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

doi:10.1007/s10483-019-2409-6

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (1): 63-84.doi: https://doi.org/10.1007/s10483-019-2409-6

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

Jinchun LAN, Qianlong ZHANG, Sha WEI, Zhike PENG, Xinjian DONG, Wenming ZHANG

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

收稿日期:2018-07-05 修回日期:2018-09-15 出版日期:2019-01-01 发布日期:2019-01-01
通讯作者: Zhike PENG E-mail:z.peng@sjtu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11632011, 11572189, and 51421092) and the China Postdoctoral Science Foundation (No. 2016M601585)

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

Jinchun LAN, Qianlong ZHANG, Sha WEI, Zhike PENG, Xinjian DONG, Wenming ZHANG

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

Received:2018-07-05 Revised:2018-09-15 Online:2019-01-01 Published:2019-01-01
Contact: Zhike PENG E-mail:z.peng@sjtu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11632011, 11572189, and 51421092) and the China Postdoctoral Science Foundation (No. 2016M601585)

摘要/Abstract

摘要： 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.

关键词: birth function, dead function, effection-diffusion eqation.upper-lower solutions, timedependent orthogonal bases, polynomial chaos, uncertainty quantification, stochastic response surface approximation

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.

Key words: dead function, birth function, effection-diffusion eqation.upper-lower solutions, stochastic response surface approximation, uncertainty quantification, timedependent orthogonal bases, polynomial chaos

中图分类号:

60H35

Jinchun LAN, Qianlong ZHANG, Sha WEI, Zhike PENG, Xinjian DONG, Wenming ZHANG. Uncertainty quantification for stochastic dynamical systems using time-dependent stochastic bases[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(1): 63-84.

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

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

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