Stochastic sensitivity analysis using preconditioning approach

Abstract

Purpose

High‐dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for capturing the high‐dimensional relationships between sets of input and output model variables. It is an efficient formulation of the system response, if higher‐order cooperative effects are weak, allowing the physical model to be captured by the lower‐order terms. The paper's aim is to develop a new computational tool for estimating probabilistic sensitivity of structural/mechanical systems subject to random loads, material properties and geometry.

Design/methodology/approach

When first‐order HDMR approximation of the original high‐dimensional limit state is not adequate to provide the desired accuracy to the sensitivity analysis, this paper presents an enhanced HDMR (eHDMR) method to represent the higher‐order terms of HDMR expansion by expressions similar to the lower‐order ones with monomial multipliers. The accuracy of the HDMR expansion can be significantly improved using preconditioning with a minimal number of additional input‐output samples without directly invoking the determination of second‐ and higher‐order terms. As a part of this effort, the efficacy of HDMR, which is recently applied to uncertainty analysis, is also demonstrated. The method is based on computing eHDMR approximation of system responses and score functions associated with probability distribution of a random input. Surrogate model is constructed using moving least squares interpolation formula. Once the surrogate model form is defined, both the probabilistic response and its sensitivities can be estimated from a single probabilistic analysis, without requiring the gradients of performance functions.

Findings

The results of two numerical examples involving mathematical function and structural/solid‐mechanics problems indicate that the sensitivities obtained using eHDMR approximation provide significant accuracy when compared with the conventional Monte Carlo method, while requiring fewer original model simulations.

Originality/value

This is the first time where application of eHDMR concepts is explored in the stochastic sensitivity analysis. The present computational approach is valuable to the practical modelling and design community.

Citation

Chowdhury, R. and Adhikari, S. (2010), "Stochastic sensitivity analysis using preconditioning approach", Engineering Computations, Vol. 27 No. 7, pp. 841-862. https://doi.org/10.1108/02644401011073683