APPLICATION OF COUPLED RKHS-HDMR TO STOCHASTIC MECHANICS AND RELIABILITY

Abstract eng:
A generic high dimensional model representation (HDMR) method is presented for approximating the limit state/performance function in terms of functions of lower dimensions and for going beyond the tensor-product formulation. Within the framework of reproducing kernel Hilbert space (RKHS) interpolation techniques, HDMR is formulated for approximation of the original limit state/performance function. RKHS provides rigorous and effective framework for smooth multivariate interpolation of scattered data points leading to asymptotically convergent solutions. HDMR technique in conjunction with a successive multilevel decomposition technique provides efficient and accurate procedures for reducing a multidimensional interpolation problem to smaller, independent subproblems. Numerical illustrations of RKHS-HDMR with applications to the structural/mechanical systems are given. The proposed RKHS-HDMR is intimately related to Gordon’s blending-function methods for multivariate interpolation and approximation. The general findings in this paper and their illustration provide a foundation for further applications to the reliability and system safety.

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