modeling and identification of unsteady airwake

The Pennsylvania State University

The Graduate School

MODELING AND IDENTIFICATION OF

UNSTEADY AIRWAKE DISTURBANCES ON ROTORCRAFT

A Thesis in

Aerospace Engineering

by

Sade M. Sparbanie

2008 Sade M. Sparbanie

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

December 2008

ii

The thesis of Sade M. Sparbanie was reviewed and approved* by the following:

Joseph F. Horn

Associate Professor of Aerospace Engineering

Thesis Advisor

Jack W. Langelaan

Assistant Professor of Aerospace Engineering

George Lesieutre

Professor of Aerospace Engineering

Head of the Department of Aerospace Engineering

*Signatures are on file in the Graduate School

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ABSTRACT

Shipboard operations can be among the most difficult missions for rotorcraft

pilots. Ordinary tasks such as precision hovering and landing can become increasingly

difficult when performed in the unsteady winds that develop behind ship superstructures

and above a moving ship deck. Often, the increased pilot workload is the limiting factor

in determining whether a particular task can be performed in certain wind-over-deck

conditions. In recent years, research has been performed to identify the ship gusts that are

affecting pilots. If the unsteady winds can be identified, then gust rejection tools can be

developed to help reduce pilot workload, and to make missions safer. Additionally, from

accurate wind information, high fidelity real time simulations can be developed to test

new engineering designs and to train naval pilots.

This study further investigates gust identification methods by applying new

engineering tools to develop offline and online gust identification processes. In the

offline environment, aircraft time history data is used to develop colored noise filters that

capture the spectral properties of the ship airwake gusts. When the continuous filter is

transformed to a discrete transfer function, and excited with a white noise input, the

power spectral density of the filtered output matches the power spectral properties of the

stochastic portion of the unsteady airwake gusts.

Although the offline gust identification method is successful, it can become

computationally intensive to develop gust identification filters for every ship airwake

condition a particular helicopter may encounter. As a result, an online identification

method is examined. In this initial feasibility study, a sixth order autoregressive Burg

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model is used to determine colored noise filter coefficients in a real-time simulation

environment. Initial results shows that the spectral properties of the filters converge to

key peaks that were evident in the offline filter fitting method.

In this study, the gust identification principles used to identify the stochastic

airwake properties are then applied to create a real time simulation airwake model.

Previous approaches to developing airwake simulation models of the shipboard

environment employed computational fluid dynamics. Often the memory restrictions

placed on the size of data allowed for the real time simulation applications either limited

the fidelity of the CFD solution, or the length of unrepeatable data created. By relying on

a grid of stochastic filters, which are excited with a random white noise, the

computational effort is significantly reduced and guaranteed not to show noticeable

repetitions in flight simulation data. The stochastic airwake is tested by performing

simulated flight trajectories, as well as using piloted simulation testing at Sikorsky

Aircraft. Initial results suggest similar pilot workload, demonstrating the feasibility and

accuracy of the stochastic airwake simulation model.

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TABLE OF CONTENTS

LIST OF FIGURES................................................................................................. 7

LIST OF TABLES .................................................................................................. 15

ACKNOWLEDGEMENTS..................................................................................... 16

Chapter 1 Introduction............................................................................................ 1

1.1 Motivation .................................................................................................. 1

1.2 Literature Review ....................................................................................... 2

1.2.1 Ship Airwake Modeling Through Experimental Testing .................... 2

1.2.2 Computational Fluid Dynamics Ship Airwake Models ...................... 3

1.2.3 Gust Disturbance Identification......................................................... 4

1.2.4 Stability Augmentation System Control for Gust Rejection ............... 4

1.2.5 Model Following Control Architecture for Gust Rejection ................ 5

1.2.6 Trailing Edge Gust Rejection Controller ........................................... 7

1.3 Focus of Current Research .......................................................................... 8

1.3.1 Disturbance Identification in Offline and Online Environments......... 8

1.3.2 Simulation Modeling of Airwakes using Stochastic Filters ................ 9

Chapter 2 Simulation Environment ......................................................................... 10

2.1 Genhel-PSU................................................................................................ 10

2.2 CFD Airwakes Used with Genhel-PSU ....................................................... 12

2.2.1 USS Winston S. Churchill Destroyer (DDG-81)................................ 12

2.2.2 USS Peleliu (LHA-5) Tarawa Class Solutions................................... 14

2.3 Simulation Hover Locations used with Genhel-PSU ................................... 15

2.4 Sikorsky GENHEL ..................................................................................... 16

2.4.1 MTE Definition................................................................................. 17

2.4.2 Cooper Harper Rating Scale .............................................................. 18

Chapter 3 Stochastic Filter Theory.......................................................................... 19

3.1 General Theory........................................................................................... 19

3.2 Previous Filter Design................................................................................. 20

3.3 New Design Methodology .......................................................................... 23

3.4 Offline Filter Fitting Results ....................................................................... 26

3.5 Discrete Filter Generation ........................................................................... 33

3.6 Equivalent Body Gusts Transformed to Local Velocity Disturbances.......... 36

3.7 Initial Simulation Results ............................................................................ 38

Chapter 4 Online Identification of Stochastic Filters ............................................... 42

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4.1 Previous Work ............................................................................................ 42

4.2 Burg Autoregressive Spectral Estimation .................................................... 43

4.3 Real Time Workshop / Implementation into Genhel-PSU ........................... 46

4.4 Results of Burg AR Model.......................................................................... 49

Chapter 5 Simulation Modeling of Airwakes Using Stochastic Filters..................... 52

5.1 Motivation .................................................................................................. 52

5.2 Stochastic Filter Grid Design ...................................................................... 53

5.3 Implementation into GENHEL-PSU ........................................................... 58

5.4 Genhel-PSU Stochastic Airwake Results..................................................... 62

5.5 Implementation into Sikorsky GENHEL and Piloted Results ...................... 71

Chapter 6 Conclusions ............................................................................................ 76

6.1 Analysis Summary...................................................................................... 76

6.2 Recommendations for Future Work ............................................................ 80

6.2.1 Equivalent Gusts ............................................................................... 81

6.2.2 Stochastic Airwake Model Limitations.............................................. 81

Bibliography............................................................................................................ 83

Appendix A Settings for Genhel-PSU..................................................................... 87

Appendix B Offline Stochastic Filter Fitting Results............................................... 89

B.1 Windowing Comparison............................................................................. 89

B.2 Filter Fit Comparison ................................................................................. 92

B.3 LHA Filter Fits: 30 knots / 0 deg ................................................................ 96

B.4 LHA Filter Fits: 30 knots / 30 deg .............................................................. 99

B.5 DDG-81 Filter Fits: 25 knots / 0 deg........................................................... 103

B.6 DDG-81 Initial Simulation Results............................................................. 106

B.7 LHA 30 kts / 0 deg Initial Simulation Results............................................. 111

B.8 LHA 30 kts / 30 deg Initial Simulation Results........................................... 116

Appendix C Online AR Filter Results ..................................................................... 122

C.1 Online Burg AR Model Fitting Results....................................................... 122

Appendix D Stochastic Simulation Modeling Results ............................................. 126

D.1 Genhel-PSU Simulation Hovering Results ................................................. 126

D.2 Genhel-PSU Simulation Trajectory Maneuver Results ............................... 141

D.3 Sikorsky GENHEL Piloted Simulation Results .......................................... 148

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LIST OF FIGURES

Figure 1.1: MFC Architecture.................................................................................. 6

Figure 1.2: Airwake Compensator Comparisons using a Model Following

Controller. [Horn, Bridges, 2007]. .................................................................... 7

Figure 2.1: DDG-81 stationed in Virginia Beach, VA. [Sparbanie, 2008]................ 12

Figure 2.2: Dimensions of the CFD airwake behind the DDG-81 ship...................... 13

Figure 2.3: USS Peleliu (LHA 5) ............................................................................. 14

Figure 2.4: Top View of the LHA Class Ship Outlining Landing Spot 8 .................. 15

Figure 2.5: Approximate Hover Location behind a DDG-81. ................................... 16

Figure 2.6: Visuals used with Sikorsky’s GENHEL during Piloted Simulations.

[Geiger, et al., 2008] ......................................................................................... 17

Figure 2.7: Cooper-Harper Rating Scale .................................................................. 18

Figure 3.1: PSD of the Lateral Gust, v, using the filter fitting method by [Horn,

Bridges, and Lee, 2006]. ................................................................................... 23

Figure 3.2: Longitudinal Equivalent Gust Velocity for the Windowing

Comparison ...................................................................................................... 27

Figure 3.3: Vertical Velocity Equivalent Body Gust for the Filter Design

Comparison ...................................................................................................... 28

Figure 3.4: Roll Rate Equivalent Body Gust for the Filter Design Comparison ........ 29

Figure 3.5: Vertical Velocity Equivalent Body Gust: LHA 30 kts / 0 deg................. 30

Figure 3.6: Yaw Rate Equivalent Body Gust: LHA 30 kts / 0 deg ............................ 30

Figure 3.7: Lateral Velocity Equivalent Body Gust: LHA 30 kts / 30 deg ............... 31

Figure 3.8: Pitch Component Equivalent Body Gust for LHA 30 kts / 30 deg .......... 31

Figure 3.9: Initial Simulation: Longitudinal Velocity Equivalent Body Gust for

DDG-81............................................................................................................ 40

Figure 3.10: Initial Simulation: Longitudinal Velocity PSD for DDG-81 ................. 40

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Figure 3.11: Initial Simulation: Vertical Velocity Equivalent Body Gust for DDG-

81 ..................................................................................................................... 41

Figure 3.12: Initial Simulation: Vertical Velocity PSD for DDG-81......................... 41

Figure 4.1: AR Filter Diagram [Orfandis, 1988] ...................................................... 44

Figure 4.2: High Level View of the Gust Filter Identification Controller.................. 47

Figure 4.3: Gust Identification using a Burg AR Estimator ...................................... 48

Figure 4.4: Online AR Filter Convergence for the Roll Rate Equivalent Gust .......... 50

Figure 4.5: Online AR Filter Convergence for the Pitch Rate Equivalent Gust ........ 50

Figure 5.1: Schematic of the x-y coordinate grid. ..................................................... 55

Figure 5.2: Schematic of the x-z coordinate grid. ..................................................... 57

Figure 5.3: Three Dimensional View of the Stochastic Filter Grid. .......................... 58

Figure 5.4: Genhel-PSU Coordinate System Diagram.............................................. 59

Figure 5.5: Aircraft Position and Nearest Eight Grid Points ..................................... 60

Figure 5.6: Lateral Stick Input for 439-0-42 Location .............................................. 64

Figure 5.7: Longitudinal Stick Input for 454-0-52.................................................... 64

Figure 5.8: Collective Stick Input for 454-0-52........................................................ 65

Figure 5.9: Pedal Inputs for 544-37-58..................................................................... 65

Figure 5.10: Longitudinal Velocity of Gust acting on the Fuselage center for 439-

0-42.................................................................................................................. 66

Figure 5.11: Lateral Velocity of Gust acting on the Fuselage center for 454-0-52 .... 67

Figure 5.12: Vertical Velocity of Gust acting on the Fuselage center for 439-0-42... 67

Figure 5.13: Pedal Input for Trajectory Path 1 ......................................................... 70

Figure 5.14: Collective Stick Input for Trajectory Path 2 ......................................... 70

Figure 5.15: Pilot HQR assessment for various Airwake conditions......................... 72

Figure 5.16: Lateral Stick Input for Pilot 4............................................................... 73

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Figure 5.17: Longitudinal Stick for Pilot 5............................................................... 74

Figure 5.18: Pedal Input for Pilot 6 .......................................................................... 74

Figure B.1: u - Velocity Component for the Windowing Comparison ...................... 89

Figure B.2: v - Velocity Component for the Windowing Comparison ...................... 90

Figure B.3: w - Velocity Component for the Windowing Comparison ..................... 90

Figure B.4: p - Rotational Component for the Windowing Comparison ................... 91

Figure B.5: q - Velocity Component for the Windowing Comparison ...................... 91

Figure B.6: r - Velocity Component for the Windowing Comparison....................... 92

Figure B.7: u - Velocity Component for the Filter Design Comparison .................... 93

Figure B.8: v - Velocity Component for the Filter Design Comparison .................... 93

Figure B.9: w - Velocity Component for the Filter Design Comparison ................... 94

Figure B.10: p - Roll Component for the Filter Design Comparison......................... 94

Figure B.11: q - Pitch Component for the Filter Design Comparison........................ 95

Figure B.12: r - Yaw Component for the Filter Design Comparison......................... 95

Figure B.13: u - Velocity Component for LHA 30 kts / 0 deg .................................. 96

Figure B.14: v - Velocity Component for LHA 30 kts / 0 deg .................................. 97

Figure B.15: w - Velocity Component for LHA 30 kts / 0 deg ................................. 97

Figure B.16: p - Roll Component for LHA 30 kts / 0 deg......................................... 98

Figure B.17: q - Pitch Component for LHA 30 kts / 0 deg........................................ 98

Figure B.18: r – Yaw Component for LHA 30 kts / 0 deg ........................................ 99

Figure B.19: u - Velocity Component for LHA 30 kts / 30 deg ................................ 100

Figure B.20: v - Velocity Component for LHA 30 kts / 30 deg ................................ 100

Figure B.21: w - Velocity Component for LHA 30 kts / 30 deg ............................... 101

Figure B.22: p - Roll Component for LHA 30 kts / 30 deg....................................... 101

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Figure B.23: q - Pitch Component for LHA 30 kts / 30 deg...................................... 102

Figure B.24: r - Yaw Component for LHA 30 kts / 30 deg....................................... 102

Figure B.25: u - Velocity Component for DDG-81 25 kts / 0 deg............................. 103

Figure B.26: v - Velocity Component for DDG-81 25 kts / 0 deg............................. 104

Figure B.27: w - Velocity Component for DDG-81 25 kts / 0 deg............................ 104

Figure B.28: p - Roll Component for DDG-81 25 kts / 0 deg ................................... 105

Figure B.29: q - Pitch Component for DDG-81 25 kts / 0 deg.................................. 105

Figure B.30: r - Yaw Component for DDG-81 25 kts / 0 deg ................................... 106

Figure B.31: u - Velocity Component for DDG-81 Initial Simulation Results .......... 107

Figure B.32: v - Velocity Component for DDG-81 Initial Simulation Results .......... 107

Figure B.33: w - Velocity Component for DDG-81 Initial Simulation Results ......... 108

Figure B.34: p – Roll Component for DDG-81 Initial Simulation Results ................ 108

Figure B.35: q - Pitch Component for DDG-81 Initial Simulation Results ............... 109

Figure B.36: r - Yaw Component for DDG-81 Initial Simulation Results................. 109

Figure B.37: u - Velocity PSD of the DDG-81 Initial Simulation Results................. 110

Figure B.38: v - Velocity PSD of the DDG-81 Initial Simulation Results................. 110

Figure B.39: w - Velocity PSD of the DDG-81 Initial Simulation Results................ 111

Figure B.40: u - Velocity Component for LHA 30 kts / 0 deg Initial Simulation

Results.............................................................................................................. 112

Figure B.41: v - Velocity Component for LHA 30 kts / 0 deg Initial Simulation

Results.............................................................................................................. 112

Figure B.42: w - Velocity Component for LHA 30 kts / 0 deg Initial Simulation

Results.............................................................................................................. 113

Figure B.43: p - Roll Component for LHA 30 kts / 0 deg Initial Simulation

Results.............................................................................................................. 113

Figure B.44: q - Pitch Component for LHA 30 kts / 0 deg Initial Simulation

Results.............................................................................................................. 114

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Figure B.45: r - Yaw Component for LHA 30 kts / 0 deg Initial Simulation

Results.............................................................................................................. 114

Figure B.46: u - Velocity PSD of the LHA 30 kts / 0 deg Initial Simulation

Results.............................................................................................................. 115

Figure B.47: v - Velocity PSD of the LHA 30 kts / 0 deg Initial Simulation

Results.............................................................................................................. 115

Figure B.48: w - Velocity PSD of the LHA 30 kts / 0 deg Initial Simulation

Results.............................................................................................................. 116

Figure B.49: u - Velocity Component for LHA 30 kts / 30 deg Initial Simulation

Results.............................................................................................................. 117

Figure B.50: v - Velocity Component for LHA 30 kts / 30 deg Initial Simulation

Results.............................................................................................................. 117

Figure B.51: w - Velocity Component for LHA 30 kts / 30 deg Initial Simulation

Results.............................................................................................................. 118

Figure B.52: p - Roll Component for LHA 30 kts / 30 deg Initial Simulation

Results.............................................................................................................. 118

Figure B.53: q - Pitch Component for LHA 30 kts / 30 deg Initial Simulation

Results.............................................................................................................. 119

Figure B.54: r - Yaw Component for LHA 30 kts / 30 deg Initial Simulation

Results.............................................................................................................. 119

Figure B.55: u - Velocity PSD of the LHA 30 kts / 30 deg Initial Simulation

Results.............................................................................................................. 120

