William A. Crossley

Aerodynamic and Aeroacoustic Optimization of Rotorcraft Airfoils via a Parallel Genetic Algorithm

A parallel genetic algorithm (GA) methodology was developed to generate a family of two-dimensional airfoil designs that address rotorcraft aerodynamic and aeroacoustic concerns. The GA operated on 20 design variables, whichconstitutedthecontrolpointsforasplinerepresentingtheairfoilsurface.TheGAtookadvantageofavailable computer resources by operating in either serial mode, where the GA and function evaluations were run on the same processor or “ manager/worker” parallel mode, where the GA runs on the manager processor and function evaluations areconducted independently on separate workerprocessors. The multiple objectives of this work were to minimizethedrag and overall noiseof the airfoil. Constraintswereplaced on liftcoefe cient, moment coefe cient, andboundary-layerconvergence.TheaerodynamicanalysiscodeXFOILprovidedpressureandsheardistributions in addition to liftand drag predictions. Theaeroacousticanalysis code, WOPWOP, provided thicknessand loading noise predictions. The airfoils comprising the resulting Pareto-optimal set exhibited favorable performance when compared with typical rotorcraft airfoils under identical design conditions using the same analysis routines. The relationship between the quality of results and the analyses used in the optimization is also discussed. The new airfoil shapes could provide starting points for further investigation.

Using the Two-Branch Tournament Genetic Algorithm for Multiobjective Design

The two-branch tournament genetic algorithm is presented as an approach to determine a set of Pareto-optimal solutions to multiobjective design problems. Because the genetic algorithm searches using a population of points rather than using a point-to-point search, it is possible to generate a large numher of solutions to multiobjective problems in a single run of the algorithm. The two-branch tournament and its implementation in a genetic algorithm (GA) to provide these solutions are discussed. This approach differs from most traditional methods for GA-based multiobjective design ; it does not require the nondominated ranking approach nor does it require additional fitness manipulations. A multiobjective mathematical benchmark problem and a 10-bar truss problem were solved to illustrate how this approach works for typical multiobjective problems. These problems also allowed comparison to published solutions. The two-branch GA was also applied to a problem combining discrete and continuous variables to illustrate an additional advantage of this approach for multiobjective design problems. Results of all three problems were compared to those of single-objective approaches providing a measure of how closely the Pareto-optimal set is estimated by the two-branch GA. Finally, conclusions were made about the benefits and potential for improvement of this approach.

Empirically-Derived Population Size and Mutation Rate Guidelines for a Genetic Algorithm with Uniform Crossover

The Genetic Algorithm (GA) is employed by different users to solve many problems; however, various challenges and issues surround the appropriate form and parameter settings of the GA. One of these issues is the conflict between theory and experiment regarding the crossover operator. Experimental results suggest that the uniform crossover can provide better results for optimization, so many users wish to employ this approach. Unlike for the single-point crossover GA, no established set of guidelines exists to assist in choosing appropriate population sizes and mutation rates when using the uniform crossover. This paper presents the results of an empirical study to determine such guidelines by examining several parameter combinations on four mathematical functions and one engineering design problem. The resulting guidelines appear to be valid over these test problems. They are presented and discussed, with the intent that they may provide assistance to users of GAs with uniform crossover.

Topology Design of Planar Cross-Sections with a Genetic Algorithm: Part 1--Overcoming the Obstacles

Using a topology approach gives an engineer freedom to design a structure of any shape and connectivity. In this way, no a priori knowledge of the shape or geometry of the design is needed when the problem is being formulated. The binary chromosome design storage and global search capabilities of the Genetic Algorithm (GA) make it a powerful tool for solving topology design problems. Previous researchers have experimented with the GA for topology design, and some have indicated that methodology issues prevented wider application. Among these issues are chromosome crossover method, enforcement of design connectivity, and appropriate structural analysis. The research described in this paper investigated the use of a GA for topology design of planar cross-sections under bending and torsion. Chromosome crossover method was investigated for this class of problems, and methods of enforcing connected designs were studied. The research shows that, with proper structural modeling and appropriate choice of crossover and connectivity, a GA can perform topology design for bending and torsional elements. Successful cases are presented and discussed.

Spacecraft Reliability-Based Design Optimization Under Uncertainty Including Discrete Variables

computationally expensive sampling techniques. The computational cost of optimization approaches becomes prohibitivewhenconsideringdiscretetechnology andredundancychoicesasvariables.Thisworkpresentsagenetic algorithm with Monte Carlo sampling for probabilistic reliability-based design optimization of satellite systems. In thisapproach,confidence-levelconstraintsensurethatsystemreliabilityrequirementsaremetwithhighprobability. Thegeneticalgorithm–MonteCarlosamplingapproachiscomparedtoadeterministic margin-basedapproachthat enforcesmarginsorsafetyfactorsonthereliabilityofindividualcomponents.Thecomparisonshowsthatthegenetic algorithm–Monte Carlo sampling approach produces satellite designs that have low launch mass (a surrogate for cost) while achieving reliability requirements at specified high confidence levels, while the genetic algorithm– deterministic margin-based approach produces heavy satellite designs with excessive redundancy. Based on this work, extensions of a genetic algorithm-based approach for discrete optimization under uncertainty that may require less computational effort appear possible.

