Global sensitivity analysis by polynomial dimensional decomposition

• Published in: Reliability engineering & system safety Vol. 96; no. 7; pp. 825 - 837
• Main Author: Rahman, Sharif
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.07.2011; Elsevier
• Subjects: ANOVA; Applied sciences; Approximation; Computation; Convergence; Curse of dimensionality; Decomposition; Deterioration; Dimension reduction; Exact sciences and technology; Experimental design; Mathematical analysis; Mathematical models; Mathematics; Operational research and scientific management; Operational research. Management science; Orthogonal polynomials; Probability and statistics; Probability theory and stochastic processes; Reliability theory. Replacement problems; Sciences and techniques of general use; Sensitivity analysis; Sensitivity index; Statistics; Stochastic processes; Dimension reduction; Curse of dimensionality; ANOVA; Orthogonal polynomials; Sensitivity index; Chaos; Decomposition method; Global analysis; Probability distribution; Polynomial method; Stochastic process; Optimization; Uncertain system; Nonsmooth analysis; Smooth function; Convergence rate; System analysis; Dimensionality; Integration; Sensitivity analysis; Statistical analysis; Polynomial decomposition; Variance analysis; Computational complexity; Orthogonal polynomial; Stochastic analysis; Sampling methods; State dependence
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2011.03.002

This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol's method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent.