Uncertainty quantification for model parameters and hidden state variables in Bayesian dynamic linear models

Nguyen, Luong Ha; Gaudot, Ianis; Goulet, James‐A.

doi:10.1002/stc.2309

Cited by 4 publications

(5 citation statements)

References 45 publications

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“…Equation ( 20) is the objective function, which aims to maximize the joint probability density of observations (Equation ( 21)). Any optimization algorithm, 52 such as batch gradient descent, can be implemented to search for the optimal solution. The termination criterion is based on the log-likelihood value as follows:…”

Section: Bayesian Dynamic Linear Modelsmentioning

confidence: 99%

SHM-informed life-cycle intelligent maintenance of fatigue-sensitive detail using Bayesian forecasting and Markov decision process

Lai

Dong

Smyl

2023

Structural Health Monitoring

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Civil and maritime engineering systems must be efficiently managed to control the failure risk at an acceptable level as their performance is gradually degraded throughout the operational life, caused by fatigue and corrosion. Structural health monitoring develops a timely capability to assess the structural condition and performance metrics. However, using actual long-term monitoring data to guide the life-cycle management under stochastic environments has not been sufficiently studied. To realize an optimal maintenance strategy within the service life, an integrated monitoring-based optimal management framework is developed on the basis of the partially observable Markov decision processes (POMDPs) and Bayesian forecasting. In the proposed framework, the stochastic fatigue processes are quantified by the state transition matrix. The Bayesian dynamic linear model is embedded in POMDPs as a continuous observation part to forecast the cycling impacts and estimate the deterioration rate using long-term dynamic strain responses. In addition, making use of the special features of the problem considered in this paper, an adaptive discretization strategy is proposed to alleviate the complexity of large discrete observed spaces in the POMDP. The applicability and feasibility of the framework are evaluated by intelligent maintenance of fatigue-sensitive components with real-world monitoring data. After solving the POMDP by an efficient offline solver, the results obtained in this paper demonstrate that structural interventions are uneconomical to extend the life when a welded detail is approaching its end of life due to the normal service. Furthermore, if multiple interventions are available, the framework can find optimal maintenance actions based on the trade-off between long-term utility and the corresponding cost. This framework as the prototype could also be adjusted to aid life-cycle intelligent maintenance of other types of components under different deterioration scenarios.

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Section: Bayesian Dynamic Linear Modelsmentioning

confidence: 99%

SHM-informed life-cycle intelligent maintenance of fatigue-sensitive detail using Bayesian forecasting and Markov decision process

Lai

Dong

Smyl

2023

Structural Health Monitoring

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“…The complete model matrices A , C , Q , and R required for state estimation using the Kalman filter are described in Appendix B. The vector of unknown parameters which need to be estimated using an optimization algorithm 8,17,41 is given by

θ = {[σ_{w}^{LT} σ_{w}^{AR} σ_{w}^{TP} σ_{v}]}^{⊺},

where

σ_{w}^{monospaceLT}

is the standard deviation of the local trend,

σ_{w}^{monospaceAR}

is the standard deviation of the AR process,

σ_{w}^{monospaceTP}

is the standard deviation of the local trend (TP) in TM, and σ v is the standard deviation for the observation error. The initial parameter and the optimized parameter values using Newton‐Raphson 8 optimization technique by maximizing the joint log‐likelihood 42 are

\begin{matrix} {bold-italicθ}_{0} = & {false[1 0^{- 6} 0.1 1 0^{- 6} 1 false]}^{⊺}, \\ bold-italic θ^{*} = & {false[2.16 \times 1 0^{- 6} 0.092 6.5 \times 1 0^{- 7} 0.054 false]}^{⊺} . \end{matrix}

…”

Section: Applied Examplesmentioning

confidence: 99%

The Gaussian multiplicative approximation for state‐space models

Deka

Nguyen

Amiri

et al. 2021

Structural Contr & Hlth

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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.

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“…The model construction consists in pre‐defining a vector of hidden state variables included in the model for interpreting the data. Examples of model construction are illustrated in several case studies . The warm‐up is employed for approximating the initial distribution for each model parameter.…”

Section: Rao‐blackwellized Particle Filtermentioning

confidence: 99%

“…Examples of model construction are illustrated in several case studies. 41,42 The warm-up is employed for approximating the initial distribution for each model parameter. For this purpose, it can employ either the Markov chain Monte Carlo or Laplace approximation.…”

Section: Framework Architecturementioning

confidence: 99%

“…For this purpose, it can employ either the Markov chain Monte Carlo or Laplace approximation . The details for the application of these methods to BDLMs are described by Nguyen et al This step ensures that the algorithm does not waste particles at places where the model parameter values are unlikely. Note that the warm‐up step is operated in a batch learning procedure with a small training period.…”

Section: Rao‐blackwellized Particle Filtermentioning

confidence: 99%

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Real‐time anomaly detection with Bayesian dynamic linear models

Nguyen

Goulet

2019

Struct Control Health Monit

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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.

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Uncertainty quantification for model parameters and hidden state variables in Bayesian dynamic linear models

Cited by 4 publications

References 45 publications

SHM-informed life-cycle intelligent maintenance of fatigue-sensitive detail using Bayesian forecasting and Markov decision process

SHM-informed life-cycle intelligent maintenance of fatigue-sensitive detail using Bayesian forecasting and Markov decision process

The Gaussian multiplicative approximation for state‐space models

Real‐time anomaly detection with Bayesian dynamic linear models

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