Functional Series Expansions and Quadratic Approximations for Enhancing the Accuracy of the Wiener Path Integral Technique
Publication: Journal of Engineering Mechanics
Volume 146, Issue 7
Abstract
A novel Wiener path integral (WPI) technique is developed for determining the response of stochastically excited nonlinear oscillators. This is done by employing functional series expansions in conjunction with quadratic approximations. The technique can be construed as an extension and enhancement in terms of accuracy of the standard (semiclassical) WPI solution approach where only the most probable path connecting initial and final states is considered for determining the joint response probability density function (PDF). In contrast, the technique developed herein accounts also for fluctuations around the most probable path, thus yielding an increased accuracy degree. An additional significant advantage of the proposed enhancement as compared to the most probable path approach relates to the fact that low-probability events (e.g., failure probabilities) can be estimated directly in a computationally efficient manner by determining only a few points of the joint response PDF. Specifically, the normalization step in the standard approach, which requires the evaluation of the joint response PDF over its entire effective domain, is circumvented. The performance of the technique is assessed in several numerical examples pertaining to various oscillators exhibiting diverse nonlinear behaviors, where analytical results are set vis-à-vis pertinent Monte Carlo simulation data.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
I. A. Kougioumtzoglou gratefully acknowledges the support through his CAREER award by the CMMI Division of the National Science Foundation (Award No. 1748537).
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 7 • July 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Oct 11, 2019
Accepted: Jan 17, 2020
Published online: Apr 27, 2020
Published in print: Jul 1, 2020
Discussion open until: Sep 27, 2020
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