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Data-Driven Uncertainty Quantification and Propagation in Structural Dynamics Inverse Problems

Sedehi, Omid | 2019

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  1. Type of Document: Ph.D. Dissertation
  2. Language: English
  3. Document No: 52297 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Rahimzadeh Rofooei, Fayaz; Katafygiotis, Lambros
  7. Abstract:
  8. This study opens up new horizons in data-driven structural identification methods offering extensive improvements over the existing time-/frequency-domain probabilistic methods. It pushes forward a holistic Bayesian statistical framework to integrate the existing formulations under a hierarchical setting aiming to quantify both the identification precision and the ensemble variability prompted due to model errors. Since the computation of the posterior distributions in hierarchical models is expensive and cumbersome, novel marginalization strategies, asymptotic approximations, and maximum a posteriori estimations are proposed offering mathematical formulations for the uncertainty quantification and propagation. For the first time, the connection between the ensemble covariance matrix and hyper distribution parameters is characterized through approximate estimations. This interesting finding addresses relevant concerns relating to the outcome of the mainstream Bayesian methods in capturing the stochastics variability from multiple data sets. Moreover, numerical and experimental examples are used to demonstrate the method and to compare it with the existing Bayesian formulations for both model updating and response predictions.The joint estimation of the state and input in linear time-invariant dynamical systems is revisited proposing novel sequential Bayesian formulations. An appealing feature of the proposed method is the promise it holds up for updating the covariance matrices of the process and measurement noise in real-time using asymptotic approximations. It also mitigates the low-frequency drift components appearing in estimations of the state and input using the zero-mean Gaussian white noise assumptions for describing the variation of the input forces across discrete time intervals. Experimental and numerical examples are next employed to illustrate the efficacy and efficiency of the proposed methodologies. Contrary to the present methods that produce significant low-frequency drifts while using noisy acceleration response-only measurements, the proposed method offers accurate predictions. This Bayesian filtering technique proposed for the reconstruction of the state and input forces can be used in the emerging fatigue prognosis frameworks
  9. Keywords:
  10. Probabilistic Methods ; Bayesian Method ; Uncertainty Quantification ; Uncertainty Propagation ; Bayesian Filtering ; Model Updating ; Response Prediction

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