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In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive estimation of a multidimensional integral — known as the marginal likelihood or as the model evidence (i.e., the probability of observing the measured data given the model) — over the multidimensional parameter domain. This study presents efficient approaches for estimating this marginal likelihood by transforming it into a one-dimensional integral that is subsequently evaluated using a quadrature rule at multiple adaptively-chosen iso-likelihood contour levels. Three different algorithms are proposed to estimate the probability mass at each adapted likelihood level using samples from importance sampling, stratified sampling, and Markov chain Monte Carlo (MCMC) sampling, respectively. The proposed approach is illustrated — with comparisons to Monte Carlo, nested, and MultiNest sampling — through four numerical examples. The first, an elementary example, shows the accuracies of the three proposed algorithms when the exact value of the marginal likelihood is known. The second example uses an 11-story building subjected to an earthquake excitation with an uncertain hysteretic base isolation layer with two models to describe the isolation layer behavior. The third example considers flow past a cylinder when the inlet velocity is uncertain. Based on the these examples, the method with stratified sampling is by far the most accurate and efficient method for complex model behavior in low dimension, particularly considering that this method can be implemented to exploit parallel computation. In the fourth example, the proposed approach is applied to heat conduction in an inhomogeneous plate with uncertain thermal conductivity modeled through a 100 degree-of-freedom Karhunen–Loève expansion. The results indicate that MultiNest cannot efficiently handle the high-dimensional parameter space, whereas the proposed MCMC-based method more accurately and efficiently explores the parameter space. The marginal likelihood results for the last three examples — when compared with the results obtained from standard Monte Carlo sampling, nested sampling, and MultiNest algorithm — show good agreement. 

Large-scale seismic structural tests are crucial to validating both structural design methodologies and the effectiveness of seismic isolation devices. However, considering the significant costs of such tests, it is essential to leverage data from completed tests by taking advantage of numerical models of the tested structures, updated using data collected from the experiments, to complete additional studies that may be difficult, unsafe or impossible to physically test. However, updating complex numerical models poses its own challenges. The first contribution of this paper is to develop a multi-stage model updating method suitable for high-order models of base-isolated structures, which is motivated and evaluated through modeling and model updating of a full-scale four-story base-isolated reinforced-concrete frame building that was tested in 2013 at the NIED E-Defense laboratory in Japan. In most studies involving model updating, all to-be-updated parameters are typically updated simultaneously; however, given the observation that the superstructure in this study predominantly moves as a rigid body in low-frequency modes and the isolation layer plays a minor role in all other modes, this study proposes updating parameters in stages: first, the linear superstructure parameters are updated so that its natural frequencies and mode shapes match those identified via a subspace system identification of the experimental building responses to low-level random excitations; then, the isolation-layer device linear parameters are updated so that the natural frequencies, damping ratios and mode shapes of the three isolation modes match. These two stages break a large-scale linear model updating problem into two smaller problems, thereby reducing the search space for the to-be-updated parameters, which generally reduces computational costs regardless of what optimization algorithm is adopted. Due to the limited instrumentation, the identified modes constitute only a subset of all the modes; to match each identified mode with a FEM mode, a procedure is proposed to compare each identified mode with a candidate set of FEM modes and to select the best match, which is a second contribution. Further, nonlinear isolation-layer device models are proposed, updated and validated with experimental data. Finally, combining the isolation-layer devices' nonlinear models with the updated superstructure linear FEM, the final result is a data-calibrated nonlinear numerical model that will be used for further studies of controllable damping and validation of new design methodologies, and is being made available for use by the research community, alleviating the dearth of experimentally-calibrated numerical models of full-scale base-isolated buildings with lateral-torsional coupling effects.