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    A Kriging–NARX Model for Uncertainty Quantification of Nonlinear Stochastic Dynamical Systems in Time Domain

    Source: Journal of Engineering Mechanics:;2020:;Volume ( 146 ):;issue: 007
    Author:
    Biswarup Bhattacharyya
    ,
    Eric Jacquelin
    ,
    Denis Brizard
    DOI: 10.1061/(ASCE)EM.1943-7889.0001792
    Publisher: ASCE
    Abstract: A novel approach, referred to as sparse Kriging–NARX (KNARX), is proposed for the uncertainty quantification of nonlinear stochastic dynamical systems. It combines the nonlinear autoregressive with exogenous (NARX) input model with the high fidelity surrogate model Kriging. The sparsity in the proposed approach is introduced in the NARX model by reducing the number of polynomial bases using the least-angle regression (LARS) algorithm. Sparse KNARX captures the nonlinearity of a problem by the NARX model, whereas the uncertain parameters are propagated using the Kriging surrogate model, and LARS makes the model efficient. The accuracy and the efficiency of the sparse KNARX was measured through uncertainty quantification applied to three nonlinear stochastic dynamical systems. The time-dependent mean and standard deviation were predicted for all the numerical examples. Instantaneous stochastic response characteristics and maximum absolute response were also predicted. All the results were compared with the full scale Monte Carlo simulation (MCS) results and a mean error was calculated for all the numerical problems to measure the accuracy. All the results had excellent agreement with the MCS results at a very limited computational cost. The efficiency of the sparse KNARX also was measured by the CPU time and the required number of surrogate model evaluations. In all instances, sparse KNARX outperformed other state-of-the-art methods, which justifies the applicability of this model for nonlinear stochastic dynamical systems.
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      A Kriging–NARX Model for Uncertainty Quantification of Nonlinear Stochastic Dynamical Systems in Time Domain

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    contributor authorBiswarup Bhattacharyya
    contributor authorEric Jacquelin
    contributor authorDenis Brizard
    date accessioned2022-01-30T19:32:51Z
    date available2022-01-30T19:32:51Z
    date issued2020
    identifier other%28ASCE%29EM.1943-7889.0001792.pdf
    identifier urihttp://yetl.yabesh.ir/yetl1/handle/yetl/4265517
    description abstractA novel approach, referred to as sparse Kriging–NARX (KNARX), is proposed for the uncertainty quantification of nonlinear stochastic dynamical systems. It combines the nonlinear autoregressive with exogenous (NARX) input model with the high fidelity surrogate model Kriging. The sparsity in the proposed approach is introduced in the NARX model by reducing the number of polynomial bases using the least-angle regression (LARS) algorithm. Sparse KNARX captures the nonlinearity of a problem by the NARX model, whereas the uncertain parameters are propagated using the Kriging surrogate model, and LARS makes the model efficient. The accuracy and the efficiency of the sparse KNARX was measured through uncertainty quantification applied to three nonlinear stochastic dynamical systems. The time-dependent mean and standard deviation were predicted for all the numerical examples. Instantaneous stochastic response characteristics and maximum absolute response were also predicted. All the results were compared with the full scale Monte Carlo simulation (MCS) results and a mean error was calculated for all the numerical problems to measure the accuracy. All the results had excellent agreement with the MCS results at a very limited computational cost. The efficiency of the sparse KNARX also was measured by the CPU time and the required number of surrogate model evaluations. In all instances, sparse KNARX outperformed other state-of-the-art methods, which justifies the applicability of this model for nonlinear stochastic dynamical systems.
    publisherASCE
    titleA Kriging–NARX Model for Uncertainty Quantification of Nonlinear Stochastic Dynamical Systems in Time Domain
    typeJournal Paper
    journal volume146
    journal issue7
    journal titleJournal of Engineering Mechanics
    identifier doi10.1061/(ASCE)EM.1943-7889.0001792
    page04020070
    treeJournal of Engineering Mechanics:;2020:;Volume ( 146 ):;issue: 007
    contenttypeFulltext
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