Tracking time-varying properties using quasi time-invariant models with Bayesian dynamic programming - Yang, Yanping (2024)
Tracking the temporal variation of the properties of a system is relevant in different settings when data of extended duration is available, e.g., anomaly detection, condition monitoring, and trend identification. One simple approach is to divide the data into non-overlapping segments and then identify the model properties of each segment individually using a time-invariant model within the segment. The potential change of the system is then investigated by tracking the variations of model properties from one segment to another. In this context, a dynamic programming approach has been developed recently that determines the ‘best partitioning’ of data segments, between which a change of model parameters takes place in the sense of Bayesian model selection. As a change can result when any one of the parameters has changed in a statistically significant manner, a basic question is concerned with what constitutes a suitable model that meets specific monitoring objectives. E.g., should all or only some of the parameters be allowed to change? Motivated by this, a quasi time-invariant (QTI) modeling methodology is proposed in this work where only some (rather than all) parameters are allowed to change across data segments. Computational issues associated with this new class of models are addressed, e.g., the efficient calculation of posterior most probable value and covariance matrix, and Bayesian evidence in the context of dynamic programming. Focusing on modal property (natural frequencies, damping ratios, etc.) tracking with ambient data, the proposed methodology with QTI model is investigated with synthetic and laboratory data; and applied to field data of a tall building during a typhoon event. The results from field data are compared with those from existing methods.