Figure B.56: v - Velocity PSD of the LHA 30 kts / 30 deg Initial Simulation

Results.............................................................................................................. 120

Figure B.57: w - Velocity PSD of the LHA 30 kts / 30 deg Initial Simulation

Results.............................................................................................................. 121

Figure C.1: Identified Longitudinal Gust Velocity Gust Filters ................................ 122

Figure C.2: Identified Lateral Gust Velocity Gust Filters ........................................ 123

Figure C.3: Identified Vertical Gust Velocity Gust Filters....................................... 123

Figure C.4: Identified Roll Rate Gust Filters ........................................................... 124

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Figure C.5: Identified Pitch Rate Gust Filters.......................................................... 124

Figure C.6: Identified Yaw Rate Gust Filters .......................................................... 125

Figure D.1: Lateral Sick Input at 439-0-42............................................................... 127

Figure D.2: Longitudinal Sick Input at 439-0-42...................................................... 127

Figure D.3: Collective Stick Input at 439-0-42......................................................... 128

Figure D.4: Pedal Input at 439-0-42......................................................................... 128

Figure D.5: Longitudinal Velocity acting on Fuselage at 439-0-42........................... 129

Figure D.6: Lateral Velocity acting on Fuselage at 439-0-42.................................... 129

Figure D.7: Vertical Velocity acting on Fuselage at 439-0-42.................................. 130

Figure D.8: Lateral Sick Input at 454-0-52............................................................... 130

Figure D.9: Longitudinal Sick Input at 454-0-52...................................................... 131

Figure D.10: Collective Stick Input at 454-0-52....................................................... 131

Figure D.11: Pedal Input at 454-0-52....................................................................... 132

Figure D.12: Longitudinal Velocity acting on Fuselage at 454-0-52......................... 132

Figure D.13: Lateral Velocity acting on Fuselage at 454-0-52.................................. 133

Figure D.14: Vertical Velocity acting on Fuselage at 454-0-52 ................................ 133

Figure D.15: Lateral Sick Input at 545-31-33........................................................... 134

Figure D.16: Longitudinal Sick Input at 545-31-33.................................................. 134

Figure D.17: Collective Stick Input at 545-31-33..................................................... 135

Figure D.18: Pedal Input at 545-31-33..................................................................... 135

Figure D.19: Longitudinal Velocity acting on Fuselage at 545-31-33....................... 136

Figure D.20: Lateral Velocity acting on Fuselage at 545-31-33................................ 136

Figure D.21: Vertical Velocity acting on Fuselage at 545-31-33 .............................. 137

Figure D.22: Lateral Sick Input at 454-37-58........................................................... 137

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Figure D.23: Longitudinal Sick Input at 454-37-58.................................................. 138

Figure D.24: Collective Stick Input at 454-37-58..................................................... 138

Figure D.25: Pedal Input at 454-37-58..................................................................... 139

Figure D.26: Longitudinal Velocity acting on Fuselage at 454-37-58....................... 139

Figure D.27: Lateral Velocity acting on Fuselage at 454-37-58................................ 140

Figure D.28: Vertical Velocity acting on Fuselage at 454-37-58 .............................. 140

Figure D.29: Three Dimensional View of Trajectory Path 1..................................... 142

Figure D.30: Aircraft Position Time History of Trajectory Path 1 ............................ 143

Figure D.31: Lateral Stick Input for Trajectory Path 1 ............................................. 143

Figure D.32: Longitudinal Stick Input for Trajectory Path 1 .................................... 144

Figure D.33: Collective Stick Input for Trajectory Path 1 ........................................ 144

Figure D.34: Pedal input for Trajectory Path 1......................................................... 145

Figure D.35: Three Dimensional View of Trajectory Path 2..................................... 145

Figure D.36: Aircraft Position Time History of Trajectory Path 2 ............................ 146

Figure D.37: Lateral Stick Input for Trajectory Path 2 ............................................. 146

Figure D.38: Longitudinal Stick Input for Trajectory Path 2 .................................... 147

Figure D.39: Collective Stick Input for Trajectory Path 2 ........................................ 147

Figure D.40: Pedal input for Trajectory Path 2......................................................... 148

Figure D.41: Lateral Stick Input for Pilot 1.............................................................. 149

Figure D.42: Longitudinal Stick Input for Pilot 1..................................................... 149

Figure D.43: Collective Stick Input for Pilot 1 ......................................................... 150

Figure D.44: Pedal Input for Pilot 1 ......................................................................... 150



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LIST OF TABLES

Table 3.1: Gust Filters Derived for DDG81 Hover Location, WOD: 25kts / 0deg .... 32

Table 3.2: Gust Filters Derived for LHA LS 8, WOD: 30kts / 0deg ........................ 32

Table 3.3: Gust Filters Derived for LHA LS 8, WOD: 30kts / 30deg....................... 32

Table A.1: DDG-81 Hover Coordinates ................................................................... 87

Table A.2: LHA Hover Coordinates ........................................................................ 87

Table A.3: Genhel-PSU Matlab GUI Interface......................................................... 88

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ACKNOWLEDGEMENTS

This research was supported by the Center for Rotorcraft Innovation (CRI) under

contract (WBS 2007-B-01-02.3-P3) with Sikorsky Aircraft Corporation and NAVAIR under

the SBIR contract (N68335-07-C00310) with Barron Associates. I would like to extend

additional thanks to Derek Geiger of Sikorsky Aircraft Corporation and Jared Cooper of

Barron Associates for their help. The thesis also uses CFD airwake data for the DDG-81

provided by NAVAIR Advanced Aerodynamics branch (AIR-4.3.2.1) under a Memorandum

of Agreement with Penn State. I would like to thank Dr. Susan Polsky for her help in

providing access and understanding of the DDG-81 airwake data.

I would also like to thank my advisor, Dr. Joseph F. Horn, for his guidance over the

past two years. From course work to research he has always taken the time to answer my

questions and teach me the fundamentals necessary to pursue a career that I will enjoy for

years to come. I am very grateful to have had the opportunity to be one of his students.

My graduate education would not have been the same if it weren’t for my coworkers.

I would like to extend my gratitude to Derek Bridges for his time and patience while teaching

me how to use the simulator and for his advice on research over the past year. Additional

thanks to Wei Guo, Conor Marr, Pamela Montanye, Sana Safraz, and Eric Tobias, I have

learned much from each of you. I am also thankful to all the coworkers and friends who have

kept graduate school fun in-between long hours at the office.

Finally, I would like to thank my parents. Without their love and support, I would not

be here today.

Chapter 1

Introduction

1.1 Motivation

Shipboard operations continue to be among the most challenging for maritime

rotorcraft pilots. The unsteady airwake behind a ship requires pilots to continuously

compensate for gust disturbances, resulting in high pilot workload. In addition to the

unsteady air flow, the ship deck is rolling and pitching, and at times the pilots have to be

prepared to fly in adverse weather conditions. With the environmental factors considered,

the ordinary tasks such as takeoff, landing, and precision hovering become increasingly

difficult and dangerous while at sea.

Often high pilot workload is the limiting factor when determining the allowable

sea state and wind-over-deck (WOD) conditions for particular rotorcraft and ship

combinations. In order to provide a quick response in critical situations, it is of high

interest of the Navy to extend these flight envelopes. Significant work has been

completed in recent years to accurately model the ship board environment and to develop

gust alleviation controls to improve pilot workload. Accurate simulations allow for pilot

training, simulation of experimental gust alleviation controllers, and partial development

of the WOD envelope [1]. With continuous research effort, flight envelopes will be

extended, and flying conditions for pilots can be made safer.

2

1.2 Literature Review

1.2.1 Ship Airwake Modeling Through Experimental Testing

Several researchers have experimented with developing ship airwakes for flight

simulations models through full-scale testing and model-scale testing. Full scale testing is

costly in terms of time and money. As a result, other methods are used in an effort to

supplement the majority of flight tests. Model-scale testing is an alternative, but can

present an obstacle if the wind tunnel can not meet the required Reynolds number for the

scaled model [2]. Early attempts to accurately model a ship airwake were conducted

through wind tunnel experiments by Healey [3]. Healey was able to make a preliminary

database, but found it difficult to accurately measure the turbulence close to the ship.

Clement, et al. also comments that wind tunnel tests are good for defining the steady

winds around the ship, but can not provided definitive results for ship-induced turbulence

[4].

When the means are available, simulations derived from wind tunnel data (or

computational efforts) can be evaluated with limited full scale flight testing. An example

of such testing was the V-22 Osprey during initial ship deck flights [5]. The pilots felt the

simulation was not representative of the disturbances they were facing in flight. As a

result the flight test data was reduced to provide insight on discrepancies between the

simulation model and actual flight.

3

1.2.2 Computational Fluid Dynamics Ship Airwake Models

A common alternative to experimental testing is computational fluid dynamics

(CFD). Polsky and Bruner examined a time-accurate ship airwake for the LHA class ship

[6]. The study used COBALT, an unstructured grid solver that relies on the Navier-

Stokes equations. Woodson and Ghee used the same solver to examine the DDG-81 ship

and compared CFD results with wind tunnel testing [7]. Polsky, et al. examined minor

discrepancies between the CFD and wind tunnel tests to build confidence in CFD airwake

solutions using the COBALT solver [8]. At Penn State, a parallel flow solver, PUMA2

was used to examine airwake solutions behind LHA class ships [9]. PUMA2 uses a finite

volume formulation of the Euler/Navier-Stokes equations.

Additional advances in CFD airwake solutions have been made by Zan [10]. He

suggested that a detailed time varying solution is important in high-fidelity simulations.

He also states that a new CFD model should be created for each wind direction because

the angle that the wind comes across the deck will affect the simulation significantly.

Forrest, et al. examined the shipboard problem in more detail by testing several WOD

conditions on two separate ships, using FLUENT CFD solvers [11]. The study

determined that geometric details that result in medium to large scale flow should be

considered to achieve an accurate airwake model. Finally, Shipman, et al. define the

modeling parameters that are most sensitive in generating a CFD ship airwake [12]. The

paper examines the tradeoff between the computing power required to produce the CFD

airwake versus the required fidelity of the simulation. The majority of the airwake

dynamics are characterized by bluff body shedding of the main ship geometries;

4

however, a high fidelity solution would require additional details to be included.

Parameters that can be modified are grid size and the resolution of boundary layers.

Depending on the intended use of the CFD solution, computing power can be reduced by

concentrating efforts on computing very detailed solutions directly downstream of critical

structures such as a large ship mast or a deck’s edge.

1.2.3 Gust Disturbance Identification

Along with flight simulation, researchers have been trying to design systems to

help reject gust disturbances. In doing so, the first step is to identify the gusts that are

creating disturbances on the aircraft. Labows, Blanken, and Tishcler presented a study

that reduced flight test data of a UH-60 BLACK HAWK to a low speed turbulence model

[13]. The study first extracted the remnant aircraft rates caused by the atmospheric

disturbances, and then fit a von Karman turbulence model to the power spectral density

(PSD) of the equivalent gusts. The idea is if white noise is fed through this filter, the

resultant noise would be representative of the actual test data. The work was continued by

Lursardi, et al. and it was determined that the parametric turbulence models are scalable

for varying levels of turbulence and wind directions [14].

1.2.4 Stability Augmentation System Control for Gust Rejection

Horn, Bridges, and Lee applied the concepts presented in [13,14] to alleviate pilot

workload during shipboard operations [15]. The study used the UH-60 BLACK HAWK

5

GENHEL model hovering in an LHA airwake. The controller design was constrained to

represent a limited authority Stability Augmentation System (SAS). The first design step

was to determine the equivalent aircraft gusts acting on the aircraft, and to model the

spectral properties with a von Karman turbulence model. The SAS was then designed

using H2 synthesis to reject gust disturbances based on the von Karman turbulence

models. The simulation indicated a significant reduction in pilot control activity and

angular motion of the aircraft when using an optimized SAS. The drawback to this design

was that the optimized SAS changed the frequency response of the vehicle to the pilot

input. In other words, if the pilot entered an input at the same frequency of a known gust,

then it too would be filtered out since the SAS controller was designed to reject

disturbances occurring at specific frequencies.

1.2.5 Model Following Control Architecture for Gust Rejection

To differentiate between desired pilot input and the gust disturbances, Horn and

Bridges developed model-following control (MFC) architecture to be used in gust

rejection [16]. The study used the same gust identification principals presented in [15].

This MFC architecture uses feed-forward compensation to track pilot inputs and when

engaged, implements feed-back compensation to reject gust disturbances. The advantage

to using this control architecture allows for the gust disturbance rejection to be turned on

or off as needed, as well as easily substituting new compensators for different airwakes.

Overall, the commands generated are based on angular rate tracking error. The controller

6

uses a simple model following design with the closed-loop attitude dynamics as the plant

model. The basic MFC architecture is presented in Fig. 1.1.

Overall, Horn and Bridges found there was an improvement in the aircraft

handling qualities. Additionally, the fluctuations in the aircraft’s angular rates and

attitudes were significantly reduced. The reduction in angular rates is visible in Fig. 1.2.

In this figure the red line represents the airwake compensator off, and the blue line

represents the airwake compensator on.

Figure 1.1: MFC Architecture

7

1.2.6 Trailing Edge Gust Rejection Controller

A recent feasibility studied was performed by Montanye [17] to use active trailing

edge flaps as a gust alleviation controller. The study implemented a model following

controller that used the swashplate and pedals to ensure that the vehicle follows the

desired response to pilot inputs. Unlike studies by Horn, the airwake compensator rejects

airwake disturbances with trailing edge flaps and a H2 controller. The study was

implemented with a UH-60 BLACK HAWK GENHEL model and an LHA airwake. The

initial results suggest that trailing edge flaps are capable of reducing the magnitude of the

vehicle angular gust response in the roll and pitch axes.

Figure 1.2: Airwake Compensator Comparisons using a Model Following Controller.

[Horn, Bridges, 2007].

8

1.3 Focus of Current Research

This research provides further investigation of ship airwake identification

principles in offline and online environments. Additionally, using the theory from the

airwake identification methods, this study examines an alternative simulation of ship

airwake disturbances.

1.3.1 Disturbance Identification in Offline and Online Environments

This first goal of this research is to accurately identify airwake characteristics.

This study modifies the principles of [13,14,15,16] by applying modern tools offered in

recent releases of MATLAB. The new methodology guarantees stable filter development

and constrains the PSD filter fit to the frequency range that affects handling qualities of

pilots. This process is done in an offline environment; relying on previously generated

time histories of the aircraft flight dynamics from a simulation performed in Genhel-PSU.

While this paper focuses using results from an aircraft simulation model, the filter design

process can also be applied to flight test data.

Offline gust identification provides useful information in rejecting gusts for a

particular ship and airwake condition; however, it would require significant effort to

analyze aircraft time histories for every helicopter, ship, and WOD condition. As a result,

it is ideal to develop an online learning algorithm that will identify the properties of the

airwake gusts during flight. This research presents an initial feasibility study of an

autoregressive model used for online gust identifications. The system presented could

9

then be used in coordination with an adaptive controller to improve gust rejection during

flight in future applications.

1.3.2 Simulation Modeling of Airwakes using Stochastic Filters

Finally, although the CFD solutions presented in Section 1.2.2 can provide an

accurate environment, the computing power required to implement detailed solutions can

be a limiting factor in real-time simulation applications. The large velocity databases

typically have to be loaded into memory prior to the start of a simulation. Consequently,

the length of the simulation is usually limited to 40-60 seconds of data in an effort to

keep the database at a manageable size. To achieve longer simulations, the airwake can

be cycled, but it produces noticeable repetitions in flight data.

Chapter 2

Simulation Environment

This study required the use of rotorcraft simulation models capable of interacting

with several ship airwake models. The majority of the simulation tests utilized Genhel-

PSU, a FORTRAN based simulation of a UH-60A BLACK HAWK. A secondary

simulation environment used was a version of GENHEL maintained by Sikorsky

Aircraft. This chapter will review the simulation environments as well as their

corresponding airwake models.

2.1 Genhel-PSU

The primary flight dynamics model used for this research is Genhel-PSU.

GENHEL (GENeral HELicopter) is a Fortran-based simulation that was initially created

at Sikorsky Aircraft Corporation and documented under contract with the U.S. Army /

NASA Ames Research Center [18]. The simulation was provided to Penn State VLRCOE

by the Rotorcraft Division of NASA Ames. Several modifications have been made to the

code, resulting in the version called Genhel-PSU [19]. These changes include network

communications to interact with other programs and computers, incorporating user-

defined controllers, a graphical user interface, generation of high order linear models, and

the addition of shipboard interface modules [20]. With these advancements, Genhel-PSU

is capable of running real-time piloted simulations of ship-based operations.

11

Although there have been updates to GENHEL to meet current research needs,

the basic mathematical models of the aerodynamics and flight dynamics is mostly

unchanged from the original version. The simulation is a nonlinear model of the UH-60A

that includes accurate models of the main rotor, fuselage aerodynamics, horizontal and

vertical tail surfaces, servo and sensor models, landing gear, and mechanical flight

controls. The main rotor model also includes blade flapping, lagging, and hub rotational

degrees of freedom. The helicopter position, velocity, and acceleration are calculated at

every time step by summing each of the six forces and moments at the center of gravity.

