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Nonlinear Stochastic Modelling and Updating in Structural Dynamics Using Bayesian Inference / PUSHPA PANDEY

Swansea University Author: PUSHPA PANDEY

DOI (Published version): 10.23889/SUThesis.69945

Abstract

The modelling of nonlinear dynamic systems has become increasingly important across various engineering disciplines due to the complexity and uncertainty inherent in real-world structures. Traditional deterministic models, while useful, often fail to capture the full range of dynamic behaviours, esp...

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Published: Swansea University, Wales, UK 2025
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
Supervisor: Khodaparast, H. H., and Friswell, M. I.
URI: https://cronfa.swan.ac.uk/Record/cronfa69945
first_indexed 2025-07-10T14:05:59Z
last_indexed 2025-07-11T05:02:56Z
id cronfa69945
recordtype RisThesis
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In response, there has been a growing trend towards incorporating stochastic modelling techniques to account for uncertainties and provide more robust predictions. By integrating probabilistic methods with data-driven approaches like machine learning, researchers are able to enhance the accuracy and reliability of models, particularly in &#xFB01;elds like aerospace, mechanical, and civil engineering. These advancements not only improve model &#xFB01;delity but also offer new ways to quantify and mitigate risks in the design and operation of complex systems. This research introduces a methodology for developing stochastic models of nonlinear dynamic systems, using both analytical and deep learning-based approaches. The focus is on updating these models with experimental data to better capture the uncertainties inherent in jointed structures, which exhibit complex behaviours such as frictional nonlinearity and geometric distortions. Traditional deterministic models often fall short in accurately representing these systems, necessitating the use of stochastic modelling frameworks to incorporate probabilistic elements and quantify uncertainties. Key components of the framework include system identi&#xFB01;cation using time series data corresponding to experimental backbone curves&#x2014;representations of the system&#x2019;s nonlinear vibrational behaviour&#x2014;as inputs for model development. This process is facilitated by the Sparse Identi&#xFB01;cation of Nonlinear Dynamics (SINDy), which constructs data-driven models by leveraging the sparse nature of many physical systems. A phase-locked loop (PLL) is later implemented to extract backbone curves based on the concept of maintaining the resonance condition during vibration testing, aiding in accurate backbone curve generation. These curves serve as the foundation for stochastic model updating, achieved through Bayesian inference and Markov Chain Monte Carlo (MCMC) techniques. To optimize computational performance, the study incorporates a deep learning model as a surrogate for the more time-intensive analytical models within the MCMC framework. This hybrid approach balances the physical interpretability of analytical models with the computational ef&#xFB01;ciency of data-driven techniques, enabling faster and more accurate pre-dictions. Both deterministic and stochastic models are validated against experimental data from a benchmark system, con&#xFB01;rming the reliability of the framework in capturing complex, nonlinear dynamics. This novel integration of analytical modelling, deep learning, and Bayesian updating provides a comprehensive and &#xFB02;exible solution for the stochastic modelling of nonlinear mechanical systems. 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I.</supervisor><degreelevel>Doctoral</degreelevel><degreename>Ph.D</degreename><degreesponsorsfunders>EPSRC doctoral training grant</degreesponsorsfunders><apcterm/><funders>EPSRC doctoral training grant</funders><projectreference/><lastEdited>2025-07-10T15:11:10.4054617</lastEdited><Created>2025-07-10T14:38:52.3967184</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering</level></path><authors><author><firstname>PUSHPA</firstname><surname>PANDEY</surname><order>1</order></author></authors><documents><document><filename>69945__34738__d04a5e80cc324c88a87416d407410299.pdf</filename><originalFilename>2025_Pandy_P.final.69945.pdf</originalFilename><uploaded>2025-07-10T15:03:53.9149818</uploaded><type>Output</type><contentLength>200332</contentLength><contentType>application/pdf</contentType><version>E-Thesis &#x2013; open access</version><cronfaStatus>true</cronfaStatus><documentNotes>Copyright: The author, Pushpa Pandey, 2025</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807>
spelling 2025-07-10T15:11:10.4054617 v2 69945 2025-07-10 Nonlinear Stochastic Modelling and Updating in Structural Dynamics Using Bayesian Inference 8cecb434236d6e98b699f181c1525826 PUSHPA PANDEY PUSHPA PANDEY true false 2025-07-10 The modelling of nonlinear dynamic systems has become increasingly important across various engineering disciplines due to the complexity and uncertainty inherent in real-world structures. Traditional deterministic models, while useful, often fail to capture the full range of dynamic behaviours, especially when systems are subject to nonlinearities such as friction, hysteresis, or geometric irregularities. In response, there has been a growing trend towards incorporating stochastic modelling techniques to account for uncertainties and provide more robust predictions. By integrating probabilistic methods with data-driven approaches like machine learning, researchers are able to enhance the accuracy and reliability of models, particularly in fields like aerospace, mechanical, and civil engineering. These advancements not only improve model fidelity but also offer new ways to quantify and mitigate risks in the design and operation of complex systems. This research introduces a methodology for developing stochastic models of nonlinear dynamic systems, using both analytical and deep learning-based approaches. The focus is on updating these models with experimental data to better capture the uncertainties inherent in jointed structures, which exhibit complex behaviours such as frictional nonlinearity and geometric distortions. Traditional deterministic models often fall short in accurately representing these systems, necessitating the use of stochastic modelling frameworks to incorporate probabilistic elements and quantify uncertainties. Key components of the framework include system identification using time series data corresponding to experimental backbone curves—representations of the system’s nonlinear vibrational behaviour—as inputs for model development. This process is facilitated by the Sparse Identification of Nonlinear Dynamics (SINDy), which