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1. 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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2. A Comparative Study of Frequency-domain Finite Element Updating Approaches Using Different Optimization Procedures

   DONG, Xinjun; WANG, Yang (July 2016, EWSHM)

   In order to achieve a more accurate finite element (FE) model for an as-built structure, experimental data collected from the actual structure can be used to update selected parameters of the FE model. The process is known as FE model updating. This research compares the performance of two frequency-domain model updating approaches. The first approach minimizes the difference between experimental and simulated modal properties, such as natural frequencies and mode shapes. The second approach minimizes modal dynamic residuals from the generalized eigenvalue equation involving stiffness and mass matrices. Both model updating approaches are formulated as an optimization problem with selected updating parameters as optimization variables. This research also compares the performance of different optimization procedures, including a nonlinear least-square, an interior-point and an iterative linearization procedure. The comparison is conducted using a numerical example of a space frame structure. The modal dynamic residual approach shows better performance than the modal property difference approach in updating model parameters of the space frame structure. 

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3. Structural health monitoring using extremely compressed data through deep learning

   https://doi.org/10.1111/mice.12517  

   Azimi, Mohsen; Pekcan, Gokhan (November 2019, Computer-Aided Civil and Infrastructure Engineering)

   Abstract This study introduces a novel convolutional neural network (CNN)‐based approach for structural health monitoring (SHM) that exploits a form of measured compressed response data through transfer learning (TL)‐based techniques. The implementation of the proposed methodology allows damage identification and localization within a realistic large‐scale system. To validate the proposed method, first, a well‐known benchmark model is numerically simulated. Using acceleration response histories, as well as compressed response data in terms of discrete histograms, CNN models are trained, and the robustness of the CNN architectures is evaluated. Finally, pretrained CNNs are fine‐tuned to be adaptable for three‐parameter, extremely compressed response data, based on the response mean, standard deviation, and a scale factor. The performance of each CNN implementation is assessed using training accuracy histories as well as confusion matrices, along with other performance metrics. In addition to the numerical study, the performance of the proposed method is demonstrated using experimental vibration response data for verification and validation. The results indicate that deep TL can be implemented effectively for SHM of similar structural systems with different types of sensors. 

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4. On gain design in virtual output feedback for model updating

   https://doi.org/10.1007/978-981-13-8331-1  

   Ulriksen, M; Bernal, D. (January 2019, Proceedings of the 13th International Conference on Damage Assessment of Structures)

   The set of equations to be solved for parameter estimation in model updating has no unique solution when, as will often be the case in structural applications, the dimensionality of the model exceeds the number of target parameters estimated from experiments. One approach for enlarging the target space is to create closed-loop systems that, in addition, can be designed with pole sensitivities favorable for updating the model. The present paper will focus on designing gains for model updating using a recently proposed virtual implementation of output feedback, which allows computation of several closed-loop systems, from a single open loop realization and removes the constraint of closed-loop stability. The gains are designed through an eigenstructure assignment procedure, in which the model parameters of interest in the updating are divided into two different classes; one where the pole sensitivities with respect to the parameters are to be enhanced and one where they are to be reduced. A numerical example with a structural system is presented that demonstrates the merit of the proposed gain design procedure. 

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5. Nonlinear Structural Model Parameter Updating Using Residual Drift Measurements from Sequential Seismic Events

   https://doi.org/10.1061/JSENDH.STENG-15117  

   De, Budhaditya; Burton, Henry V (October 2025, Journal of Structural Engineering)

   Model parameter updating can enhance the use of nonlinear structural response simulation to guide decision-making in the post-earthquake environment. Since most structures in high seismic regions are not instrumented with sensors, the response history during ground shaking is usually not available after an earthquake. Nevertheless, technologies such as Light Detection and Ranging (LiDAR) and drone-mounted imaging devices have increased the feasibility of measuring residual deformations after the shaking has subsided. It is within this context that a framework for performing nonlinear structural model parameter updating based only on residual drift measurements is proposed. The considered setting is one where a structure is subjected to a sequence of ground motions (without repairs), whereby after each event, the structural model parameters are updated using a Bayesian formulation and the measured residual drift. The methodology is demonstrated by using experimental data from a reinforced concrete bridge pier subjected to six back-to-back ground motions with significant residual drifts recorded after the third, fourth and fifth records in the sequence. The results showed that the updating procedure is able to incrementally (after each record) improve the accuracy of both the concrete and steel model parameters which also enhanced the estimates of the simulated peak and residual drifts. 

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