Surrogate-based Analysis and Optimization

Recent progress in flapping wing aerodynamics and aeroelasticity

The custom in surrogate-based modeling of complex engineering problems is to fit one or more surrogate models and select the one surrogate model that performs best. In this paper, we extend the utility of an ensemble of surrogates to (1) identify regions of possible high errors at locations where predictions of surrogates widely differ, and (2) provide a more robust approximation approach. We explore the possibility of using the best surrogate or a weighted average surrogate model instead of individual surrogate models. The weights associated with each surrogate model are determined based on the errors in surrogates. We demonstrate the advantages of an ensemble of surrogates using analytical problems and one engineering problem. We show that for a single problem the choice of test surrogate can depend on the design of experiments.

Ensemble of surrogates

Response surface approximation of Pareto optimal front in multi-objective optimization

Approximate mathematical models (metamodels) are often used as surrogates for more computationally intensive simulations. The common practice is to construct multiple metamodels based on a common training data set, evaluate their accuracy, and then to use only a single model perceived as the best while discarding the rest. This practice has some shortcomings as it does not take full advantage of the resources devoted to constructing different metamodels, and it is based on the assumption that changes in the training data set will not jeopardize the accuracy of the selected model. It is possible to overcome these drawbacks and to improve the prediction accuracy of the surrogate model if the separate stand-alone metamodels are combined to form an ensemble. Motivated by previous research on committee of neural networks and ensemble of surrogate models, a technique for developing a more accurate ensemble of multiple metamodels is presented in this paper. Here, the selection of weight factors in the general weighted-sum formulation of an ensemble is treated as an optimization problem with the desired solution being one that minimizes a selected error metric. The proposed technique is evaluated by considering one industrial and four benchmark problems. The effect of different metrics for estimating the prediction error at either the training data set or a few validation points is also explored. The results show that the optimized ensemble provides more accurate predictions than the stand-alone metamodels and for most problems even surpassing the previously reported ensemble approaches.

Ensemble of metamodels with optimized weight factors

Modern computational and experimental tools for aerodynamics and propulsion applications have matured to a stage where they can provide substantial insight into engineering processes involving fluid flows, and can be fruitfully utilized to help improve the design of practical devices. In particular, rapid and continuous development in aerospace engineering demands that new design concepts be regularly proposed to meet goals for increased performance, robustness and safety while concurrently decreasing cost. To date, the majority of the effort in design optimization of fluid dynamics has relied on gradient-based search algorithms. Global optimization methods can utilize the information collected from various sources and by different tools. These methods offer multi-criterion optimization, handle the existence of multiple design points and trade-offs via insight into the entire design space, can easily perform tasks in parallel, and are often effective in filtering the noise intrinsic to numerical and experimental data. However, a successful application of the global optimization method needs to address issues related to data requirements with an increase in the number of design variables, and methods for predicting the model performance. In this article, we review recent progress made in establishing suitable global optimization techniques employing neural network and polynomial-based response surface methodologies. Issues addressed include techniques for construction of the response surface, design of experiment techniques for supplying information in an economical manner, optimization procedures and multi-level techniques, and assessment of relative performance between polynomials and neural networks. Examples drawn from wing aerodynamics, turbulent diffuser flows, gas-gas injectors, and supersonic turbines are employed to help demonstrate the issues involved in an engineering design context. Both the usefulness of the existing knowledge to aid current design practices and the need for future research are identified.

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Global Design Optimization for Aerodynamics and Rocket Propulsion Components

There is growing interest to adopt supersonic turbines for rocket propulsion. However, this technology has not been actively investigated in the United States for the last three decades. To aid design improvement, a global optimization framework combining the radial-basis neural network (NN) and the polynomial response surface (RS) method is constructed for shape optimization of a two-stage supersonic turbine, involving O(10) design variables. The design of the experiment approach is adopted to reduce the data size needed by the optimization task. The combined NN and RS techniques are employed. A major merit of the RS approach is that it enables one to revise the design space to perform multiple optimization cycles. This benefit is realized when an optimal design approaches the boundary of a predefined design space. Furthermore, by inspecting the influence of each design variable, one can also gain insight into the existence of multiple design choices and select the optimum design based on other factors such as stress and materials consideration.

