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

Struct Control Health Monit

Goulet

2021

Self Cite

The early detection of anomalies associated with changes in the behavior of structures is important for ensuring their serviceability and safety. Identifying anomalies from monitoring data is prone to false and missed alarms due to the uncertain nature of the infrastructure responses' dependency on external factors such as temperature and loading. Existing anomaly detection strategies typically rely on univariate threshold values and disregard the planning horizon in the context of decision making. This paper proposes an anomaly detection framework that combines the interpretability of existing Bayesian dynamic linear models, a particular form of state-space models, with the longterm planning ability of reinforcement learning. The new framework provides (a) reinforcement learning formalism for anomaly detection in Bayesian dynamic linear models, (b) a method for simulating anomalies with respect to its height, duration, and time of occurrence, and (c) a method for quantifying anomaly detectability. The potential of the new framework is demonstrated on monitoring data collected on a bridge in Canada. The results show that the framework is able to detect real anomalies that were known to have occurred, as well as synthetic anomalies.

Section: Empirical Model Estimationmentioning

confidence: 99%

{boldx}_{t}^{monospaceKR}

models the reversible periodic patterns for each observation 36 . Here, we use 10 hidden control points for the kernel regression which results in the vector

{boldx}_{t}^{monospaceKR} = {([], x_{t, 0}^{monospaceKR} x_{t, 1}^{monospaceKR} \dots x_{t, 10}^{monospaceKR})}^{⊺}

consisting in 10 hidden state variables.…”

Section: Case Studymentioning

confidence: 99%

Anomaly detection using state‐space models and reinforcement learning

Khazaeli

Struct Control Health Monit

Goulet

2021

Self Cite

“…This case study is conducted on the traffic‐load data 23,43,44 recorded on the Tamar bridge in the United Kingdom. Correctly modeling traffic data are required for removing its effect on structural responses.…”

Section: Applied Examplesmentioning

confidence: 99%

“…These components capture the irreversible pattern which can be used to identify an anomaly in the behavior of the structure 22 . Periodic (PD) and kernel regression (KR) components are used to identify external effects having periodic pattern that can be, respectively, harmonic or non‐harmonic in nature 23 . The autoregressive component (AR) is used in combination with these components to capture the residuals, that is, any physical phenomenon that is not captured by the other structured components.…”

Section: Introductionmentioning

confidence: 99%

The Gaussian multiplicative approximation for state‐space models

Deka

Structural Contr & Hlth

Amiri

et al. 2021

Summary Applications such as structural health monitoring (SHM) often rely on the analysis of time‐series using methods such as state‐space models (SSM). In this paper, we propose an analytical method called the Gaussian multiplicative approximation (GMA) that is applicable to multiplicative state‐space models that are often encountered in practical SHM applications. The method enables the analytical inference of the mean vector and the covariance matrix for the product of two hidden states in the transition and/or observation models using linear estimation theory and the online estimation of model parameters as hidden states. The potential of combining the GMA and Bayesian dynamic linear models (BDLM) is illustrated through the development of (1) a generic component called online autoregressive that can estimate both the state variable and the parameter together; (2) a generic component called trend multiplicative for multiplicative seasonality model to identify non‐harmonic periodic pattern whose amplitude changes linearly with time; and (3) a generic component called double kernel regression to identify non‐harmonic periodic pattern that involves the product of two periodic kernel regression components. The SHM‐based case studies presented confirm that the GMA exceeds the performance of the existing nonlinear Kalman filter methods in terms of accuracy along with the computational cost.

“…The model of both case studies consists in a vector of hidden state variables that includes a baseline (B) component, a local trend (LT), a local acceleration (LA), a kernel‐regression (KR) component with a period of 365.24 days, and an autoregressive (B) component. The structural behavior over time is described by the baseline.…”

Section: Case Studiesmentioning

confidence: 99%

Real‐time anomaly detection with Bayesian dynamic linear models

Struct Control Health Monit

Goulet

2019

Self Cite

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.