constructs data-driven models by leveraging the sparse nature of many physical systems. A phase-locked loop (PLL) is later implemented to extract backbone curves based on the concept of maintaining the resonance condition during vibration testing, aiding in accurate backbone curve generation. These curves serve as the foundation for stochastic model updating, achieved through Bayesian inference and Markov Chain Monte Carlo (MCMC) techniques. To optimize computational performance, the study incorporates a deep learning model as a surrogate for the more time-intensive analytical models within the MCMC framework. This hybrid approach balances the physical interpretability of analytical models with the computational efficiency of data-driven techniques, enabling faster and more accurate pre-dictions. Both deterministic and stochastic models are validated against experimental data from a benchmark system, confirming the reliability of the framework in capturing complex, nonlinear dynamics. This novel integration of analytical modelling, deep learning, and Bayesian updating provides a comprehensive and flexible solution for the stochastic modelling of nonlinear mechanical systems. By enabling more accurate uncertainty quantification, the framework holds significant promise for applications in engineering fields where joint structures are prevalent, such as aerospace, automotive, and civil engineering. E-Thesis Swansea University, Wales, UK Nonlinear dynamics, system identification, backbone curve, Bayesian analysis, stochastic modelling 2 6 2025 2025-06-02 10.23889/SUThesis.69945 A selection of content is redacted or is partially redacted from this thesis to protect sensitive and personal information. COLLEGE NANME COLLEGE CODE Swansea University Khodaparast, H. H., and Friswell, M. I. Doctoral Ph.D EPSRC doctoral training grant EPSRC doctoral training grant 2025-07-10T15:11:10.4054617 2025-07-10T14:38:52.3967184 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering PUSHPA PANDEY 1 69945__34738__d04a5e80cc324c88a87416d407410299.pdf 2025_Pandy_P.final.69945.pdf 2025-07-10T15:03:53.9149818 Output 200332 application/pdf E-Thesis – open access true Copyright: The author, Pushpa Pandey, 2025 true eng
title Nonlinear Stochastic Modelling and Updating in Structural Dynamics Using Bayesian Inference
spellingShingle Nonlinear Stochastic Modelling and Updating in Structural Dynamics Using Bayesian Inference
PUSHPA PANDEY
title_short Nonlinear Stochastic Modelling and Updating in Structural Dynamics Using Bayesian Inference
title_full Nonlinear Stochastic Modelling and Updating in Structural Dynamics Using Bayesian Inference
title_fullStr Nonlinear Stochastic Modelling and Updating in Structural Dynamics Using Bayesian Inference
title_full_unstemmed Nonlinear Stochastic Modelling and Updating in Structural Dynamics Using Bayesian Inference
title_sort Nonlinear Stochastic Modelling and Updating in Structural Dynamics Using Bayesian Inference
author_id_str_mv 8cecb434236d6e98b699f181c1525826
author_id_fullname_str_mv 8cecb434236d6e98b699f181c1525826_***_PUSHPA PANDEY
author PUSHPA PANDEY
author2 PUSHPA PANDEY
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publishDate 2025
institution Swansea University
doi_str_mv 10.23889/SUThesis.69945
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
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description The modelling of nonlinear dynamic systems has become increasingly important across various engineering disciplines due to the complexity and uncertainty inherent in real-world structures. Traditional deterministic models, while useful, often fail to capture the full range of dynamic behaviours, especially when systems are subject to nonlinearities such as friction, hysteresis, or geometric irregularities. In response, there has been a growing trend towards incorporating stochastic modelling techniques to account for uncertainties and provide more robust predictions. By integrating probabilistic methods with data-driven approaches like machine learning, researchers are able to enhance the accuracy and reliability of models, particularly in fields like aerospace, mechanical, and civil engineering. These advancements not only improve model fidelity but also offer new ways to quantify and mitigate risks in the design and operation of complex systems. This research introduces a methodology for developing stochastic models of nonlinear dynamic systems, using both analytical and deep learning-based approaches. The focus is on updating these models with experimental data to better capture the uncertainties inherent in jointed structures, which exhibit complex behaviours such as frictional nonlinearity and geometric distortions. Traditional deterministic models often fall short in accurately representing these systems, necessitating the use of stochastic modelling frameworks to incorporate probabilistic elements and quantify uncertainties. Key components of the framework include system identification using time series data corresponding to experimental backbone curves—representations of the system’s nonlinear vibrational behaviour—as inputs for model development. This process is facilitated by the Sparse Identification of Nonlinear Dynamics (SINDy), which constructs data-driven models by leveraging the sparse nature of many physical systems. A phase-locked loop (PLL) is later implemented to extract backbone curves based on the concept of maintaining the resonance condition during vibration testing, aiding in accurate backbone curve generation. These curves serve as the foundation for stochastic model updating, achieved through Bayesian inference and Markov Chain Monte Carlo (MCMC) techniques. To optimize computational performance, the study incorporates a deep learning model as a surrogate for the more time-intensive analytical models within the MCMC framework. This hybrid approach balances the physical interpretability of analytical models with the computational efficiency of data-driven techniques, enabling faster and more accurate pre-dictions. Both deterministic and stochastic models are validated against experimental data from a benchmark system, confirming the reliability of the framework in capturing complex, nonlinear dynamics. This novel integration of analytical modelling, deep learning, and Bayesian updating provides a comprehensive and flexible solution for the stochastic modelling of nonlinear mechanical systems. By enabling more accurate uncertainty quantification, the framework holds significant promise for applications in engineering fields where joint structures are prevalent, such as aerospace, automotive, and civil engineering.
published_date 2025-06-02T05:29:32Z
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score 11.089386

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