Uncertainty propagation analysis by an extended sparse grid technique

Abstract

In this paper, an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle, aiming at improving the solving accuracy of the high-order moments and hence the fitting accuracy of the probability density function (PDF) of the system response. The proposed method incorporates the extended Gauss integration into the uncertainty propagation analysis. Moreover, assisted by the Rosenblatt transformation, the various types of extended integration points are transformed into the extended Gauss-Hermite integration points, which makes the method suitable for any type of continuous distribution. Subsequently, within the sparse grid numerical integration framework, the statistical moments of the system response are obtained based on the transformed points. Furthermore, based on the maximum entropy principle, the obtained first four-order statistical moments are used to fit the PDF of the system response. Finally, three numerical examples are investigated to demonstrate the effectiveness of the proposed method, which includes two mathematical problems with explicit expressions and an engineering application with a black-box model.

Keywords

uncertainty propagation analysis / extended sparse grid / maximum entropy principle / extended Gauss integration / Rosenblatt transformation / high-order moments analysis

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Acknowledgments

This work was supported by the National Science Fund for Distinguished Young Scholars (Grant No. 51725502), the major program of the National Natural Science Foundation of China (Grant No. 51490662), and the National Key Research and Development Project of China (Grant No. 2016YFD0701105).

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