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1. Experimental Model Updating of a Full-Scale Concrete Frame Structure

   https://doi.org/10.13133/9788893771146  

   Liu, Xi; Dong, Xinjun; wang, Yang; Muhanna, Rafi; Fedele, Francesco (January 2019, 14th International Workshop on Advanced Smart Materials and Smart Structures Technology)

   In structural analysis, it is common practice to construct a finite element (FE) model of an as-built structure using nominal material properties and idealized boundary conditions. However, behaviors of the FE model generally differ from the as-built structure in the field. To minimize the differences, selected parameters of the FE model can be updated using experimental measurements from the as-built structure. This paper investigates the FE model updating of a full-scale concrete frame structure with over a thousand degrees-of-freedom. Given experimental measurements obtained during a shaker test, frequency-domain modal properties of the concrete structure are identified. A non-convex optimization problem is then formulated to update parameter values of the FE model by minimizing the difference between the experimentally identified modal properties and those generated from the FE model. The selected optimization variables include concrete elastic moduli of the columns, beams and slabs. Upon model updating, the modal properties of the FE model can match better with the experimentally identified modal properties. 

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2. Parameters identification of cable stayed footbridges using Bayesian inference

   https://doi.org/doi.org/10.1007/s11012-019-01019-  

   Pepi, C. (August 2019, Meccanica)

   Numerical modeling of actual structural systems is a very complex task mainly due to the lack of complete knowledge on the involved parameters. Simplified assumptions on the uncertain geometry, material properties and boundary conditions make the numerical model response differ from the actual structural response. Improvements of the finite element (FE) models to obtain accurate response predictions can be achieved by vibration based FE model updating which uses experimental measures to minimize the differences between the numerical and experimental modal features (i.e. natural frequencies and mode shapes). Within this context, probabilistic model updating procedures based on the Bayes’ theorem were recently proposed in the literature in order to take into account the uncertainties affecting the structural parameters and their influence on the structural response. In this paper, a novel framework to efficiently estimate the posterior marginal PDF of the selected model parameters is proposed. First, the main dynamic parameters to be used for model updating are identified by ambient vibration tests on an actual structural system. Second, a first numerical FE model is developed to perform initial sensitivity analysis. Third, a surrogate model based on polynomial chaos is calibrated on the initial FE model to significantly reduce computational costs. Finally, the posterior marginal PDFs of the chosen model parameters are estimated. The effectiveness of the proposed method is demonstrated using a FE numerical model describing a curved cable-stayed footbridge located in Terni (Umbria Region, Central Italy). 

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3. Parameters identification of cable stayed footbridges using Bayesian inference

   https://doi.org/doi.org/10.1007/s11012-019-01019-x  

   Chiara Pepi, C. (August 2019, Meccanica)

   Numerical modeling of actual structural systems is a very complex task mainly due to the lack of complete knowledge on the involved parameters. Simplified assumptions on the uncertain geometry, material properties and boundary conditions make the numerical model response differ from the actual structural response. Improvements of the finite element (FE) models to obtain accurate response predictions can be achieved by vibration based FE model updating which uses experimental measures to minimize the differences between the numerical and experimental modal features (i.e. natural frequencies and mode shapes). Within this context, probabilistic model updating procedures based on the Bayes’ theorem were recently proposed in the literature in order to take into account the uncertainties affecting the structural parameters and their influence on the structural response. In this paper, a novel framework to efficiently estimate the posterior marginal PDF of the selected model parameters is proposed. First, the main dynamic parameters to be used for model updating are identified by ambient vibration tests on an actual structural system. Second, a first numerical FE model is developed to perform initial sensitivity analysis. Third, a surrogate model based on polynomial chaos is calibrated on the initial FE model to significantly reduce computational costs. Finally, the posterior marginal PDFs of the chosen model parameters are estimated. The effectiveness of the proposed method is demonstrated using a FE numerical model describing a curved cable-stayed footbridge located in Terni (Umbria Region, Central Italy). 

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4. A variational Bayesian inference technique for model updating of structural systems with unknown noise statistics

   https://doi.org/10.3389/fbuil.2023.1143597  

   Nabiyan, Mansureh-Sadat; Sharifi, Mahdi; Ebrahimian, Hamed; Moaveni, Babak (April 2023, Frontiers in Built Environment)

   Dynamic models of structural and mechanical systems can be updated to match the measured data through a Bayesian inference process. However, the performance of classical (non-adaptive) Bayesian model updating approaches decreases significantly when the pre-assumed statistical characteristics of the model prediction error are violated. To overcome this issue, this paper presents an adaptive recursive variational Bayesian approach to estimate the statistical characteristics of the prediction error jointly with the unknown model parameters. This approach improves the accuracy and robustness of model updating by including the estimation of model prediction error. The performance of this approach is demonstrated using numerically simulated data obtained from a structural frame with material non-linearity under earthquake excitation. Results show that in the presence of non-stationary noise/error, the non-adaptive approach fails to estimate unknown model parameters, whereas the proposed approach can accurately estimate them. 

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5. Adjoint- and Hybrid-Based Hessians for Optimization Problems in System Identification

   https://doi.org/10.1115/1.4040072  

   Nandi, Souransu; Singh, Tarunraj (October 2018, Journal of Dynamic Systems, Measurement, and Control)

   An adjoint sensitivity-based approach to determine the gradient and Hessian of cost functions for system identification of dynamical systems is presented. The motivation is the development of a computationally efficient approach relative to the direct differentiation (DD) technique and which overcomes the challenges of the step-size selection in finite difference (FD) approaches. An optimization framework is used to determine the parameters of a dynamical system which minimizes a summation of a scalar cost function evaluated at the discrete measurement instants. The discrete time measurements result in discontinuities in the Lagrange multipliers. Two approaches labeled as the Adjoint and the Hybrid are developed for the calculation of the gradient and Hessian for gradient-based optimization algorithms. The proposed approach is illustrated on the Lorenz 63 model where part of the initial conditions and model parameters are estimated using synthetic data. Examples of identifying model parameters of light curves of type 1a supernovae and a two-tank dynamic model using publicly available data are also included. 

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