Additional specifics are outlined in [18].

To simulate ship-board landing missions, Genhel-PSU provides many options.

There are visuals and CFD data for the Winston Churchill Destroyer (DDG-81) with

WOD condition of 25 kts/0 deg, and the Peleliu LHA class ship with WOD conditions of

30 kts/0 deg and 30 kts/30 deg. Each of the airwake solutions can be scaled for different

wind speeds. For added accuracy of the simulation environment, ship motion has also

been added. The user can select to model a ship moving at constant speed and heading as

well as selecting added time-varying motion for a particular sea state. A semi-analytical

method that calculates the heave, roll, and pitch motion using sum of sine equations is

outlined in [21,22] and is implemented into Genhel-PSU in [23].

In the absence of experienced pilots, Genhel-PSU offers a pilot model that will fly

a prescribed trajectory without the need for human inputs [24]. The pilot model is a

closed-loop control law that was designed to emulate a human pilot. This multi-input,

multi-output (MIMO) control law is scheduled with airspeed to follow the trajectory path

that was defined by a set of position, speed, altitude, and heading terms. This pilot model

12

is used to hover at specific points within the ship airwakes to gather simulation data

throughout this study.

2.2 CFD Airwakes Used with Genhel-PSU

2.2.1 USS Winston S. Churchill Destroyer (DDG-81)

The Winston-Churchill Destroyer (DDG-81) provides the navy with multi-

mission offensive and defensive capabilities. The ship is 505 ft long and 59 ft wide and

can achieve 30 plus knots at sea [25]. The ship can carry two Sea Hawks, a variant of the

UH-60 BLACK HAWK. A visual of the DDG-81 ship deck is made available in Genhel-

PSU’s visual library and it can be flown with a CFD airwake of the DDG-81.

Figure 2.1: DDG-81 stationed in Virginia Beach, VA. [Sparbanie, 2008].

13

The CFD model used with Genhel-PSU was developed by NAVAIR using cell-

centered finite volume Navier-Stokes solver called Cobalt [26]. The CFD model was

originally developed and documented by Woodson and Ghee [7] and further investigated

by Polsky, et al. [8]. Within these papers, the CFD model is validated with wind tunnel

results. The nominal CFD WOD condition is 25 kts at 0 deg wind. The CFD data can be

scaled to simulate other wind speeds, but only for deck winds of 0 deg.

The CFD analysis used a trapezoidal shaped grid, fanning out in height and width.

The first plane is aligned with the hangar doors and measures 264.7 ft by 196.86 ft. The

final plane is 817 ft behind the hangar doors and measures 1640.5 ft by 524.96 ft. The

detailed grid shown in Fig. 2.2 has 55 x-planes with each plane consisting of 77 y-points

and 61 z-points. At each grid point there are time-varying u, v, and w velocity

components. The airwake contains data for 60 seconds, with a time step of 0.01 seconds

[27].

Figure 2.2: Dimensions of the CFD airwake behind the DDG-81 ship.

14

2.2.2 USS Peleliu (LHA-5) Tarawa Class Solutions

The USS Peleliu is a US Naval LHA Tarawa-class amphibious assault ship that

has been used in attack missions, carrying several helicopters ranging from CH-53 Super

Sea Stallions to CH-46 Sea Knights as well as AV-8B Harrier jets [28]. The deck is 820

ft long and 106 ft wide.

The LHA class ship airwake solution was calculated with PUMA 2, a modified

version of a Parallel Unstructured Maritime Aerodynamics (PUMA) CFD solver [9,

29,30]. This solver uses a finite volume formulation of the integral form of the Euler and

Navier-Stokes equations for three-dimensional, compressible, unsteady/steady solutions

for complex geometries [9].

The nominal case used for simulation is a CFD solution around landing spot 8.

The user can select either a WOD condition of 30 knots with 0 degree winds or 30 knots

with 30 degree winds. The solutions can be scaled to seek solutions at different wind

Figure 2.3: USS Peleliu (LHA 5)

15

speeds. Landing spot 8 is depicted in Fig. 2.4, and is known to be one of the most

difficult places to land on the ship in 30 deg winds due to the added wind turbulence of a

cross wind breaking around the super structure on the deck.

2.3 Simulation Hover Locations used with Genhel-PSU

The main hover location selected for the DDG-81 in this study was for the aircraft

to hover within CFD airwake coordinate system at 430 ft behind the origin, centered

along the midline of the ship, and 31.3 ft above the origin of the airwake. This relates to

roughly 205 ft behind and 28 ft above the center of the DDG-81 ship in Genhel-PSU.

The red dot in Fig. 2.5 represents the approximate hover location for the center of

fuselage.

Figure 2.4: Top View of the LHA Class Ship Outlining Landing Spot 8

16

For repeatability of these simulations, the specifics of the trajectory files and

Genhel-PSU settings used for these hover maneuvers and are outlined in Appendix A.

2.4 Sikorsky GENHEL

Sikorsky GENHEL is a modular object-oriented code that can be readily modified

to represent different rotorcraft. It also has the capability to interact with a ship flow field

and ship motion modules. For this study, a S-92 fly-by-wire (FBW) aircraft was flown in

different ship airwakes. The S-92 FBW aircraft was chosen based on the deck size of the

DDG-81 and because Sikorsky Aircraft has already validated the aircraft’s simulation

model. The ship airwakes used with Sikorsky GENHEL is the same CFD airwake for the

DDG-81 that was provided by NAVAIR to PSU for simulations with Genhel-PSU.

Figure 2.5: Approximate Hover Location behind a DDG-81.

(x,y,z) = (389.95, y ,16.40)

(x,y,z) = (389.95, y ,10.11)(x,y,z) = (470.42, y ,13.29)

(x,y,z) =

(389.38, y , 27.40)

x = 429.3 ft

17

2.4.1 MTE Definition

For evaluation of the stochastic airwake grid, trained pilots were used in a fixed

based simulator. To evaluate the pilot workload in the turbulent flow-field, the pilots

were instructed to fly the Maritime Task Element (MTE) presented in [27]. The MTE

consisted of a standard approach to the back of the ship, and a precision hover task over

the landing spot on the ship deck. The maneuver begins at a 70 ft hover approximately

400-500 ft behind the ship. The pilot moves towards the back of the ship with a closure

rate of 6-10 kts. After the pilot performs a smooth flare over the fantail, the pilot has

about 10 sec to begin the stable hover maneuver. The 30 sec hover should be directly

over the landing spot at a gear height of 9-13 ft. Marginal and desired performance

standards were defined by visual cues seen by the pilots. A snapshot of the visuals that

the pilot would see can be seen in Fig. 2.6.

Figure 2.6: Visuals used with Sikorsky’s GENHEL during Piloted Simulations. [Geiger,

et al., 2008]

18

2.4.2 Cooper Harper Rating Scale

To numerically evaluate the pilot workload during the simulation performing the

MTE above, the pilots were asked to asses the current simulation run on the Cooper-

Harper Rating Scale [31]. The scale rates pilot work from 1 to 10, where 1 is the least

amount of work, and 10 means the aircraft is uncontrollable. If the pilot maintains

desirable tolerances, as defined by the above MTE, then the rating falls between 1 and 3.

If the pilot maintains adequate performance, the HQR rating falls between 4 and 6. The

Cooper-Harper Rating Scale is in Fig. 2.7.

Figure 2.7: Cooper-Harper Rating Scale

Chapter 3

Stochastic Filter Theory

It is desirable to accurately identify the airwake characteristics of the flow field

behind a ship at sea. The method presented by Labows [13] and Lusardi [14] offers an

offline method to extract equivalent gusts and to estimate the peak characteristics through

a colored noise filter. The method modified and implemented by Horn, Bridges, and Lee

[15] and again by Horn and Bridges [16] to reject gust disturbances in a model following

control architecture. This chapter explores their work further and refines the colored

noise filter.

3.1 General Theory

The airwake flow field can be divided into deterministic and stochastic

components. The deterministic component is the mean velocity of the wind. The

stochastic component can be modeled as a set of stochastic colored noise filters. For any

given point in space, there are six gust filters; three for the translational components and

three for rotational gusts.

If one can isolate the turbulence of the air, then the stochastic component of the

airwake can be modeled as a random process. It is assumed that the airwake will repeat

itself over a range of frequencies, and as a result, the airwake can be characterized by

averaging the estimates of the power spectrum using periodograms [32]. When the

20

estimated linear system is excited with an uncorrelated white noise, the resulting signal

should have similar frequency domain properties as the stochastic signal of the original

airwake.

3.2 Previous Filter Design

The first revision of stochastic filter design produced by Horn, Bridges, and Lee

[15] used a method that resulted in a design similar to the Von Karman turbulence model.

The first step was performing simulated hovers over the ship deck using the pilot model

discussed in Section 2.1. During the simulation, the aircraft’s rigid body states, state

derivatives, and control inputs were recorded. To isolate the airwake, the aircraft open-

loop dynamics had to be accounted for. A high order linearized model was developed that

took the form of:

where x is the state vector, u is the pilot inputs, and w is the equivalent disturbance

vector. Here the state vector is defined as:

The control input vector is:

GwBuAxx ++=& Eq. 3.1

Trqpwvux ][ θφ= Eq. 3.2

21

and the equivalent disturbance vector is:

The components of the disturbance vector represent the average gust velocity over

the body of the vehicle as well as the spatial variation modeled as equivalent angular

rates.

Using the pseudo-inverse of the G matrix from a reduced 9-state linear model, the

disturbance vector can be found.

The time histories of the equivalent gusts are produced and the mean value is

subtracted for each of the six airwake components. The mean value is considered the

deterministic portion and can be included again during real time simulation.

The last step taken was to derive a transfer function, that when stimulated with the

uncorrelated white noise vector, a disturbance would be created that had similar spectral

T

pedcolllonglatu ][ δδδδ= Eq. 3.3

[ ]Tgggggg rqpwvuw = Eq. 3.4

( )BuAxxGw −−= +&

Eq. 3.5

22

properties as the airwake observed during the simulation hovers. To do this, the PSD of

the equivalent gusts were computed. Then a filter similar to the von Karman turbulence

model was fitted to the PSD. The filter is shown Eq. 3.6.

In Eq. 3.6, the intensity factor,σ , the length scale, L , and the coefficients ia , ib ,

are selected to fit the PSD over the frequency range of 0.1 to 40 rad/sec. The parameters

were fit using a nonlinear least-squares routine to reduce the error between the fitting

filter and the equivalent gusts. The parameter V in this equation is the reference speed of

the nominal wind condition.

Horn, Bridges, and Lee [15] found desirable results from this approach and are

outlined in Fig. 3.1. The red line is the PSD of the equivalent gusts, and the blue line is

the filter designed to match the spectral properties the equivalent gust.

( )3

3

2

21

2

21

1

14

+

++

++

=

sV

Las

V

Las

V

La

sV

Lbs

V

Lb

V

L

sH

σ

Eq. 3.6

23

3.3 New Design Methodology

In an effort to achieve a smoother fit, the filter fitting routines have been modified

to use newer functions included in recent releases of MATLAB. In doing so, the effort

used Welch’s Method for spectrum fitting. The Welch method is a modification of the

Barlett procedure that can directly compute the power spectrum estimate using Fast

Fourier Transforms (FFTs) [32]. It uses periodogram estimates based on splitting time

series of overlapped segments multiplied by data windows. The window is applied to the

data segments before computation of the periodograms.

Figure 3.1: PSD of the Lateral Gust, v, using the filter fitting method by [Horn, Bridges,

and Lee, 2006].

24

Another change to the filter fitting routine is that the system examines four

window sizes: 512, 1024, 2048, and 4096, where the time step was 0.01 sec. The final

PSD is an average of each PSD resulting from the four window sizes. This was done in

an effort to minimize the effect of window size selection, and to assure a consistent filter

fit through any data set. Moreover, using four different window sizes allows one to

accurately capture a wide range of frequencies. A smaller window would allow one to

capture high frequency information, whereas a larger window would highlight smaller

frequencies.

The colored filter was also modified. Previously the filter was designed after the

von Karman gust models, and now a simple third order system is designed with poles and

damping coefficients. The benefit to the change in filter fitting method is that the poles

and damping coefficients can easily be constrained. Moreover, there is one less parameter

to optimize during the filter fitting routine. The transfer function that is fitted to the

equivalent gust’s PSD now takes the form:

In Eq. 3.6, K is a gain, zζ and pζ are damping ratios, nz

ω and npω are natural

frequencies, and p is a pole. Each of these parameters were constrained and given an

initial guess for the non-linear least squares fit. Overall, constraining the parameters was

an advantage because the filters were guaranteed to be stable. Additionally, placing

( ) ( )( ) ( )psss

ssKsG

npnpp

nznzz

+++

++=

22

22

2

2

ωωζ

ωωζ Eq. 3.7

25

constraints allowed for the filter fit to avoid high frequency modes which can create

problems in numerical implementation.

Finally, different windowing methods were examined. Welch’s method was

applied using Hamming, Hann, and Blackman windows. The general form of the

windowing techniques were documented in MATLAB’s help files, and are outlined by

the Eqs. 3.8- 3.10.

Hamming Window:

Hann Windowing:

Blackman Windowing:

In all of these equations, the window length, L, is N +1, where N is the width in

samples. The parameter n is an integer between zero and N .

( ) NnN

nnw ≤≤

−= 0,

2cos46.054.0

π

Eq. 3.8

( ) NnN

nnw ≤≤

−= 0,

2cos1

21

π

Eq. 3.9

( ) NnN

n

N

nnw ≤≤

+

−= 0,

4cos08.0

2cos5.042.0

ππ

Eq. 3.10

26

3.4 Offline Filter Fitting Results

Initial filter fitting results were generated from the UH-60A performing a standard

hover for the DDG-81 ship airwake with a WOD condition of 25 kts / 0 deg. The hover

specifications were outlined in Section 2.3 and the corresponding Genhel-PSU settings

are outlined in Appendix A.

The first examination is if the various windowing techniques had an effect on the

colored filter generation while using Welch’s Method. Figure 3.2 shows the PSD of the

longitudinal equivalent gust velocity vector as well as the resulting filters generated from

the Hamming, Hann, and Blackman windowing techniques. The equivalent gust vector

was extracted from simulation hover time history data, as outlined in Eqs. 3.1-3.5. The

PSD of the equivalent gust was found using a Hamming window. The filters were

generated using the filter fit outlined in Eq. 3.7 and followed the windowing Eqs. 3.8-

3.10.

Figure 3.2 figure suggests that each of these windowing techniques will generate

very similar stochastic gust filters. Additional results for the v, w, p, q, r components can

also be found in Appendix B. Since the windowing technique does not affect our results,

this study will arbitrarily pick the Hamming Windowing for the rest of the filter fitting

results presented in this chapter.

27

Next, the new filter fitting method is compared to the filter fitting method in [16].

They both use Welch’s method and Hamming windowing, but the change in filter models

as described in Eqs. 3.6 and 3.7 are being examined. With the new filter fitting method, it

is desired that the filter fits be smoother through the frequency range of 0.4 to 10 rad/sec.

For the older filter fit, initial guesses were made for each of the filter fits. The

intensity factor,σ ,was initialized at 3. The length scale, L , was set to 10. The coefficients

in the numerator were set to 2.7478 and 0.3398. The coefficients in the denominator were

set to 2.9958, 1.9754, and 0.1539. A nonlinear least squares routine was used to

determine the filter coefficients that minimized the error between the equivalent gusts and

the filter fit.

100

101

10-2

10-1

100

101

102

103

104

Windowing Comparision for DDG81 25kt / 0 deg Hover

Freq (rad/sec)

u -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts

Hamming

Hann

Blackman

Figure 3.2: Longitudinal Equivalent Gust Velocity for the Windowing Comparison

28

For the new filter fit, the lower and upper bounds on the damping ratios were

constrained to be 0.1 and 2. Additionally, the natural frequencies and the pole location

were forced to be between 0.4 and 20 rad/sec. The gain K was constrained between 0 and

1000. Finally, an initial guess of 1 for each of the five parameters yielded the best results.

Again, a nonlinear least squares routine was used to determine the filter coefficients that

minimized the error between the equivalent gusts and the filter fit.

Two examples of the filter fits are seen in Figs. 3.3-3.4. One can see the new filter

design yielded better results. Additional results can be seen Section B.2.

100

101

10-2

10-1

100

101

102

103

Freq (rad/sec)

w -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts

Old Filter Design

New Filter Design

Figure 3.3: Vertical Velocity Equivalent Body Gust for the Filter Design Comparison

29

Finally, to demonstrate the filter design process can be used for any airwake and

WOD condition, the new filter design that used Welch’s method and Hamming

windowing was applied to two new airwake conditions. A hover, using the pilot model,

was performed in the LHA airwake for WOD conditions of 30 kts / 0 deg and 30 kts / 30

deg. The trajectory file information used to command a hover above landing spot 8, and

the settings for Genhel-PSU, is tabulated in Appendix A. A sampling of the results for the

extracted equivalent gusts and corresponding filter fits are in Figures 3.5-3.8. A figure for

every equivalent gust and filter fit can be seen in Appendix B. The final filter found for

each airwake and WOD conditions are outline in Tables 3.1-3.3.

