Towards ‘h-p adaptive’ generalized ANOVA

Abstract

This paper presents a novel ‘h-p adaptive’ generalized analysis of variance decomposition (G-ANOVA) for high dimensional stochastic computations. Firstly, an iterative scheme based on variance based global sensitivity analysis is proposed to determine the optimal polynomial order and important component functions (p adaptivity) of G-ANOVA. Then, a homotopy algorithm is employed to determine the unknown expansion coefficients. Moreover, a novel distribution adaptive sequential experimental design (h-adaptivity) is utilized at each step and the accuracy of the G-ANOVA based surrogate model is computed using leave one out statistical test. It is observed that significantly less number of component functions are retained. As a consequence, the proposed approach is highly efficient and is applicable for solving problems involving large number of stochastic dimensions. Implementation of the proposed approach has been illustrated with four high dimensional applied mechanics problems. The proposed approach is found to yield accurate and efficient results. Finally, the proposed approach has been applied for structural reliability analysis of a large scale real life problem.