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Sparse Bayesian machine learning for the interpretable identification of nonlinear structural dynamics: Towards the experimental data-driven discovery of a quasi zero stiffness device

Tanmoy Chatterjee Orcid Logo, Alexander Shaw Orcid Logo, Michael Friswell, Hamed Haddad Khodaparast Orcid Logo

Mechanical Systems and Signal Processing, Volume: 205, Start page: 110858

Swansea University Authors: Alexander Shaw Orcid Logo, Michael Friswell, Hamed Haddad Khodaparast Orcid Logo

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DOI (Published version): 10.1016/j.ymssp.2023.110858

Abstract

Data-driven discovery of governing laws for complex nonlinear structural dynamic systems remains a challenging issue of paramount importance. This work addresses the above issue by leveraging the available noisy data and integrating sparse Bayesian machine learning (ML) techniques to discover the go...

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Published in: Mechanical Systems and Signal Processing
ISSN: 0888-3270 1096-1216
Published: Elsevier BV 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa64766
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This work addresses the above issue by leveraging the available noisy data and integrating sparse Bayesian machine learning (ML) techniques to discover the governing equations. The problem of discovery is re-cast as the automatic relevance determination of models (model selection) from the library of potential candidate basis terms and their coefficients are determined (parameter identification) using sparse Bayesian linear regression. Two sparsity promoting ML algorithms based on relevance vector machines have been employed. Both these approaches use Bayesian statistics and quantify the uncertainty associated with the model predictions. Results from four representative numerical examples of nonlinear structural dynamics illustrate excellent performance of both proposed approaches. The results have been validated with the true governing equations and time response data. Comparison has also been made with a recent and popular sparse discovery approach. 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spelling v2 64766 2023-10-18 Sparse Bayesian machine learning for the interpretable identification of nonlinear structural dynamics: Towards the experimental data-driven discovery of a quasi zero stiffness device 10cb5f545bc146fba9a542a1d85f2dea 0000-0002-7521-827X Alexander Shaw Alexander Shaw true false 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false f207b17edda9c4c3ea074cbb7555efc1 0000-0002-3721-4980 Hamed Haddad Khodaparast Hamed Haddad Khodaparast true false 2023-10-18 AERO Data-driven discovery of governing laws for complex nonlinear structural dynamic systems remains a challenging issue of paramount importance. This work addresses the above issue by leveraging the available noisy data and integrating sparse Bayesian machine learning (ML) techniques to discover the governing equations. The problem of discovery is re-cast as the automatic relevance determination of models (model selection) from the library of potential candidate basis terms and their coefficients are determined (parameter identification) using sparse Bayesian linear regression. Two sparsity promoting ML algorithms based on relevance vector machines have been employed. Both these approaches use Bayesian statistics and quantify the uncertainty associated with the model predictions. Results from four representative numerical examples of nonlinear structural dynamics illustrate excellent performance of both proposed approaches. The results have been validated with the true governing equations and time response data. Comparison has also been made with a recent and popular sparse discovery approach. Finally, the proposed framework is applied to real datasets that were generated from an in-house designed experimental setup of a quasi zero stiffness device and good performance has been observed. Journal Article Mechanical Systems and Signal Processing 205 110858 Elsevier BV 0888-3270 1096-1216 Sparse Bayesian, Interpretable, Machine learning, Nonlinear structural dynamics, Relevance vector machines 15 12 2023 2023-12-15 10.1016/j.ymssp.2023.110858 http://dx.doi.org/10.1016/j.ymssp.2023.110858 COLLEGE NANME Aerospace Engineering COLLEGE CODE AERO Swansea University All the authors gratefully acknowledge the support of the Engineering and Physical Sciences Research Council, United Kingdom through the award of a Programme Grant “Digital Twins for Improved Dynamic Design”, grant number EP/R006768. 