Since this process works well, it should also be noted that the same process can be

applied to data collected during precision hovers maneuvers performed in flight testing of

full scaled aircraft.

100

101

10-4

10-3

10-2

10-1

100

101

Freq (rad/sec)

p -

Roll

Com

ponent [(

rad/s

)2]

Equivalent Gusts

Old Filter Design

New Filter Design

Figure 3.4: Roll Rate Equivalent Body Gust for the Filter Design Comparison

30

100

101

10-3

10-2

10-1

100

101

102

103

LHA Landing Spot 8: WOD Case: 30kts / 0deg

Freq (rad/sec)

w -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts

Welch / Hamming Filter

Figure 3.5: Vertical Velocity Equivalent Body Gust: LHA 30 kts / 0 deg

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

r -

Yaw

Com

ponent [(

rad/s

)2]

Equivalent Gusts


Figure 3.6: Yaw Rate Equivalent Body Gust: LHA 30 kts / 0 deg

31

100

101

10-1

100

101

102

103

104


Freq (rad/sec)

v -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts


Figure 3.7: Lateral Velocity Equivalent Body Gust: LHA 30 kts / 30 deg

100

101

10-4

10-3

10-2

10-1

100

101

102


Freq (rad/sec)

q -

Pitch C

om

ponent [(

rad/s

)2]

Equivalent Gusts


Figure 3.8: Pitch Component Equivalent Body Gust for LHA 30 kts / 30 deg

32

Table 3.1: Gust Filters Derived for DDG81 Hover Location, WOD: 25kts / 0deg

17958.02034.006506.0

26.33717.1197.0:

23

2

+++

++

sss

ssu

14771.01175.003711.0

179.105297.0007704.0:

23

2

+++

++

sss

ssp

17268.03531.006054.0

62.32477.11911.0:

23

2

+++

++

sss

ssv

14829.01262.003304.0

5583.00182.000322.0:

23

2

+++

++

sss

ssq

108.13706.007942.0

21.14391.11154.0:

23

2

+++

++

sss

ssw

16784.02818.005642.0

969.10699.001152.0:

23

2

+++

++

sss

ssr

Table 3.2: Gust Filters Derived for LHA LS 8, WOD: 30kts / 0deg

15478.01558.004946.0

896.77888.005844.0:

23

2

+++

++

sss

ssu

13036.0116.002419.0

299.001723.0002257.0:

23

2

+++

++

sss

ssp

1681.27087.02971.0

59.26445.13561.0:

23

2

+++

++

sss

ssv

13388.01362.002443.0

2412.001108.0001022.0:

23

2

+++

++

sss

ssq

1952.1145.12503.0

83.14305.32155.0:

23

2

+++

++

sss

ssw

1396.46638.04856.0

883.11175.002368.0:

23

2

+++

++

sss

ssr

Table 3.3: Gust Filters Derived for LHA LS 8, WOD: 30kts / 30deg

16776.02017.006615.0

64.67146.55576.0:

23

2

+++

++

sss

ssu

13921.01277.003402.0

075.21224.00119.0:

23

2

+++

++

sss

ssp

1127.28238.02247.0

1.120468.9366.1:

23

2

+++

++

sss

ssv

16801.02663.006962.0

197.21419.001553.0:

23

2

+++

++

sss

ssq

1567.3037.3708.1

3.1051.119427.8:

23

2

+++

++

sss

ssw

1218.15853.01661.0

106.97991.008261.0:

23

2

+++

++

sss

ssr

33

3.5 Discrete Filter Generation

It is the goal of this research to not only identify the airwake spectral properties,

but to also use the spectral information to produce a real time simulation environment. In

a real time application, the continuous filters will need to be transformed into discrete

filters. In this paper, the Tustin approximation method is applied [33]. The z-transform of

a continuous transfer function is approximated as:

Where the continuous frequency variable is estimated as:

In Eq. 3.12, T is the sample period. To demonstrate implementation, let’s take a standard

4th order continuous transfer function:

Substituting the z-transformation into Eq. 3.13, one can find the discrete transfer

function:

( ) ( )'sHzH = Eq. 3.11

1

12'

+

−=

z

z

Ts Eq. 3.12

εδχβα +⋅+⋅+⋅+⋅

+⋅+⋅+⋅′=

sss

dscsbsaKsH

234

23

s)( Eq. 3.13

34

A simplification of Eq. 3.14 leads to:

When the terms are expanded, Eq. 3.15 can be expressed as:

Where the coefficients i

k are expressed as:

( )εδχβα +

+

−+

+

−+

+

−+

+

−

+

+

−+

+

−+

+

−′

=

1

12

1

12

1

12

1

12

1

12

1

12

1

12

234

23

z

z

Tz

z

Tz

z

Tz

z

T

dz

z

Tc

z

z

Tb

z

z

TaK

zH Eq. 3.14

( ) ( ) ( ) ( )( )( ) ( )

( ) ( ) ( ) ( ) ( )( )( ) ( )

+++−⋅+

+−⋅++−⋅+−⋅

+++−⋅+

+−⋅++−⋅′

=

−−−

−−−−−

−−−

−−−−

4143113

2121213141

4143113

21212131

1112

114118116

1112

114118

)(

zTzzT

zzTzzTz

zdTzzcT

zzbTzzaTK

zHd

εδ

χβα

Eq. 3.15

4

10

3

9

2

8

1

76

4

5

3

4

2

3

1

21)(−−−−

−−−−

++++

++++′=

zkzkzkzkk

zkzkzkzkkKzH Eq. 3.16

35

For numerical implementation, one can solve for the output based on the previous

input values, previous output values, and the coefficients of the continuous transfer

function. The standard discrete transfer function is the output ( )zY divided by the

input ( )zX .

Cross multiplication leads to:

Then, to find the current output based on the previous inputs and outputs, the outputi

y is:

432

10

43

9

42

8

43

7

432

6

432

5

43

4

42

3

43

2

432

1

24816

441664

6896

441664

24816

248

4416

68

4416

248

TTTTk

TTTk

TTk

TTTk

TTTTk

dTcTbTaTk

dTcTaTk

dTbTk

dTcTaTk

dTcTbTaTk

εδχβα

εδβα

εχα

εδβα

εδχβα

+−+−=

+−+−=

+−=

++−−=

++++=

+−+−=

+−=

+−=

++−=

+++=

Eq. 3.17

( )( ) 4

10

3

9

2

8

1

76

4

5

3

4

2

3

1

21)(−−−−

−−−−

++++

++++′==

zkzkzkzkk

zkzkzkzkkK

zX

zYzH Eq. 3.18

( ) ( ) ( ) ( ) ( )[ ]( ) ( ) ( ) ( ) ( )4321

4321

109876

54321

−+−+−+−+

=−+−+−+−+′

kykkykkykkykkyk

kxkkxkkxkkxkkxkK Eq. 3.19

36

For implementation, a normally distributed random number vector is applied to

Eq. 3.20. The resulting output vector should have the same disturbance output as the

continuous transfer function when excited by the same random number vector.

3.6 Equivalent Body Gusts Transformed to Local Velocity Disturbances

Since the continuous filters were derived from extracted equivalent body gusts,

then the derived filters create equivalent body gusts when excited by a white noise vector.

For non-linear simulations, the equivalent body gusts need to be transformed into local

velocity disturbances. The local longitudinal, lateral, and vertical velocities due to the

stochastic component of the airwake can be found applying the following relations:

In Eq. 3.21, Xpos, Ypos, and Zpos are the components of a position vector of the

local component compared to the fuselage center of the aircraft. Moreover, Ubwake, Vbwake,

Wbwake, Pbwake, Qbwake, and Rbwake are the equivalent body gusts found at each time step by

[ ]

6

410`392817

453423121

k

ykykykyk

xkxkxkxkxkK

y iiii

iiiii

i

−−−−

−−−−

−−−−

++++′

= Eq. 3.20

posbwakeposbwakebwakes



ypxqww

zpxrvv

zqyruu

+−=

++=

+−=

Eq. 3.21

37

exciting the corresponding discrete transfer function filter. To find the total local velocity

of the airwake acting on component of the aircraft, then a time-averaged airwake value

also needs to be included.

In this study, the time-averaged airwake value is found from averaging the CFD

airwake velocity over the span of the time history for a particular location within the

airwake. It should be clarified that in Genhel-PSU, the airwake CFD files do not include

the steady nominal wind. For the DDG-81 WOD condition of 25 kts / 0 deg, the steady

nominal wind is 25 kts. For Genhel-PSU, it should be noted that the steady nominal wind

condition is a second deterministic airwake component, and is added into the final local

velocity under another variable name.

Finally, when computing the fuselage center local velocities, the u, v, and w

velocities due to the stochastic component of the airwake are simply the u, v, and w

equivalent body gusts. This is because the position vector would be zeros. To perform an

initial simulation testing of the stochastic filters, it is ideal to apply this simplification.

TAs

TAs

TAs

www

vvv

uuu

+=

+=

+=

Eq. 3.22

38

3.7 Initial Simulation Results

It is the purpose of this study to be able to recreate similar gusts as the CFD

simulation data in terms of the spectral properties of the velocity data when the linear

filters designed above are excited with white noise. In an initial implementation effort,

the continuous filters in Tables 3.1- 3.3 were excited with white noise in the SIMULINK

environment. Additionally, the continuous filters were transformed to discrete filters

using the Tustin approximation method described in Section 3.5. The discrete filters were

excited with the same white noise input vector as the continuous filters. The output of

discrete and continuous filters was then compared to the time history of the equivalent

gust vectors that were used in the derivation of the continuous filters. Finally, the time

history of the CFD velocity vectors that acted on the fuselage center during simulation

was plotted against the offline simulation results. When using the CFD velocity data set,

the mean velocity component was subtracted out such that only the stochastic gusts were

being compared. For frequency analysis, the PSD of the velocity components of the

continuous filters, discrete filters, extract equivalent gusts, and CFD velocity vectors

were found.

A full set of figures showing the comparison of the velocity vectors for the

translational and rotational axes for the DDG-81 with WOD conditions of 25 kts / 0 deg,

LHA 30 kts / 0 deg and LHA 30 kts / 30 deg can be found in Appendix Sections B.6-B.8.

For discussion purposes, the longitudinal and vertical velocity vectors for the DDG-81

will be examined as well as the corresponding PSD plots.

39

The longitudinal velocity component of the DDG-81 airwake is presented in

Fig. 3.9. The dark blue line is the results from exciting the Tustin discrete filter. The

green line depicts the disturbance from the continuous filter that was excited in the

SIMULINK environment. The red line represents the equivalent gusts determined by

removing the aircraft’s dynamics from the simulation results. Finally, the light blue line

is the stochastic portion of the CFD gust that acted on the center of the fuselage during

simulation. Overall Fig. 3.9 shows fairly good agreement. To examine the frequency

response, the PSD of each data set is taken in Fig. 3.10. The figure demonstrates similar

spectral properties and validates the continuous and discrete filters.

Next, the vertical velocity component of the DDG-81 airwake is examined in

Fig. 3.11. There is a discrepancy in the stochastic portion of the CFD gust as compared to

the equivalent gusts, continuous filter, and discrete filter results. Since the filters match

the equivalent gusts, one can pin point the error relating to accurately developing the

equivalent gusts and not in the filter fitting routines or the method of filter excitation.

When examining Fig. 3.12, it is clear that the magnitude of the PSD of the CFD gust is

not being accurately captured in the equivalent gusts. A possible source of error could be

the accuracy of the reduced order linear model. This is a key component in accurately

developing this method for industry applications and should be examined further. This

topic is presented as a suggestion for future work and is discussed further in Section 6.2.

40

0 20 40 60 80 100 120-15

-10

-5

0

5

10

15DDG-81 Hover Location: WOD Case: 25kts / 0deg

time [s]

u -

Velo

city C

om

ponent [(f

t/s)]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure 3.9: Initial Simulation: Longitudinal Velocity Equivalent Body Gust for DDG-81

100

101

10-4

10-2

100

102

104

DDG-81 Hover Location: WOD Case: 25kts / 0deg

Freq (rad/sec)

u -

Velo

city C

om

ponent [(f

t/s)2

]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure 3.10: Initial Simulation: Longitudinal Velocity PSD for DDG-81

41

0 20 40 60 80 100 120-15

-10

-5

0

5

10

time [s]

w -

Velo

city C

om

ponent [(f

t/s)]


Tustin

Simulink

Equivalent Gust

CFD Gust

Figure 3.11: Initial Simulation: Vertical Velocity Equivalent Body Gust for DDG-81

100

101

10-4

10-2

100

102

104


Freq (rad/sec)

w -

Velo

city C

om

ponent [(f

t/s)2

]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure 3.12: Initial Simulation: Vertical Velocity PSD for DDG-81

Chapter 4

Online Identification of Stochastic Filters

Developing a database of stochastic filters for every airwake condition that a

helicopter might encounter would require significant effort. As a result, it is also of

interest to develop an online learning algorithm that will learn and possibly reject gusts

during flight. This research study demonstrates an initial feasibility of an autoregressive

method used for online stochastic gust identification.

4.1 Previous Work

An initial feasibility study that was conducted by Horn, et al, [34] investigated

online learning algorithms to determine the deterministic and stochastic portions of a

CFD ship airwake. The study relied on a SIMULINK based tiltrotor simulation [35,36]

that used a composite airwake model of an LHA amphibious assault ship. The airwake

model incorporated time-averaged data provided by NAVAIR and Von Karman gust

models developed by Horn.

For identifying the stochastic airwake, the study used a Burg autogressive model.

In general, an autogressive model was selected for computational efficiency. Also, the

autogressive model is attractive because it does not require the time-domain data to be

transformed into the frequency domain. Overall, the study concluded that a 6th order

model is the minimum order model that would accurately estimate the stochastic airwake.

43

The paper then compared the online results of a 6th

order autogressive model to

benchmark filters found offline. The online filter results demonstrated convergence to

key peaks in the handling qualities frequency range when examining the magnitude plots

of the generated filters.

To continue this study, a 6th order Burg autoregressive model is implemented into

a real-time simulation environment in an effort to estimate the stochastic portion of a

CFD airwake. Successful integration can lead to future developments of an online

adaptive controller rejecting gust disturbances during flight. This goal is lucrative,

although it could be faced with opposition in industry as the new controller would have to

be proven to be robust in all flight conditions. A second motivation to this process is that

during flight, an external computer could be connected to the flight control system to

compute autogressive filters as a means to store data about the airwake behind a ship. As

a result, only the final filter coefficient values would need to be stored. This would

elevate the need to store large time histories of the aircraft dynamics during flight, as well

as minimizing the computational effort required to develop the filters in an offline

environment. The filters of the airwakes gathered during actual flights can then be used to

develop gust rejection controllers or to verify airwake simulations.

4.2 Burg Autoregressive Spectral Estimation

The Burg autoregressive model is a method to estimate the spectral properties of a

data signal by processing blocks of data at a time [37]. The Burg model offers an

advantage over other block estimation methods as it guarantees the generation of

44

minimum phase filters [38]. Additionally, Orfandis [38] states a rule of thumb that the

Burg model should work better than other autogressive models for short time histories of

data. Overall, all the methods will improve as the data records become longer.

As discussed in Chapter 3, the stochastic component of the airwake can be

estimated as a filter, that when excited by a white noise, recreates a disturbance similar to

the measured stochastic airwake in terms of the spectral properties. Orfandis presents the

signal modeling process as depicted in Fig. 4.1 where +pe is a prediction error sequence

that is approximately white, ( )zA is the prediction error filter that places poles, and n

y is

the disturbance output.

The optimal forward and backward predictors are defined by:

Where ( )ne p

+ and ( )ne p

− are found from filtering n

y through a prediction-error filter and

its reverse.

Figure 4.1: AR Filter Diagram [Orfandis, 1988]

( )[ ] ( )[ ] minmin22

== −+neEandneE pp Eq. 4.1

45

The Burg method then minimizes the least squares of both the forward and

backward prediction errors when determining the filter coefficients of ( )zA . When

solving for the filter coefficients, the Levinson-Durbin recursion must be used. The

Levinson-Durbin recursion is defined by:

Where the reflection coefficient,P

γ , is solved by:

In MATLAB, the autogressive filter solves for the Burg AR model and presents

the final filter as:

( ) pnppnpnpnp yayayayne −−−+ ++++= L2211

( ) npppnppnppnp yayayayne ++++= +−+−−−

L2211

Eq. 4.2

−

=

−

−−

−−

−−

−

−

−

1

011

1,1

2,1

1,1

,

1,1

2,1

1,1

,

1,

2,

1,

p

pp

pp

p

pp

pp

p

p

pp

pp

p

p

a

a

a

a

a

a

a

a

a

a

a

MMMγ Eq. 4.3

( ) ( )

( ) ( )[ ]∑

∑−

=

−−

+−

−−

−

=

+−

−+

−

=1

2

1

2

1

1

1

1

1

12

N

pn

pp

p

N

pn

p

p

nene

nene

γ Eq. 4.4

46

Where the order of A(z) is p, and G is a scalar gain. When the Burg estimator

block is used in the SIMULINK environment, a vector of A coefficients are returned,

along with the scalar G.

