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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
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Alexander Shaw ,
Michael Friswell,
Hamed Haddad Khodaparast
Mechanical Systems and Signal Processing, Volume: 205, Start page: 110858
Swansea University Authors:
Alexander Shaw , Michael Friswell, Hamed Haddad Khodaparast
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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...
| Published in: | Mechanical Systems and Signal Processing |
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| ISSN: | 0888-3270 1096-1216 |
| Published: |
Elsevier BV
2023
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa64766 |
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| 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 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. |
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| Keywords: |
Sparse Bayesian, Interpretable, Machine learning, Nonlinear structural dynamics, Relevance vector machines |
| College: |
Faculty of Science and Engineering |
| Funders: |
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. |
| Start Page: |
110858 |