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Failure probability estimation of linear time varying systems by progressive renement of reduced order models

Dasgupta, A and Ghosh, D (2019) Failure probability estimation of linear time varying systems by progressive renement of reduced order models. In: SIAM-ASA Journal on Uncertainty Quantification, 7 (3). pp. 1007-1028.

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Official URL: https://doi.org/10.1137/18M1165840


Estimation of failure probabilities is computationally expensive, and the usage of reduced order models (ROM) holds a promise in reducing this cost. However, such an attempt also requires development of new algorithms to minimize the error due to approximation by ROMs. In this work, a novel iterative algorithm is proposed for estimating failure probabilities of parametrically uncertain linear dynamical systems using ROMs. The key idea in this algorithm is to progressively localize the training domain of the ROM in the domain of random parameters. While the algorithm is generic in nature, particularly a proper orthogonal decomposition based ROM is used here and found to be very effiective. Through a detailed numerical study implementing the proposed algorithm, two variants of the ROM|global and local|are explored and a considerable cost gain over a full-scale model is observed. The algorithm also performed well in estimating a low probability of failure. Being dependent on a statistical simulation, this algorithm has inherent potential to be easily and efficiently parallelized.

Item Type: Journal Article
Publication: SIAM-ASA Journal on Uncertainty Quantification
Publisher: Society for Industrial and Applied Mathematics Publications
Additional Information: The copyright for this article belongs to Society for Industrial and Applied Mathematics Publications.
Keywords: Beams and girders; Dynamical systems; Iterative methods; Linear control systems; Monte Carlo methods; Probability; Time varying systems, Failure Probability; Failure probability estimation; Linear dynamical systems; Linear time-varying systems; Proper orthogonal decompositions; Reduced order models; Statistical simulation; Surrogate model, Approximation algorithms
Department/Centre: Division of Mechanical Sciences > Civil Engineering
Date Deposited: 07 Dec 2022 06:23
Last Modified: 07 Dec 2022 06:23
URI: https://eprints.iisc.ac.in/id/eprint/78278

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