4.3 Real Time Workshop / Implementation into Genhel-PSU

To test the Burg model in a real-time simulation environment, Genhel-PSU had to

be modified. A controller was implemented into Genhel-PSU in which it accepted current

pilot commands, actuator commands, sensor outputs, trim values at initialization, and an

off or on switch from Genhel-PSU. If the switch is on, the controller will determine the

filter coefficients that best estimate the airwake properties by using a 6th

order Burg

autogressive model. The coefficients from the Burg model are written to a file.

Additionally, the controller simulates the general UH-60A BLACK HAWK mechanical

control system with SAS, so the controller passes out the actuator commands that are

used to move the swashplate in Genhel-PSU.

To develop the code for the controller, MATLAB’s Real Time Workshop (RTW)

complier was used. This is a picture to code approach that relied on SIMULINK models

of the UH-60 mechanical controls (with SAS) and of the Burg autoregressive model. The

RTW controller is developed as a dynamic link library (DLL) file that can be loaded by

Genhel-PSU during the initialization of the controller. The benefit of using a DLL file is

( )( ) ( ) p

p zpaza

GzH

−− ++++=

1211

L Eq. 4.5

47

that Genhel-PSU does not have to be recompiled every time a new DLL file is

implemented.

The UH-60A mechanical controls were validated by comparing the unaltered

Genhel-PSU model with simulation results of the RTW DLL file. The high level view of

the RTW controller can be seen in Fig. 4.2.

The gust filter identification block accepts the actuator commands as well as the

aircraft dynamics (sensor commands) at every time step of 0.01 sec. The gust

identification block first determines the equivalent body gusts as developed in Chapter 3.

Each extracted equivalent body gust is sampled at 20 Hz, or at every 0.05 sec, and is then

Figure 4.2: High Level View of the Gust Filter Identification Controller

48

passed to a buffer. The buffer collects 600 samples, or 30 sec, of equivalent gust vectors.

The buffer has an overlap of 560 samples, so that there is a smooth transition in filter

coefficients from one time step to the next. The deterministic portion of the equivalent

gusts (the mean of the signal) is then subtracted from the data set since the autoregressive

filter should only be estimating the stochastic winds. The signal is then sent to a 6th order

Burg autoregressive estimator block that is provided in the signal processing toolbox in

SIMULINK. The Burg model will determine new filter coefficients every 2 sec. The flow

chart for this process can be seen in Fig. 4.3.

The filter coefficients determined during the gust filter identification routine is

then sent to Genhel-PSU workspace, and written to a file at each time step. Since the

Burg autoregressive model will only update the filter coefficients every 2 sec, the

coefficients will be repeated in the output data file for 200 lines. For the initial feasibility

Figure 4.3: Gust Identification using a Burg AR Estimator

49

study, this did not create a problem in data processing. In future applications it may

become necessary to modify the code to only write when the filters are updated, or

perhaps only as needed as determined by other parameters. For large data collections

(hours of flight test data at several hover locations), it would become cumbersome to

have to handle and process unnecessarily large files.

4.4 Results of Burg AR Model

The autogressive model was implemented into Genhel-PSU and tested in the

DDG-81 airwake with a WOD condition of 25 kts / 0 deg. For this simulation, a new

linear model was developed to initialize the SIMULINK diagram used for RTW code

generation. The RTW was then used to generate a DLL file that was loaded into the

controls directory of Genhel-PSU. Once the DLL is loaded, Genhel-PSU is set to hover in

the selected wind condition with no additional SAS controllers turned on. Since the RTW

controller already estimates the UH-60A Mechanical system with SAS, adding additional

SAS to the controller would be adding additional SAS and skewing the results.

When the simulation is completed, the Burg AR model coefficients are examined

at every 20 seconds. To do so, the coefficients at each selected time step was used to

develop a filter. The frequency response of the transfer function was then compared to

the offline filter results found in Chapter 3. Over a short period time, one would expect

the Burg AR model to converge to the stochastic filter models determined in the offline

environment. Plots for each equivalent body gust can be found in Appendix C. Selected

figures for the DDG-81 CFD airwake and Burg AR Model are presented in Figs. 4.4-4.5.

50

100

101

-30

-25

-20

-15

-10

-5

0

5

10

15

20

pg (

dB

)

DDG81 25 kts 0 deg / AR Burg Method - 6th Order

Frequency (rad/sec)

Off-line

20 sec

40 sec

60 sec

80 sec

100 sec

120 sec

Figure 4.4: Online AR Filter Convergence for the Roll Rate Equivalent Gust

100

101

-35

-30

-25

-20

-15

-10

-5

0

5

10

qg (

dB

)


Frequency (rad/sec)

Off-line

20 sec

40 sec

60 sec

80 sec

100 sec

120 sec

Figure 4.5: Online AR Filter Convergence for the Pitch Rate Equivalent Gust

51

Overall, all of the figures show convergence to a given filter in the online

environment; however, the convergence isn’t always to the filter found in the offline

environment. One draw back to the Burg AR model is that it analyzes the entire

spectrum, whereas the filter fitting technique in Chapter 3 was able to constrain the filter

fit to a frequency range between 0.4 and 10 rad/sec. This overall fitting method by the

Burg method may capture peaks at higher frequencies that are not of interest, and

providing a slightly worse filter fit through the frequencies that affect handling qualities

the most.

Even though the Burg method tends to capture the PSD within the spectral filter

over a larger range of frequencies, the Burg method still demonstrates convergence to

peaks at the same frequencies as the offline filter results. Sometimes, the magnitudes of

the PSDs from the Burg model are slightly lower than the offline filter results.

Chapter 5

Simulation Modeling of Airwakes Using Stochastic Filters

This chapter discusses the simulation modeling of an airwake using stochastic

filters. First, the motivation of this research effort is reviewed. Then, the details of the

simulation modeling and the code used for implementation into Genhel-PSU are

discussed. Finally, the simulation results from using this airwake in Genhel-PSU and

Sikorsky GENHEL are examined.

5.1 Motivation

In an effort to improve the simulation model of the shipboard environment, this

study examines replacing the detailed CFD-based ship airwake models presented in

Chapter 2 with a grid of stochastic filters. By relying on a CFD model, 3-axis velocity

data had to be stored into memory prior to running a simulation. Due to memory

requirements, limitations were placed on the length of the airwake and/or the fidelity of

the simulation. With these limitations, the CFD airwake is usually limited to 40-60

seconds of data. To run longer simulations, the airwake can be repeated; however, there

are noticeable repetitions in flight simulation data.

To reduce the dependence on memory requirements, this research moves towards

using a grid of stochastic filters that will be excited by random white noise input. For this

simulation environment, only the filter coefficients and time averaged CFD data for the

53

entire grid need to be stored into to memory. The benefits are that the airwake is no

longer constrained by memory requirements and that the airwake can be run indefinitely

without noticeable repetitions of data. Additionally, this approach could be used to

develop a stochastic airwake model derived from experimental data. This offers an

alternative to relying solely on a CFD model that may have uncertainties.

5.2 Stochastic Filter Grid Design

For an initial feasibility study of the stochastic airwake, a new grid design was

developed. At each grid point, the stochastic filter coefficients for the translational and

rotational axes are known. If the aircraft is in between a set of grid points, then the

stochastic filter coefficients would be interpolated. To minimize the dependence on

computing power requirements, but trying to create an accurate environment, it was

decided to design a grid around the desired landing path for a pilot performing a

shipboard landing. For this design, there is a condensed cluster of filters near the ship

deck, and sparsely placed filters near the start of the pilot’s approach. This was done

because the airwake is more turbulent behind hangar doors than 800 ft back. By selecting

a less detailed grid in areas expected to have a smaller changes velocity data, the

computational effort will be further reduced.

The grid was defined by first creating a vector of x-coordinate locations which

specified the distances behind the ship deck for each y-z grid plane. For this grid, there

are 11 equally spaced grid points with lower and upper bounds at x-airwake coordinates

of 424 and 574 ft. Then there are an additional four equally spaced coordinates behind

54

them with an upper bound of x-coordinate of 1000 ft. Overall, this would create a vector

ix , of length 15. Again, the vector ix ensured that the details of the ship airwake would

be preserved in the area with the highest turbulence near the ship deck, and allowed for

reduced computing power further out away from the deck where the ship airwake tends to

have smaller changes in disturbance characteristics.

Next, a matrix of x-y coordinates was defined using a constant change in the

parameter β . The vector of β angles is derived from the relationship of a desired y

coordinate with the x midpoint coordinate of 574 ft. The jβ vector is defined as:

In Eq. 5.1, 1Px is the midpoint x value of 574 feet. The variable 1Py is the

maximum y value at the midpoint 1Px . For this grid, yP1 was selected to be 80 ft. The

vector jβ is selected to have a length of 3. This would create angle of zero degrees at the

center line of the ship, and two angles extending in the positive direction. When creating

the full matrix x-y matrix, the y-values from the positive side of the grid will be mirrored

across the center line of the ship to create a symmetric grid. Finally, ny in Eq. 5.1 is

defined as ( )1−j .

The y-coordinate values are a function of the jβ vector and the ix vector. The x-

y matrix of size ( )ij , is found computing Eq. 5.2.

( ) ( )1tan

tan 11

1

1

11 −−

=

−−

j

n

PP

P

Pj i

y

xy

x

yβ Eq. 5.1

55

The x-y matrix is then mirrored about the center line of the ship to create a

symmetric x-y matrix of size [ ]( )ij ,12 − . The x-y coordinate grid can be seen in Fig. 5.1.

In this figure, the black circles represent the x-y coordinate location for a particular set of

translational and rotational equivalent gust body filters.

Next a matrix of x-z coordinates was defined. This used a similar approach to the

x-y coordinate matrix, but employed a constant change in a parameter α . The vector of

( )jiij xy βtan, = Eq. 5.2

500 600 700 800 900 1000

-200

-150

-100

-50

0

50

100

150

200

x (ft)

y (

ft)

Figure 5.1: Schematic of the x-y coordinate grid.

56

α angles is derived from the relationship between the difference in the upper and lower

bound of the z-axis when compared to the x axis. The kα vector is defined as:

In Eq. 5.3, the parameter min0Pz is the lower limit of the z-coordinates and is

defined as 24.2 feet. This was set from the lowest possible grid point that allowed the

aircraft to trim in Genhel-PSU while running the CFD DDG-81 airwake. The upper

bound of the z-axis at location 1x , is the parameter max0Pz . It is defined as 60 ft, which

gave adequate room to hover in the z-axis. The vector kα has a length of 5, and nz is

defined to be ( )1−k .

The z-coordinate values are a function of the kα vector and the ix vector. The x-z

matrix of size ( )ik , is found computing Eq. 5.4.

The x-z coordinate grid can be seen Fig. 5.2. In this figure, the black circles

represent the x-z coordinate location for a particular set of translational and rotational

equivalent gust body filters.

( )1

tan

tan0

min0max01

0

min0max01 −

−

−

−=

−

−k

n

P

PP

P

PP

ki

z

x

zz

x

zzα

Eq. 5.3

( ) min0, tan Pkiik zxz += α Eq. 5.4

57

Incorporating the x-y and x-z matrices together, a three dimensional matrix can be

composed. The grid concentrated around typical areas that the pilot would fly during the

approach to a landing on the back of the destroyer and also allowed significant space for

the pilot to deviate from the desired flight path. A three dimensional view of the

stochastic grid can be seen in Fig. 5.3.

400 500 600 700 800 900 10000

50

100

150

x (ft)

z (

ft)

Figure 5.2: Schematic of the x-z coordinate grid.

58

5.3 Implementation into GENHEL-PSU

To implement the stochastic airwake into Genhel-PSU, additional code had to be

written. The original method for incorporating airwake effects was that first the entire

CFD airwake was read into memory. Then, each aircraft component would call the

memory to determine the local airwake velocity by interpolating the x, y, and z velocities

in time and with a weighted position coordinate.

The new modifications will first read in stochastic and deterministic airwake

grids. The stochastic grid is the same as what was presented in Section 5.2. The

deterministic airwake is simply the time averaged solution of the CFD airwake, so the

grid used for deterministic portion is the same grid file as the CFD airwake that is

500

600

700

800

900

1000

-100

0

100

50

100

x (ft)

y (ft)

z (

ft)

Figure 5.3: Three Dimensional View of the Stochastic Filter Grid.

59

presented in Section 2.2.1. Also during initialization, a file containing the stochastic filter

coefficients for each stochastic grid point is read in, as well as a file with the u, v, and w

time averaged velocities for each deterministic grid points.

Finally, to excite the stochastic filters during flight, a white noise source is

required. During the initialization of Genhel-PSU, an arbitrarily long random number

vector for each six stochastic components is read into memory. The built in random

number generator in FORTRAN is not used because the white noise source must be

normally distributed. MATLAB offers a randn command that can be used to create a

normally distributed vector. Saving the MATLAB workspace of six normally distributed

vectors to a text file provides a quick solution for the initial implementation effort.

After Genhel-PSU is initialized, the stochastic airwake program is called at every

time step by main aerodynamic module. The stochastic airwake subroutine accepts the

fuselage location and translates it from North, East, Down (NED) coordinates to airwake

coordinates. For visualization, the aircraft, ship, and airwake coordinate system is

illustrated in Fig. 5.4.

Figure 5.4: Genhel-PSU Coordinate System Diagram

60

Once in airwake coordinates, the program determines the aircraft’s location both

in the stochastic and deterministic grids. Additionally, the nearest 8 grid points from each

grid are determined. Figure 5.5 shows the aircraft fuselage’s position within either grid

system. Note that the grid will fan out in both the y and z coordinates in both the

stochastic and deterministic airwake grids.

The airwake program then needs to determine the local stochastic filter

coefficients. The nearest eight grid points’ filter coefficients are read from the stochastic

filter matrix. A location-weighted interpolation is performed to find the stochastic filter

coefficients for the local point in the stochastic airwake grid. The local coefficients are

then passed into a Tustin subroutine with a newly selected random number. The

subroutine follows the methodology of Section 3.5. This subroutine also requires the last

four Tustin routine outputs and the last four random numbers. These values are saved into

two arrays from time step to time step, and are updated after each Tustin calculation. The

new Tustin output is the current stochastic airwake velocity component. Since the

Figure 5.5: Aircraft Position and Nearest Eight Grid Points

61

stochastic filters are derived in the aircraft’s body coordinates, the current stochastic

component is considered to be the stochastic airwake velocity acting on the center of the

fuselage in body coordinates.

Next, the deterministic velocity is determined. Similar to the stochastic method, a

location-weighted interpolation is performed to find the local time averaged velocities.

Since the local time averaged velocities are in airwake coordinates, the values are

transformed into body coordinates. The u, v, w deterministic components are then added

to the stochastic u, v, w components. The summation of the time averaged velocities and

the stochastic local components are then stored into a global ‘body wake’ variable. In

Genhel-PSU, the u component is called UBWAKE. The other five components have

similar variable names.

Each aerodynamic component (Fuselage, Main Rotor, Tail Rotor, Tail) will rely

on these ‘body wake’ variables to determine the local component velocity. Since the

global variables are actually the equivalent body gusts (plus the time averaged velocity

components), it is necessary to transform the equivalent body gusts to the local

component velocities using the Eqs. 3.21-3.22. Note that it is technically incorrect to pass

the time averaged values through Eq. 3.21; however, since these variables are only faced

with addition and subtraction and would eventually be added through Eq. 3.22, this

implementation method should be okay. Additionally, since in the Genhel-PSU airwake

environment differentiates between the mean steady wind and airwake turbulence

velocities, the mean steady wind will then need to be added to the final stochastic and

time averaged velocities to find the total wind velocity for aerodynamic calculations.

62

Overall, this program methodology should provide a good first implementation of

a stochastic airwake; however, there are known limitations of the program. First, the

aircraft must remain inside the airwake. The simulation will not store zeros into the

output and input vectors of for the Tustin subroutine when the subroutine is not called. As

a result, when the aircraft moves out of the airwake, and then reenters, it will rely on

information from a few time steps ago. Second, this program assumes the aircraft is at the

same attitude at which the helicopter had during the hover maneuver performed to

generate the continuous filters. If the aircraft nears the back of the ship with sideslip, or a

nose down attitude, then the simulation may not provide an accurate estimation of aircraft

disturbances. Finally, the length of unrepeated flight simulation data is dependent on the

length of the random number vectors read into memory at the start of simulation.

5.4 Genhel-PSU Stochastic Airwake Results

To test the stochastic airwake code, a simulated hover was performed in the

stochastic airwake and at the corresponding location within the DDG-81 CFD airwake.

