Bayesian-network-based system identification of spatial distribution of structural parameters

Structural deterioration or damage in civil infrastructures may results in severe losses of properties and human lives. To prevent such situations, structure health monitoring (SHM) technologies have been developed in recent decades. As one of the SHM technologies, so-called system identification (SI) methods aim to estimate structural parameters by minimizing an error function consisting of measured and calculated responses of a structure under the same loading condition. Such optimization-based SI algorithms may suffer from ill-posedness of the inverse problem, which may result in non-uniqueness of solutions or non-stability of the optimization process. In this paper, in order to avoid issues related to ill-posedness, an SI method based on the Bayesian Network (BN) technology is developed, especially for probabilistic identification of spatial distribution of structural parameters. Utilizing graph theories, a BN describes random variables by nodes connected by links, which represent conditional probability tables (CPT) explaining the probabilistic relationship between the linked nodes. For effective SI using BN, this study proposes a BN graph model, which employs a bi-variate Gaussian function as a shape function describing the spatial distribution of a structural parameter with a small number of parameters. The parameters of the Gaussian (shape) function are considered as nodes in the BN to describe various spatial distribution patterns using a small number of parent nodes. Using this modeling approach, the number of the BN nodes is not affected by the size of the finite element (FE) mesh. Thus, the approach prevents the BN graph from growing to an intractable size even if the FE analysis requires smaller meshes to improve the accuracy of the structural analysis. Using the constructed BN, information on applied loads, and observed structural responses, a BN inference algorithm effectively updates the prior distribution of spatial distribution parameters to the posterior distribution. The proposed method is tested and demonstrated by numerical examples. Using a variety of structural deterioration scenarios, the SI results by the proposed method are compared with those by maximum likelihood estimation (MLE), and an FE-updating method. During the test, the influences of measurement errors, and incomplete/missing data on the performance of the methods are also investigated. The results show that the proposed SI approach is more stable and robust than the other tested methods, and potentially has more merits that are worth investigating in future research.