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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

A 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.

Patnaik, Surya N.↗
NASA NTRS1991

Optimal design of solidification processes

An optimal design algorithm is presented for the analysis of general solidification processes, and is demonstrated for the growth of GaAs crystals in a Bridgman furnace. The system is optimal in the sense that the prespecified temperature distribution in the solidifying materials is obtained to maximize product quality. The optimization uses traditional numerical programming techniques which require the evaluation of cost and constraint functions and their sensitivities. The finite element method is incorporated to analyze the crystal solidification problem, evaluate the cost and constraint functions, and compute the sensitivities. These techniques are demonstrated in the crystal growth application by determining an optimal furnace wall temperature distribution to obtain the desired temperature profile in the crystal, and hence to maximize the crystal's quality. Several numerical optimization algorithms are studied to determine the proper convergence criteria, effective 1-D search strategies, appropriate forms of the cost and constraint functions, etc. In particular, we incorporate the conjugate gradient and quasi-Newton methods for unconstrained problems. The efficiency and effectiveness of each algorithm is presented in the example problem.

Dantzig, Jonathan A.↗
NASA NTRS1991

Sensitivity analysis, approximate analysis, and design optimization for internal and external viscous flows

A gradient-based design optimization strategy for practical aerodynamic design applications is presented, which uses the 2D thin-layer Navier-Stokes equations. The strategy is based on the classic idea of constructing different modules for performing the major tasks such as function evaluation, function approximation and sensitivity analysis, mesh regeneration, and grid sensitivity analysis, all driven and controlled by a general-purpose design optimization program. The accuracy of aerodynamic shape sensitivity derivatives is validated on two viscous test problems: internal flow through a double-throat nozzle and external flow over a NACA 4-digit airfoil. A significant improvement in aerodynamic performance has been achieved in both cases. Particular attention is given to a consistent treatment of the boundary conditions in the calculation of the aerodynamic sensitivity derivatives for the classic problems of external flow over an isolated lifting airfoil on 'C' or 'O' meshes.

Taylor, Arthur C., III↗
NASA NTRS2003

Design Optimization of Composite Structures under Uncertainty

Design optimization under uncertainty is computationally expensive and is also challenging in terms of alternative formulation. The work under the grant focused on developing methods for design against uncertainty that are applicable to composite structural design with emphasis on response surface techniques. Applications included design of stiffened composite plates for improved damage tolerance, the use of response surfaces for fitting weights obtained by structural optimization, and simultaneous design of structure and inspection periods for fail-safe structures.

Haftka, Raphael T.↗
NASA NTRS2018

Multidisciplinary Design Optimization and Cruise Mach Number Study of Truss-Braced Wing Aircraft

The Subsonic Ultra Green Aircraft Research (SUGAR) Phase III was led by Dr. Rakesh K. Kapania and Dr. Joseph A. Schetz at the Multidisciplinary Analysis and Design Center for Advanced Vehicles, Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg VA. The research was performed from December 2014 to December 2015. Three major areas were investigated: Multidisciplinary Design Optimization (MDO) studies of truss braced wing (TBW) and strut braced wing (SBW) vehicles at cruise Mach numbers of 0.7 and 0.8 for a flight mission similar to current market single aisle configurations. The performance and the characteristics of the optimized vehicles were compared to the SUGAR Phase II TBW vehicle. These results were obtained without applying any of the extended transonic aerodynamic and aeroelastic tools that will be discussed later. It was found that the cruise Mach number has a large effect on the best “truss” configuration. At Mach 0.7, an SBW has a better fuel consumption and better take-off gross weight (TOGW). However, at Mach 0.8, the TBW is superior because the jury strut aids in satisfying the flutter constraint; Two-dimensional, steady, transonic aerodynamic analysis of the Boeing Airfoil J (BACJ) airfoil was performed for a range of thickness ratios, Mach numbers and lift coefficients. Reynolds-averaged Navier-Stokes (RANS) equations were solved to obtain the lift-curve slope, wave drag coefficient, the location of the center of pressure and to predict the separation at the trailing edge, which may lead to buffeting. One of the goals was to develop a database of lift-curve slope and the location of center of pressure, which could be used in a transonic aeroelastic analysis. Another goal was to compare the wave drag coefficients to those predicted by Lock’s fourth-power law and also to compare the transonic effects obtained from RANS simulations to those predicted by the Korn equations. A third goal was to develop a buffet boundary, which can be integrated into the MDO framework to prevent the optimized designs from probable buffeting; A state-space transonic aeroelastic analysis tool was developed, which can incorporate the nonlinear transonic effects in the unsteady aerodynamics but is yet computationally cheap when used within the VT MDO framework. The aeroelastic analysis uses Leishman- Beddoes (LB) indicial functions, which generated a state-space representation of the aeroelastic system. The indicial functions allow the incorporation of data for steady lift-curve slope and location of the center of pressure. Thus, the steady transonic effects are included, and the unsteady aerodynamic responses are a linearization about the steady results. The aeroelastic approach discretizes the wing into numerous strips, which results in a large eigenvalue problem as each strip has eight augmented aerodynamic states as per the LB theory. Thus, to reduce the computation expense, a reduced order model (ROM) was developed. The approach was validated using a few examples.

