Dimension adaptive finite difference decomposition using multiple sparse grids for stochastic computation

The present study aims to investigate uncertainty quantification followed by reliability analysis of structure with homogeneous non-normal random fields. In stochastic finite element formulation, these continuous fields are discretized by different methods (e.g. Karhunen-Loève Expansion) which transformed it into a set of random variables. However, this discretization often leads to large number of random variables, especially for multiple random fields. With this in view, two different meta-model based approaches are presented in this study using high dimensional model representation (HDMR) for efficient stochastic computation. First, an adaptive multiple finite difference HDMR (AMFD-HDMR) is proposed that decomposes the original performance function into summands of smaller dimensions. These subfunctions are modeled by polynomial chaos expansion (PCE) using moving least square technique which utilizes the benefits of orthogonality of the basis functions and provides adaptive interpolation between the support points. These support points are generated in a sparse grid framework based on the hierarchial tensor products of the sub-grids and the appropriate statistical properties. An iterative scheme is developed with the aim to create new support points in the desired locations such as most probable failure point and/or maxima/minima. Later, a dimension adaptive multiple finite difference HDMR (dAMFD-HDMR) is proposed utilizing sensitivity analysis to further improve the efficiency and accuracy. In the second proposal, an intermittent HDMR formulation is suggested based on the individual and mutual contributions of the significant dimensions. Once the meta-model is built, Monte Carlo simulation is performed over it, thus bypassing the time exhaustive computation of the original performance function. Numerical studies are carried out using composite plate to prove the merits of the proposed algorithms compared to other methods available in the literature.