E-Thesis 304 views 72 downloads
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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Swansea University, Wales, UK
2025
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| 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 |
| 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, 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. |
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| Item Description: |
A selection of content is redacted or is partially redacted from this thesis to protect sensitive and personal information. |
| Keywords: |
Nonlinear dynamics, system identification, backbone curve, Bayesian analysis, stochastic modelling |
| College: |
Faculty of Science and Engineering |
| Funders: |
EPSRC doctoral training grant |