A Kernel-Based Method for Modeling Non-harmonic Periodic Phenomena in Bayesian Dynamic Linear Models

Modeling periodic phenomena with accuracy is a key aspect to detect abnormal behavior in time series for the context of Structural Health Monitoring. Modeling complex non-harmonic periodic pattern currently requires sophisticated techniques and significant computational resources. To overcome these limitations, this paper proposes a novel approach that combines the existing Bayesian Dynamic Linear Models with a kernel-based method for handling periodic patterns in time series. The approach is applied to model the traffic load on the Tamar Bridge and the piezometric pressure under a dam. The results show that the proposed method succeeds in modeling the stationary and non-stationary periodic patterns for both case studies. Also, it is computationally efficient, versatile, self-adaptive to changing conditions, and capable of handling observations collected at irregular time intervals.