A Combined Nonstationary Kriging and Support Vector Machine Method for Stochastic Eigenvalue Analysis of Brake Systems

Abstract

This paper presents a new metamodel approach based on nonstationary kriging and a support vector machine to efficiently predict the stochastic eigenvalue of brake systems. One of the difficulties in the mode-coupling instability induced by friction is that stochastic eigenvalues represent heterogeneous behavior due to the bifurcation phenomenon. Therefore, the stationarity assumption in kriging, where the response is correlated over the entire random input space, may not remain valid. In this paper, to address this issue, Gibb’s nonstationary kernel with step-wise hyperparameters was adopted to reflect the heterogeneity of the stochastic eigenvalues. In predicting the response for unsampled input, the support vector machine-based classification is utilized. To validate the performance, a simplified finite element model of the brake system is considered. Under various types of uncertainties, including different friction coefficients and material properties, stochastic eigenvalue problems are investigated. Through numerical studies, it is seen that the proposed method improves accuracy and robustness compared to conventional stationary kriging.

Keywords

• brake systems
• stochastic complex eigenvalue analysis
• nonstationary kriging
• support vector machine