Kapania, Rakesh K.↗
NASA NTRS1992

Multidisciplinary design optimization using response surface analysis

Aerospace conceptual vehicle design is a complex process which involves multidisciplinary studies of configuration and technology options considering many parameters at many values. NASA Langley's Vehicle Analysis Branch (VAB) has detailed computerized analysis capabilities in most of the key disciplines required by advanced vehicle design. Given a configuration, the capability exists to quickly determine its performance and lifecycle cost. The next step in vehicle design is to determine the best settings of design parameters that optimize the performance characteristics. Typical approach to design optimization is experience based, trial and error variation of many parameters one at a time where possible combinations usually number in the thousands. However, this approach can either lead to a very long and expensive design process or to a premature termination of the design process due to budget and/or schedule pressures. Furthermore, one variable at a time approach can not account for the interactions that occur among parts of systems and among disciplines. As a result, vehicle design may be far from optimal. Advanced multidisciplinary design optimization (MDO) methods are needed to direct the search in an efficient and intelligent manner in order to drastically reduce the number of candidate designs to be evaluated. The payoffs in terms of enhanced performance and reduced cost are significant. A literature review yields two such advanced MDO methods used in aerospace design optimization; Taguchi methods and response surface methods. Taguchi methods provide a systematic and efficient method for design optimization for performance and cost. However, response surface method (RSM) leads to a better, more accurate exploration of the parameter space and to estimated optimum conditions with a small expenditure on experimental data. These two methods are described.

Unal, Resit↗
NASA NTRS1990

Design optimization of gas generator hybrid propulsion boosters

A methodology used in support of a contract study for NASA/MSFC to optimize the design of gas generator hybrid propulsion booster for uprating the National Space Transportation System (NSTS) is presented. The objective was to compare alternative configurations for this booster approach, optimizing each candidate concept on different bases, in order to develop data for a trade table on which a final decision was based. The methodology is capable of processing a large number of independent and dependent variables, adjusting the overall subsystems characteristics to arrive at a best compromise integrated design to meet various specified optimization criteria subject to selected constraints. For each system considered, a detailed weight statement was generated along with preliminary cost and reliability estimates.

Weldon, Vincent↗
NASA NTRS1990

Design Optimization of Gas Generator Hybrid Propulsion Boosters

A methodology used in support of a study for NASA/MSFC to optimize the design of gas generator hybrid propulsion booster for uprating the National Space Transportation System (NSTS) is presented. The objective was to compare alternative configurations for this booster approach, optimizing each candidate concept on different bases, in order to develop data for a trade table on which a final decision was based. The methodology is capable of processing a large number of independent and dependent variables, adjusting the overall subsystems characteristics to arrive at a best compromise integrated design to meet various specific optimization criteria subject to selected constraints. For each system considered, a detailed weight statement was generated along with preliminary cost and reliability estimates.

Weldon, Vincent↗
NASA NTRS2002

Turbomachinery Airfoil Design Optimization Using Differential Evolution

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine and compared to earlier methods. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Madavan, Nateri K.↗
NASA NTRS2002

Turbomachinery Airfoil Design Optimization Using Differential Evolution

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Madavan, Nateri K.↗
NASA NTRS2001

Simultaneous Aerodynamic and Structural Design Optimization (SASDO) for a 3-D Wing

The formulation and implementation of an optimization method called Simultaneous Aerodynamic and Structural Design Optimization (SASDO) is shown as an extension of the Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) method. It is extended by the inclusion of structure element sizing parameters as design variables and Finite Element Method (FEM) analysis responses as constraints. The method aims to reduce the computational expense. incurred in performing shape and sizing optimization using state-of-the-art Computational Fluid Dynamics (CFD) flow analysis, FEM structural analysis and sensitivity analysis tools. SASDO is applied to a simple. isolated, 3-D wing in inviscid flow. Results show that the method finds the saine local optimum as a conventional optimization method with some reduction in the computational cost and without significant modifications; to the analysis tools.

Gumbert, Clyde R.↗
NASA NTRS2000

Preliminary Design Optimization For A Supersonic Turbine For Rocket Propulsion

In this study, we present a method for optimizing, at the preliminary design level, a supersonic turbine for rocket propulsion system application. Single-, two- and three-stage turbines are considered with the number of design variables increasing from 6 to 11 then to 15, in accordance with the number of stages. Due to its global nature and flexibility in handling different types of information, the response surface methodology (RSM) is applied in the present study. A major goal of the present Optimization effort is to balance the desire of maximizing aerodynamic performance and minimizing weight. To ascertain required predictive capability of the RSM, a two-level domain refinement approach has been adopted. The accuracy of the predicted optimal design points based on this strategy is shown to he satisfactory. Our investigation indicates that the efficiency rises quickly from single stage to 2 stages but that the increase is much less pronounced with 3 stages. A 1-stage turbine performs poorly under the engine balance boundary condition. A portion of fluid kinetic energy is lost at the turbine discharge of the 1-stage design due to high stage pressure ratio and high-energy content, mostly hydrogen, of the working fluid. Regarding the optimization technique, issues related to the design of experiments (DOE) has also been investigated. It is demonstrated that the criteria for selecting the data base exhibit significant impact on the efficiency and effectiveness of the construction of the response surface.

