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The Genetic Algorithm as an Automated Methodologyfor Helicopter Conceptual DesignWLLIAM A. CROSSLEY a & DAVID H. LAANANEN ba School of Aeronautics and Astronautics, Purdue University, 1282 Grissom Hall, WestLafayette, IN, 47909-1282, USAb Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe,AZ, 85287-6106, USAVersion of record first published: 15 Mar 2007.

To cite this article: WLLIAM A. CROSSLEY & DAVID H. LAANANEN (1997): The Genetic Algorithm as an Automated Methodologyfor Helicopter Conceptual Design, Journal of Engineering Design, 8:3, 231-250

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Journal of Engineering Design, Vol. 8, No. 3, 1997

The Genetic Algorithm as an Automated Irriethodology for Helicopter Conceptual Design

WILLIAM A. CROSSLEY & DAVID H. LAANANEN

SUMMARY The genetic algorirhm (GA) is a search algorirhm that mimics the pamrns of natural selection and reproduction displayed by biologi'cal populations. The GA's operation as a non-calculus-based search and optimization method makes it a good candidare for use in conceptual design. This paper presents a discussion of the use of a G A as an automated approach to conceptual design of helicopters. To accomplish this task, a G A war combined with an industry-standard helicopter sizing code. This resulting genetic algorithm-based design code mas then used to generare conceptual designs for the medium 113 replacement helicopter and a hypothetical attack helicopter. Results of these design e f fom are discussed, providing insight into the use of a G A to automate the conceptual design of helicopters.

1. Introduction

?"he genetic algorithm (GA) imitates the processes of natural selection and reproduction that are seen in biological populations. Because 'survival-of-the-finest' behavior

is analogous to optimization, the GA has begun to find application to optimal design problems. The GA is not calculus based and has features that make it well suited to

performing conceptual design tasks. In fact, the search behavior of the GA allows it to automate the conceptual design process. The work described in this paper involved

using a GA, coupled with a helicopter-industry conceptual design analysis code, to perform an automated search through a defined design space. Two different helicopter

rnissions were used, and the GA generated high-quality designs for both problems. The manner in which these designs were generated was then compared with the approach

of human design engineers to the same problems.

1.1 The GA

The GA is a probabilistically guided search method, developed originally in the 1970s as a computer science tool to improve programming suuctures and program performance. It was later realized that this algorithm also had applications in other fields, including game theory, process planning, claassifier systems, machine learning and function optimization [I]. Features of GAS have recently (since the late 1980s) been exploited as search and optimization routines in aerospace engineering problems [2].

W. A. Crossley, School of Aeronautics and Astronautics, Purdue University, 1282 Grissom Hall, West Iafayene, IN 47909-1282, USA. D. H. Laananen, Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106, USA. E-mail: [email protected] and [email protected].

0954-48281971030231-20 @I997 Carfax Publishing Ltd

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232 W. A. Crossley & D. H. Laananen

This concept, which resulted from work by Holland [3], has been expanded by many others and has now developed into an accepted search and optimization technique.

The idea of 'survival of the fittest' can be considered analogous to optimization; an organism well adapted to its environment is more fit in nature, while an aircraft with lower weight could be considered more fit in the GA. Because of this analogy, GAS have been used for optimization, yet they differ from the familiar calculus-based optimization routines in four major ways (adapted from Goldberg [I]):

(1) GAS work with a coding of the design variables and parameters in the problem, rather than with the actual parameters themselves.

(2) GAS make use of a population-type search. Many different design points are evaluated during each iteration, instead of moving from one point to the next.

(3) GAS need only a fitness or objective function value. No derivatives or gradients are necessary.

(4) GAS use probabilistic transition rules to find new points for exploration rather than using deterministic rules based on gradient information.

The mimicry of nature in GAS includes representing points in a design or search space as if they were individual organisms. Design variables, the 'genes' of a given design, are mapped into binary strings. These strings are then concatenated to form the 'chromosome' for a combination of variables that represent an individual design point. The GA works with these binary chromosomes, rather than with the actual design parameters. Binary coding is generally used, although other alphabets and coding schemes have been used [I]. This coding feature allows for a simultaneous use of discrete, integer and continuous design variables in one problem [4].

Further matching the processes seen in nature, the GA works with a population of points rather than one single point. To begin the GA, an initial generation is created by randomly placing '1's and '0's along the chromosomes for a given population size. For example, a population of 30 individuals will have 30 different chromosome strings. Unlike natural populations, GAS typically maintain the same population size throughout their execution. In a simple GA, two 'parents' are selected to produce two 'children' so that the number of individuals in the population will not vary with successive generations.

From the initial population, parents are selected based on the survival-of-the-fittest approach. Each member of the population has its binary chromosome decoded to the corresponding design variables. The combination of design variables represented by that chromosome is evaluated to' find a fitness value, which is analogous to the objective function in a traditional numerical optimization problem. Individuals with better fitness values are more likely to sunrive and be used as parents for the next generation. For this work, a tournament selection routine was used. In this approach, two potential parents are chosen and their fitness values are compared. The individual with a better fitness is selected, in this case lower weight, because the helicopter design problem has an objective of minimum weight.

Once parents have been selected, the reproduction process is camed out using two operators, cross-over and mutation. Both of these operations mirror processes observed in natural reproduction. The approach used for this work is the uniform cross-over, where each bit is examined for cross-over with a 50% probability. For example, a 'fair coin' is tossed for the first bit location; if heads results, then the first bit of parent 1 becomes the first bit of child 1, and the first bit of parent 2 becomes the first bit of child 2. Conversely, if tails results, the first bit of parent 1 becomes the first bit of child 2, and the first bit of parent 2 becomes the first bit of child 1. This process then produces

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Genetic Algorithm for Conceptual Design 233

nu0 offspring which become pan of the next generation. Each child contains 'genetic material' from each parent, representing features of the two parent designs.

