On Novel Approaches to Model-Based Structural Health Monitoring

Structural health monitoring (SHM) strategies have classically fallen into two main categories of approach: model-driven and data-driven methods. The former utilises physics-based models and inverse techniques as a method for inferring the health state of a structure from changes to updated parameters; hence defined as inverse model-driven approaches. The other frames SHM within a statistical pattern recognition paradigm. These methods require no physical modelling, instead inferring relationships between data and health states directly. Although successes with both approaches have been made, they both suffer from significant drawbacks, namely parameter estimation and interpretation difficulties within the inverse model-driven framework, and a lack of available full-system damage state data for data-driven techniques. Consequently, this thesis seeks to outline and develop a framework for an alternative category of approach; forward model-driven SHM. This class of strategies utilise calibrated physics-based models, in a forward manner, to generate health state data (i.e. the undamaged condition and damage states of interest) for training machine learning or pattern recognition technologies. As a result the framework seeks to provide potential solutions to these issues by removing the need for making health decisions from updated parameters and providing a mechanism for obtaining health state data. In light of this objective, a framework for forward model-driven SHM is established, highlighting key challenges and technologies that are required for realising this category of approach. The framework is constructed from two main components: generating physics-based models that accurately predict outputs under various damage scenarios, and machine learning methods used to infer decision bounds. This thesis deals with the former, developing technologies and strategies for producing statistically representative predictions from physics-based models. Specifically this work seeks to define validation within this context and propose a validation strategy, develop technologies that infer uncertainties from various sources, including model discrepancy, and offer a solution to the issue of validating full-system predictions when data is not available at this level. The first section defines validation within a forward model-driven context, offering a strategy of hypothesis testing, statistical distance metrics, visualisation tools, such as the witness function, and deterministic metrics. The statistical distances field is shown to provide a wealth of potential validation metrics that consider whole probability distributions. Additionally, existing validation metrics can be categorised within this fields terminology, providing greater insight. In the second part of this study emulator technologies, specifically Gaussian Process (GP) methods, are discussed. Practical implementation considerations are examined, including the establishment of validation and diagnostic techniques. Various GP extensions are outlined, with particular focus on technologies for dealing with large data sets and their applicability as emulators. Utilising these technologies two techniques for calibrating models, whilst accounting for and inferring model discrepancies, are demonstrated: Bayesian Calibration and Bias Correction (BCBC) and Bayesian History Matching (BHM). Both methods were applied to representative building structures in order to demonstrate their effectiveness within a forward model-driven SHM strategy. Sequential design heuristics were developed for BHM along with an importance sampling based technique for inferring the functional model discrepancy uncertainties. The third body of work proposes a multi-level uncertainty integration strategy by developing a subfunction discrepancy approach. This technique seeks to construct a methodology for producing valid full-system predictions through a combination of validated sub-system models where uncertainties and model discrepancy have been quantified. This procedure is demonstrated on a numerical shear structure where it is shown to be effective. Finally, conclusions about the aforementioned technologies are provided. In addition, a review of the future directions for forward model-driven SHM are outlined with the hope that this category receives wider investigation within the SHM community

A probabilistic framework for forward model-driven SHM

A challenge for many structural health monitoring (SHM) technologies is the lack of available damage state data. This problem arises due to cost implications of damaging a structure in addition to issues associated with the feasibility and safety of testing a structure in multiple damage scenarios. Many data-driven approaches to SHM are successful when the appropriate damage state data is available, however the problem of obtaining data for various damage states of interest restricts their use in industry. Forward model-driven approaches to SHM seek to aid this challenge. This methodology uses validated physical models to generate predictions of the system at different damage states, providing machine learning strategies with training data, to infer decision bounds. An ideal forward model-driven SHM framework is one in which one or more physical models are able to produce predictions that are statistically representative of data obtained from the physical structure. Validation of these physical models requires observational data. As a result, validation is performed on a component or sub-system level where damage state data can be more easily obtained. This methodology requires the combination of several low-level physical models via a multi-level uncertainty integration technique. This paper outlines such a framework using uncertainty quantification technologies and statistical methods for combining low-level probabilistic models whilst accounting of discrepancies that may occur in interactions with other low-level models. The method contains several statistical techniques for accounting for model discrepancies that may occur at any point throughout the modelling process. Model discrepancies arise due to missing physics or simplifications and result in the model deviating from the observed physics even when the ‘true’ parameters of the model are known. By accounting for model discrepancies throughout the framework the approach allows for further insight into model form errors whilst also improving the techniques ability to produce statistically representative predictions across damage states. The paper presents the key stages highlighting the relevant technologies and application considerations. Additionally, a discussion of integration with current data-driven approaches and the appropriate machine learning tools is given for a forward model-driven SHM approach