James D. Guptill

COMPARATIVE EVALUATION OF DIFFERENT OPTIMIZATION ALGORITHMS FOR STRUCTURAL DESIGN APPLICATIONS

Non-linear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Centre, a project was initiated to assess the performance of eight different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using the eight different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems, however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with Sequential Unconstrained Minimizations Technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.

Neural Network and Regression Approximations in High-Speed Civil Aircraft Design Optimization

Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Centers Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Centers CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.

Optimization for Aircraft Engines with Regression and Neural-Network Analysis Approximators

Surya N. PatnaikOhio Aerospace InstituteCleveland, Ohio 44142James D. Guptill, Dale A. Hopkins, and Thomas M. LavelleNational Aeronautics and Space AdministrationGlenn Research CenterCleveland, Ohio 44135SUMMARYThe NASA Engine Performance Program (NEPP) can configure and analyze almost any type of gas turbineengine that can be generated through the interconnection of a set of standard physical components. In addition, thecode can optimize engine performance by changing adjustable variables under a set of constraints. However, forengine cycle problems at certain operating points, the NEPP code can encounter difficulties: nonconvergence in thecurrently implemented Powells optimization algorithm and deficiencies in the Newton-Raphson solver duringengine balancing. A project was undertaken to correct these deficiencies. Nonconvergence was avoided through acascade optimization strategy, and deficiencies associated with engine balancing were eliminated through neuralnetwork and linear regression methods. An approximation-interspersed cascade strategy was used to optimize theengines operation over its flight envelope. Replacement of Powells algorithm by the cascade strategy improved theoptimization segment of the NEPP code. The performance of the linear regression and neural network methods asalternative engine analyzers was found to be satisfactory. This report considers two examples--a supersonic mixed-flow turbofan engine and a subsonic waverotor-topped engine--to illustrate the results, and it discusses insightsgained from the improved version of the NEPP code.INTRODUCTIONThe NASA Engine Performance Program (NEPP) is a gas-turbine engine-cycle simulation code. This code canconfigure and analyze almost any type of gas turbine engine that can be generated through the interconnection ofa set of standard physical components: propeller, inlet, ducts, combustor, fan, compressors, turbines, shafts, heatexchangers, flow splitters, subsonic mixers and/or supersonic ejectors, nozzles and water injectors or gas generators.The engine can he designed for different types of fuels: standard hydrocarbon jet fuel and cryogenic fuel and slurries.For thermodynamic analysis, built-in curve fits can be generated from empirical data available in NEPP. For theanalysis of jet and rocket fuels, an auxiliary chemical equilibrium composition model is available (ref. 1). The NEPPcode has been successfully used to simulate a wide range of engines from turboshaft and turboprops to airturbo-rockets and supersonic variable-cycle engines. A description of the NEPP program, with typical input files for a setof engine configurations, is given in references 2 and 3. Since its inception (ref. 4), the NEPP program has beencontinuously undergoing improvement to keep pace with the advanced gas turbine engines envisioned for the 21 stcentury. NEPP simulation has decreased engine cycle analysis time and improved engine model fidelity.The NEPP code has a numerical optimization capability to increase engine performance. The program allowsthe maximization or minimization of a cost function for a set of independent variables subjected to a number ofspecified behavior parameters of the engine, which act as the constraints. In the NEPP code, the resulting optimiza-tion problem is solved using Powells method (ref. 5), which was developed in the early sixties. It has been observedthat for certain engine problems Powells method can produce an overdesign condition with fewer active constraintsthan the correct optimum solution or can experience convergence difficulties. A project was undertaken to correctthe optimization-related deficiency in the NEPP code by augmenting it with a cascade optimization strategy that wasNASA/TM----2000-209177 1

Subsonic Aircraft Design Optimization with Neural Network and Regression Approximators

The Flight-Optimization-System (FLOPS) code encountered difficulty in analyzing a subsonic aircraft. The limitation made the design optimization problematic. The deficiencies have been alleviated through use of neural network and regression approximations. The insight gained from using the approximators is discussed in this paper. The FLOPS code is reviewed. Analysis models are developed and validated for each approximator. The regression method appears to hug the data points, while the neural network approximation follows a mean path. For an analysis cycle, the approximate model required milliseconds of central processing unit (CPU) time versus seconds by the FLOPS code. Performance of the approximators was satisfactory for aircraft analysis. A design optimization capability has been created by coupling the derived analyzers to the optimization test bed CometBoards. The approximators were efficient reanalysis tools in the aircraft design optimization. Instability encountered in the FLOPS analyzer was eliminated. The convergence characteristics were improved for the design optimization. The CPU time required to calculate the optimum solution, measured in hours with the FLOPS code was reduced to minutes with the neural network approximation and to seconds with the regression method. Generation of the approximators required the manipulation of a very large quantity of data. Design sensitivity with respect to the bounds of aircraft constraints is easily generated.