Mutation occurs on an infrequent basis in both nature and the GA algorithm. By including mutation, the population will help to delay the condition where all individuals become so similar to each other that no further improvement is possible. When a mutation occurs in an individual, one bit along the binary string is either switched from a '1' to a '0' or from a '0' to a '1'. This operator is quite simple, and typical GA programs use mutation probabilities in the range 0.1-1.0%. In spite of its simplicity, mutation can force a population out of a nearly static condition by introducing new patterns in the binary strings not seen in the population.

In spite of the reliance of GAS on probabilistic methods, they are not merely random searches. Because the selection operator favors individuals with high fitness values, the offspring genLration will contain binary string characteristics similar to those of their parents. Eventually, certain patterns associated with high fitness values begin to dominate future generations. Individuals in the GA population exchange information firom their respective strings, but the 'building blocks' associated with the highly fit individuals propagate through future populations with increasing frequency, because individuals with these binary string patterns will have higher fimesses and be more likely to sunrive and reproduce. In spite of the seemingly high number of fitness evaluations required by the GA, the search power is significantly greater than that of a purely random search, resulting in a rather powerful and fast search and global optimization routine.

1.2 Helicopter Conceptual Design

In general, the rotorcraft design process proceeds from a set of requirements to conceptual design, followed by preliminary design, then detailed design, resulting in a description from which an aircraft could be manufactured [5, 61. Conceptual design addresses the issues of configuration arrangement, size, weight and performance of the aircraft. This conceptual design process may be further decomposed into the phases of selection and sizing.

During the selection phase of conceptual design, the process is usually fluid, with many changes and new ideas introduced and discussed by a team of engineers and designers. Typically, the standard practice utilizes brainstorming sessions to generate new ideas and concepts [6]. From these ideas and concepts, a selection or evaluation session narrows the scope of the different concepts. A design team participating in these sessions will make decisions about the helicopter configuration and arrangement based cln qualitative factors as well as results from quantitative, analytical models. The selection of concepts and configurations can be affected by the design team's experience, personal preferences or biases, and external influences (i.e. politics, economics, history) [7]. The concept or arrangement resulting from this selection may be the design that 'feels right', not necessarily one that has been objectively and quantitatively selected as a good design.

After the concept has been selected, the helicopter's major design parameters are sized to meet required characteristics. Mission analysis determines the amount of fuel required, and the aircraft's empty weight is calculated. In this iterative process, the gross weight of a specified combination of design variables is calculated based on an initial approximation of the gross weight. The newly calculated weight then becomes the next approximation, and the process repeats until the approximated and calculated

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weights have converged to the same value. Computerized sizing codes have been introduced to speed up this process.

Common in industry, government and academic rotorcraft design exercises is the use of the sizing codes HESCOMP [8] and VASCOMP I1 [9]. These computer programs are used because of their ability to estimate weight, required propulsive power and physical dimensions of given aircraft configurations to meet specified requirements. HESCOMP is used to analyze the performance of traditional helicopters, and VASCOMP is used for other rotorcraft configurations such as tiltrotors. Unfomately, this program cannot make decisions regarding configuration or major design parameters; it only provides a design point, a description of an aircraft for a given configuration and set of parameters. For a given configuration, several of these design points are calculated by varying the input design parameters. These design points can be used to describe the design solution space in a carpet plot that describes how gross weight varies with design parameters. The addition of constraints to the carpet plot resmcts the allowable solutions and leads to identification of an optimal design point which can perform a desired mission, meets all performance constraints, and has the lowest possible gross weight. Although low cost is generally a principal objective in aircraft design, cost is difficult to quantlfy in the conceptual design phase; however, lower weight typically suggests lower monetary cost [ 5 ] . This graphical process of optimization for lowest gross weight is normally limited to three major design variables to allow for graphical depiction of the design space. In general, this process is also limited to a single objective optimization for minimum weight.

Some work has been conducted towards coupling numerical optimization routine, to currently existing sizing codes (see, for example, Schliecher [lo]). These numerical optimization routines, such as CONMIN [l 11, are calculus based and, therefore, have difficulties with discontinuous or non-smooth functions and often find locally optimal designs. The inability to handle discrete, integer and continuous design variables simultaneously also limits these methods to function only as configuration suing tools.

2. Design Problems

The two design problems used in this exercise are the proposed US Navy medium lift replacement (MLR) helicopter [12] and a hypothetical high-speed attack helicopter [13]. The MLR helicopter mission requires an aircraft which can carry 24 Marines from a ship to an on-shore drop zone, return to the ship and carry 24 more Marines to the drop zone without refuelling. Figure 1 displays a more detailed mission description.

The attack helicopter mission involves carrying 1274 lb of ordnance from a forward base of operations and attacking ground targets, as illustrated in Fig. 2.

2.1 Design Variables and Coding

The design variables for both problems are encoded into binary chromosomes for use with the GA. Eight different concept variables are mapped into binary strings, as presented in Table I. Also, three engine performance maps were used as discrete variables, as presented in Table 11. Note that the binary code requires an even number of mapping relationships, which results in a redundant mapping of the GLC 38 engine. In a situation like this, the redundant mapping of a discrete variable will introduce some bias into the initial randomly generated population. This first population will have more designs that use the GLC 38 engine performance map; however, the bias is soon

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La,tn arrive SO nmi

40 min

R e p u t wilhout rcfucl. lus

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FIG. 1. MLR helicopter amphibious troop lift design mission.

