Surrogate-Based Design Optimization with Adaptive Sequential Sampling

Mehmani, Ali; Zhang, Jie; Chowdhury, Souma; Messac, Achille

doi:10.2514/6.2012-1527

Cited by 11 publications

(7 citation statements)

References 32 publications

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“…The utility of the knowledge of the local and global accuracy of a surrogate goes beyond validation of the surrogate for application. Such knowledge can be crucial (i) for domain exploration, (ii) for further improvement of the surrogate using direct or sequential sampling (adaptive sampling 12 or active learning 13 ), (iii) for assessing the reliability (and updating) of the optimal design obtained through surrogate based optimization, 14,15 and (iv) for quantifying the uncertainty (and user confidence) associated with the surrogate. Other possible applications include surrogate model selection, and the construction of weighted surrogate model and conservative surrogate model.…”

Section: A Approximation Modelsmentioning

confidence: 99%

Quantifying Regional Error in Surrogates by Modeling its Relationship with Sample Density

Mehmani

Chowdhury

Zhang

et al. 2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Approximation models (or surrogate models) provide an efficient substitute to expensive physical simulations and an efficient solution to the lack of physical models of system behavior. However, it is challenging to quantify the accuracy and reliability of such approximation models in a region of interest or the overall domain without additional system evaluations. Standard error measures, such as the mean squared error, the cross-validation error, and the Akaikes information criterion, provide limited (often inadequate) information regarding the accuracy of the final surrogate. This paper introduces a novel and model independent concept to quantify the level of errors in the function value estimated by the final surrogate in any given region of the design domain. This method is called the Regional Error Estimation of Surrogate (REES). Assuming the full set of available sample points to be fixed, intermediate surrogates are iteratively constructed over a sample set comprising all samples outside the region of interest and heuristic subsets of samples inside the region of interest (i.e., intermediate training points). The intermediate surrogate is tested over the remaining sample points inside the region of interest (i.e., intermediate test points). The fraction of sample points inside region of interest, which are used as intermediate training points, is fixed at each iteration, with the total number of iterations being pre-specified. The estimated median and maximum relative errors within the region of interest for the heuristic subsets at each iteration are used to fit a distribution of the median and maximum error, respectively. The estimated statistical mode of the median and the maximum error, and the absolute maximum error are then represented as functions of the density of intermediate training points, using regression models. The regression models are then used to predict the expected median and maximum regional errors when all the sample points are used as training points. Standard test functions and a wind farm power generation problem are used to illustrate the effectiveness and the utility of such a regional error quantification method.

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Section: A Approximation Modelsmentioning

confidence: 99%

Quantifying Regional Error in Surrogates by Modeling its Relationship with Sample Density

Mehmani

Chowdhury

Zhang

et al. 2013

54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

Self Cite

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“…Typically, there are four main steps in constructing a surrogate model: (1) choosing the appropriate method for performing the design of experiments (DoE); (2) evaluating the response of high fidelity simulation model at the sampling points; (3) determining the proper surrogate model to fit the responses in the previous step; and (4) validating the accuracy of the surrogate model [8] .…”

Section: Aero-structure Optimization Based On Surrogate Modelmentioning

confidence: 99%

“…Some popular surrogate modeling methods are Polynomial Response Surfaces, Kriging Model, Moving Least Square, radial basis functions, neural networks, and hybrid surrogate modeling [8] . These methods mentioned above have been widely applied in many areas, such as aerospace engineering and automotive design [9] .…”

Section: Aero-structure Optimization Based On Surrogate Modelmentioning

confidence: 99%

Multidisciplinary design optimization of composite wing by parametric modeling

Liang

Zhu

et al. 2013

Proceedings 2013 International Conference on Mechatronic Sciences, Electric Engineering and Computer (MEC)

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In order to take into account the different requirements in aerodynamic and structural discipline, the optimization of a composite wing design is conducted using multidisciplinary design optimization (MDO) method. The geometry model of the wing is generated automatically through a parametric-modeling approach. The computational fluid dynamics (CFD) grid is generated automatically from parametric modeling using CATIA and ICEM CFD, followed by automatic flow analysis using FLUENT. The structural finite element analysis (FEA) grid is generated automatically by the parametric methods of CATIA and MSC/Patran. The structure is optimized by MSC/Nastran, and the aerodynamic load is transferred from the CFD grid to the FEA grid using the inverse distance weighted (IDW) interpolation method. The response surface method is applied for optimization and the optima of the current surrogate model is used to update the sample points. The developed MDO framework is applied to a wing optimization problem, and the optimization design result demonstrates this method could reduce the wing's structural weight.

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“…The major challenge arising in using surrogate models or low fidelity models in optimization (i.e., surrogatebased design optimization) is the fidelity of these models which may lead to introducing false optima. 24 Model management strategies have been investigated in surrogate-based optimization to build a high quality surrogate. Forrester et al 25 combined Kriging with a Bayesian model for multi-fidelity optimization based on the EGO (Efficient Global Optimization) and demonstrated the approach using a wing aerodynamic design problem.…”

Section: A Variable Fidelity Optimizationmentioning

confidence: 99%

Managing Variable Fidelity Models in Population-based Optimization using Adaptive Model Switching

Mehmani

Chowdhury

Messac

2014

15th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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This paper proposes a novel model management technique to be applied in populationbased heuristic optimization. This technique adaptively selects different computational models (both physics-based and statistical models) to be used during optimization, with the overall goal to end with high fidelity solutions in a reasonable time period. For example, in optimizing an aircraft wing to obtain maximum lift-to-drag ratio, one can use low-fidelity models such as given by the vortex lattice method, or a high-fidelity finite volume model (that solves the full Navier-Stokes equations), or a surrogate model that substitutes the high-fidelity model.The information from models with different levels of fidelity is integrated into the heuristic optimization process using a novel model-switching metric. In this context, models could be surrogate models, low-fidelity physics-based analytical models, and medium-to-high fidelity computational models (based on grid density). The model switching technique replaces the current model with the next higher fidelity model, when a stochastic switching criterion is met at a given iteration during the optimization process. The switching criteria is based on whether the uncertainty associated with the current model output dominates the latest improvement of the fitness function. In the case of the physics-based models, the uncertainty in their output is quantified through an inverse assessment process by comparing with high-fidelity model responses or experimental data (if available). To determine the fidelity of surrogate models, the Predictive Estimation of Model Fidelity (PEMF) method is applied. The effectiveness of the proposed method is demonstrated by applying it to airfoil optimization with the objective to maximize the lift to drag ratio of the wing under different flow regimes. It was found that the tuned low fidelity model dominates the optimization process in terms of computational time and function calls.

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Surrogate-Based Design Optimization with Adaptive Sequential Sampling

Cited by 11 publications

References 32 publications

Quantifying Regional Error in Surrogates by Modeling its Relationship with Sample Density

Quantifying Regional Error in Surrogates by Modeling its Relationship with Sample Density

Multidisciplinary design optimization of composite wing by parametric modeling

Managing Variable Fidelity Models in Population-based Optimization using Adaptive Model Switching

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