Uncertainty quantification of nonlinear system stochastic response estimates based on the Wiener path integral technique: A Bayesian compressive sampling treatment

The Wiener path integral (WPI) technique for determining the stochastic response of diverse nonlinear systems is enhanced herein based on a Bayesian compressive sampling (CS) treatment. Specifically, first, sparse expansions for the system response joint probability density function (PDF) are employ...

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Bibliographic Details
Published in:Probabilistic engineering mechanics 2022-01, Vol.67, p.103193, Article 103193
Main Authors: Katsidoniotaki, Maria I., Psaros, Apostolos F., Kougioumtzoglou, Ioannis A.
Format: Article
Language:English
Subjects:
Bayesian analysis
Boundary value problems
Compressive sampling
Estimates
Monte Carlo simulation
Nonlinear system
Nonlinear systems
Nonlinearity
Path integral
Probability density functions
Sampling
Sparse representations
Stochastic dynamics
Stochastic models
Thermal expansion
Uncertainty
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Summary:The Wiener path integral (WPI) technique for determining the stochastic response of diverse nonlinear systems is enhanced herein based on a Bayesian compressive sampling (CS) treatment. Specifically, first, sparse expansions for the system response joint probability density function (PDF) are employed. Next, exploiting the localization capabilities of the WPI technique for direct evaluation of specific PDF points leads to an underdetermined linear system of equations for the expansion coefficients. Further, relying on a Bayesian CS solution formulation yields a posterior distribution for the expansion coefficient vector. In this regard, a significant advantage of the herein developed methodology relates to the fact that the uncertainty of the response PDF estimates obtained by the WPI technique is quantified. Furthermore, an adaptive scheme is proposed based on the quantified uncertainty of the estimates for optimal selection of PDF sample points. This yields considerably fewer boundary value problems to be solved as part of the WPI technique, and thus, the associated computational cost is significantly reduced. Two indicative numerical examples pertaining to a Duffing nonlinear oscillator and to an oscillator with asymmetric nonlinearities are considered for demonstrating the capabilities of the developed technique. Comparisons with pertinent Monte Carlo simulation data are included as well.
ISSN:0266-8920
1878-4275
DOI:10.1016/j.probengmech.2021.103193