Mission conducted at W f t altitude. Ausck "on-standard aunmphcrc (T= 95'0 targm

"Nao Of the E d " 9 NOEflibt (NOEI flight and hover. iO mi"

Cruirs a 99% best m g c velocity

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FIG. 2. High-speed attack helicopter mission.

cwercome if the GLC 38 engine results in poor fitness values for designs with this engine performance map.

Integer and continuous variables are mapped in a similar manner, but, because the <;A works with a coding of the variable value, these variables are actually discretized. The integer variables are discretized with a resolution of one between values, while the continuous variables may be discretized to any appropriate resolution. T o keep the helicopter design problem manageable in scope, continuous variables were mapped to short string lengths with coarse resolution. Longer suing lengths would provide better resolution but require longer processing time and more computational memory. Table 111 presents the integer and continuous variables with their minimum and maximum values, the resolution between values, and the binary string length. In this representation, a binary number of zero maps to the minimum value of a variable.

For this work, five continuous design variables were used. Rotor tip speed describes the speed of the rotor blade's tip, and this value is the product of the rotational speed c~f the rotor and the rotor radius. The rotor disk loading is the ratio of the rotorcraft's gross weight to the total area swept by the rotor disk(s); a larger value implies a smaller rotor radius for a given weight. The wing loadiig variable is used to describe the size c~f a wing, if a wing is present on the helicopter concept; similar to disk loading, this variable is calculated as the ratio of gross weight to wing platform area. The aspect ratio c~f the wing provides a measure of the 'slenderness' of the wing. The standard definition cmf aspect ratio as the wing span squared divided by the planform area was used. The ftnal continuous variable used was the blade loading. Blade loading, often referred to

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236 W. A. Crossley @ D. H. Laananen

TABLE I. Mapping of helicopter concept variables to binary snings

Binary suing

000 001 010 011 100 101 110 111

Aircraft concept

Single main rotor Single main rotor with wing Single main rotor with propeller Single main rotor with wing and propeller Tandem rotor (two main rotors) Tandem rotor with wing Tandem rotor with propeller Tandem rotor with wing and propeller

TABLE 11. Mapping of engine performance maps to binary

strings

Binary suing Engine map

00 T406 ~ r b o s h a f t 0 1 T64 Nrboshaft 10 GLC 38 turboshaft 11 GLC 38 turboshaft

as CTh, is related to the lift coefficient of the rotor blades themselves; the value used in this work is analogous to the maximum lift coefficient of a fixed wing.

As an example, a design for a winged, single-main rotor helicopter (001) with tip speed of 720 ft s - ' (OllO), disk loading of 12.5 Ib ftC2 (1101), wing loading of 300 Ib ft-2 (1 loo), wing aspect ratio of 6.0 (OlOO), maximum blade loading of 0.185 (01 lo), two engines (O), five-bladed rotor (10) and a T406 engine map (00) would be represented by the concatenated suing:

where the pipe 'I' indicates the concatenation location; it is not actually present in the

TABLE 111. Integer and continuous variable to binary suing mapping parameters for

helicopter conceptual design problem

Variable (units) Minimum Maximum Suing length

value value Resolution (bits) -

Tip speed (ft s - ') 690.0 765.0 5.0 4 Disk loading (Ib '-') 6.0 13.5 0.5 4

Wing loading (Ib ft-2) 150.0 337.5 12.5 4 Wing aspect ratio 4.0 11.5 0.5 4

Max, blade loading (CTI) 0.155 0.230 0.005 4 Number of engines 2 3 1 1 Number of blades 3 6 1 2

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binary chromosome. Each chromosome contains 28 bits; using this binary coding, 2" or 268 435 456 different parameter combinations exist in the design space.

2.2 Fimess Ewaluation

For this study, a method which evaluates the fitness of each individual string was required. As mentioned earlier, cost is difficult to quantify in the conceptual design phase. Therefore, in terms of the optimization problem, an objective function for romtorcraft conceptual design may be aircraft gross weight. The fitness evaluation must incorporate the necessary parameters to define performance and weight characteristics of the rotorcraft configuration. Additionally, this model must evaluate and account for design constraints imposed on the aircraft when providing a fimess value. Because HESCOMP [8] is a widely used helicopter sizing code, it was chosen to calculate gross weight for the fimess evaluation routine. To use this code with the GA, modifications were made to the input methods, and code was added to interpret the variables representing aircraft configuration.

The variables representing aircraft configuration required additional interpretation to properly represent the desired concept. In HESCOMP, an input variable distin- guishes between single-main rotor and tandem-rotor concepts. An additional variable signals the presence of a wing, auxiliary propulsion (in this example, a pusher propeller), both or neither. Weight factors that vary between the tandem-rotor and single-main rotor concepts must also be changed. Similarly, additional download and drag must be accounted for in the winged designs. For concepts that utilize a propeller, it!; performance is treated as a 'constant propeller', which remains the same for all dtsigns, regardless of gross weight. Use of the constant propeller reduced the number of' design variables required for the design problem.

2.3 Roblem-related Configuration Constrainls

Preliminary work to combine the GA with HESCOMP employed a reduced set of design variables, as discussed in Crossley et al. [14]. Unfortunately, this early work applied no constraints, other than maximum and minimum values of the design vs~riables that were enforced on the designs. Although the generated concepts appeared to be the best designs, their configurations included physically unrealistic combinations of some of the variables. Additional configuration constraints that were applied in the present effort were related to the number of rotor blades and to auxiliary propulsion devices.

The constraint on rotor blade number requires that a tandem-rotor configuration be restricted to at most four blades per rotor to avoid overlap and intermeshing difficulties between the two main rotors. The number of blades for a single-main rotor configuration is restricted only by the side constraints associated with the range of the vaxiable. In this exercise, six is the maximum number of rotor blades, as listed in Table 111.