Papila, Nilay↗
NASA NTRS1998

Multidisciplinary Design Optimization (MDO) Methods: Their Synergy with Computer Technology in Design Process

The paper identifies speed, agility, human interface, generation of sensitivity information, task decomposition, and data transmission (including storage) as important attributes for a computer environment to have in order to support engineering design effectively. It is argued that when examined in terms of these attributes the presently available environment can be shown to be inadequate a radical improvement is needed, and it may be achieved by combining new methods that have recently emerged from multidisciplinary design optimization (MDO) with massively parallel processing computer technology. The caveat is that, for successful use of that technology in engineering computing, new paradigms for computing will have to be developed - specifically, innovative algorithms that are intrinsically parallel so that their performance scales up linearly with the number of processors. It may be speculated that the idea of simulating a complex behavior by interaction of a large number of very simple models may be an inspiration for the above algorithms, the cellular automata are an example. Because of the long lead time needed to develop and mature new paradigms, development should be now, even though the widespread availability of massively parallel processing is still a few years away.

Sobieszczanski-Sobieski, Jaroslaw↗
NASA NTRS1992

Thermal design optimization of a segmented GFRP primary reflector for a submillimeter telescope

Results are presented of a thermal design optimization study of the segmented GFRP primary reflector of the earth-orbiting Submillimeter Imager and Line Survey telescope. The paper examines the thermal requirements of the primary reflector and the thermal environment of the telescope and describes the thermal design of the primary reflector. Particular attention is given to the geometric math model and the thermal math model of the telescope. A summary for the steady-state thermal performance of the optimized design is presented, showing that the optimized design has reduced, by an order of magnitude, structural spatial temperature gradients, which were earlier shown to be the most significant obstacle in maintaining the required telescope figure accuracy.

Tsuyuki, Glenn T.↗
NASA NTRS1974

System design optimization for a Mars-roving vehicle and perturbed-optimal solutions in nonlinear programming

Work in two somewhat distinct areas is presented. First, the optimal system design problem for a Mars-roving vehicle is attacked by creating static system models and a system evaluation function and optimizing via nonlinear programming techniques. The second area concerns the problem of perturbed-optimal solutions. Given an initial perturbation in an element of the solution to a nonlinear programming problem, a linear method is determined to approximate the optimal readjustments of the other elements of the solution. Then, the sensitivity of the Mars rover designs is described by application of this method.

Pavarini, C.↗
NASA NTRS2018

Solution of Ordinary Differential Equations in Gradient-Based Multidisciplinary Design Optimization

A gradient-based approach to multidisciplinary design optimization enables efficient scalability to large numbers of design variables. However, the need for derivatives causes difficulties when integrating ordinary differential equations (ODEs) in models. To simplify this, we propose the use of the general linear methods framework, which unifies all Runge-Kutta and linear multistep methods. This approach enables rapid implementation of integration methods without the need to differentiate each one, even in a gradient-based optimization context. We also develop a new parallel time integration algorithm that enables vectorization across time steps. We present a set of benchmarking results using a stiff ODE, a non-stiff nonlinear ODE, and an orbital dynamics ODE, and compare integration methods. In a modular gradient-based multidisciplinary design optimization context, we find that the new parallel time integration algorithm with high-order implicit methods, especially Gauss-Legendre collocation, is the best choice for a broad range of problems.

Hwang, John T.↗
NASA NTRS2018

High-Fidelity Multidisciplinary Design Optimization Methodology with Application to Rotor Blades

A multidisciplinary design optimization procedure has been developed and applied to rotorcraft simulations involving tightly-coupled, high-fidelity computational fluid dynamics and comprehensive analysis. A discretely-consistent, adjoint-based sensitivity analysis available in the fluid dynamics solver provides sensitivities arising from unsteady turbulent flows on unstructured, dynamic, overset meshes, while a complex-variable approach is used to compute structural sensitivities with respect to aerodynamic loads. The multidisciplinary sensitivity analysis is conducted through integrating the sensitivity components from each discipline of the coupled system. Accuracy of the coupled system for high-fidelity rotorcraft analysis is verified; simulation results exhibit good agreement with established solutions. A constrained gradient-based design optimization for a HART-II rotorcraft configuration is demonstrated. The computational cost for individual components of the multidisciplinary sensitivity analysis is assessed and improved.

Wang, Li↗