Assessing the actual state of structural dynamical systems based on available measurements is a crucial task in contemporary engineering applications. In this context, this presentation focuses on solving complex Bayesian model updating problems related to structural dynamical systems. By adopting Bayesian model updating with structural reliability methods, the problem of sampling the posterior distribution of the system parameters is reframed as generating samples conditioned on a specifically devised failure event. To address this problem, an advanced simulation technique is appropriately integrated with a Hamiltonian Monte Carlo scheme to obtain samples at each simulation level. In particular, the well-established subset simulation method is employed. In this setting, a candidate state is first determined by simulating the trajectory of an auxiliary dynamical system, which is then accepted or rejected based on the traditional Metropolis-Hastings rule. Such an approach has proven efficient in drawing samples from complex target distributions, and thus, it is adopted as an effective tool to explore involved domains related to challenging model updating problems.

To assess the performance of the method, a test problem and an application example associated with a nonlinear structural dynamical model are investigated. Numerical results and validation calculations indicate that the proposed approach can be regarded as a viable alternative to address a class of complex identification problems in structural dynamics, including locally identifiable cases, strictly unidentifiable models based on available data, and cases with a large number of model parameters.

Hector Jensen is a Professor Civil Engineering at the Santa Maria Technical University, Valparaiso, Chile, and Professor of Mechanical Engineering at the Catholic University of Chile, Santiago. Chile. He is a Mathematician Civil Engineer from the University of Chile, and he received his PhD in Applied Mechanics from the California Institute of Technology (CALTECH), Pasadena, USA. His research interests include Computational Stochastic Mechanics, Advanced Simulation Methods, Robust and Reliability-Based Optimization, Risk and Sensitivity Analysis, Fuzzy Analysis, Finite Element Analysis, Dynamic Sub-structuring, and Bayesian Model Updating. He has been visiting professor in several American and European universities, including University of California at Los Angeles (UCLA), California Institute of Technology (CALTECH), University of Michigan (UM), University of Innsbruck, etc. He has published numerous journal and conference papers, as well as book chapters in areas of his expertise. In addition, a book that deals with the application of reduced-order models to complex simulation-based problems has been published by Springer in 2019 (Sub-Structure Coupling for Dynamic Analysis: Application to Complex Simulation-Based Problems Involving Uncertainty). He is preparing a new book related to the Reliability, Sensitivity and Optimization of Linear Structural Systems under Stochastic Gaussian Excitation based on Advanced Simulation Techniques. He has been invited to give lectures, keynotes, semi-plenary and plenary lectures in a number of universities and international conferences. He is member of the editorial board of several journals, and he has been guest editor of different Journals, including Computers and Structures, Mechanical Systems and Signal Processing and Reliability Engineering and System Safety. He is also member of the scientific committee of many international conferences and reviewer of different journals. In 2018 he was selected by the Recruitment Program of High-end Foreign Experts of the State Administration of Foreign Affairs of the People’s Republic of China. He is listed among the top 2% scientists globally by the Stanford/Elsevier ranking list in Civil Engineering and Applied Mathematics.