The constraint on auxiliary propulsion devices is two-part. For simplicity in this problem, the constant-propeller notion was adopted as discussed previously. However, mounting a pusher propeller on a tandem-rotor transport helicopter would block access to the rear ramp door that is required for rapid exit of troops and equipment. Thus, the auxiliary propulsion for a tandem-rotor helicopter must be mounted on the wing. Two wing-mounted propellers would then be required for yaw balance, so that an allowable concept with tandem-rotor and auxiliary propulsion would have a wing and two

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TABLE IV. GA-generated designs for the MLR helicopter

Tip Disk Wing Wing Blade Number Gross Random Helicopter speed loading loading aspen loading of weight seed configuration (ft s- ') (Ib ft-') (lb ft-') ratio (CTIO) engines (Ib)

4167 Tandem,wing 765.0 11.0 150.0 6.5 0.205 2 43 227 8437 Tandem, wing 765.0 11.5 150.0 6.5 0.200 2 43 278 487 Tandem, wing 765.0 11.5 150.0 6.0 0.205 2 43 237

11512 Tandem, wing 760.0 11.5 150.0 6.0 0.205 3 43 249

propellers. In keeping with the constant-propeller notion, each propeller on the tandem concept has one half the area of a single propeller; in this way, the two smaller propellers will require the same amount of power to produce the same total thrust as the single propeller. It is of interest to note that this constraint makes infeasible the configuration of tandem rotor with propeller and no wing (1 10 in Table I). These constraints were handled via a sex-limited inheritance approach [15], which modifies the mapping of configuration strings in order to suppress infeasible configurations.

The attack helicopter design problem does not require the same configuration- related constraints that apply to the MLR helicopter design problem. Propeller place- ment in a tandem-rotor concept for an attack helicopter does not present the diaculty associated with a rear loading ramp, so all eight concepts are viable alternatives for the helicopter. Furthermore, because a single propeller could be mounted on the fuselage, two propellers on the wing are not required. The constraint on the number of rotor blades for tandem concepts is still required for the attack helicopter.

With improved constraint representation and appropriate selection of GA parameters and operators, conceptual designs of helicopters were generated to meet both the MLR and attack helicopter missions. These designs are presented in further detail in Crossley [15] and Crossley and Laananen [16].

Four different random seeds were used to initialize the GA for design generation. The MLR designs that resulted from use of the GA-based design approach are presented in Table IV. All of the designs are similar; in fact, all have four-bladed rotors and use the GLC-38 engine map. Also, the calculated gross weights, including a penalty for blade folding requirements, span a range of only 50 Ib. For conceptual design purposes, these weight differences are negligible.

These designs appear reasonable with respect to conventional design theory for large high-speed helicopters. The tandem-rotor designs require low power in hover. Tip speed impacts the weight prediction of rotor systems and drive components as well as hover performance, and a higher tip speed results in lower weight. Low wing loading on these helicopters results in fairly large area wings, but the wings, while creating a penalty for hover, off-load the main rotors in high-speed forward flight and enable both the required bank rum and the 180-knot cruise speed without the addition of heavy, auxiliary propulsion devices. The selection of high values for maximum blade loading demonstrates an increased maneuver capability. Using the GLC-38 engine map reflects choosing the most modem of the engines available.

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TABLE V. GA-generated designs for the attack helicopter -

Tip Disk Wing Wing Blade Number Gross Random Helicopter speed loading loading aspen loading of rotor weight seed configuration (ft s - ') (Ib K2) (Ib ft- ') ratio (Wu) blades (Ib)

2454 Single, wing, propeller 725.0 9.5 175.0 5.0 0.230 6 21 836 6562 Single, wing, propeller 725.0 10.5 200.0 5.0 0.220 6 21 849 5194 Single, wing, propeller 725.0 9.5 162.5 4.5 0.230 6 21807 9772 Single, wing, propeller 725.0 9.5 162.5 4.5 0.230 6 21807 -

Four designs for the high-speed attack helicopter were generated using the GA- based code. Just as in the MLR helicopter study, the designs generated for the attack helicopter are similar; all four have two engines, which use the GLC-38 engine map. The resulting designs are summarized in Table V.

These designs appear reasonable for a high-speed attack helicopter. The single main rotor allows for a smaller fuselage (less drag) than the tandem-rotor concept in an atxack helicopter, which does not require internal payload capability. A lifting wing enables the helicopter to meet the maneuver requirements without need of a large engine. The same is true for the auxiliary propulsion, which allows for the 200-knot dash capability without a large engine. Tip speed impacts both hover performance and weight prediction of rotor systems and drive components, and a higher tip speed results iri lower weight; therefore, the maximum allowable tip speed is chosen. The wings on these helicopters have reasonably large area, but the wing loading of these designs is higher than that of the AH-56A Cheyenne at about 140 Ib ftC2 [17]. (While the C,heyenne program was cancelled before full-scale production, it represents the only single-main rotor helicopter with a lifting wing and auxiliary forward propulsion ever built to specifically meet an attack mission.) Higher values of maximum blade loading capability provide better maneuverability; therefore, high blade loading values are desirable for the attack helicopter. Six-bladed rotors provide the solidity required for maneuverability at a lower weight than rotors with fewer blades and the same solidity, while still satisfying the ballistic tolerance constraint. The GLC-38 performance map again reflects the choice of the most modem engine. In all, these designs certainly appear to be good candidates for the high-speed attack requirements.

4. The GA as a Conceptual Desigd Methodology

A.utomation of the design process for increased efficiency continues to be a subject of e:ngineering design research. The conceptual design phase of the design process has oFten been ignored or overlooked by attempts at automation because of its dependence on creativity and innovation. In several instances, GAS have been described as creative or innovative [I, 181 and have been proposed as a kamework for a model of conceptual design [I 91, as discussed in this paper.

