SUPPORT VECTOR MACHINE FOR STRUCTURAL RELIABILITY ANALYSIS

• Published in: Applied mathematics and mechanics Vol. 27; no. 10; pp. 1295 - 1303
• Main Author: 李洪双 吕震宙 岳珠峰
• Format: Journal Article
• Language: English
• Published: School of Aeronautics,Northwestern Polytechnical University,Xi'an 710072,P.R.China 01.10.2006
• Subjects: Computer simulation; Learning theory; Mathematical analysis; Mathematical models; Monte Carlo methods; Neural networks; Structural reliability; Support vector machines; 固有执行函数; 支持向量机构; 经典模型; 结构可靠性; structural reliability; support vector ma-chine; implicit performance function
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-006-1001-z

Support vector machine （SVM） was introduced to analyze the reliability of the implicit performance function, which is difficult to implement by the classical methods such as the first order reliability method （FORM） and the Monte Carlo simulation （MCS）. As a classification method where the underlying structural risk minimization inference rule is employed, SVM possesses excellent learning capacity with a small amount of information and good capability of generalization over the complete data. Hence, two approaches, i.e., SVM-based FORM and SVM-based MCS, were presented for the structural reliability analysis of the implicit limit state function. Compared to the conventional response surface method （RSM） and the artificial neural network （ANN）, which are widely used to replace the implicit state function for alleviating the computation cost, the more important advantages of SVM are that it can approximate the implicit function with higher precision and better generalization under the small amount of information and avoid the ＂curse of dimensionality＂. The SVM-based reliability approaches can approximate the actual performance function over the complete sampling data with the decreased number of the implicit performance function analysis （usually finite element analysis）, and the computational precision can satisfy the engineering requirement, which are demonstrated by illustrations.