umrida: bringing uncertainty management · method of moments (perturbation method) and adjoint...

UMRIDA: Bringing Uncertainty Management

and Robust Design Methodologies to

Industrial Levels

Charles Hirsch, Dirk Wunsch, Thomas Deconinck

Numeca International

20th October 2015 3 London, United Kingdom Aerodays 2015

The role of uncertainties in Virtual Prototyping

Paradigm shift in Virtual Prototyping (VP) methodology

Virtual Prototyping (VP) has become the key technology for industry

Reduce product development cycle costs

Respond to the challenges of designing sustainable products and responding to the environmental challenges

These objectives require a highly integrated computer-based design system,

Relying on advanced massively parallel hardware, making the virtual product development and qualification process more realizable

CFD simulations are run today with a unique set of input data such as boundary conditions, physical model parameters or geometries

Real operation conditions are subject to operational and geometrical uncertainties

Uncertain operating conditions

Manufacturing tolerances or other geometric variability


The role of uncertainties in Virtual Prototyping

Paradigm shift in Virtual Prototyping (VP) methodology

New type of non-deterministic simulations are needed, where predicted quantities, such as loads, lift, drag, efficiencies, temperatures, ….

are represented by a Probability Density Function (PDF)

This PDF provides a domain of confidence associated to the considered uncertainties

This corresponds to a fundamental shift in paradigm for the whole of the VP methodology

P(h)

h

PDF of non-deterministic CFD

simulations for randomly sampled

uncertainty parameter as input

PDF of non-deterministic CFD

simulations for given PDF of

uncertainty parameter as input

Result of deterministic CFD

simulations for mean value

of measured uncertainty

parameter as input


Uncertainty Quantification and Safety Factors

Traditional approach to risk management: safety factors

Deterministic value is estimated for the load xR (requirement) and a value is provided, as best as possible, for the maximum capacity xC

On basis of which a safety factor k=xC/xR is imposed on the system

Taking the safety factor at a sufficiently high value minimizes risk

This will generally have detrimental consequences on cost and performance


Uncertainty Quantification and Safety Factors

Traditional approach to risk management: safety factors

Considering uncertainties and their PDF’s

Allows ranges (under the form of PDF’s) for requirements (loads) and capacity (resistance) to be evaluated in a rational way

Allows to define a failure region where the two PDF’s overlap. Full safety, taking into account the known uncertainties, is obtained for k>1

k>1, the design is perfectly safe (top)

k≅1, a certain risk factor will exist (middle)

k<1, a large failure region exists, which would

lead to a catastrophic design, of course to be

rejected (bottom) From: Green (2011)


UMRIDA project

UMRIDA - Uncertainty Management for Robust Industrial Design in Aeronautics

FP7 Level 1 project with a consortium of 21 partners

Comprising of universities, research institutes, industrial partners and SME’s

Project website: www.umrida.eu

Aiming at a paradigm shift in virtual prototyping away from deterministic design and towards design under uncertainties

Bridging the gap from basic research to industrial applications where large numbers of simultaneous uncertainties are accounted for

http://www.umrida.eu/


UMRIDA project

Consortium


General objectives of UMRIDA

Scientific and technical objectives

Development of innovative methods for Uncertainty Quantification (UQ)

New methods for large-scale introduction of uncertainties in Robust Design (RD)

Produce designs incorporating the major uncertainties, which are stable against variations of the uncertainty quantities

Apply UQ and RD to predefined industrial challenges with prescribed uncertainties

Creation of new generation of database, including controlled uncertainties from experiments

Validate developed methods on this database

Advance Technology Readiness Level (TRL) from currently 2-3 to 5-6

Quantifiable objective: At least 10 simultaneous uncertainties, in a turn-over time of less than 10 hours on a 100 core parallel computer

Facilitate co-operation and dissemination of UQ and RDM awareness towards European industries, research establishments and universities


Progress beyond the state of the art

Advance methods for uncertainty quantification

Method of moments (perturbation method) and adjoint based methods

Principle: Use a Taylor Series to expand output quantity around its mean

Key element is the evaluation of first and second order sensitivity derivatives

Monte-Carlo Methods (Multi-Level Monte-Carlo)