4.1 Engineering Design Process

The design process has been described in several different ways (see, for example, Cross [ Z O ] ) . A general description of the process begins with the definition of a need, which leads to an understanding of the requirements, followed by a conceptual design

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phase involving concept generation and concept evaluation. This is followed by product design where the design is often split into smaller subproblems. These subproblems are solved, and the resulting subsolutions are recombined to provide the solution for the whole design problem. For aircraft design, the product design phase is replaced by a preliminary design phase, which is then followed by a third phase, detailed design [5]. At the conclusion of detailed design, a full description from which the aircraft could be built exists. The GA follows the conceptual design approach and, in the case of helicopters as discussed in this paper, finds high-quality designs successfully.

4.2 Understanding Design Requirements

Understanding the design requirements is essential for success in any design project. These decisions about what is important in the design will determine the rest of the design process. In helicopter design, military customers provide a request for proposals , (RFP) that includes the requirements and specifications of the design. For this research, RFPs provided the design requirements for both the MLR [12] and attack [13] helicopters.

The GA possesses no feature which will automate understanding of the design requirements. However, the user of the GA must understand these requirements in order to apply the fitness evaluation correctly and define the design space, both of which affect the designs generated by the GA.

The fitness evaluation must ensure that designs which meet the requirements and which have better characteristics are assigned better fitness values. In the case of helicopter conceptual design, the sizing code HESCOMP was used to calculate the gross weight of potential aircraft designs. Requirements such as the mission description and payload capability are provided to HESCOMP through the input tiles. Constraints on the design must also be incorporated into the fitness evaluation; for the case of helicopter design, constraints were incorporated through sex-limited inheritance mapping and the use of penalty functions.

Definition of the design space also requires an understanding of the design requirements and the technology available. The design space for a GA-based design methodology music include all concepts and combinations of variables that the design engineer wishes to investigate. For this helicopter design exercise, eight different concepts were included in the design space. However, some potential concepts were not included, e.g. coaxial-rotor helicopters (counter-rotating rotors with collinear shafts) and high-speed vertical take-off and landing (VTOL) concepts like tilt rotors and tilt wings. Also, performance maps for only three engines were used. Ranges of the variables were based on the programmer's experience. The nature of these choices can be seen in the range chosen for rotor disk loading. For the attack helicopter requirements, a constraint on disk loading is required, but the choice of range in the design variable prevented selection of a disk loading which would violate the constraint.

These points indicate the need for human designers to continue to be involved in the design process,even as that process is automated. The GA is a.computationally intensive means to search complex design spaces, yet if the user can confidently reduce this design space, the GA will perform its task at less expense.

4.3 Conceptual Design

Conceptual design is the phase in the design process where the specifications and requirements of the design problem are used to fonn practical means of solution. This

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phase is generally concerned with two main activities, generation and evaluation of c:oncepts [21]. For aircraft, conceptual design begins with a set of design requirements and specifications and results in a description of an aircraft that answers the basic questions of configuration arrangement, size and weight, and performance 1.51. The c:onceptual design phase focuses on the aircraft as a whole, so that a baseline description of the aircraft is generated through the selection and sizing tasks; this aircraft is then decomposed into subsystems for further design in the preliminary and detailed clesign phases. A successful conceptual design is one which, after detailed design, will meet all the requirements and be the best conceivable design [6].

51.3.1 Concepr generation. With an understanding of the design requirements, the first c:onceptual design activity involves finding concepts that may meet these requirements. The designers must take ideas from the functional requirement space and convert them to ideas in the physical concept space [21]. This is the activity most often associated with creativity and innovation. Search features of the GA act in a way that can be <:ompared with creativity [I].

In helicopter design, concepts for the air vehicle often result from a brainstorming session in which a team of engineers discuss and propose various ideas or methods that will allow the aircraft to perform a desired mission and meet or exceed the design requirements. In the discussion of an indusny design study of the MLR helicopter, Bass and Larsen [12] describe such a session.

During the brainstorming session, various concepts involving the anti-torque, propulsion and rotor systems were proposed as potential mechanisms for creating a helicopter that could perform the MLR mission. The proposed concepts all had a basis in the previous experience and ideas of the engineers who were involved in the brainstorming session. Features that had performed well on previous helicopters or new ideas that showed potential based on analysis were proposed and combined with other features to result in a description of a helicopter that might solve the MLR design problem. This combination of ideas is central to finding a successful design. The ability to call on past experiences to generate these ideas, and the willingness to combine these features in a new or different way have been described as innovative or creative [21].

The power of the GA lies in the idea of schema processing. Schemata are pattems found in the binary code representing potential designs; schemata associated with good designs survive more often and propagate to future generations. These schemata are pattems of bits representing features of the individual design that is represented by the entire binary string. Schemata are, therefore, analogous to the ideas that human designers propose and combine to form potential helicopter concepts; as these ideas are c:ombined to form a design, the schemata are combined to form a complete individual.

The GA uses cross-over to exchange information between suings. As the cross-over c:ombines good features, better and better individuals result. Because the GA itself deals only with the binary suings, it has no information regarding what each schema represents. However, through these pattems, the GA combines ideas and features that have worked well in previous generations to find new individuals of higher fitness than their predecessors. This recombination of ideas, when seen in humans, is considered weative. In this sense, the GA generates concepts much in the same way as a team of clesign engineers.

4.3.2 Concept evaluation. Once concepts have been generated, the design team must discriminate among them. The better concepts must be identified so that further description of the design can follow. This activity often includes making 'golno-go'

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242 W. A. Crossley Q D. H. Laananen

decisions regarding acceptance of designs [21]. Human designers often pursue this activity in a qualitative or subjective manner, and designs which are considered better 'survive' the evaluation process. The GA uses the selection operator to discriminate among better individuals, each of which has been assigned a quantitative fimess value.

Because of the large scope of the design problem, the engineers on the industry team used several techniques to evaluate the design concepts generated during the brainstorming session for the design of the MLR helicopter [12]. Using evaluation matrices, the engineers made qualitative decisions about the ability of each concept to meet the helicopter's requirements. These methods then allowed assignment of a numerical score to each concept and a ranking of the concepts from best to worst. The concepts selected for further evaluation were those with the best-ranked positions.

The scope of the helicopter design problem may have created difficulties for the human designers in using qualitative evaluations, but the GA searches complex design spaces efficiently. The binary string representing each individual is decoded to provide the combination of parameters which describe each individual design. From these parameters, the fitness of each individual is determined. In the case of helicopter design, the 28-bit string is decoded into appropriate values of the nine design variables, and the fimess evaluation routine uses HESCOMP to calculate the gross weight of a helicopter with the given combination of design variables. This gross weight is used as the fitness function, and the GA uses the selection operator to discriminate among good and bad designs.

Because the GA makes use of the selection operator with the fitness function as the basis for selection, the concept evaluation process uses quantitative rather than subjective information for all of its decisions. The selection operator automates the golno-go decisions, and the GA's progression through the design space ensures that individuals with better fitness values are chosen as the 'go' concepts.

4.4 Design Space Search The GA searches through a design space differently from humans, but makes use of similar, perhaps improved, mechanisms to discover better designs. Both opportunistic behavior and parallel design efforts are displayed by the GA in its search. These same characteristics are considered beneficial in human designers.

4.4.1 Opponunkric behavior. Several researchers have shown that, in solution of a design problem, humans often display opportunistic behavior [21]. This means that designers pursue concepts and ideas that have worked well in the past and show the greatest promise for future development. The thought process of the designer, while containing alternating stages of divergent and convergent thought, follows an overall convergent path, focusing on one particular solution [ZO]. The GA mimics this opportunistic behavior.

The GA begins its search from a randomly generated initial population. The definition of the design space includes ranges of concepts and variables that provide potential solutions to the design problem, and some points in the design space represent designs that have worked well in the past. As the GA moves from generation to generation, it uses the selection, cross-over and mutation operators to move to new areas in the design space. The GA evaluates the current generation, and the best individuals are selected for future development. Parts of these best individuals are interchanged through cross-over, creating new individuals which may be better than their ancestors. This process occurs over and over, and characteristics (schemata) associated with good designs survive more frequently as the GA moves opportunisti- cally towards the best possible design in the design space.

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The opportunistic behavior of the GA can be illustrated for the MLR helicopter dcesign problem. A reduced two-dimensional view of the design space is presented in Fig. 3 using disk loading and tip speed as coordinates. For the design run starting with the random seed of 8437 (among those listed in Table IV), Fig. 3 shows the location o:f each point in the population for several selected generations. The initial, randomly generated population appears as the generation 0 plot, in which points have a fairly even dismbution throughout the design space. As the GA progresses through its run, the points in the design space begin to cluster in the area which provides the lowest- weight designs; the last generation is generation 46. Every generation has 74 individuals; in the later generations, several individuals share the same combination of disk loading and tip speed so that there appear to be a smaller number of points on the plots.

For this particular design run, the best individual has a disk loading of 11.5 lb ftC2 and a tip speed of 765 ft s- ' . The GA quickly moves the search to concentrate on the area around this point. It is interesting to note that the best design ever generated during this run was actually encountered in generation 36, and this point is not seen in the generation 40 and 46 plots.

4.4.2 Parallel design effom. The GA, by way of its population search, generates and evaluates several parallel designs. Human designers are single-concept [22] and design- firation [23] prone. It is generally accepted that if more than one concept is evaluated during conceptual design, the results of the process are better [20, 211.

Human designers following opportunistic behavior usually select one concept or idea and pursue that idea until it satisfies the design requirements. External pressure to choose a certain design, familiarity with a reduced set of the available design points, and personal experience can all impact the choices made by the human design team. While Bass and Larsen [12] contains no specific mention of these effects, an industry design team voted the single-main rotor concept to be bener than the tandem-rotor concept for the MLR helicopter. The company which conducted this study builds only single- main rotor helicopters, and its design team would obviously be more familiar wirh this type of concept. On the other hand, the GA chose a tandem-rotor design as the best helicopter for the MLR requirements.

As discussed in the previous section, the GA pursues opportunistic designs, but in the diversity of the population search the GA can also 'remember' other ideas that show some promise, as shown in the example of Fig. 4. The plots in this figure are for the design of the MLR helicopter using the seed 8437. These plots show each individual along the x-axis (74 individuals in each generation) and its configuration along the y-axis.

The initial generation is randomly generated, and all of the different concepts are well represented. As the GA begins its run, it begins to follow the opportunistic behavior and focus on the designs with tandem rotors. This choice is reasonable, as tandem rotor designs require less power to hover than single main rotor helicopters, particularly in large helicopters. The GA also begins to focus on the design with a lifting wing, which reduces the maneuver requirements of the main rotors, and an auxiliary propeller, which reduces the forward-flight requirements of the main rotors. Seeing this trend, a human designer following a single-concept design strategy may decide this is the best configuration for the MLR helicopter and discard other designs from consider- a~ion.