The PSD of the inceptor commands that were created from the pilot model are examined

and compared for both airwakes. Additionally, the PSD of the airwake velocities acting

on the aircraft at the fuselage center are examined. For confirmation of the results, the

analysis process was performed at several locations. Four of these simulated hover

comparisons are outlined in Appendix D. The four locations presented are 544-37-58,

439-0-42, 454-0-52, and 454-31-33. The numbers present the X-Y-Z airwake coordinate

positions. For example 454-31-33 was a hover performed at 454 ft behind the origin of

63

the ship, 31 ft to the starboard side of the ship, and 33 ft above the origin of the ship. For

clarity, one can reference Fig. 5.4.

Overall, the PSDs of lateral stick inputs corresponded well at lower frequencies

and tended to develop discrepancies at higher frequencies. The longitudinal inputs

showed more consistent results across the frequency range, but in specific cases exhibited

a constant a small shift in magnitude. In the collective stick input, the PSDs were

consistent between the CFD and stochastic airwakes. When examining the pedals, the

PSDs had varying results across the frequency range but suggest a correlation between

the workloads between the CFD and stochastic airwakes. Figures 5.6- 5.9 present sample

results for each inceptor input.

64

100

101

10-6

10-4

10-2

100

102

DDG-81 WOD Case: 25kts / 0deg at 439-0-42

Freq (rad/sec)

Late

ral S

tick, X

a [(%

)2]

Stochastic

CFD

Figure 5.6: Lateral Stick Input for 439-0-42 Location

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

Longitudin

al S

tick, X

b [(%

)2]

Stochastic

CFD

Figure 5.7: Longitudinal Stick Input for 454-0-52

65

100

101

10-5

10-4

10-3

10-2

10-1

100

101


Freq (rad/sec)

Colle

ctive S

tick, X

c [(

%)2

]

Stochastic

CFD

Figure 5.8: Collective Stick Input for 454-0-52

100

101

10-8

10-6

10-4

10-2

100

102


Freq (rad/sec)

Pedals

, X

p [(

%)2

]

Stochastic

CFD

Figure 5.9: Pedal Inputs for 544-37-58

66

When examining the PSDs of the airwake velocities acting on fuselage center,

clear trends emerged. The longitudinal axis PSD matched well where as the vertical axis

tended to show large discrepancies. Overall, the stochastic airwake tended to be less

violent in terms of the vertical axis. When comparing the CFD airwake and the stochastic

airwake for the lateral axis, the data tended to match at low and high frequencies, but

showed a weaker stochastic velocity in the middle of the handling qualities range.

Samples of each axis are shown in Figs. 5.10-5.12.

100

101

10-4

10-2

100

102

104


Freq (rad/sec)

U -

Velo

city a

t F

usela

ge [(f

t/sec)2

]

Stochastic

CFD

Figure 5.10: Longitudinal Velocity of Gust acting on the Fuselage center for 439-0-42

67

100

101

10-2

10-1

100

101

102

103

104


Freq (rad/sec)

V -

Velo

city a

t F

usela

ge [(f

t/sec)2

]

Stochastic

CFD

Figure 5.11: Lateral Velocity of Gust acting on the Fuselage center for 454-0-52

100

101

10-2

10-1

100

101

102

103


Freq (rad/sec)

W -

Velo

city a

t F

usela

ge [(f

t/sec)2

]

Stochastic

CFD

Figure 5.12: Vertical Velocity of Gust acting on the Fuselage center for 439-0-42

68

The discrepancies in the vertical axis and lateral axes are not clearly explained.

One source of error could be that the stochastic filters are derived from a helicopter

trimmed in a hover. The trimmed hover maneuver tends to leave the helicopter slightly

nose up and tilted in a left-wing down position. As a result, when the equivalent gusts are

extracted, there is an error in the assumption that we are fitting a filter to the direct lateral

and vertical gusts.

Although there are differences in a direct wind comparison between the CFD and

stochastic airwake solution, the goal of this study to be able to find a stochastic airwake

solution that will induce the same pilot workload. The simulated hovers near specific grid

points produced reasonable results with some inconsistencies.

To further examine the control effort required in the stochastic airwake, two

simulated approach to landings were performed. In the first trajectory path, the aircraft

started in a hover 450 ft behind the ship deck and 60 ft to the starboard side at an altitude

of 77 ft. After 30 sec, the aircraft takes 30 sec to move the aircraft to a location near the

desired landing spot. The aircraft hovers for a full minute before the end of the

simulation. The second approach is similar; however, the starting location is about 400

feet behind the ship deck, 35 ft on the port side of the ship, and at a height of 60 feet. The

trajectories were flown in both the stochastic airwake and the CFD airwake. Additionally,

to determine how much pilot workload required by the maneuver, versus how much an

airwake would affect the pilot workload, the same trajectory paths were also flown in a

steady 25 kts wind, with no airwake turbulence.

The trajectory paths and sample flight paths for the aircraft flying both maneuvers

within the stochastic airwake can be found in Appendix D. Additionally, the PSD

69

comparison of inceptor commands required to perform the maneuver in each wind

airwake condition are presented. Overall, there is remarkable agreement between the pilot

workload required in all axes between the CFD and stochastic airwakes. Additionally,

one can see that the airwake turbulence tends to affect the lateral and pedal pilot

workload more than the longitudinal axis workload. Another interesting observation is

that most of the pilot workload in the collective came from flying the maneuver, only a

slight increase in PSD magnitude was found for the airwake conditions. Two sample

figures are presented in Figs. 5.13 and 5.14. Again, a complete set of figures are shown in

Appendix D.

70

100

101

10-6

10-4

10-2

100

102

DDG-81 WOD Case: 25kts / 0deg

Freq (rad/sec)

Pedals

, X

p [(

%)2

]

Stochastic

CFD

No Airwake

Figure 5.13: Pedal Input for Trajectory Path 1

100

101

10-4

10-2

100

102

104


Freq (rad/sec)

Colle

ctive S

tick, X

c [(

%)2

]

Stochastic

CFD

No Airwake

Figure 5.14: Collective Stick Input for Trajectory Path 2

71

5.5 Implementation into Sikorsky GENHEL and Piloted Results

The stochastic filter airwake was also implemented into Sikorsky GENHEL. The

grid outlined in Section 5.2 was programmed into the real-time simulation by Sikorsky

Aircraft Corporation. Each grid point included six colored filters developed using the

mythology presented in Section 3.3, and excited with a white noise input. The simulation

was of the S-92 FBW aircraft flying in the airwake model behind a DDG-81 with a WOD

condition of 25 knots / 0 deg.

To asses the new airwake model, piloted simulations were performed. The model

was tested with six pilots; three with Navy backgrounds, three with Army backgrounds.

All pilots were new to flying the S-92 fly-by-wire type aircraft. The pilots were asked to

fly the MTE outlined in Section 2.4.1.

The piloted simulations were a smaller mission task of a larger simulation testing

program that evaluated different gust alleviation controllers as well as several airwake

models of the turbulence behind the DDG-81. The simulations presented here will only

compare the CFD airwake model provided by NAVAIR with the stochastic airwake

model, with no gust alleviation controllers active in the system. The pilots were asked to

rate the workload using the Cooper-Harper rating system for HQR values. Additionally,

the aircraft position, attitudes, rates and pilot stick/pedal input were recorded for each

simulation run.

From the piloted simulations, the pilots generally felt the stochastic airwake was

slightly more violent than the CFD airwake. In terms of HQRs, the pilots rated the

stochastic airwake case with an average of 4.75, which is nearly 0.75 higher than the

72

CFD airwake turbulence case. The consensus of the pilot comments was that the

workload was increased compared to the CFD solution; however the large 0.75 HQR

difference may be due to a HQR rating of 7 given by a single pilot. Some pilots

commented that there was a large pull on the aircraft near the hanger roof, which was not

present in their CFD case runs. A summary of HQR ratings per pilot can be seen in

Fig. 5.15.

To examine the HQRs and pilot comments more, pilot workload was analyzed by

plotting the PSD of the pilot control inputs. Figs. 5.16-5.18 show sample PSD plots of

various pilot’s input for both the CFD and stochastic filter airwakes, as well as with the

Figure 5.15: Pilot HQR assessment for various Airwake conditions

73

airwakes turned off. The data selected for this analysis is the pilots performing a 30

second hover over the landing spot. These figures show that the stochastic airwake is

fairly comparable in PSD magnitudes. When examining several of the pilots, it is clear

that once again the workload in the collective axis tends to come from the maneuver

itself. Typically in this set of data, the collective PSD for the no airwake condition

matches the CFD and stochastic airwake PSD values. Additional PSD plots can be seen

in Appendix D.3.

100

101

10-8

10-6

10-4

10-2

100

Frequency (rad/s)

PS

D o

f Late

ral S

tick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake

Figure 5.16: Lateral Stick Input for Pilot 4

74

100

101

10-6

10-4

10-2

100

102

Frequency (rad/s)

PS

D o

f Long. S

tick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake

Figure 5.17: Longitudinal Stick for Pilot 5

100

101

10-6

10-4

10-2

100

102

Frequency (rad/s)

PS

D o

f P

edals

, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake

Figure 5.18: Pedal Input for Pilot 6

75

The HQR ratings leave room for question on to why the stochastic airwake was

perceived as more difficult to fly. Although some PSD figures show comparable results,

there are a few figures that show the CFD airwake as more work, as well as some figures

showing the stochastic airwake as requiring more pilot work load. The HQR ratings

should be used as a reason to further explore possible complications.

One known problem with the Sikorsky GENHEL stochastic solution is that the

filters were generated 13 ft higher from the perceived location. (This error was corrected

in the Genhel-PSU based simulation.) The 13 ft error would most likely cause the

airwake to be more violent behind the hangar doors because there wind shear effect off

the back of the superstructure that is now 13 ft lower than expected. Additionally, a

trained pilot may not be expecting the wind sheer to occur at this height.

Another possible problem may be the random number generator for the Tustin

filter computation. At the time of simulation testing, the random number generator was a

uniformly distributed vector, and not a normally distributed noise vector. The resulting

stochastic model disturbance would not be as realistic with the uniformly distributed

vector.

Overall, both the Genhel-PSU and Sikorsky GENHEL testing show that

stochastic airwake could be developed in the manner presented in this paper to be used in

future simulation testing. Although some errors emerged in correlating the stochastic

airwake to the CFD airwake, the pilot workload induced by Genhel-PSU was very similar

between the airwakes. The piloted simulation HQR results suggested slightly higher

workload; however, it would need to be tested further to detect additional problems.

Chapter 6

Conclusions

Shipboard operations continue to be one of the most challenging for naval pilots.

The unsteady winds and moving ship deck make precision hovering and landing tasks

increasingly difficult. The pilot workload created during these tasks can often be a

limiting factor in the WOD envelop for a particular ship and aircraft combination. To

improve the handling qualities of aircraft flying in these adverse conditions, recent

research has been performed in industry to identify and reject gust disturbances. To test

flight control modifications and to train maritime pilots, significant effort has also been

put towards developing accurate real time simulation models.

This research study further investigated the shipboard landing environment by

developing tools to accurately identify the spectral properties of the stochastic winds in

both an offline and online environment. The principles from the wind identification were

then applied to create a real time stochastic simulation model that required less

computational effort than a full CFD solution.

6.1 Analysis Summary

For control law gust rejection development and accurate real time simulation

models, it is desirable to be able to accurately identify the spectral properties of the

stochastic winds affecting pilots during shipboard operations. Previous work suggested

77

fitting von Karman turbulence models to the power spectral density of an aircraft’s

equivalent airwake gust. This method was modified by changing the fitting routines to fit

an ordinary third order transfer function to the spectral properties. This technique was an

improvement because it guaranteed stable filters that were design to fit the equivalent

gusts through the frequency range that affects the handling qualities of an aircraft most

(0.4 to 10 rad/sec). Additionally, the filter fitting routines were explored by trying

different windowing techniques. It was found that the popular windowing techniques did

not affect the final filter fit.

As an initial simulation effort, the continuous gust identification filters were

transformed into discrete filters using a Tustin 4th

order model. The discrete and

continuous filters were excited with a normally distributed white noise and compared to

the extracted CFD gusts. The continuous and discrete filters provided almost identical

stochastic results. When comparing the filter results to the CFD model, the longitudinal

axis generally had the same PSD magnitudes. The lateral axis matched slightly less.

There was significant misalignment in terms of the PSD magnitudes of the vertical gusts

between the stochastic filters and CFD model.

Since it would be computationally intensive to collect data and generate filters for

every ship, aircraft, and WOD combination that an aircraft might encounter, it is

desirable to develop a gust identification technique that can be performed during flight or

in an online simulation environment. A previous study suggested Burg 6th order AR

models. To explore this subject more, the Burg models were integrated into Genhel-PSU

using generic controller that accepted a dynamic linked library file that contained a UH-

60A mechanical model (with SAS) as well as a Burg AR model used to identify filters of

78

the equivalent gusts acting on the aircraft. The DLL file was created using MATLAB’s

Real Time Workshop, which converted a SIMULINK diagram of the mechanical controls

and the gust identification techniques to code.

During real time simulations in Genhel-PSU, the Burg AR Models were capable

of identifying key spectral peaks of the gust. It was shown the Burg AR Models could be

used to store the filter coefficients in an online environment, and could be used in future

industry applications.

Finally, the gust identification principles were used to develop a stochastic model

of the DDG-81 CFD solution provided by NAVAIR. In the first third of the research, it

was found that three rotational and three translational gust filters could be defined based

on equivalent gusts. A grid was defined that focused on a typical flight path for a pilot

landing on the back of at a ship. For each grid point, the six filters were developed.

Additionally, a time-averaged velocity solution was found from the CFD solution for a

series of grid points.

A stochastic airwake code was implemented into Genhel-PSU that during

initialization, read in the stochastic airwake grid, stochastic airwake continuous filter

coefficients, time-averaged airwake grid, and time-averaged velocity values. During

flight, the aircraft’s position was used to perform a position weighted interpolation of

stochastic filter coefficients and time averaged values. The stochastic filter coefficients

were then passed to a Tustin subroutine that accepted a normally distributed white noise

input to excite the discrete filters. The stochastic wind components were added to the

time averaged components, and passed back to the general aerodynamic model to

calculate local body velocity coordinates.

79

To test the stochastic airwake model, hover simulations were performed within

the CFD airwake and the stochastic airwake. The PSD of the pilot inputs were compared

between the airwakes. It was found that they generally agreed with a few discrepancies.

The longitudinal, lateral, and vertical velocities acting on the fuselage center was also

examined. It was found the PSDs compared well for the longitudinal axis between the

CFD and stochastic airwake model. The lateral axes had some discrepancies in the

middle of the handling qualities frequency range, and the vertical axis did not match well.

During the simulation testing of the stochastic model, the aircraft was also

commanded to fly a trajectory path that included an initial hover, to fly towards the

landing spot, and then to hover for another 60 seconds. The PSD of the pilot inceptor

commands matched extremely well between the CFD and stochastic airwake model. The

success from this testing suggests that this method could be used for accurate real time

simulation environments. The benefit to such simulation models is that it is less

computationally demanding on computing requirements and that the airwake solution

would not have to be continuously cycled. In past work, repetitions in flight data were

found when the CFD solutions were repeated for longer real time simulations. Moreover,

this technique could be used to derive airwake simulation model from flight test data.

This is beneficial as CFD solutions can sometimes include uncertainties.

Finally, the stochastic airwake model was also implemented into Sikorsky

Genhel. Piloted simulations were performed where the pilots were asked to fly a specific

maritime Mission Task Element, and then to rate the pilot workload on the Cooper-

Harper Rating scale. Overall, the pilots commented that the stochastic airwake was more

violent than the CFD airwake solution. In particular, the pilots rated the stochastic

80

airwake to be 0.75 HQRs higher than the CFD solution. When examining the pilot

command inputs between the CFD and stochastic airwake, no clear indication was found

to what was causing the pilots to feel the stochastic airwake model was more violent. In

several cases, the PSD of the pilot stick commands were similar between the CFD and

stochastic airwakes. In a few cases the stochastic airwake did create more workload, but

in other cases the CFD provided to be more work also.

During analysis of the Sikorsky GENHEL results, it was realized that the filters

were generated from the CFD solution 13 ft higher than expected. As a result, the filters

were effectively 13 feet lower in real time simulation than what they should have been.

This would have created misalignment between the stochastic airwake model and the ship

visuals that the pilots relied on to perform the MTE tasks. This could be related to the

differences seen as the pilots would have felt a strong wind shear below the visual ship

superstructure instead of it being aligned with the superstructure.

6.2 Recommendations for Future Work

Although this research has made significant progress in creating accurate gust

identification models and a stochastic airwake model, a few points could be examined in

greater detail. The first relates to the equivalent gust extraction process, and the second

relates to known limitations of the programmed stochastic airwake grid within Genhel-

PSU.

81

6.2.1 Equivalent Gusts

Overall the gust identification in both the offline and online environments worked

well in evaluating the key spectral properties of the equivalent gusts. However, when the

initial simulation was run where the continuous filters from the offline identification

method was excited, there were significant discrepancies found the vertical axis as

compared to the CFD airwake gusts. Since the filter fits showed agreement between the

equivalent gusts and the generated gusts from the continuous filters, the error must fall

from the equivalent gust extraction method. It is suggested that this area be examined

further. A suggested area is to resolve whether the reduced linear model is accurately

representing the aircraft dynamics.

