Article2013

A comparative study of three collocation point methods for odd order stochastic response surface method

D. Q. Li · Shui‐Hua Jiang · Yonggang Cheng · Chuangbing Zhou

27 citations0/0 files storedSTRUCTURAL ENGINEERING AND MECHANICS

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Probabilistic and Robust Engineering Design Reliability and Maintenance Optimization Geotechnical Engineering and Analysis

Abstract

This paper aims to compare three collocation point methods associated with the odd order stochastic response surface method (SRSM) in a systematical and quantitative way. The SRSM with the Hermite polynomial chaos is briefly introduced first. Then, three collocation point methods, namely the point method, the root method and the without origin method underlying the odd order SRSMs are highlighted. Three examples are presented to demonstrate the accuracy and efficiency of the three methods. The results indicate that the condition that the Hermite polynomial information matrix evaluated at the collocation points has a full rank should be satisfied to yield reliability results with a sufficient accuracy. The point method and the without origin method are much more efficient than the root method, especially for the reliability problems involving a large number of random variables or requiring complex finite element analysis. The without origin method can also produce sufficiently accurate reliability results in comparison with the point and root methods. Therefore, the origin often used as a collocation point is not absolutely necessary. The odd order SRSMs with the point method and the without origin method are recommended for the reliability analysis due to their computational accuracy and efficiency. The order of SRSM has a significant influence on the results associated with the three collocation point methods. For normal random variables, the SRSM with an order equaling or exceeding the order of a performance function can produce reliability results with a sufficient accuracy. The order of SRSM should significantly exceed the order of the performance function involving strongly non-normal random variables.

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References

2007Global sensitivity analysis using polynomial chaos expansions 2003Modeling uncertainty in flow simulations via generalized polynomial chaos 1990A fast and efficient response surface approach for structural reliability problems 1999A new adaptive importance sampling scheme for reliability calculations 1998Stochastic Response Surface Methods (SRSMs) for Uncertainty Propagation: Application to Environmental and Biological Systems 1997An efficient method for parametric uncertainty analysis of numerical geophysical models 1999Uncertainty Analysis of Transport-Transformation Models 2004A response surface method based on weighted regression for structural reliability analysis

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