A study of adaptive penalty functions for constrained genetic algorithm-based optimization

Several potential approaches are presented that utilize adaptive penalty functions that change the value of the draw-down coefficients during a run of the genetic algorithm. A simple 1D constrained problem and a more complex 2D constrained problem were solved using the adaptive penalty strategies. A stiffened composite panel was optimized for minimum weight, subject to several constraints using the adaptive penalty methods to provide insight into how the approaches perform on an engineering problem. On the basis of these problem solutions, conclusions were drawn regarding the efficacy of adaptive penalty functions for constrained optimization. (Author)

Conceptual design of helicopters via genetic algorithm

The genetic algorithm (GA) is a computational model of natural selection and reproduction displayed by biological populations. The capabilities of GAs as search and optimization methods make them well suited to perform conceptual design tasks. A GA has been developed and combined with an industry standard sizing code specifically for helicopter conceptual design. This GA-based program was used to generate conceptual designs for three helicopter missions. Results of these efforts are discussed, providing insight into the ability of the GA to perform helicopter conceptual design.

Variable Resource Allocation Using Multidisciplinary Optimization: Initial Investigations for System of Systems

The concept of a “System of Systems” (SoS) describes a large system of multiple systems – each capable of independent operation – that have been brought together to provide capabilities beyond those of each individual constituent system. Formulating and solving an SoS design problem has become increasingly important, particularly in the aerospace and defense industries, as customers have begun to ask contractors for broad capabilities and solutions rather than for specific individual systems. Part of an SoS design problem is determining the appropriate mix of both existing and yet-to-be-designed systems. While determining an appropriate mix of existing systems falls into the category of resource allocation, including features of a yet-to-be-designed system makes the problem more complicated by requiring the allocation of a variable resource. In this paper, a simple problem using an airline wishing to investigate how a new, yet-to-be-designed aircraft will impact the fleet operating costs provides an example of this type of problem. The resulting statement is a Mixed-Integer, Non-Linear Programming (MINLP) problem. Approaches for MINLP are applied to the problem, and these methods do generate solutions but at generally high computational cost. Using a response surface approach to model the airline design portion of the problem finds good solutions at much lower computational cost. A decomposition approach analogous to those of multidisciplinary optimization is also applied to the problem, in which there is an “allocation domain” and an “aircraft design domain”, and this approach also generates solutions, but at a lower computational cost. The MDOmotivated decomposition approach appears to have promise for the allocation of variable resources challenge presented by many SoS design problems.

Nonlinear synergetic optimal controllers

Optimality properties of synergetic controllers are analyzed using the Euler-Lagrange conditions and the Hamilton-Jacobi-Bellman equation. First, a synergetic control strategy is compared with the variable structure sliding mode control. The connections of synergetic control design methodology and the methods of variable structure sliding mode control are established. In fact, the methods of sliding surface design for the sliding mode control are essential for designing invariant manifolds in the synergetic control approach. It is shown that the synergetic control strategy can be derived using tools from the calculus of variations. The synergetic control laws have a simple structure because they are derived from the associated first-order differential equation. It is also shown that the synergetic controller for a certain class of linear quadratic optimal control problems has the same structure as the one generated using the linear quadratic regulator approach by solving the associated Riccati equation. The synergetic optimal control and sliding mode control methodologies are applied to the nonlinear control of the wing-rock suppression problem. Two different wing-rock dynamic models are used to test the design of the synergetic and sliding mode controllers. The performance of the closed-loop systems driven by these controllers is analyzed and compared.

Multi-Objective Optimization of Communication Satellites with Two-Branch Tournament Genetic Algorithm

In spacecraft design, many specialized state-of-the-art design tools are employed to optimize the performance of various subsystems. However, there is no structured system-level concept-definition process. Consequently, designers usually compromise some mission goals to satisfy only one of the primary design objectives. The conceptual stage of the spacecraft design process is formulated into a multi-objective discrete optimization problem. The use of multi-objective design allows the designer to evaluate different design alternatives across the whole set of design objectives. This work addresses two key design objectives for the spacecraft design process: the minimization of total launch mass and the maximization of spacecraft overall reliability. To predict values for the objective and constraint functions, a satellite design tool, which includes a satellite sizing model and a deterministic reliability model, was built and integrated with a genetic algorithm that employs a two-branch tournament to address the dual objective problem. The multi-objective approach was successful in determining sets of discrete design parameters that would minimize the launch mass as well as maximize the reliability of a geostationary communication satellite, using specified payload requirements. The designs generated by this approach appear to fall into three regions of the tradeoff space between the satellite launch mass and the satellite reliability objectives.