However, the GA is continually searching the design space for lighter-weight designs. As the search continues, the MLR design concept with the best fitness becomes the tandem rotor with wing. The GA search has found that a variant of this

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Generation 0 Generation 5

0 0 0 0

. = = = : . . . . . i = . o 690 705 720 735 750 765

l i p Sped (A i')

6.0 t 690 705 720 735 750 765

l i p S p e d ( R i ' )



s : , , , , , , , , , , , : : I , , , , , , , , , , , , , , ,

' 10.5 10.5 0 O ! 9.0 3 9.0

-3 0 1

7.5 0

7.5

6.0 6.0

690 705 720 735 750 765 690 705 720 735 750 765

l i p S p d (R <') l i p Sped (R i')

FIG. 3. Points in the tip speeddisk loading plane of the MLR helicopter design space.

design provides better performance (lower weight) than the previously investigated concept of a tandem rotor with wing and auxiliary propulsion. The best MLR helicopter designs generated for the four different seeds are all the tandem-rotor-with-wing configuration. As the wing can reduce the rotor's requirements for lift, the ability to provide forward propulsion still exists, and the GA has found a combination of design

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(andem + wing + su.

e r n + wing

(andem

single + wing + aux

singlc + wing

single + au.

singlc

Generation 0 m o m o omo o o c m o mdem+wing+aux

o OD o 0 0 0 0 tandem + wing

0 0 0 0 tadem

0 0 moo m ~ m O O single + wing + am

o 0 0 o o 0 0 single + wing

D ~ O o o o m m o r i d s + aw;

mm mx, o single

0 10 20 30 40 50 60 70

Individual

Generation 5

I----

0 10 20 30 40 50 60 70

Individual


mdern+ wing+ aux

a - m-oo- - mdem

single + wing + au. single+ wing+aw;

ringlc + wing single + wing

single+ au. single + a w

aingle

0 10 20 30 40 SO 60 70 0 10 20 30 40 SO 60 70

Individual M v i d u a l


mndsm+ w i q + aw 1 e r n + wing + aux P " 0 0 0 0

tadem+ wing iandem+ wing

e m tadem

si@c + wing+ nlu

single + wing -

single + aw; -

sinslc + wing + nu. -

single + wing - o single + au. -

single 1 single 1 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70

Individual Mividual

FIG. 4. h4LR helicopter configurations for each individual in the population.

parameters that allows high-speed forward-fight capability without the additional !weight required by auxiliary propulsion devices.

The same behavior is exhibited by the GA when searching the design space for the attack helicopter problem. The design search by the GA using the random seed of 9772 was examined in more detail. A reduced design space representation using tip speed and disk loading was used to create the plots shown in Fig. 5. In these plots, the original design space allowed for tip speeds in the range from 690 to 765 ft s- l . A constraint on maximum rotor tip speed further limits the design space to 725 ft s-l. As seen in the h4LR design runs, the GA focuses on an area of the design space with the greatest potential. For the attack helicopter design, the space quickly focused the search around

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0 0 . . t . : : : . . . . . .

690 705 720 735 750

Tip Spkd (As")

0 0 0 0 0 0 0

0 0 0 0 0 0 0

0

P

720 735

Tip Spkd (R 8")


0 0 0

. . I . ' = 3 = : I . . , . . I , . r . . m . . r , . . . . <

690 705 720 735 750 765 690 705 720 735 750 765

Tip S p e d (R 6.') Tip Specd (R 6.')


690 705 720 735 750 765 690 705 720 735 750 765

Tip Specd (R it) Tip Spkd (R i')

FIG. 5. Points in the tip speed-disk loading plane of the attack helicopter design space.

the area containing the point with tip speed of 725 ft s- ' and disk loading of 9.5 lb ft-', the combination that was seen in the best design generated during this run.

As the GA searches the design space for the best combination of design parameters, the range of configurations rapidly narrows, as illustrated in Fig. 6. From the initial generation to the fifth generation, the GA search has already recognized that, for this

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tandcm + wing + am

tandem+ wing

tandem + aur

mndcm

single + wing+ s u

single + wing

singlc + sur

single

Generation 0

D OD m o m o o Om tandcm+wing+aw

o 0 0 o o 0 - 0 tandem+ wing

1 0 0 0 - 0 O D D tandem+ aur

0 0 m 0 o m tandem

0-0 -0 0 0 0 0 single+wing+aur

o o m o m o single + wing

m m o single + aur

o 0 0 o o single

Generation 5

, m o m m m o m om m w o 0-


tandem+wing+am o 0 0 o landem+ wing+ aur

tandsm+ wing

tandem+ a m tandsm+su

mndem tandem

single + wing + am single + wing + a u

single + n u

0 10 20 30 40 50 60 70 0 10 20 30 40 SO 60 70 M i v i d l e l Individual

Generation 20 Generation 27 mndcm + wing + nur 1 O tandcm+wing+au 1

tandrm+ wing

mndcm + Pur

randem randem singlo + wing + nul sinpla + wing + aul

single + wing single + wing o o o

single + am

single single

0 I0 20 30 40 50 60 70 0 10 20 30 40 50 60 70 M i v i d m l Individual

FIG. 6. Attack helicopter configurations for each individual in the population.

attack mission, both a lifting wing and auxiliary propulsion are required (to meet maneuver and high-speed flight requirements). Continuing through the search, the extra weight and drag of the tandem-rotor configuration make it less desirable for the attack mission, and the single main rotor with wing and auxiliary propeller becomes the configuration of choice.

4.5 GA Limitations

'The GA has displayed properties that suggest that it can be used as an automated conceptual design methodology for rotorcraft. This approach to design has limitations

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to its use; most importantly, the GA cannot replace the human element in design. These limitations manifest themselves in three major areas.

4.5.1 Fitness evaluation. To. perfom its search through a design space, the GA must have a numerical fitness value. This value becomes the sole arbiter of 'life or death' for designs during the selection operation. Intangible or unaccounted fimess concerns will not be reflected in the designs chosen as the best. In this helicopter design example, gross weight has been used as the fimess function, but helicopter designers also consider other factors such as direct operating cost, reliability and maintainability, and manufacturability when deciding on the best designs.