Shape optimization of supersonic turbines using global approximation methods

Turbine performance directly affects engine specific impulse, thrust-to-weight ratio, and cost in a rocket propulsion system. A global optimization framework combining the radial basis neural network (RBNN) and the polynomial-based response surface method (RSM) is constructed for shape optimization of a supersonic turbine. Based on the optimized preliminary design, shape optimization is performed for the first vane and blade of a 2-stage supersonic turbine, involving O(10) design variables. The design of experiment approach is adopted to reduce the data size needed by the optimization task. It is demonstrated that a major merit of the global optimization approach is that it enables one to adaptively revise the design space to perform multiple optimization cycles. This benefit is realized when an optimal design approaches the boundary of a pre-defined design space. Furthermore, by inspecting the influence of each design variable, one can also gain insight into the existence of multiple design choices and select the optimum design based on other factors such as stress and materials considerations.

/pdf/shape-optimization-of-supersonic-turbines-using-response-8p9z7tpk9j.pdf

Shape Optimization of Supersonic Turbines Using Response Surface and Neural Network Methods

A computational-fluid-dynamics-based design optimization approach, utilizing the response surface method, has been proposed for a single-element rocket injector. The overall goal of the effort is to demonstrate the integration of a set of computational and optimization tools to enable the injector designer to objectively determine the trades between performance and life during the design cycle. Using design of experiment techniques, 54 cases are selected, and computational solutions based on the Navier‐Stokes equations, finite rate chemistry, and the k‐e turbulence closure are obtained. The response surface methodology is employed as the optimization tool. Four independent design variables are selected, namely, H2 flow angle, H2 and O2 flow areas with fixed flow rates, and O2 posttip thickness. Design optimization is guided by four design objectives. The maximum temperature on the injector element oxidizer posttip, the maximum temperature on the injector face, and a combustion chamber wall temperature are chosen as life indicators. The length of the combustion zone is selected as an indicator of mixing and performance. In the context of this effort, the design optimization tools performed efficiently and reliably. In addition to establishing optimum designs by varying emphasis on the individual objectives, better insight into the interplay between design variables and their impact on the design objectives is gained. The need to include environmental design objectives early in the design phase is clearly established.

Computational-fluid-dynamics-based design optimization for single-element rocket injector

Nilay Papila', Wei Shyy', Lisa Griffin', Frank Huber* and Ken Tran §" Department of Aerospace Engineering, Mechanics & Engineering ScienceUniversity of Florida, Gainesville, FL+NASA Marshall Flight Center, Huntsville, AL: Riverbend Design Services, Palm Beach Gardens. FL" Boeing - Rocketdyne Division. Canoga Park. CAABSTRACTIn this stud,,', we present a method for optimizing, at thepreliminary design level, a supersonic turbine for rocketpropulsion system application. Single-. two- and three-stage turbines are considered v, ith the number el desienvariables increasing from h to I1 then to 15. inaccordance with the number of stages. Due to its globalnature and flexibility in handling different types ofinformation, the response surlace methodoloev tRSMI isapplied in the present stud)'. A major goat of the present,_ptimization etf_rt is to balance the desire of maximizingaerodynamic performance and mmHnizing ,.veight. I+oascertain required predictive capability t_t the P, SM. atv,'o-level domain refinement approach has been adopted."['he accuracy of the predicted optimal design pmnts basedon this ,,,trategy is shown t_3 be satistactorv. Ourinvestigation indicates that the efficiency rises qutckl>lrom single stage to 2 stages but that the increase is muchless pr{mt+unced vcith 3 stagcs. ,\ t-,+taue turbine pert;,+rmsp_+tll-ly under thc engine hai,:tllCe i_ouildi.tl_, c,>ndltitln. [1__,i,_,mficant [_ortlon of fluid kinetic energy ts Io_,t at theturbine discharge of the l-stage design due to high stagepressure ratio and high-enerev content, mostly hvdrooen_t the working t]uid. Regarding the <_ptimizationtechnique, issues related t_3 the dc,slgn _,[

/pdf/preliminary-design-optimization-for-a-supersonic-turbine-for-4z2bynqj0e.pdf

Nilay Papila

Papers

Global Design Optimization for Aerodynamics and Rocket Propulsion Components

Shape optimization of supersonic turbines using global approximation methods

Shape Optimization of Supersonic Turbines Using Response Surface and Neural Network Methods

Computational-fluid-dynamics-based design optimization for single-element rocket injector

Preliminary Design Optimization for a Supersonic Turbine for Rocket Propulsion