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Uncertainty quantification for stochastic dynamical systems using time-dependent stochastic bases

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Abstract

A novel method based on time-dependent stochastic orthogonal bases for stochastic response surface approximation is proposed to overcome the problem of significant errors in the utilization of the generalized polynomial chaos (GPC) method that approximates the stochastic response by orthogonal polynomials. The accuracy and effectiveness of the method are illustrated by different numerical examples including both linear and nonlinear problems. The results indicate that the proposed method modifies the stochastic bases adaptively, and has a better approximation for the probability density function in contrast to the GPC method.

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Authors and Affiliations

  1. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Jinchun Lan, Qianlong Zhang, Sha Wei, Zhike Peng, Xinjian Dong & Wenming Zhang

Authors
  1. Jinchun Lan
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  2. Qianlong Zhang
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  3. Sha Wei
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  4. Zhike Peng
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  5. Xinjian Dong
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  6. Wenming Zhang
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Corresponding author

Correspondence to Zhike Peng.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11632011, 11572189, and 51421092) and the China Postdoctoral Science Foundation (No. 2016M601585)

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Lan, J., Zhang, Q., Wei, S. et al. Uncertainty quantification for stochastic dynamical systems using time-dependent stochastic bases. Appl. Math. Mech.-Engl. Ed. 40, 63–84 (2019). https://doi.org/10.1007/s10483-019-2409-6

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  • DOI: https://doi.org/10.1007/s10483-019-2409-6

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2010 Mathematics Subject Classification

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