Design and analysis of computer experiments

Booker, Andrew J.

doi:10.2514/6.1998-4757

Cited by 52 publications

(27 citation statements)

References 25 publications

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“…[3][4][5][6][7][8][9][10][11][12][13][14][15][16] The effectiveness of these techniques is closely tied to topics such as design of experiments (DOE), both from general statistics as well as the specific circumstances of computational experiments, as can be seen in various example applications. 15,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] Multidisciplinary analysis and optimization (MDA/MDO), including formal optimization, coupled system theory, and sensitivity analysis, is also relevant to this research work. Traditional optimization has a long history, rooted in mathematical programming, and has well developed tools.…”

Section: Background and Related Workmentioning

confidence: 99%

Reduced-Order Techniques for Sensitivity Analysis and Design Optimization of Aerospace Systems

Parrish

2015

AIAA Journal

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This work proposes a new method for using reduced order models in lieu of high fidelity analysis during the sensitivity analysis step of gradient based design optimization.The method offers a reduction in the computational cost of finite difference based sensitivity analysis in that context. The method relies on interpolating reduced order models which are based on proper orthogonal decomposition. The interpolation process is performed using radial basis functions and Grassmann manifold projection. It does not require additional high fidelity analyses to interpolate a reduced order model for new points in the design space.The interpolated models are used specifically for points in the finite difference stencil during sensitivity analysis.The proposed method is applied to an airfoil shape optimization (ASO) problem and a transport wing optimization (TWO) problem. The errors associated with the reduced order models themselves as well as the gradients calculated from them are evaluated. The effects of the method on the overall optimization path, computation times, and function counts are also examined.

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Section: Background and Related Workmentioning

confidence: 99%

Reduced-Order Techniques for Sensitivity Analysis and Design Optimization of Aerospace Systems

Parrish

2015

AIAA Journal

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“…13,14 The validity of the kriging model is not dependent on the existence of random error and may be better suited for applications involving computer experiments because it can either "honor the data," providing an exact interpolation, or "smooth the data." 15 Booker 16 contrasts traditional DOE and R S modeling with DACE models. In the "classical" design and analysis of physical experiments, random variation is accounted for by spreading the sample points out in the design space and by taking multiple data points (replicates), see Figure 1.…”

Section: Frame Of Referencementioning

confidence: 99%

“…Booker, et al 22 solve a 31 variable helicopter rotor structural design problem; Booker 16 expands the problem to include 56 variables to examine the aeroelastic and dynamic response of the rotor. Osio and Amon 20 use a multistage DACE modeling strategy to design an embedded electronic package which has 5 design variables.…”

Section: Engineeringmentioning

confidence: 99%

Comparison of response surface and kriging models for multidisciplinary design optimization

Simpson

Korte

Mauery

et al. 1998

7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization

372

178

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In this paper, we compare and contrast the use of second-order response surface models and kriging models for approximating non-random, deterministic computer analyses. After reviewing the response surface method for constructing polynomial approximations, kriging is presented as an alternative approximation method for the design and analysis of computer experiments. Both methods are applied to the multidisciplinary design of an aerospike nozzle which consists of a computational fluid dynamics model and a finite-element model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations, and four optimization problems are formulated and solved using both sets of approximation models. The second-order response surface models and kriging models-using a constant underlying global model and a Gaussian correlation function-yield comparable results.

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“…the current approximation employed as a surrogate objective, and a design criterion, one obtains some fraction of new design sites using one criterion and the balance using the other. An implementation of this Balanced Local-Global Search (BLGS) was described by Booker et al (1995) and employed by Booker (1996), Booker et al (1996), and Booker et al (1998).…”

Section: Merit Functionsmentioning

confidence: 99%

“…Frank (1995) offered an optimizer's perspective on this methodology, suggesting that the "minimalist approach" of minimizing a singlef is not likely to yield satisfactory results, and proposed several sequential modeling strategies as alternatives. Booker (1996) studied several industrial applications of DACE and two alternative approaches.…”

Section: Introductionmentioning

confidence: 99%

Using approximations to accelerate engineering design optimization

Torczon

Trosset

1998

7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization

101

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Optimization problems that arise in engineering design are often characterized by several features that hinder the use of standard nonlinear optimization techniques. Foremost among these features is that the functions used to define the engineering optimization problem usually require the solution of differential equations, a process which is itself computationally intensive. Within a standard nonlinear optimization algorithm, the solution of these differential equations is required for each iteration of the algorithm. To mitigate such expense, an attractive alternative is to replace the computationally intensive objective with a less expensive surrogate.In conformance with engineering practice, we draw a crucial distinction between surrogate models and surrogate approximations. Surrogate models are auxiliary simulations that are less physically faithful, but also less computationally expensive, than the expensive simulation that is regarded as "truth." An instructive example is the use of an equivalent-plate analysis method in lieu of a finite element analysis, e.g. to analyze a wing-box of a high-speed civil transport. Surrogate models exist independently of the expensive simulation and can provide new information about the physical phenomenon of interest without requiring additional runs of the expensive simulation.Surrogate approximations are algebraic summaries obtained from previous runs of the expensive simulation. Examples include the low-order polynomials favored in response surface methodology (RSM) and the kriging estimates employed in the design and analysis of computer experiments (DACE). Once the approximation has been constructed, it is typically inexpensive to evaluate.When surrogates are available, be they models or approximations, the optimizer hopes to use them to facilitate the search for a solution to the engineering optimization problem. Our ultimate goal is to design robust optimization algorithms, but we would like to do so in ways that allow us to make effective use of the information that good surrogates can provide. Toward this end, we adopt the perspective that the surrogate can be used to accelerate the optimization technique by exploiting the trends that such surrogates tend to identify. We do not worry about accuracy in the surrogate until it becomes clear either that the optimization technique is in the neighborhood of a minimizer or that the surrogate is not doing a sufficiently good job of identifying trends in the objective.We consider a methodology that constructs a sequence of approximations to the objective. We concentrate on approaches such as DACE, that krige known values of the objective, but our general strategy is also amenable to other classes of approximations. We make use of pattern search techniques to handle the optimization, though other approaches are possible. We choose pattern search techniques because they can be easily amended to exploit surrogates, * Department of Computer Science, College of William & Mary, Williamsburg, VA 23187-8795 (e-mail: va@cs...

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Design and analysis of computer experiments

Cited by 52 publications

References 25 publications

Reduced-Order Techniques for Sensitivity Analysis and Design Optimization of Aerospace Systems

Reduced-Order Techniques for Sensitivity Analysis and Design Optimization of Aerospace Systems

Comparison of response surface and kriging models for multidisciplinary design optimization

Using approximations to accelerate engineering design optimization

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