Also, the GA must have unbiased fitness values for all design points in the space to provide accurate helicopter designs. Because the fitness evaluation will be programmed by humans, the biases of the design engineer with respect to certain concepts can be reflected in definition of the fitness function. Using HESCOMP to provide gross weight as the fitness function for helicopter design presents a great challenge in this area on account of its use of statistical equations to predict the weights of the helicopter's components [8]. Inputs to these equations vary between the single-main rotor and tandem-rotor concepts, and subjectively assigned values such as 'advanced technology factors' are frequently used to modify the predicted weights of components. The results of the GA may be changed by altering the inputs to the weight equations.

4.5.2 Design space definition. The design space in which the GA searches must be exhaustive to provide a search of all possible concepts and variable combinations. At the same time, the design space needs to be small enough that the problem is manageable from the points of view of programming and computational expense. The design engineer using the GA-based design approach can impact the results of the search by not including potential variables or configurations.

The helicopter design exercises demonstrate this idea, as the eight configurations included in the design space do not include coaxial-rotor configurations. While few coaxial-rotor helicopters exist, a coaxial-rotor attack helicopter has been built to provide high-speed forward flight and good maneuverability [24]. This concept was not included in the design of the high-speed attack helicopter discussed here. Exclusion of the coaxial-rotor configuration obviously prevents the GA from selecting this type of concept, which might provide a lighter-weight design.

Similarly, the design space cannot be expanded during the design search. There is no way for the GA to evaluate a coaxial-rotor concept if it has not been included in the design space. Ranges of continuous and integer variables also cannot be exceeded. If side constraints are not imposed through design requirements, the ranges used in the design space act as side limits and may prevent the GA from finding a potential value that provides better performance.

4.5.3 Convergence. Convergence is an important issue, especially when helicopter design is posed in the form of an optimization problem. As seen in the previously discussed work, the use of the pseudo-random number generator may produce a different 'best' design for each random seed, a result that may cause concern about which of the generated designs are truly the best.

This condition occurs because the GA does not use gradient information to conduct its search through the design space. Although this trait affords the ability to find good design points in complex, non-convex and even discontinuous design spaces, it unfor-

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runately leaves the GA unable to determine whether the design it has generated is globally optimal. The ability to search a wide domain has resulted in a sacrifice in the ability to guarantee convergence as an optimization routine.

Convergence to a 'best' conceptual design is also suspect in the typical industry design process. The use of subjective decision-making to reduce the design process time is common in industry studies, as discussed in Bass and Larsen [12]. The procedures used for conceptual design provide no information to demonstrate optimality, so the lack of optimality information from the GA limits its use as a design methodology only as it limits the traditional conceptual design process.

Generally, the GA provides more information about potential designs in less time than traditional methods, so several different designs generated by the GA may provide information about good designs or about inaccuracies in design space or fitness evaluations. Astute design engineers can use the results of several different GA runs and make further decisions about the designs by applying criteria not represented in calculation of the fimess function. This approach actually can make the limitation of the GA's convergence into an asset for conceptual design.

!i. Conclusions

IL a result of the work described here, it may be concluded that the GA can assist the design engineer to work more efficiently by automating some of the selection and sizing tasks required for helicopter conceptual design. For the two conceptual design studies that have been described, results generated using the GA-based design approach appear to be high-quality designs. Although the GA employs search methods different from those of human designers, it does utilize mechanisms such as opportunistic behavior and parallel design efforts that are considered desirable in humans. Finally, automation of the conceptual design phase with a GA approach has some limitations; these all require some human interaction to complete a design search.

REFERENCES

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[2] KRISHNAKUMAR, K. (1993) Genetic Algorithms-A Robust Optimization Tool (Washington, DC, AIAA Paper 93-03 15).

[3] HOLLAND, J.H. (1992) Adapration in Natural and Anificial Systems (Cambridge, MA, MIT Press).

[4] h, C.-Y. & HAJELA, P. (1992) Genetic algorithms in optimization problems with discrete and integer design variables, Engineering Optimization, 19, pp. 309-327.

[5] RAYMER, D.P. (1989) Aircraft Design: A Conceptual Approach (Washington, DC, AIAA Education Series).

[6] TORENBEEK, E. (1988) Synthesis of Subsonic A i ~ l a n e Design (Nowell, MA, Kluwer Academic Publishers).

[7] MC~~ASTERS, J.H. (1985) Some Thoughu on Design Education (Washington, DC, A I M Paper 85-3079).

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[9] SCHOEN, A.H. er al. (1980) User's Manual for VASCOMP II, the V/STOL

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250 W. A. Crossley D. H. Laananen

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[12] BASS, S.M. & LARSEN, S.D. (1995) Concept selection of a new design to meet the . medium lift replacement (MLR) helicopter requirements, in: Proceedings of the American Helicopter Society Vertical Ltj? Aircraft Design Conference, American Helicopter Society San Francisco Bay Area Chapter, San Francisco, CA, pp. 1.5-1-1.5-15.

[13] McDomell Douglas Helicopter Company (1993) Studmt Design Competitwn Request for Proposal, American Helicopter Society, Alexandria, VA.

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[I61 CROSSLEY, W.A. & LAANANEN, D.H. (1996) Conceptual design of helicopters via genetic algorithm, Journal of Aircraft, 33, pp. 1062-1070.

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[20] CROSS, N. (1989) Engineering Design Methodr (Chichester, Wiley). [21] UWN, D.G. (1992) The Mechanical Design Process (New York, McGraw-Hill). [22] FINGER, S. & DIXON, J.R. (1989) A review of research in mechanical engineering

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pdf for helicopter

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