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Bayesian Model Class Selection and Peobabilistic System Identification Considering Model Complexity

Ameri Fard Nasrand, Mohammad Ali | 2021

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53780 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mahsuli, Mojtaba
  7. Abstract:
  8. This research proposes a Bayesian model selection framework using the stochastic filtering for rapid Bayesian identification of structures under seismic excitations. Structural identification after an earthquake at a regional scale entails a high computational effort. For rapid damage detection on a regional scale, using simplified and low-cost structural models is preferred over complex finite element models, due to the large amount of information needed for finite element modeling of numerous structures within a region as well as the high computational cost of such models. Timoshenko beams, shear beams, and shear buildings are examples of simplified structural models used in this study to represent the dynamic behavior of building structures. Such models demand a small computational effort thanks to a small set of governing parameters and the availability of analytical solutions. However, this simplicity leads to more uncertainty in the model prediction. This poses the dilemma of prediction accuracy versus the model complexity. To balance the two, this research suggests a Bayesian model selection framework, which determines the best simplified model class for each building in a region to be employed in system identification for rapid damage detection in the aftermath of future earthquakes. This boosts the resourcefulness as a component of community resilience. The proposed framework features a novel cumulative evidence function comprising a cumulative likelihood function and a cumulative penalty term. The former rewards a model for a higher likelihood given the observed measurements of the building response. This is counteracted by the latter term that penalizes the model for complexity, e.g., for a higher number of governing parameters. Evidence is determined through a probabilistic system identification method, here, the extended Kalman filter (EKF). The measured responses of each building are then employed to compute the evidence function for a host of model classes. The proposed framework is also employed to determine the optimal tuning parameters of the EKF by maximizing the cumulative evidence function. Synthetic examples are presented to verify the accuracy of the proposed framework. Finally, the framework is validated through two real‐world applications that feature the Millikan Library in Passadena, California and the ANX building in Tsukuba, Japan, and the results are compared with those of past studies
  9. Keywords:
  10. Kalman Filters ; Bayesian Framework ; Probabilistic Systems ; Rapid Damage Detection ; Bayesian Model Selection ; Filter Tuning ; Resilience Enhancement

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