An adaptive filtering-based solution for the Bayesian modal identification formulation

The online identification of the dynamic properties of large structures is an integral part of structural health monitoring. The success of any vibration-based condition monitoring system requires a computationally efficient identification procedure with the potential to be used online. Computational efficiency and automation are the two fundamental requirements of an effective identification procedure. In this study, we propose a solution of a Bayesian-based formulation for the online extraction of structural modal parameters using output-only data. The proposed algorithm uses a Bayesian maximum a posteriori (MAP) estimation; the objective function is defined as a posterior probabilistic density estimation of the dynamic parameters obtained from observations. The conditional probability distribution function (PDF) is computed using a Bayesian approach to minimum mean-square estimation. To reduce the computational costs, we propose to employ an adaptive filtering technique where expansion and truncation of the conditional PDF are implemented to consider the measurement time series as finite-order Markov processes. The methodology is validated through analyses of two documented examples. Comparison with traditional identification methods clearly shows the superiority of the proposed algorithm. The findings demonstrate that the Bayesian-based methodology provides reliable modal parameter identification in dynamic systems, even for data with high noise content.