Support vector regression based metamodeling for structural reliability analysis

• Published in: Probabilistic engineering mechanics Vol. 55; pp. 78 - 89
• Main Authors: Roy, Atin, Manna, Ramkrishna, Chakraborty, Subrata
• Format: Journal Article
• Language: English
• Published: Barking Elsevier Ltd 01.01.2019; Elsevier Science Ltd
• Subjects: Algorithms; Artificial neural networks; Computer simulation; Empirical analysis; Finite element analysis; Finite element method; Kernel functions; Kriging; Mathematical models; Metamodel; Metamodels; Monte Carlo simulation; Neural networks; Optimization; Parameter optimization; Parameters; Polynomials; Regression analysis; Regularization; Reliability; Reliability analysis; Reliability engineering; Response surface methodology; Statistical analysis; Structural reliability; Support vector machines; Support vector regression; Support vector regression; Reliability analysis; Parameter optimization; Metamodel
• DOI: 10.1016/j.probengmech.2018.11.001
• ISSN: 0266-8920

Various metamodeling approaches e.g. polynomial response surface method artificial neural network, Kriging method etc. have been emerged as an effective alternative for solving computationally challenging complex reliability analysis problems involving finite element response analysis. However, such approaches are primarily based on the principle of empirical risk minimization. The support vector machine for regression i.e. the support vector regression (SVR) which is based on structural risk minimization has revealed improved abilities of response approximation using small sample learning. The implementation of SVR model requires to optimize a loss function involving the loss function parameter, regularization parameter and also kernel function parameter(s) to tackle nonlinear problems. The success of SVR largely depends on proper choice of such parameters. A simple yet effective algorithm by solving an optimization sub-problem to minimize the mean square error value obtained by cross-validation method is investigated in the present study to construct SVR model for structural reliability analysis. The effectiveness of the algorithm is demonstrated numerically by comparing various computed statistical metrics obtained by the most accurate direct Monte Carlo Simulation (MCS) technique. The performance of SVR based metamodel to estimate the reliability is also studied by comparing the results with the direct MCS based results.