Probabilistic damage detection and identification of coupled structural parameters using Bayesian model updating with added mass. (24th October 2022) - Zeng, Jice; Kim, Young Hoon
Highlights: Using vibration data, both mass and stiffness are updated with addressing the coupling effect. Multiple Markov chains are parallelly run to estimate complex posterior PDF. Damage location and severity are reliably and probabilistically identified using vibration data. Abstract: Damage detection inevitably involves uncertainties originated from measurement noise and modeling error. It may cause incorrect damage detection results if not appropriately treating uncertainties. To this end, vibration-based Bayesian model updating (VBMU) is developed to utilize vibration responses or modal parameters to estimate structural parameters and the associated uncertainties of those estimates. However, traditional VBMU often assumes that mass is well known and invariant because simultaneous identification of mass and stiffness may yield an unidentifiable problem due to the coupling effect of the mass and stiffness. In addition, the posterior PDF in VBMU is usually approximated by single Markov Chain Monte Carlo (MCMC), leading to a low acceptance rate and limited capability for complex structures. This paper proposed a novel VBMU to address the coupling effect and identify mass and stiffness by adding known mass. Two vibration data sets are acquired from original and modified systems with added mass, giving the new characteristic equations. Then, the posterior PDF is reformulated by measured data and predicted counterparts from new characteristic equations. For efficiently approximating the posterior PDF, Differential Evolutionary Adaptive Metropolis (DREAM) algorithm is adopted to draw samples by running multiple Markov chains parallelly to enhance acceptance rate and sufficiently explore possible solutions. Finally, a numerical example with a ten-story shear building and a laboratory-scale three-story frame structure are utilized to demonstrate the efficacy of the proposed VBMU framework. The results show that the proposed method can successfully identify both mass and stiffness, and their uncertainties. Reliable probabilistic damage detection can also be achieved.