Bayesian dynamic programming approach for tracking time-varying model properties in SHM

Structural health monitoring (SHM) quite often involves continually tracking the temporal variation of some properties of interest, where statistical information about variations under normal situation can be obtained and potential anomalies may be detected for further attention. Structural-related properties such as natural frequency and stiffness often need to be identified with a physics-based model that relates them to measured data. Conventional approaches empirically divide data into non-overlapping segments with equal lengths and identify the model parameters within each segment based on a time-invariant model. Potentially time-varying model properties are then investigated based on the variation of identified results from one data segment to another. Challenges do exist, e.g., how to choose segment length to balance modeling error and identification accuracy, how to set criterion for anomaly detection, etc., which should be addressed with proper extraction of probabilistic information from data. In this work, the SHM problem is formulated as a Bayesian model selection problem, where the data can be ‘partitioned’ in an arbitrary manner, whose optimal choice, and hence points of significant change, are determined together with the model inference process by maximizing the probabilistic evidence supported by data. An efficient algorithm based on dynamic programming is proposed to determine the optimal partitioning and associated piecewise-constant properties, which is otherwise computationally prohibitive. The methodology is applied to tracking modal properties, e.g., natural frequency and damping ratio, of structures using output-only ambient vibration data. It is investigated with synthetic data and then applied to field data of a tall building during a typhoon event.