Quantification of the uncertainty in forecasts using structural health monitoring data: A Bayesian approach

The advancement in structural health monitoring technology has been evolving from monitoring-based diagnosis to monitoring-based prognosis. While vibration-based methods using fast-varying structural response data (e.g. acceleration) have enjoyed thriving developments for structural health diagnosis over the past decades, a methodological framework suitable for handling both slow-varying structural response data (e.g. strain and displacement) and fast-varying structural response data in time series is more favourable for structural health prognosis. This proposal is aimed at developing a unified framework for estimation and forecasting of structural health in connection with slow-varying and fast-varying time series monitoring data. In recognising their flexibility, state space models consisting in observation equation and system equation will be formulated in terms of dynamic linear model and its extensions in the Bayesian context to underpin the desired methodological framework. The dynamic linear model is an elegant system approach to handling time series data from a Bayesian perspective. In contrast to classical autoregressive and moving average (ARMA) models which rest on stationarity, the dynamic linear model in the Bayesian context accommodates both stationary and non-stationary time series data. It is able to directly capture features of time series data, such as trend, seasonality, and regression effects. More importantly, the dynamic linear model allows for the description of temporary or permanent shifts in time series parameters that occur abruptly, which is necessary for outlier and damage detection in structural health monitoring paradigm. While uncertainty is inevitable in time series monitoring data and in forecasts based on time series data, the Bayesian approach provides a perfect tool for representing the uncertainty in time series models and quantifying the uncertainty in forecasts in line with time series data. The Bayesian calculation of complex systems has become tractable since the advent of Markov chain Monte Carlo (MCMC) methods.In this research project, generic dynamic linear models in the Bayesian context will first be developed which enable the representation and forecast of both slow-varying and fast-varying structural response time series data, catering for the description of trend, seasonality, and regression effects. Then, in the Bayesian forecasting and dynamic modelling context, methods for detecting outliers and detecting changes in parameter regimes will be developed for application to structural health monitoring. Field monitoring data from an instrumented bridge and from an in-service high-speed train will be applied for examining the forecast accuracy and verifying the outlier and damage/defect detection and distinction capabilities.