The first step in data-driven approaches to Structural Health Monitoring (SHM) is that of damage detection. This is a problem that has been well studied in laboratory conditions. Yet, SHM remains an academic topic, not yet widely implemented in industry. One of the main reasons for this is arguably the difficulty in dealing with Environmental and Operational Variabilities (EOVs), which have a tendency to influence damage-sensitive features in ways similar to damage itself. A large number of the methods developed for SHM applications make use of linear Gaussian models for various tasks including dimensionality reduction, density estimation and system identification. A wide range of linear Gaussian models can be formulated as special cases of a general class of probabilistic graphical models, or Bayesian networks. The work presented here discusses how Bayesian networks can be used systematically to approach different types of damage detection problems, through their likelihood function. A likelihood evaluates the probability that an observation belongs to a particular model. If this model correctly captures the undamaged state of the system, then a likelihood can be used as a novelty index, which can point to the presence of damage.
Likelihood functions can be systematically exploited for damage detection purposes across the vast range of linear Gaussian models. One of the key benefits of this fact is that simple models can easily be extended to mixtures of linear Gaussian models. It is shown how this approach can be effective in dealing with operational and environmental variabilities. This thesis thus provides a point of view on performing novelty detection under this wide class of models systematically with their likelihood functions. Models that are typically used for other purposes can become powerful novelty detectors in this view. The relationship between Principal Component Analysis (PCA) and Kalman filters is a good example of this. Under the graphical model perspective these two models are a simple variation of each other, where they model data with and without time dependence. Provided these models are trained with representative data from a non-damaged system, their likelihood function presents a useful novelty index. Their limitation to modelling linear Gaussian data can be overcome through the mixture modelling interpretation. Through graphical models, this is a straightforward extension, but one that retains a probabilistic interpretation.
The impact of this interpretation is that environmental and operational variability, as well as potential nonlinearity, in SHM features can be captured by these models. Even though the interpretation changes depending on the model, the likelihood function can consistently be used as a damage indicator, throughout models like Gaussian mixtures, PCA, Factor Analysis, Autoregressive models, Kalman filters and switching Kalman filters. The work here focuses around these models. There are various ways in which these models can be used, but here the focus is narrowed to exploring them as novelty detectors, and showing their application in different contexts. The context in this case refers to different types of SHM data and features, as this could be either vibration, acoustics, ultrasound, performance metrics, etc.
%The thesis divides into three main sections. The first presents an overview and scope, with introductions to SHM data, machine learning and the use of likelihood functions for novelty detection.
This thesis provides a discussion on the theoretical background for probabilistic graphical models, or Bayesian networks. Separate chapters are dedicated to the discussion of Bayesian networks to model static and dynamic data (with and without temporal dependencies, respectively). Furthermore, three different application examples are presented to demonstrate the use of likelihood function inference for damage detection. These systems are a simulated mass-spring-damper system, with varying stiffness in its non-damaged condition, and with a cubic spring nonlinearity. This system presents a challenge from the point of view of the characterisation of the changing environment in terms of global stiffness and excitation energy. It is shown how mixtures of PCA models can be used to tackle this problem if frequency domain features are used, and mixtures of linear dynamical systems (Kalman filters) can be used to successfully characterise the baseline undamaged system and to identify the presence of damage directly from time domain measurements. Another case study involves the detection of damage on the Z-24 bridge. This is a well-studied problem in SHM research, and it is of interest due to the nonlinear stiffness effect due to temperature changes. The features used here are the first four natural frequencies of the bridge. It is demonstrated how a Gaussian mixture model can characterise the undamaged condition, and its likelihood is able to accurately predict the presence of damage. The third case study involves the prediction of various stages of damage on a wind turbine bearing. This is an experimental laboratory investigation - and the problem is also tackled with a Gaussian mixture model. This problem is of interest because the lowest damage level seeded in the bearing was subsurface yield. This is of great relevance to the wind turbine community, as detecting this level of damage is currently not feasible. Features from Acoustic Emission (AE) measurements were used to train a Gaussian mixture model. It is shown that the likelihood function of this model can correctly predict the presence of damage.
