Frequency response-based structural damage detection using Gibbs sampler

The frequency response function (FRF)-based deterministic damage detection method is well established, but there are some practical difficulties when considering uncertainty associated with measurement noise. To address this measurement uncertainty, a probabilistic damage detection algorithm is presented based on the FRF and Bayesian statistical theory. This method is oriented to the incomplete FRF data, where only row data of the complete FRF matrix at different frequencies are required. This means that abundant data can be utilized in one experiment to achieve probabilistic analysis, avoiding the inconvenience of multiple measurements. First, a Bayesian linear regression model is presented to relate the damage coefficient to the measured FRF. Then, the statistical characteristics of the damage coefficient are obtained from the conditional probability distribution by using the Gibbs sampler, a special form of the Markov chain Monte Carlo (MCMC) method. The probability of damage existence (PDE) for each element is determined according to the probability distributions of the damage coefficient before and after damage. The proposed approach has the merits that it not only estimates the specific value of the damage coefficient but also analyses the corresponding uncertainty. A truss structure and a shear steel frame are, respectively, numerically and experimentally analyzed using the proposed approach with different assumed damage scenarios. The influences of the noise level and frequency number on the detection results are also investigated. The research results indicate that the proposed method has strong noise immunity and robustness. (C) 2019 Elsevier Ltd. All rights reserved.