Abstract
The Bayesian model updating approach (BMUA) benefits from identifying the most probable values of structural parameters and providing uncertainty quantification. However, the traditional BMUA is often used to update stiffness only with the assumption of well-known mass, which allows unidentifiable cases induced by the coupling effect of mass and stiffness to be circumvented and may not be optimal for structures experiencing damages in both mass and stiffness. In this paper, the new BMUA tailored to estimating both mass and stiffness is presented by using two measurement states (original and modified systems). A new eigenequation with a stiffness-modified system is formulated to address the coupling effect of mass and stiffness. The posterior function is treated using an asymptotic approximation method, giving the new objective functions with stiffness modification. Analytical formulations of modal parameters and structural parameters are then derived by a linear optimization method. In addition, the covariance matrix of uncertain parameters is determined by the inverse of the Hessian matrix of the objective function. The performance of the proposed BMUA is evaluated through two numerical examples in this study; a probabilistic damage estimation is also implemented. The results show the proposed BMUA is superior to the traditional one in mass and stiffness updating.
Highlights
The proposed Bayesian model updating approach (BMUA) can accurately identify mass and stiffness parameters
The updated frequencies by the proposed BMUA have a highly acceptable agreement and the error is less than 2%, with actual values in two damage cases, as shown in Table 4 and Figure 4
It can be attributed to the coupling effect of mass and stiffness existing in traditional Bayesian that governs the accuracy of the updated results when simultaneously updating mass and stiffness
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The coupling effect has been recently successfully addressed and achieved acceptable results in identifying mass and stiffness It still requires certain prior information and quantifying parameter uncertainties remains a challenge. Ding et al [42] proposed an evolutionary-based model updating approach to simultaneously update structural parameters, mass and stiffness, while only partial uncertainty due to measurement noise was available. A novel Bayesian model updating framework is proposed to address the coupling effect for simultaneously updating mass and stiffness, as well as quantifying parameter uncertainties. The new eigenequations are reformulated by two sets of measured data acquired from an original system and a stiffness-modified system, which aims to address the coupling effect of mass and stiffness, giving the new prior PDF and new posterior PDF.
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