Model selection for dynamic reduction-based structural health monitoring following the Bayesian evidence approach

Abstract

Abstract There usually exist multitudinous finite element (FE) models with varying level of complexity which can be developed from the engineering judgment for the purpose of structural system identification and health monitoring. By following the theory of Bayesian evidence statistic, this paper proposes a methodology to investigate the issues of FE model-class selection for choosing suitable parameterized structural models utilized in dynamic reduction-based structural health monitoring (SHM). By employing the concept of information divergence, the amount of information needed to be extracted from the measured data is explicitly quantified during the procedure of FE model updating-based structural health monitoring. Then, for achieving a trade-off between the complexity of a parameterized FE model class and that of its corresponding information-theoretic interpretation, such information is utilized for penalizing the complexity of model class to ensure that a relatively simple parameterization scheme can be achieved. The proposed methodology consists of calibration and subsequent monitoring stages, and the information obtained in the former stage is utilized as pseudo-data which is learned by the latter stage to improve the model parameter estimation by implementing the delayed rejection adaptive Metropolis algorithm. Through numerical case studies conducted for a four-storey two-bay steel frame structure considering semi-rigid connections as well as laboratory experiment performed for a two-storey bolt-connected steel frame model, the feasibility and validity of proposed methodology is demonstrated.