6.2.2 Stochastic Airwake Model Limitations

When programmed, the stochastic airwake subroutine for Genhel-PSU was

developed with known limitations:

First, the subroutine assumes the aircraft is at the same attitude at which the

helicopter had during the hover maneuver performed to generate the continuous filters. If

the aircraft nears the back of the ship with sideslip, or a nose down attitude, then the

simulation may not provide an accurate estimation of the stochastic aircraft disturbances.

Secondly, the time averaged airwake values are passed in through the body wake

variables (eg. UBWAKE). This assumption also requires the aircraft is aligned with the

ship axes. If the aircraft is in a side slip 90 degrees to the right, then the u-component

time averaged solution is still being added to from the nose of the aircraft, and not from

82

the side of the aircraft. It is suggested that this be reprogrammed to first assume that the

body wake variables are actually in ship airwake coordinates (instead of body

coordinates.) This might be a reasonable assumption since the body coordinates are fairly

well aligned with the ship axes with the filters are derived.

Next, the stochastic airwake grid should be expanded to include more grid points.

It is known that the PSD of the CFD airwake changes rapidly in magnitude along the

vertical axis over the ship deck. It is suggested to add more grid points to create a tighter

grid above the ship deck. Additionally, adding points to the left and right of the ship deck

would allow for simulated trajectories to approach the back of the ship at various angles

instead of just shallow sideslip maneuvers.

Finally, the length of unrepeated flight simulation data is dependent on the length

of the random number vectors read into memory at the start of simulation. The stochastic

airwake subroutine requires a set of random number vectors to be read into simulation

because the built in random number generators in FORTRAN are not normally

distributed. Future work in this area should involve developing a subroutine that

calculates a normally distributed random number vector series during real time

simulation. With this subroutine included, Genhel-PSU could run indefinitely without

noticeable repetitions in flight data.

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22. Jensen, J.J., Mansour, A.E., and Olsen, A.S., “Estimations of Ship Motions Using

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in Airwakes,” Ph.D. Thesis, Department of Aerospace Engineering, The

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Forum, Montreal, Canada, May 2008.

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Appendix A

Settings for Genhel-PSU

Table A.1: DDG-81 Hover Coordinates

Airwake Coordinates:

X 430

Y 0

Z 0

Trajectory File (Flight Gear Off):

X -204.8525

Y 0

Z 27.8683

Trajectory File (Flight Gear On):

X -204.8525

Y 0

Z 14.6754

Standard WOD Condition 25 kts / 0 deg

Table A.2: LHA Hover Coordinates

Trajectory File (Flight Gear Off):

X -307.9400

Y -46.2500

Z 93.7773

Trajectory File (Flight Gear On):

X -307.9400

Y -46.2500

Z 87.6999

Standard WOD Conditions: 30 knots / 30 deg

30 knots / 0 deg

88

Table A.3: Genhel-PSU Matlab GUI Interface

Initial Conditions

Location: Other

Latitude [deg N] 0.02

Longitude [deg W] 0.02

X-Offset [ft] Set by Trajectory File

Y-Offset [ft] Set by Trajectory File

Z-Offset [ft] Set by Trajectory File

Altitude [ft] Set by Trajectory File

Speed [kt] Set by Trajectory File

χ [deg] 0

γ [deg] 0

ψ [deg] 0

Weight/CG Location

Weight [lb] 16825.0

Fuse. Station CG [in] 355.0

Waterline CG [in] 248.2

Buttline CG [in] 0.0

Control Settings

Pilot Model - ON Roll SAS – ON

Analog SAS – ON Pitch SAS – ON

Digital SAS – ON Yaw SAS – ON

ECU – ON Automatic Stabilator Control – ON

Controller: UH-60 Mech (All other settings OFF)

Other Settings

Inflow Model: Pitt-Peters

Blade Segments: 30

Output Decimation: 1

Zero Sideslip Speed [kts]: 60

Ground Effect: Turned On

Time Step [s], [deg]: 0.01, 15.4699

Turbulence: Airwake

Wind Speed, Direction: Set by Airwake Selections

Appendix B

Offline Stochastic Filter Fitting Results

B.1 Windowing Comparison

The PSDs of the equivalent gusts were found using Welch’s Method and three

different types of windowing techniques to determine which windowing technique would

provide the best filter fit. The analysis used the UH-60A hovering in the DDG81 with a

WOD condition of 25kts / 0deg at the hover location described in Appendix A,

Table A.1.

100

101

10-2

10-1

100

101

102

103

104


Freq (rad/sec)

u -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts

Hamming

Hann

Blackman

Figure B.1: u - Velocity Component for the Windowing Comparison

90

100

101

10-2

10-1

100

101

102

103

104


Freq (rad/sec)

v -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts

Hamming

Hann

Blackman

Figure B.2: v - Velocity Component for the Windowing Comparison

100

101

10-2

10-1

100

101

102

103


Freq (rad/sec)

w -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts

Hamming

Hann

Blackman

Figure B.3: w - Velocity Component for the Windowing Comparison

91

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

p -

Roll

Com

ponent [(

rad/s

)2]

Equivalent Gusts

Hamming

Hann

Blackman

Figure B.4: p - Rotational Component for the Windowing Comparison

100

101

10-5

10-4

10-3

10-2

10-1

100

101


Freq (rad/sec)

q -

Pitch C

om

ponent [(

rad/s

)2

Equivalent Gusts

Hamming

Hann

Blackman

Figure B.5: q - Velocity Component for the Windowing Comparison

92

B.2 Filter Fit Comparison

The PSDs of the equivalent gusts were found using Welch’s Method with

Hamming windowing. Two types of filter designs were tested. The analysis used the UH-

60A hovering in the DDG81 with a WOD condition of 25kts / 0deg at the hover location

described in Appendix A, Table A.1.

100

101

10-5

10-4

10-3

10-2

10-1

100

101


Freq (rad/sec)

r -

Yaw

Com

ponent [(

rad/s

)2]

Equivalent Gusts

Hamming

Hann

Blackman

Figure B.6: r - Velocity Component for the Windowing Comparison

93

100

101

10-2

10-1

100

101

102

103

104

Freq (rad/sec)

u -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts

Old Filter Design

New Filter Design

Figure B.7: u - Velocity Component for the Filter Design Comparison

100

101

10-2

10-1

100

101

102

103

104

Freq (rad/sec)

v -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts

Old Filter Design

New Filter Design

Figure B.8: v - Velocity Component for the Filter Design Comparison

94

100

101

10-2

10-1

100

101

102

103

Freq (rad/sec)

w -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts

Old Filter Design

New Filter Design

Figure B.9: w - Velocity Component for the Filter Design Comparison

100

101

10-4

10-3

10-2

10-1

100

101

Freq (rad/sec)

p -

Roll

Com

ponent [(

rad/s

)2]

Equivalent Gusts

Old Filter Design

New Filter Design

Figure B.10: p - Roll Component for the Filter Design Comparison

95

100

101

10-5

10-4

10-3

10-2

10-1

100

101

Freq (rad/sec)

q -

Pitch C

om

ponent [(

rad/s

)2]

Equivalent Gusts

Old Filter Design

New Filter Design

Figure B.11: q - Pitch Component for the Filter Design Comparison

100

101

10-5

10-4

10-3

10-2

10-1

100

101

Freq (rad/sec)

r -

Yaw

Com

ponent [(

rad/s

)2]

Equivalent Gusts

Old Filter Design

New Filter Design

Figure B.12: r - Yaw Component for the Filter Design Comparison

96

B.3 LHA Filter Fits: 30 knots / 0 deg


Hamming windowing. The analysis used the UH-60A hovering in the LHA airwake

above landing spot 8 with a WOD condition of 30 kts / 0 deg at the hover location

described in Appendix A.

100

101

10-2

10-1

100

101

102

103


Freq (rad/sec)

u -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts


Figure B.13: u - Velocity Component for LHA 30 kts / 0 deg

97

100

101

10-3

10-2

10-1

100

101

102

103


Freq (rad/sec)

v -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts


Figure B.14: v - Velocity Component for LHA 30 kts / 0 deg

100

101

10-3

10-2

10-1

100

101

102

103


Freq (rad/sec)

w -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts


Figure B.15: w - Velocity Component for LHA 30 kts / 0 deg

98

100

101

10-5

10-4

10-3

10-2

10-1

100

101


Freq (rad/sec)

p -

Roll

Com

ponent [(

rad/s

)2]

Equivalent Gusts


Figure B.16: p - Roll Component for LHA 30 kts / 0 deg

100

101

10-5

10-4

10-3

10-2

10-1

100


Freq (rad/sec)

q -

Pitch C

om

ponent [(

rad/s

)2]

Equivalent Gusts


Figure B.17: q - Pitch Component for LHA 30 kts / 0 deg

99

B.4 LHA Filter Fits: 30 knots / 30 deg


Hamming windowing. The analysis used the UH-60A hovering in the LHA airwake

above landing spot 8 with a WOD condition of 30 kts / 30 deg at the hover location

described in Appendix A.

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

r -

Yaw

Com

ponent [(

rad/s

)2]

Equivalent Gusts


Figure B.18: r – Yaw Component for LHA 30 kts / 0 deg

100

100

101

10-1

100

101

102

103

104

105


Freq (rad/sec)

u -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts


Figure B.19: u - Velocity Component for LHA 30 kts / 30 deg

100

101

10-1

100

101

102

103

104


Freq (rad/sec)

v -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts


Figure B.20: v - Velocity Component for LHA 30 kts / 30 deg

101

100

101

10-1

100

101

102

103

104


Freq (rad/sec)

w -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts


Figure B.21: w - Velocity Component for LHA 30 kts / 30 deg

100

101

10-4

10-3

10-2

10-1

100

101

102


Freq (rad/sec)

p -

Roll

Com

ponent [(

rad/s

)2]

Equivalent Gusts


Figure B.22: p - Roll Component for LHA 30 kts / 30 deg

102

100

101

10-4

10-3

10-2

10-1

100

101

102


Freq (rad/sec)

q -

Pitch C

om

ponent [(

rad/s

)2]

Equivalent Gusts


Figure B.23: q - Pitch Component for LHA 30 kts / 30 deg

100

101

10-3

10-2

10-1

100

101

102

103


Freq (rad/sec)

r -

Yaw

Com

ponent [(

rad/s

)2]

Equivalent Gusts


Figure B.24: r - Yaw Component for LHA 30 kts / 30 deg

103

B.5 DDG-81 Filter Fits: 25 knots / 0 deg


Hamming windowing. The analysis used the UH-60A hovering in the DDG-81 airwake

with a WOD condition of 25 kts / 0 deg at the hover location described in Appendix A.

100

101

10-2

10-1

100

101

102

103

104


Freq (rad/sec)

u -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts


Figure B.25: u - Velocity Component for DDG-81 25 kts / 0 deg

104

100

101

10-2

10-1

100

101

102

103

104


Freq (rad/sec)

v -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts


Figure B.26: v - Velocity Component for DDG-81 25 kts / 0 deg

100

101

10-2

10-1

100

101

102

103


Freq (rad/sec)

w -

Velo

city C

om

ponent [(

ft/s

)2]

Equivalent Gusts


Figure B.27: w - Velocity Component for DDG-81 25 kts / 0 deg

105

100

101

10-4

10-3

10-2

10-1

100

101

102


Freq (rad/sec)

p -

Roll

Com

ponent [(

rad/s

)2]

Equivalent Gusts


Figure B.28: p - Roll Component for DDG-81 25 kts / 0 deg

100

101

10-5

10-4

10-3

10-2

10-1

100


Freq (rad/sec)

q -

Pitch C

om

ponent [(

rad/s

)2]

Equivalent Gusts


Figure B.29: q - Pitch Component for DDG-81 25 kts / 0 deg

106

B.6 DDG-81 Initial Simulation Results

The analysis used the UH-60A hovering in the DDG-81 airwake with a WOD

condition of 25kts / 0deg at the hover location described in Appendix A. The dark blue

line is the results from the Tustin discrete filter. The green line depicts the disturbance

from the continuous filter that was excited in the SIMULINK environment. The red line

depicts the equivalent gusts determined by removing the aircraft’s dynamics from the

simulation results. Finally, the light blue line is the stochastic portion of the CFD gust

that acted on the center of the fuselage during simulation.

100

101

10-5

10-4

10-3

10-2

10-1

100

101


Freq (rad/sec)

r -

Yaw

Com

ponent [(

rad/s

)2]

Equivalent Gusts


Figure B.30: r - Yaw Component for DDG-81 25 kts / 0 deg

107

0 20 40 60 80 100 120-15

-10

-5

0

5

10


time [s]

u -

Velo

city C

om

ponent [(f

t/s)]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.31: u - Velocity Component for DDG-81 Initial Simulation Results

0 20 40 60 80 100 120-15

-10

-5

0

5

10


time [s]

v -

Velo

city C

om

ponent [(f

t/s)]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.32: v - Velocity Component for DDG-81 Initial Simulation Results

108

0 20 40 60 80 100 120-15

-10

-5

0

5

10

time [s]

w -

Velo

city C

om

ponent [(f

t/s)]


Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.33: w - Velocity Component for DDG-81 Initial Simulation Results

0 20 40 60 80 100 120-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

time [s]

p -

Velo

city C

om

ponent [r

ad/s

]


Tustin

Simulink

Equivalent Gust

Figure B.34: p – Roll Component for DDG-81 Initial Simulation Results

109

0 20 40 60 80 100 120-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

time [s]

q -

Velo

city C

om

ponent [r

ad/s

]


Tustin

Simulink

Equivalent Gust

Figure B.35: q - Pitch Component for DDG-81 Initial Simulation Results

0 20 40 60 80 100 120-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

time [s]

r -

Velo

city C

om

ponent [r

ad/s

]


Tustin

Simulink

Equivalent Gust

Figure B.36: r - Yaw Component for DDG-81 Initial Simulation Results

110

100

101

10-4

10-2

100

102

104


Freq (rad/sec)

u -

Velo

city C

om

ponent [(f

t/s)2

]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.37: u - Velocity PSD of the DDG-81 Initial Simulation Results

100

101

10-4

10-2

100

102

104


Freq (rad/sec)

v -

Velo

city C

om

ponent [(

ft/s

)2]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.38: v - Velocity PSD of the DDG-81 Initial Simulation Results

111

B.7 LHA 30 kts / 0 deg Initial Simulation Results

The analysis used the UH-60A hovering in the LHA airwake with a WOD

condition of 30 kts / 0 deg at the hover location described in Appendix A. The dark blue






100

101

10-4

10-2

100

102

104


Freq (rad/sec)

w -

Velo

city C

om

ponent [(f

t/s)2

]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.39: w - Velocity PSD of the DDG-81 Initial Simulation Results

112

0 20 40 60 80 100 120-4

-3

-2

-1

0

1

2

3

4

5LHA Landing Spot 8: WOD Case: 30kts / 0deg

u -

Velo

city C

om

ponent [ft/s]

time [s]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.40: u - Velocity Component for LHA 30 kts / 0 deg Initial Simulation Results

0 20 40 60 80 100 120-4

-3

-2

-1

0

1

2


v -

Velo

city C

om

ponent [ft/s]

time [s]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.41: v - Velocity Component for LHA 30 kts / 0 deg Initial Simulation Results

113

0 20 40 60 80 100 120-4

-3

-2

-1

0

1

2

3

time [s]

w -

Velo

city C

om

ponent [ft/s]


Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.42: w - Velocity Component for LHA 30 kts / 0 deg Initial Simulation Results

0 20 40 60 80 100 120-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

time [s]

p -

Velo

city C

om

ponent [r

ad/s

]


Tustin

Simulink

Equivalent Gust

Figure B.43: p - Roll Component for LHA 30 kts / 0 deg Initial Simulation Results

114

0 20 40 60 80 100 120-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

time [s]

q -

Velo

city C

om

ponent [r

ad/s

]


Tustin

Simulink

Equivalent Gust

Figure B.44: q - Pitch Component for LHA 30 kts / 0 deg Initial Simulation Results

0 20 40 60 80 100 120-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

time [s]

r -

Velo

city C

om

ponent [r

ad/s

]


Tustin

Simulink

Equivalent Gust

Figure B.45: r - Yaw Component for LHA 30 kts / 0 deg Initial Simulation Results

115

100

101

10-3

10-2

10-1

100

101

102

103


Freq (rad/sec)

u -

Velo

city C

om

ponent [(f

t/s)2

]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.46: u - Velocity PSD of the LHA 30 kts / 0 deg Initial Simulation Results

100

101

10-4

10-2

100

102

104


Freq (rad/sec)

v -

Velo

city C

om

ponent [(

ft/s

)2]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.47: v - Velocity PSD of the LHA 30 kts / 0 deg Initial Simulation Results

116

B.8 LHA 30 kts / 30 deg Initial Simulation Results

The analysis used the UH-60A hovering in the LHA airwake with a WOD

condition of 30 kts / 30 deg at the hover location described in Appendix A. The dark blue






