Technical Papers
Apr 30, 2021

Uncertainty Quantification of Locally Nonlinear Dynamical Systems Using Neural Networks

Publication: Journal of Computing in Civil Engineering
Volume 35, Issue 4

Abstract

Models are often given in terms of differential equations to represent physical systems. In the presence of uncertainty, accurate prediction of the behavior of these systems using the models requires understanding the effect of uncertainty in the response. In uncertainty quantification, statistics such as mean and variance of the response of these physical systems are sought. To estimate these statistics, sampling-based methods like Monte Carlo often require many evaluations of the models’ governing differential equations for multiple realizations of the uncertainty. However, for large complex engineering systems, these methods become computationally burdensome as the solution of the models’ governing differential equations for such systems is expensive. In structural engineering, an otherwise linear structure often contains spatially local nonlinearities with uncertainty present in them. A standard nonlinear solver for them with sampling-based methods for uncertainty quantification incurs significant computational cost for estimating the statistics of the response. To ease this computational burden of uncertainty quantification of large-scale locally nonlinear dynamical systems, a method is proposed herein that decomposes the response into two parts: response of a deterministic nominal linear system and a corrective term. This corrective term is the response from a pseudoforce that contains the nonlinearity and uncertainty information. In this paper, neural network, a recently popular tool for universal function approximation in the scientific machine-learning community due to the advancement of computational capability as well as the availability of open-source packages, is used to estimate the pseudoforce. Since only the nonlinear and uncertain pseudoforce is modeled using the neural networks, the same network can be used to predict a different response of the system, and no new network is required to train if the statistics of a different response are sought.

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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. Available data and source codes include: (1) training and validation data sets, (2) trained neural networks, and (3) source codes for training and evaluation of the neural networks.

Acknowledgments

The author thanks Dr. Mahmoud Kamalzare for kindly providing the finite-element model of the 100-DOF building in Example 2 and Dr. Erik A. Johnson and Dr. Steven F. Wojtkiewicz for kindly providing the finite-element model of the 20-story building in Example 3.

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Go to Journal of Computing in Civil Engineering
Journal of Computing in Civil Engineering
Volume 35Issue 4July 2021

History

Received: Sep 23, 2020
Accepted: Dec 10, 2020
Published online: Apr 30, 2021
Published in print: Jul 1, 2021
Discussion open until: Sep 30, 2021

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Postdoctoral Associate, Smead Dept. of Aerospace Engineering Sciences, Univ. of Colorado, Boulder, CO 80303. ORCID: https://orcid.org/0000-0002-1974-6123. Email: [email protected]

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