Application of Support Vector Machine-Based Classification Extremum Method in Flexible Mechanism

The computational efficiencies of traditional reliability methods, such as Monte Carlo (MC), are extremely low. There are also some shortcomings for surrogate model (SM)-based methods, e.g., the sample points of the quadratic polynomial (QP)-MC grow exponentially with the increases of random variables and the artificial neural network (ANN)-MC may exhibit overfitting with limited sample numbers, etc. However, the characteristic of support vector machine (SVM) is that it specifically fits for small samples and has strong learning and good generalization abilities so that it can obtain an optimal solution even with limited samples. In this case, a high-efficiency and high-accuracy dynamic reliability framework called as SVM-based classification extremum method (SVM-CEM) combining SVM classification theory with random probability model based on optimization idea is proposed, which is very suitable for the flexible mechanism (FM) that has few samples. First, an implicit limit state equation (LSE) of dynamic response and a reliability model with multiple failure modes for FM are established. The kernel function is introduced in building the model, the solution of optimal classification hyperplane is translated into a dual problem of convex quadratic programming optimization, which is regarded as the surrogate model of FM's dynamic response extreme value (DREV). Then, this method is used to analyze the dynamic reliability of FM's maximum angular acceleration (MAA). Finally, to reveal the validity of this method, SVM-CEM is compared with MC, QP-MC, and ANN-MC. The conclusion is that the computational efficiency of SVM-CEM is better than that of MC, QP-MC, and ANN-MC ensuring the computational accuracy. The proposed SVM-CEM in dynamic reliability analysis has important guiding significance for the application of FM's practical engineering.