100

101

10-3

10-2

10-1

100

101

102

103


Freq (rad/sec)

w -

Velo

city C

om

ponent [(f

t/s)2

]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.48: w - Velocity PSD of the LHA 30 kts / 0 deg Initial Simulation Results

117

0 20 40 60 80 100 120-25

-20

-15

-10

-5

0

5

10

15

20


u -

Velo

city C

om

ponent [ft/s]

time [s]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.49: u - Velocity Component for LHA 30 kts / 30 deg Initial Simulation Results

0 20 40 60 80 100 120-30

-20

-10

0

10

20


v -

Velo

city C

om

ponent [ft/s]

time [s]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.50: v - Velocity Component for LHA 30 kts / 30 deg Initial Simulation Results

118

0 20 40 60 80 100 120-30

-25

-20

-15

-10

-5

0

5

10

15

20

time [s]

w -

Velo

city C

om

ponent [ft/s]


Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.51: w - Velocity Component for LHA 30 kts / 30 deg Initial Simulation Results

0 20 40 60 80 100 120-1.5

-1

-0.5

0

0.5

1

1.5

time [s]

p -

Velo

city C

om

ponent [r

ad/s

]


Tustin

Simulink

Equivalent Gust

Figure B.52: p - Roll Component for LHA 30 kts / 30 deg Initial Simulation Results

119

0 20 40 60 80 100 120-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

time [s]

q -

Velo

city C

om

ponent [r

ad/s

]


Tustin

Simulink

Equivalent Gust

Figure B.53: q - Pitch Component for LHA 30 kts / 30 deg Initial Simulation Results

0 20 40 60 80 100 120-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

time [s]

r -

Velo

city C

om

ponent [r

ad/s

]


Tustin

Simulink

Equivalent Gust

Figure B.54: r - Yaw Component for LHA 30 kts / 30 deg Initial Simulation Results

120

100

101

10-2

100

102

104

106


Freq (rad/sec)

u -

Velo

city C

om

ponent [(f

t/s)2

]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.55: u - Velocity PSD of the LHA 30 kts / 30 deg Initial Simulation Results

100

101

10-2

100

102

104

106


Freq (rad/sec)

v -

Velo

city C

om

ponent [(

ft/s

)2]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.56: v - Velocity PSD of the LHA 30 kts / 30 deg Initial Simulation Results

121

100

101

10-2

10-1

100

101

102

103

104


Freq (rad/sec)

w -

Velo

city C

om

ponent [(f

t/s)2

]

Tustin

Simulink

Equivalent Gust

CFD Gust

Figure B.57: w - Velocity PSD of the LHA 30 kts / 30 deg Initial Simulation Results

Appendix C

Online AR Filter Results

Appendix C outlines the results found using online filter fitting methods to

estimate the airwake properties.

C.1 Online Burg AR Model Fitting Results

This section outlines the results using an online Burg AR Model to fit gust filters

to the UH-60A hovering in the DDG-81 airwake at the standard hover location outlined

in Appendix A.

100

101

-10

0

10

20

30

40

50

60

ug (

dB

)


Frequency (rad/sec)

Off-line

20 sec

40 sec

60 sec

80 sec

100 sec

120 sec

Figure C.1: Identified Longitudinal Gust Velocity Gust Filters

100

101

-20

-10

0

10

20

30

40

vg (

dB

)


Frequency (rad/sec)

Off-line

20 sec

40 sec

60 sec

80 sec

100 sec

120 sec

Figure C.2: Identified Lateral Gust Velocity Gust Filters

100

101

-30

-20

-10

0

10

20

30

40

50

wg (

dB

)


Frequency (rad/sec)

Off-line

20 sec

40 sec

60 sec

80 sec

100 sec

120 sec

Figure C.3: Identified Vertical Gust Velocity Gust Filters

124

100

101

-30

-25

-20

-15

-10

-5

0

5

10

15

20

pg (

dB

)


Frequency (rad/sec)

Off-line

20 sec

40 sec

60 sec

80 sec

100 sec

120 sec

Figure C.4: Identified Roll Rate Gust Filters

100

101

-35

-30

-25

-20

-15

-10

-5

0

5

10

qg (

dB

)


Frequency (rad/sec)

Off-line

20 sec

40 sec

60 sec

80 sec

100 sec

120 sec

Figure C.5: Identified Pitch Rate Gust Filters

125

100

101

-40

-30

-20

-10

0

10

20

r g (

dB

)


Frequency (rad/sec)

Off-line

20 sec

40 sec

60 sec

80 sec

100 sec

120 sec

Figure C.6: Identified Yaw Rate Gust Filters

Appendix D

Stochastic Simulation Modeling Results

This appendix outlines the results of the simulation modeling results from the

stochastic airwake that was implemented in Genhel-PSU and Sikorsky’s Genhel.

D.1 Genhel-PSU Simulation Hovering Results

This section presents the results from performing a simulated hover at four spots

within the stochastic airwake model. The results are compared to results of the same

maneuver performed the DDG-81 CFD airwake that the stochastic filters were derived

from. The case names in each figure explain the X-Y-Z location in the airwake

coordinate system that the hover was performed at. For example, 454-31-33 relates to

454 feet behind the origin of the ship, 31 feet to the starboard side of the ship’s center

line, and 33 feet above the bottom of the ship. Each section presents the PSD of pilot

stick inputs to maintain the hover as well as PSD of the winds acting on the center of the

aircraft’s fuselage.

127

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

Late

ral S

tick, X

a [(%

)2]

Stochastic

CFD

Figure D.1: Lateral Sick Input at 439-0-42

100

101

10-5

10-4

10-3

10-2

10-1

100

101


Freq (rad/sec)

Longitudin

al S

tick, X

b [(%

)2]

Stochastic

CFD

Figure D.2: Longitudinal Sick Input at 439-0-42

128

100

101

10-5

10-4

10-3

10-2

10-1

100

101


Freq (rad/sec)

Colle

ctive S

tick, X

c [(

%)2

]

Stochastic

CFD

Figure D.3: Collective Stick Input at 439-0-42

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

Pedals

, X

p [(

%)2

]

Stochastic

CFD

Figure D.4: Pedal Input at 439-0-42

129

100

101

10-4

10-2

100

102

104


Freq (rad/sec)

U -

Velo

city a

t F

usela

ge [(f

t/sec)2

]

Stochastic

CFD

Figure D.5: Longitudinal Velocity acting on Fuselage at 439-0-42

100

101

10-2

10-1

100

101

102

103

104


Freq (rad/sec)

V -

Velo

city a

t F

usela

ge [(f

t/sec)2

]

Stochastic

CFD

Figure D.6: Lateral Velocity acting on Fuselage at 439-0-42

130

100

101

10-2

10-1

100

101

102

103


Freq (rad/sec)

W -

Velo

city a

t F

usela

ge [(f

t/sec)2

]

Stochastic

CFD

Figure D.7: Vertical Velocity acting on Fuselage at 439-0-42

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

Late

ral S

tick, X

a [(%

)2]

Stochastic

CFD


131

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

Longitudin

al S

tick, X

b [(%

)2]

Stochastic

CFD


100

101

10-5

10-4

10-3

10-2

10-1

100

101


Freq (rad/sec)

Colle

ctive S

tick, X

c [(

%)2

]

Stochastic

CFD


132

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

Pedals

, X

p [(

%)2

]

Stochastic

CFD


100

101

10-4

10-2

100

102

104


Freq (rad/sec)

U -

Velo

city a

t F

usela

ge [(f

t/sec)2

]

Stochastic

CFD


133

100

101

10-2

10-1

100

101

102

103

104


Freq (rad/sec)

V -

Velo

city a

t F

usela

ge [(f

t/sec)2

]

Stochastic

CFD


100

101

10-4

10-2

100

102

104


Freq (rad/sec)

W -

Velo

city a

t F

usela

ge [(f

t/sec)2

]

Stochastic

CFD


134

100

101

10-8

10-6

10-4

10-2

100

102


Freq (rad/sec)

Late

ral S

tick, X

a [(%

)2]

Stochastic

CFD


100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

Longitudin

al S

tick, X

b [(%

)2]

Stochastic

CFD


135

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

Colle

ctive S

tick, X

c [(

%)2

]

Stochastic

CFD


100

101

10-8

10-6

10-4

10-2

100

102


Freq (rad/sec)

Pedals

, X

p [(

%)2

]

Stochastic

CFD


136

100

101

10-3

10-2

10-1

100

101

102

103


Freq (rad/sec)

U -

Velo

city a

t F

usela

ge [(f

t/sec)2

]

Stochastic

CFD


100

101

10-3

10-2

10-1

100

101

102

103


Freq (rad/sec)

V -

Velo

city a

t F

usela

ge [(f

t/sec)2

]

Stochastic

CFD


137

100

101

10-3

10-2

10-1

100

101

102

103


Freq (rad/sec)

W -

Velo

city a

t F

usela

ge [(f

t/sec)2

]

Stochastic

CFD


100

101

10-8

10-6

10-4

10-2

100


Freq (rad/sec)

Late

ral S

tick, X

a [(%

)2]

Stochastic

CFD


138

100

101

10-8

10-6

10-4

10-2

100


Freq (rad/sec)

Longitudin

al S

tick, X

b [(%

)2]

Stochastic

CFD


100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

Colle

ctive S

tick, X

c [(

%)2

]

Stochastic

CFD


139

100

101

10-8

10-6

10-4

10-2

100

102


Freq (rad/sec)

Pedals

, X

p [(

%)2

]

Stochastic

CFD


100

101

10-4

10-2

100

102

104


Freq (rad/sec)

U -

Velo

city a

t F

usela

ge [(f

t/sec)2

]

Stochastic

CFD


140

100

101

10-3

10-2

10-1

100

101

102

103


Freq (rad/sec)

V -

Velo

city a

t F

usela

ge [(f

t/sec)2

]

Stochastic

CFD


100

101

10-4

10-2

100

102

104


Freq (rad/sec)

W -

Velo

city a

t F

usela

ge [(f

t/sec)2

]

Stochastic

CFD


141

D.2 Genhel-PSU Simulation Trajectory Maneuver Results

This section presents the results from performing a simulation in which the

helicopter was prescribed a desired trajectory. The pilot model, described in Section 2.1,

emulated a pilot flying the desired flight path. This section presents the trajectory path

and PSDs of stick inputs for two separate flight paths. The first hover started aft and to

the starboard side of the desired landing spot. The aircraft then flew forward and ended in

a final hover near the desired landing spot. The second trajectory path was similar, but

started on the port side of the ship and at a different height. The flight path ended near the

desired landing spot. The aircraft positions are offset in the x-axis by 225 ft in the x-axis

and 3.4 feet in the z-axis due to the coordinate differences between the airwake origin and

Genhel-PSU ship origin.

142

-1000

100-600-400-200

-50

0

50

100

150

North-South Position (xN) [ft]

East-West Position (yE) [ft]

Altitud

e (

h)

[ft]

Flight Path

Trajectory Path

Figure D.29: Three Dimensional View of Trajectory Path 1

143

0 20 40 60 80 100 120-1000

-500

0

XN [ft]

0 20 40 60 80 100 120-100

0

100

YE [ft]

0 20 40 60 80 100 1200

50

100

h [ft]

Time [s]

Figure D.30: Aircraft Position Time History of Trajectory Path 1

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

Late

ral S

tick, X

a [(%

)2]

Stochastic

CFD

No Airwake

Figure D.31: Lateral Stick Input for Trajectory Path 1

144

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

Longitudin

al S

tick, X

b [(%

)2]

Stochastic

CFD

No Airwake

Figure D.32: Longitudinal Stick Input for Trajectory Path 1

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

Colle

ctive S

tick, X

c [(

%)2

]

Stochastic

CFD

No Airwake

Figure D.33: Collective Stick Input for Trajectory Path 1

145

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

Pedals

, X

p [(

%)2

]

Stochastic

CFD

No Airwake

Figure D.34: Pedal input for Trajectory Path 1

-100-50

050

100

-600

-400

-200

-50

0

50

100

150

(YE) [ft]

(XN) [ft]

Altitud

e (

h)

[ft]

Flight Path

Trajectory Path

Figure D.35: Three Dimensional View of Trajectory Path 2

146

0 20 40 60 80 100 120-1000

-500

0X

N [ft]

0 20 40 60 80 100 120-50

0

50

YE [ft]

0 20 40 60 80 100 1200

50

100

h [ft]

Time [s]

Figure D.36: Aircraft Position Time History of Trajectory Path 2

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

Late

ral S

tick, X

a [(%

)2]

Stochastic

CFD

No Airwake

Figure D.37: Lateral Stick Input for Trajectory Path 2

147

100

101

10-4

10-3

10-2

10-1

100

101

102


Freq (rad/sec)

Longitudin

al S

tick, X

b [(%

)2]

Stochastic

CFD

No Airwake

Figure D.38: Longitudinal Stick Input for Trajectory Path 2

100

101

10-4

10-2

100

102

104


Freq (rad/sec)

Colle

ctive S

tick, X

c [(

%)2

]

Stochastic

CFD

No Airwake

Figure D.39: Collective Stick Input for Trajectory Path 2

148

D.3 Sikorsky GENHEL Piloted Simulation Results

This section presents the PSDs of piloted inputs for each of the six pilots for

piloted simulations performed with Sikorsky GENHEL model. The stochastic airwake

model is compared to the CFD airwake model for the DDG-81 with a WOD condition of

25 knots / 0 deg.

100

101

10-6

10-4

10-2

100

102


Freq (rad/sec)

Pedals

, X

p [(

%)2

]

Stochastic

CFD

No Airwake

Figure D.40: Pedal input for Trajectory Path 2

149

100

101

10-8

10-6

10-4

10-2

100

Frequency (rad/s)

PS

D o

f Late

ral S

tick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake

Figure D.41: Lateral Stick Input for Pilot 1

100

101

10-8

10-6

10-4

10-2

100

102

Frequency (rad/s)

PS

D o

f Long. S

tick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake

Figure D.42: Longitudinal Stick Input for Pilot 1

150

100

101

10-6

10-4

10-2

100

102

104

Frequency (rad/s)

PS

D o

f C

oll.

Stick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake

Figure D.43: Collective Stick Input for Pilot 1

100

101

10-8

10-6

10-4

10-2

100

102

Frequency (rad/s)

PS

D o

f P

edals

, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake

Figure D.44: Pedal Input for Pilot 1

151

100

101

10-8

10-6

10-4

10-2

100

Frequency (rad/s)

PS

D o

f Late

ral S

tick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


100

101

10-6

10-5

10-4

10-3

10-2

10-1

100

Frequency (rad/s)

PS

D o

f Long. S

tick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


152

100

101

10-3

10-2

10-1

100

101

102

103

Frequency (rad/s)

PS

D o

f C

oll.

Stick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


100

101

10-5

10-4

10-3

10-2

10-1

100

101

Frequency (rad/s)

PS

D o

f P

edals

, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


153

100

101

10-6

10-5

10-4

10-3

10-2

10-1

100

Frequency (rad/s)

PS

D o

f Late

ral S

tick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


100

101

10-6

10-4

10-2

100

102

Frequency (rad/s)

PS

D o

f Long. S

tick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


154

100

101

10-6

10-4

10-2

100

102

104

Frequency (rad/s)

PS

D o

f C

oll.

Stick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


100

101

10-6

10-4

10-2

100

102

Frequency (rad/s)

PS

D o

f P

edals

, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


155

100

101

10-8

10-6

10-4

10-2

100

Frequency (rad/s)

PS

D o

f Late

ral S

tick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


100

101

10-6

10-4

10-2

100

102

Frequency (rad/s)

PS

D o

f Long. S

tick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


156

100

101

10-4

10-2

100

102

104

Frequency (rad/s)

PS

D o

f C

oll.

Stick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


100

101

10-6

10-4

10-2

100

102

Frequency (rad/s)

PS

D o

f P

edals

, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


157

100

101

10-5

10-4

10-3

10-2

10-1

100

Frequency (rad/s)

PS

D o

f Late

ral S

tick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


100

101

10-6

10-4

10-2

100

102

Frequency (rad/s)

PS

D o

f Long. S

tick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


158

100

101

10-4

10-2

100

102

104

Frequency (rad/s)

PS

D o

f C

oll.

Stick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


100

101

10-8

10-6

10-4

10-2

100

102

Frequency (rad/s)

PS

D o

f P

edals

, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


159

100

101

10-6

10-4

10-2

100

102

Frequency (rad/s)

PS

D o

f Late

ral S

tick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


100

101

10-5

10-4

10-3

10-2

10-1

100

101

Frequency (rad/s)

PS

D o

f Long. S

tick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


160

100

101

10-4

10-2

100

102

104

Frequency (rad/s)

PS

D o

f C

oll.

Stick, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


100

101

10-6

10-4

10-2

100

102

Frequency (rad/s)

PS

D o

f P

edals

, [(

%)2

]

No Airwake

CFD Airwake

Stochastic Airwake


modeling and identification of unsteady airwake

Documents