Adaptive explicit decision functions for probabilistic design and optimization using support vector machines

Basudhar, Anirban; Missoum, Samy

doi:10.1016/j.compstruc.2008.02.008

Cited by 186 publications

(88 citation statements)

References 16 publications

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“…A wide variety of surrogate modeling techniques have been reported in the literature, which include: (i) Polynomial Response Surface Model (PRSM) (Myers and Montgomery 2002), (ii) Kriging (Giunta and Watson 1998; Sakata et al 2003;Simpson 1998;Cressie 1993), (iii) Radial Basis Functions (RBF) (Hardy 1971;Jin et al 2001;Cherrie et al 2002;Hussain et al 2002), (iv) Extended Radial Basis Functions (E-RBF) Messac 2005, 2006;Zhang et al 2010a, b, c), (v) Artificial Neural Networks (ANN) (Duda et al 2000;Yegnanarayana 2004), and (vi) Support Vector Regression (SVR) (Clarke et al 2005;Vapnik 1995;Duda et al 2000;Basudhar and Missoum 2008). In the literature, the accuracy and effectiveness of various surrogate models for linear, nonlinear, smooth, and noisy responses have also been investigated (Forrester and Keane 2009;Queipo et al 2005;Wang and Shan 2007;Simpson et al 2008).…”

Section: Surrogate Modeling Reviewmentioning

confidence: 99%

An adaptive hybrid surrogate model

Zhang

Chowdhury

Messac

2012

Struct Multidisc Optim

121

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The determination of complex underlying relationships between system parameters from simulated and/or recorded data requires advanced interpolating functions, also known as surrogates. The development of surrogates for such complex relationships often requires the modeling of high dimensional and non-smooth functions using limited information. To this end, the hybrid surrogate modeling paradigm, where different surrogate models are combined, offers an effective solution. In this paper, we develop a new high fidelity surrogate modeling technique that we call the Adaptive Hybrid Functions (AHF). The AHF formulates a reliable Crowding Distance-Based Trust Region (CD-TR), and adaptively combines the favorable characteristics of different surrogate models. The weight of each contributing surrogate model is determined based on the local measure of accuracy for that surrogate model in the pertinent trust region. Such an approach is intended to exploit the advantages of each component surrogate. This approach seeks to simultaneously capture the global trend of the function as well as the local deviations. In this paper, the AHF combines four component surrogate models: (i) the Quadratic Response Surface Model (QRSM), (ii) the Radial Basis Functions (RBF), (iii) the Extended Radial Basis Functions (E-RBF), and (iv) the Kriging model. The AHF is applied to standard test problems and to a complex engineering design problem. Subsequent evaluations of the Root Mean Squared Error (RMSE) and the Maximum Absolute Error (MAE) illustrate the promising potential of this hybrid surrogate modeling approach.

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Section: Surrogate Modeling Reviewmentioning

confidence: 99%

An adaptive hybrid surrogate model

Zhang

Chowdhury

Messac

2012

Struct Multidisc Optim

121

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“…Since this estimation is repeated for multiple design configurations examined within the optimization algorithm, these approaches ultimately impose a prohibitive computational cost for applications involving computationally expensive models. To address this challenge, soft computing approaches such as surrogate models and support vector machine have been incorporated within the stochastic-simulation-based estimation of the system reliability in RBDO to replace expensive numerical models (Basudhar and Missoum 2008;Dubourg et al 2011;Missoum et al 2007;Papadrakakis and Lagaros 2002). These approaches, though, could similarly face challenges for applications with large number of model parameters as the required number of evaluations of the expensive models to support the adopted soft-computing techniques is large.…”

Section: Introductionmentioning

confidence: 99%

Non-parametric stochastic subset optimization for design problems with reliability constraints

Jia

Taflanidis

Beck

2015

Struct Multidisc Optim

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The Non-Parametric Stochastic Subset Optimization (NP-SSO) is a recently developed algorithm appropriate for optimization problems that use reliability criteria as objective function and involve computationally expensive numerical models for the engineering system under consideration. This paper discusses its extension to reliability-based design optimization (RBDO) applications involving reliability criteria as a design constraint. The foundation of NP-SSO is the formulation of an augmented problem where the design variables are artificially considered as uncertain. In this context, the reliability of the engineering system is proportional to an auxiliary probability density function related to the design variables. NP-SSO is based on simulation of samples from this density and approximation of this reliability through kernel density estimation (KDE) using these samples. The RBDO problem is then solved using this approximation for evaluating the reliability constraints over the entire design domain and identifying the feasible region satisfying them. To improve computational efficiency, an iterative approach is proposed; at the end of each iteration, a new reduced search space is identified with reliability satisfying relaxed constraints, until the algorithm converges to the feasible design domain satisfying the desired constraints. A second refinement stage after initial convergence is also proposed to further improve the accuracy of the identified feasible region. A non-parametric characterization of the search space using a framework based on multivariate boundary KDE and support vector machine is established. To further improve the efficiency of the stochastic sampling stage, an adaptive selection of the number of samples required for the KDE approximation is proposed.

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“…All points in the newly selected set were evaluated, and the classifier retrained. This strategy is similar to that of [13] in that it ensures that successive selected points are located on the classification boundary, but are distant from existing sampled points and each other. Adaptive sampling was carried out for a total of four iterations yielding a final total of 30 data points.…”

Section: Adaptive Sampling Studymentioning

confidence: 99%

Constrained classification for infrastructure threat assessment

Lennox

Glascoe

2011

2011 IEEE International Conference on Technologies for Homeland Security (HST)

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Abstract-Validated computer simulation is an important aspect of critical infrastructure vulnerability assessment. The high computational cost of such models limits the number of threat scenarios that may be directly evaluated, which leads to a need for statistical emulation to predict outcomes for additional scenarios. Our particular area of interest is statistical methods for emulating complex computer codes that predict if a particular tunnel/explosive configuration results in the breaching of an underground transportation tunnel. In this case, there is considerable a priori information as to the properties of this breach classification boundary. We propose a constrained classifier, in the form of a parametric support vector machine, that allows us to incorporate expert knowledge into the shape of the decision boundary. We demonstrate the effectiveness of this technique with both a simulation study and by applying the method to a tunnel breach data set. This analysis reveals that constrained classification can offer substantial benefits for small sample sizes. The technique may be used either to provide a final classification result in the face of extremely limited data or as an interim step to guide adaptive sampling.

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Adaptive explicit decision functions for probabilistic design and optimization using support vector machines

Cited by 186 publications

References 16 publications

An adaptive hybrid surrogate model

An adaptive hybrid surrogate model

Non-parametric stochastic subset optimization for design problems with reliability constraints

Constrained classification for infrastructure threat assessment

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