Bayesian Calibration of Hysteretic Parameters with Consideration of the Model Discrepancy for Use in Seismic Structural Health Monitoring

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.

Nonlinear model updating through a hierarchical Bayesian modeling framework

“…The posterior distributions of the hyper parameters are also computed according to the analytical solutions derived in Eqs. ( 26)- (31), as shown in Fig. 10.…”

“…The Bouc-Wen (BW) model is widely used in dynamical structures to represent the hysteretic behavior of nonlinear systems [22,31]. It was initially proposed by Bouc [56], subsequently modified by Wen [57] and thereafter extended by other researchers in the literature [58][59][60].…”

“…Song et al proposed a Bayesian model updating methodology for dynamical systems with geometric nonlinearities based on the nonlinear normal modes extracted from broadband vibration data [30]. Ceravolo et al employed a Bayesian uncertainty quantification framework for the identification of hysteretic parameters with consideration of the model discrepancy in seismic structural health monitoring [31]. More investigations for nonlinear model updating based on the Bayesian techniques can be found in the literature [32][33][34][35][36][37][38][39].…”

Special Issue on Novel Approaches for Structural Health Monitoring

“…In the study reported in [8], the authors investigate model-driven seismic structural health monitoring procedures, based on a Bayesian uncertainty quantification framework. The variety of schemes and uncertainties that are typical of civil structures make the prediction of their actual mechanical behaviour and structural performance a difficult task.…”