Multiple-input Multiple-Output Support Vector Machine For Structural Reliability Design

The structural reliability design is one of the important contents of reliability engineering. It has been one of the most important methods of structural design, with its theory of reliability for the indeterminacies of engineering structures. Though the theory of reliability analysis for simple structure or structure systems has been mature, only a few of them are fit for the situations that have multiple variables or multiple limit state functions. Existing methods figured out these problems usually have low efficiency and low precision, especially in the case of small samples and high dimension.Support vector machine(SVM) algorithm, developed in recent twenty years, has good learning performance of small sample. SVM also has great advantages in dealing with nonlinear and high dimension problems. SVM has been used to deal with reliability analysis, combining with some basic reliability analysis methods, such as Monte Carlo Simulation(MCS) and First Order Second Moment(FORM). But these methods are only for structural reliability analysis problem with single limit state function. A multi-input multi-output support vector machine(MIMO-SVM), which based on the standard SVM, is a method for multiple out target. And the functions approximated by MIMO-SVM have high efficiency and high precision.This paper presents a methodology for structural reliability analysis of multiple LSFs using MIMO-SVM. MIMO-SVM is used to construct a surrogate model for all multiple LSFs, and this MIMO-SVM model is only trained from one data set with one calculation process. Then, the article proposes two methods of reliability based design optimization(RBDO) based on MIMO-SVM. Using a set of training data, the SVM surrogate model is trained and established for all probabilistic constraints in a design optimization problem. Furthermore, the SVM surrogate model is unique, i.e., its construction procedure does not need the repeating sampling. Considering the effect on the failure probability, caused by the prediction accuracy of SVM, the probabilistic support vector machine(PSVM) method is introduced into the structure reliability assessment method, with a conservative reliability assessment. And then the structure reliability assessment method based PSVM is served as RBDO.