Principle: Perform high number of deterministic simulations with sampled parameters and evaluate output quantities on different levels

Polynomial chaos or collocation methods (Intrusive and non-intrusive)

Principle: Expand the solution into a polynomial chaos or an interpolating polynomial

Non-intrusive formulation allows to solve a set of uncoupled simulations

Combination with sparse grid formulation or regression based approaches to tackle many simultaneous uncertainties



Characterization of most influential uncertainties and dimension reduction

Quantify input uncertainties

Mean and standard deviation of output PDF is dependent on shape of input PDF

Need for a method to derive correct information on input PDF from generally scarce experimental data

Identify most important uncertainties

Use approaches like SS-ANOVA, Morris Method, PCA, Sobol indices, Karhunen-Loeve expansion

Use adjoint technique to reduce number of uncertainties and then run PCM or MC

Surrogate models or Reduced order models

Reduce cost of UQ and RD methods



Advances in robust design and optimization methodologies

Objective are designs which are less sensitive to variation of conditions/parameters due to uncertainties

Robust design problems: design insensitive to small changes

Reliability-based design problems: design with probability of failure less than an acceptable value

Design under uncertainties is a new field of research

Unclear so far how to enforce robustness, robust objective/constraint formulations and dependence on used optimizers

Inverse multi-objective robust design

Optimize mean output performance

Maximize standard deviation or tolerance on input variables

While keeping the required constraints satisfied


Validation database with prescribed uncertainties

Construction of unique validation database with prescribed uncertainties

The FP7 UMRIDA project (www.umrida.eu) on Uncertainty Management for Robust Industrial Design in Aeronautics includes the creation of a validation database with prescribed uncertainties

Industrial multiphysics challenges defined by industrial project partners

Advance Technology Readiness Level to “Advanced/Applied”

Quantifiable objective: At least 10 simultaneous uncertainties, in a turn-over time of less than 10 hours on a 100 core parallel computer

Specific focus on multidisciplinary applications such as

FSI, CHT, combustion, aero-acoustics

Uncertainties provided by industry experts

Contains also one experimental set-up with controlled uncertainties during measurement campaign

http://www.umrida.eu/



UMRIDA validation database: Basic Challenges (1/3)

BC-01:

NUMECA

BC-02:

NUMECA

Description:

• NODESIM-CFD test case

• NASA Rotor 37

Uncertainties:

• Inlet Pt, outlet pressure

• Geometrical: tip clearances

• Symmetric beta-pdf

• Blade thickness, blade angle, ... in

10 sections

• LE angle, twist distribution, non-

uniformity of blade spacing

Description:

• NODESIM-CFD test case

• RAE 2822 airfoil

• Mach = 0.734

• Angle of incidence 2.79°

• Reynolds = 6.5 e6

Uncertainties:

• Angle of incidence: std 0.1°

• Thickness-to-chord ratio: std 0.005

• Mach number: std 0.005

• Uncertainties with either a uniform

or normal distributed PDF




BC-03:

DLR

BC-04:

EADS

Description:

• DLR-F6 wing/body

• From Drag prediction workshop

(DPW III) with/without fairing

• ATAAC test case

• M = 0.75

• Re = 5e6

• CL = 0.5

Uncertainties:

• Mach number

• Angle of attack

• Reynolds number

• Wing thickness

• LE shape

Description:

• F11 (KH3Y) TO2 Configuration

• Flap setting on a three-element

high-lift airfoil

• M = 0.1715, Re = 11e5

• AoA = 9.6°

• Slat deflection = 20°

• Flap deflection = 22°

Uncertainties:

• Uncertainties: flap deflection

i) Gaussian distribution with mean

notional setting and s=2% of flap

chord

ii) Beta PDF with mean equal to

notional setting and +-2% of flap

chord




BC-05:

STANFORD

CIRA

Description:

• New experimental data on shock

boundary layer interaction with

uncertainties

• Test configuration is a 24°

compression wedge in a Mach 2

flow

Uncertainties:

• Distributed geometrical uncertainty

of the upstream wall

• Controlled geometrical modifications

to introduce flow perturbations

• Validation of UQ simulation for

shock location by MC with hundreds

of sampled configurations



UMRIDA validation database: Industrial Challenges (1/5)

