Article2008

A polynomial dimensional decomposition for stochastic computing

140 citations0/0 files storedInternational Journal for Numerical Methods in Engineering

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Probabilistic and Robust Engineering Design Mathematical functions and polynomials Gaussian Processes and Bayesian Inference

Abstract

Abstract This article presents a new polynomial dimensional decomposition method for solving stochastic problems commonly encountered in engineering disciplines and applied sciences. The method involves a hierarchical decomposition of a multivariate response function in terms of variables with increasing dimensions, a broad range of orthonormal polynomial bases consistent with the probability measure for Fourier‐polynomial expansion of component functions, and an innovative dimension‐reduction integration for calculating the coefficients of the expansion. The new decomposition method does not require sample points as in the previous version; yet, it generates a convergent sequence of lower‐variate estimates of the probabilistic characteristics of a generic stochastic response. The results of five numerical examples indicate that the proposed decomposition method provides accurate, convergent, and computationally efficient estimates of the tail probability of random mathematical functions or the reliability of mechanical systems. Copyright © 2008 John Wiley & Sons, Ltd.

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References

1991Stochastic Finite Elements: A Spectral Approach 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations 1999General foundations of high‐dimensional model representations 2004A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics 2003Theorems and examples on high dimensional model representation 2004A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics 1997A state-of-the-art report on computational stochastic mechanics 1997An efficient method for parametric uncertainty analysis of numerical geophysical models

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