Graph-Theoretic-Approach-Assisted Gaussian Process for Nonlinear Stochastic Dynamic Analysis under Generalized Loading
Publication: Journal of Engineering Mechanics
Volume 145, Issue 12
Abstract
We present a novel framework for nonlinear stochastic dynamic analysis under generalized (Gaussian and non-Gaussian) loading. First, the actual system involving high-dimensional stochastic inputs is reduced to multiple low-dimensional systems by using graph structure. Subsequently, Gaussian process (GP) is utilized as a surrogate for the low-dimensional systems. The GP associated with the low-dimensional systems obtained using the graph-theoretic approach can be trained in parallel, and hence the proposed approach is highly efficient. In order to illustrate the performance of the proposed approach, four nonlinear stochastic dynamic problems have been solved. All the problems selected are high dimensional in number of stochastic dimensions. Results obtained using the proposed approach are compared with benchmark solutions obtained using Monte Carlo simulation. It is observed that the proposed approach yields highly accurate results for all the problems. Moreover, the number of training points required is also quite a bit less, indicating that the proposed approach is highly efficient.
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Acknowledgments
The authors acknowledge the computing facility provided by the Center for Research Computing, University of Notre Dame, and the support from Council of Scientific and Industrial Research, Government of India, via Grant No. 22(0712)/16/EMR-II.
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Published In
Journal of Engineering Mechanics
Volume 145 • Issue 12 • December 2019
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©2019 American Society of Civil Engineers.
History
Received: Nov 18, 2018
Accepted: Apr 22, 2019
Published online: Sep 30, 2019
Published in print: Dec 1, 2019
Discussion open until: Feb 29, 2020
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