Abstract
Bayesian model calibration techniques are commonly employed in the characterization of nonlinear dynamic systems, as they provide a conceptual and effective framework to deal with model uncertainties, experimental errors and procedure assumptions. This understanding has resulted in the need to introduce a model discrepancy term to account for the differences between model-based predictions and real observations. Indeed, the goal of this work is to investigate model-driven seismic structural health monitoring procedures based on a Bayesian uncertainty quantification framework, and thus make relevant considerations for its use in the seismic structural health monitoring, focusing on masonry structures. Specifically, the Bayesian inference has been applied to the calibration of nonlinear hysteretic systems to both provide: (i) most probable values (MPV) of the parameters following the calibration; and (ii) estimates of the model discrepancy posterior distribution. The effect of the model discrepancy in the calibration is first illustrated recurring to a single degree of freedom using a Bouc–Wen type oscillator as a numerical benchmark. The model discrepancy is then introduced for calibrating a reference nonlinear Bouc–Wen model derived from real data acquired on a monitored masonry building. The main novelty of this study is the application of the framework of uncertainty quantification on models representing data measured directly on masonry structures during seismic events.
Highlights
Models play a key role in simulating the behavior of engineering structures, though even very detailed models may fail to represent critical mechanisms
I horizontal and vertical dotted lines in the plots represent the calibrated reference value of the initial and vertical dotted lines in the plots represent the calibrated reference value of the initial stiffness. This realistic case study has shown that a Gaussian discrepancy term, with null mean and. This realistic case study has shown that a Gaussian discrepancy term, with null mean and unknown unknown variance, is an effective choice to tackle the model inaccuracy rising for low levels of variance, is an effective choice to tackle the model inaccuracy rising for low levels ofwith degradation when
The well-known Bayesian inversion framework was first illustrated through a numerical benchmark of a SDOF Bouc–Wen type oscillator, and applied to a reference model derived from a calibrated 2-DOFs system of a real monitored masonry building hit by the 2016 Central Italy earthquake
Summary
Models play a key role in simulating the behavior of engineering structures, though even very detailed models may fail to represent critical mechanisms. The variety of schemes and uncertainties that are typical of civil structures makes the prediction of the actual mechanical behavior and structural performance a difficult task. All this being said, computer simulations are useful engineering tools to design complex systems and to assess their performance [1,2,3]. Accurate modelling of the structural systems requires them to be calibrated and validated with direct observations and measured experimental data [4]. Most calibration methods are essentially regression techniques that estimate the model parameters based on the outputs, and eventually on the input, by means of various optimization algorithms.
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