IC-01:

TURBOMECA

IC-02:

EADS-IW

Description:

• Database of pressure signal

recods taken in the combustor

• Existence of thermo-acoustic

instabilities by high amplitude of

pressure measurements

Uncertainties:

• Varying operating conditions and

geometrical definitions of the

combustion chamber

• Uncertainties in the acoustic

boundary conditions for the

Helmholtz solver

Description:

• Undertainty in the determination

of design loads

• Aerodynamic force distribution

across the full flight envelope

• Landing gear data for loads

• Stiffness distribution

• Mass distribution

Uncertainties:

• Quantify uncertainties in all

process inputs

• Propagate these through loads

calculations and evaluate variance

of design loads estimations

• Within practicle time-scales on

~100 processor cluster




Industrial challenges

IC-03:

DASSAULT

IC-04:

SATURN

Description:

• Falcon jet configuration

• Fuselage, wing, nacelle, tail, ...

Uncertainties:

• Robustness/operational

uncertainties (free stream Mach, AoA,

Reynolds number)

• Geometrical uncertainties (wing

spanwise twist distribution)

Description:

• Fan stage for FSI optimization

Uncertainties:

• Leading/Trailing edge radius

• Inlet angle, output edge middle

line angle

• Blade thickness/angle

• Section deflection in several

sections





IC-05:

SATURN

IC-06:

AAEM

Description:

• Cooled turbine blade

Uncertainties:

• Operational uncertainties

• P1*abs, T1*abs

• P2*rel, T2*rel

• Turbulence parameters

Description:

• RD procedure for optimal design

of acoustic panels installed in

typical business-jet aero-engine

intakes

Uncertainties:

• Manufacturing tolerances (facing-

sheet effective open area, hole

diameters and shape)

• Uncertainties on acoustic

parameters identifying the operative

environment





IC-07:

MAN

IC-08:

CIRA/

DASSAULT

Description:

• Industrial compressor stage

Uncertainties:

• Operational uncertainties (gas

properties, pressure, temperatures)

• Manufacturing (surface roughness,

deformation due to heat treatment)

• Lifetime (erosion, fouling)

Description:

• Supersonic/Transonic laminar

flow design of business jet aircraft

• Design of swept wing and

airframe with a large extension of

laminar flow in their working

conditions

Uncertainties:

• Uncertainties in modelling the

laminar/turbulent transition process

combined with geometrical

uncertainties





IC-09:

RRD

Description:

• High Pressure Compressor blade

design

Uncertainties:

• Uncertainties in boundary

conditions and geometrical shape


Other objectives of UMRIDA

Co-operation and dissemination

Increase awareness, understanding in EU industry and academia

Organization of two workshops

Allowing quantitative comparison between UQ and RDM approaches on industrial challenges defined within the project

Best Practice Guides (BPG) for industrial aeronautical users

Based on gained experience and workshop outcomes

Broad exploitation and communication towards industry, academia and public

Book containing most significant advances within UMRIDA will be published at end of project


Examples of progress within UMRIDA

Operational and geometrical uncertainties in turbomachinery design

5 simultaneous uncertainties: geometrical (tip gap, LE angle, LE radius)

and 2 operational

Automatic modification of tip gap



Operational and geometrical uncertainties in turbomachinery design

Total pressure ratio over mass flow Influence of uncertainties on

solution

Computational effort



Application of surrogate based Monte-Carlo to CHT in turbine blade

Uncertainty Quantification is based on

surrogate model built covering the design and

uncertain space.


Overview of speed up by UQ methods developped


Summary

After 24 months significant progress has been done

A new generation of database including uncertainty definitions has been set-up

Several partners successfully demonstrated the capability of the UQ methods to meet the UMRIDA quantifiable objective during the UQ-workshop at project mid-term

Significant speed-ups could be reach for the entire range of methods applied

Several methods have been introduced into engineering tools and are now available for daily use by design engineers

These UQ methods are now introduced into the optimization process with the goal of robust and reliable designs


Thank you!

www.umrida.eu

umrida: bringing uncertainty management · method of moments (perturbation method) and adjoint...

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