2023-11-27T14:17:58.0155070 2023-10-18T08:45:09.3440820 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering Tanmoy Chatterjee 0000-0002-9374-7992 1 Alexander Shaw 0000-0002-7521-827X 2 Michael Friswell 3 Hamed Haddad Khodaparast 0000-0002-3721-4980 4 64766__28810__260e18fc1efc4f0bad9e00b69e1a4113.pdf 64766.pdf 2023-10-18T08:51:31.2509595 Output 9636294 application/pdf Version of Record true © 2023 The Author(s). Published by Elsevier Ltd. Distributed under the terms of a Creative Commons Attribution 4.0 International License (CC BY 4.0). true eng http://creativecommons.org/licenses/by/4.0/
title Sparse Bayesian machine learning for the interpretable identification of nonlinear structural dynamics: Towards the experimental data-driven discovery of a quasi zero stiffness device
spellingShingle Sparse Bayesian machine learning for the interpretable identification of nonlinear structural dynamics: Towards the experimental data-driven discovery of a quasi zero stiffness device
Alexander Shaw
Michael Friswell
Hamed Haddad Khodaparast
title_short Sparse Bayesian machine learning for the interpretable identification of nonlinear structural dynamics: Towards the experimental data-driven discovery of a quasi zero stiffness device
title_full Sparse Bayesian machine learning for the interpretable identification of nonlinear structural dynamics: Towards the experimental data-driven discovery of a quasi zero stiffness device
title_fullStr Sparse Bayesian machine learning for the interpretable identification of nonlinear structural dynamics: Towards the experimental data-driven discovery of a quasi zero stiffness device
title_full_unstemmed Sparse Bayesian machine learning for the interpretable identification of nonlinear structural dynamics: Towards the experimental data-driven discovery of a quasi zero stiffness device
title_sort Sparse Bayesian machine learning for the interpretable identification of nonlinear structural dynamics: Towards the experimental data-driven discovery of a quasi zero stiffness device
author_id_str_mv 10cb5f545bc146fba9a542a1d85f2dea
5894777b8f9c6e64bde3568d68078d40
f207b17edda9c4c3ea074cbb7555efc1
author_id_fullname_str_mv 10cb5f545bc146fba9a542a1d85f2dea_***_Alexander Shaw
5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
f207b17edda9c4c3ea074cbb7555efc1_***_Hamed Haddad Khodaparast
author Alexander Shaw
Michael Friswell
Hamed Haddad Khodaparast
author2 Tanmoy Chatterjee
Alexander Shaw
Michael Friswell
Hamed Haddad Khodaparast
format Journal article
container_title Mechanical Systems and Signal Processing
container_volume 205
container_start_page 110858
publishDate 2023
institution Swansea University
issn 0888-3270
1096-1216
doi_str_mv 10.1016/j.ymssp.2023.110858
publisher Elsevier BV
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering
url http://dx.doi.org/10.1016/j.ymssp.2023.110858
document_store_str 1
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description Data-driven discovery of governing laws for complex nonlinear structural dynamic systems remains a challenging issue of paramount importance. This work addresses the above issue by leveraging the available noisy data and integrating sparse Bayesian machine learning (ML) techniques to discover the governing equations. The problem of discovery is re-cast as the automatic relevance determination of models (model selection) from the library of potential candidate basis terms and their coefficients are determined (parameter identification) using sparse Bayesian linear regression. Two sparsity promoting ML algorithms based on relevance vector machines have been employed. Both these approaches use Bayesian statistics and quantify the uncertainty associated with the model predictions. Results from four representative numerical examples of nonlinear structural dynamics illustrate excellent performance of both proposed approaches. The results have been validated with the true governing equations and time response data. Comparison has also been made with a recent and popular sparse discovery approach. Finally, the proposed framework is applied to real datasets that were generated from an in-house designed experimental setup of a quasi zero stiffness device and good performance has been observed.
published_date 2023-12-15T14:17:58Z
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