Least square support vector machine for structural reliability analysis

Monte-Carlo Simulation (MCS) is a powerful tool in solving reliability problems. However, it is time-consuming use for the complex structural engineering problems. Another commonly used method, First-Order Second Moment Method (FOSM) usually requires the values and derivatives of limit state function. This paper presents two types of Least Square Support Vector Machine (LS-SVM) based reliability analysis methods, i.e. LS-SVM-based MCS and LS-SVM-based FOSM. In the first method, LS-SVM is adopted to replace the limit state function and enhance the efficiency of computing. In the second method, LS-SVM is adopted to approximate the limit state function and its partial derivatives which FOSM requires. Thus, based on the LS-SVM, both methods are substantially improved in efficiency. To assess the validity of this methodology, three structural examples are studied and discussed. The results prove that the LS-SVM based new methods are effective in structural reliability analysis problems involving the implicit limit state function.