Input-State Estimation of Inelastic Structural Systems: Theoretical Framework and Experimental Validation
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Fahed, Nadine
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Abstract
System identification through online estimation algorithms allows for a comprehensive understanding, prediction, and assessment of the intricate behaviors exhibited by complex in-situ systems in a variety of applications. This model-based technique leverages the system's noisy output data and integrates existing mathematical physics-based models to infer the unknown inputs or unobservable dynamic states. The adoption of these online techniques in real-world settings has gained momentum over the past several years, owing to their ease of implementation, the robustness and reliability of the results, and the continuous advancements in sensing technologies. Furthermore, when structural systems are loaded beyond their elastic limit, they exhibit inelastic behavior which necessitates different methods to accommodate this complex nonlinear phenomenon. This dissertation contributes to this research area by developing a robust framework that integrates hysteretic models with nonlinear stochastic filtering methods to quantify the input characteristics of systems exhibiting inelastic behavior due to material plasticity.
Towards this goal, an input-state estimator for linear systems is first established. The estimator is designed to reduce the dependency on heuristically chosen input statistics by incorporating an online input covariance updating routine. Numerical and experimental validation is conducted, the results of which highlighted the robustness of the estimator in successfully tracking the input and state time history for various initialized input statistics. The estimator is then extended to nonlinear systems using an Extended Kalman framework. To efficiently model the system dynamics in the presence of hysteresis or plastic deformation, two modeling approaches of the continuum system are explored: an equivalent single degree of freedom formulation combined with a uniaxial Bouc-Wen model and a planar multiaxial hysteretic beam model. A comprehensive numerical validation of the proposed framework is conducted to gain insight into the performance of the inelastic models and the estimation algorithm. The results underscored the effectiveness of the proposed estimator and integrated models in successfully characterizing the input and states in the presence of nonlinearities in the system. Finally, the framework is experimentally validated using data collected from a beam subjected to an impact at its midspan. The novel estimator, along with the integrated models, adequately tracked the impulsive load. As such, these efforts represent an important contribution to the experimental validation of joint input-state estimation methods for inelastic continuum structures subjected to high-rate dynamic inputs.
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2024-12-09
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Dissertation (PhD)