Summary The detection of changes in structural behaviour over time, that is, anomalies, is an important aspect in structural safety analysis. This paper proposes an anomaly detection method that combines the existing Bayesian Dynamic Linear Models framework with the Switching Kalman Filter theory. The key aspect of this method is its capacity to detect anomalies based on the prior probability of an anomaly, a generic anomaly model, as well as transition probabilities between a normal and an abnormal state. Moreover, the approach operates in a semisupervised setup where normal and abnormal state labels are not required to train the model. The potential of the new method is illustrated on the displacement data recorded on a dam in Canada. The results show that the approach succeeded in identifying the anomaly caused by refection work, without triggering any false alarm. It also provided the specific information about the dam's health and conditions.

Summary A key goal in structural health monitoring is to detect abnormal events in a structure's behavior by interpreting its observed responses over time. The goal is to develop an anomaly detection method that (a) is robust towards false alarm and (b) capable of performing real‐time analysis. The majority of anomaly detection approaches are currently operating over batches of data for which the model parameters are assumed to be constant over time and to be equal to the values estimated during a fixed‐size training period. This assumption is not suited for the real‐time anomaly detection where model parameters need to be treated as time‐varying quantities. This paper presents how this issue is tackled by combining Rao‐Blackwellized particle filter (RBPF) with the Bayesian dynamic linear models (BDLMs). The BDLMs, which is a special case of state‐space models, allow decomposing time series into a vector of hidden state variables. The RBPF employs the sequential Monte Carlo method to learn model parameters continuously as the new observations are collected. The potential of the new approach is illustrated on the displacement data collected from a dam in Canada. The approach succeeds in detecting the anomaly caused by the refection work on the dam as well as the artificial anomalies that are introduced on the original dataset. The new method opens the way for monitoring the structure's health and conditions in real time.

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.

In Structural Health Monitoring, non-harmonic periodic hidden covariate typically arises when an observed structural response depends on unobserved external effects such as temperature or loading. This paper addresses this challenge by proposing a new extension to Bayesian Dynamic Linear Models (BDLMs) for handling situations where non-harmonic periodic hidden covariates may influence the observed responses of structures. The potential of the new approach is illustrated on the data recorded on a dam in Canada. A model employing the proposed approach is compared to another that only uses a superposition of harmonic hidden components available from the existing BDLMs. The comparative study shows that the proposed approach succeeds in estimating hidden covariates and has a better predictive performance than the existing method using a superposition of harmonic hidden components.

Summary The quantification of uncertainty associated with the model parameters and the hidden state variables is a key missing aspect for the existing Bayesian dynamic linear models. This paper proposes two methods for carrying out the uncertainty quantification task: (a) the maximum a posteriori with the Laplace approximation procedure (LAP‐P) and (b) the Hamiltonian Monte Carlo procedure (HMC‐P). A comparative study of LAP‐P with HMC‐P is conducted on simulated data as well as real data collected on a dam in Canada. The results show that the LAP‐P is capable to provide a reasonable estimation without requiring a high computation cost, yet it is prone to be trapped in local maxima. The HMC‐P yields a more reliable estimation than LAP‐P, but it is computationally demanding. The estimation results obtained from both LAP‐P and HMC‐P tend to the same values as the size of the training data increases. Therefore, a deployment of both LAP‐P and HMC‐P is suggested for ensuring an efficient and reliable estimation. LAP‐P should first be employed for the model development and HMC‐P should then be used to verify the estimation obtained using LAP‐P.