Quantifying the value of information transfer in population-based SHM

Population-based structural health monitoring (PBSHM), seeks to address some of the limitations associated with data scarcity that arise in traditional SHM. A tenet of the population-based approach to SHM is that information can be shared between sufficiently-similar structures in order to improve predictive models. Transfer learning techniques, such as domain adaptation, have been shown to be a highly-useful technology for sharing information between structures when developing statistical classifiers for PBSHM. Nonetheless, transfer-learning techniques are not without their pitfalls. In some circumstances, for example if the data distributions associated with the structures within a population are dissimilar, applying transfer-learning methods can be detrimental to classification performance -- this phenomenon is known as negative transfer. Given the potentially-severe consequences of negative transfer, it is prudent for engineers to ask the question `when, what, and how should one transfer between structures?'. The current paper aims to demonstrate a transfer-strategy decision process for a classification task for a population of simulated structures in the context of a representative SHM maintenance problem, supported by domain adaptation. The transfer decision framework is based upon the concept of expected value of information transfer. In order to compute the expected value of information transfer, predictions must be made regarding the classification (and decision performance) in the target domain following information transfer. In order to forecast the outcome of transfers, a probabilistic regression is used here to predict classification performance from a proxy for structural similarity based on the modal assurance criterion.

Sharing Information Between Machine Tools to Improve Surface Finish Forecasting

At present, most surface-quality prediction methods can only perform single-task prediction which results in under-utilised datasets, repetitive work and increased experimental costs. To counter this, the authors propose a Bayesian hierarchical model to predict surface-roughness measurements for a turning machining process. The hierarchical model is compared to multiple independent Bayesian linear regression models to showcase the benefits of partial pooling in a machining setting with respect to prediction accuracy and uncertainty quantification.

A decision framework for selecting information-transfer strategies in population-based SHM

Decision-support for the operation and maintenance of structures provides significant motivation for the development and implementation of structural health monitoring (SHM) systems. Unfortunately, the limited availability of labelled training data hinders the development of the statistical models on which these decision-support systems rely. Population-based SHM seeks to mitigate the impact of data scarcity by using transfer learning techniques to share information between individual structures within a population. The current paper proposes a decision framework for selecting transfer strategies based upon a novel concept -- the expected value of information transfer -- such that negative transfer is avoided. By avoiding negative transfer, and by optimising information transfer strategies using the transfer-decision framework, one can reduce the costs associated with operating and maintaining structures, and improve safety.

When is an SHM problem a Multi-Task-Learning problem?

Multi-task neural networks learn tasks simultaneously to improve individual task performance. There are three mechanisms of multi-task learning (MTL) which are explored here for the context of structural health monitoring (SHM): (i) the natural occurrence of multiple tasks; (ii) using outputs as inputs (both linked to the recent research in population-based SHM (PBSHM)); and, (iii) additional loss functions to provide different insights. Each of these problem settings for MTL is detailed and an example is given.

Towards risk-informed PBSHM: Populations as hierarchical systems

The prospect of informed and optimal decision-making regarding the operation and maintenance (O&M) of structures provides impetus to the development of structural health monitoring (SHM) systems. A probabilistic risk-based framework for decision-making has already been proposed. However, in order to learn the statistical models necessary for decision-making, measured data from the structure of interest are required. Unfortunately, these data are seldom available across the range of environmental and operational conditions necessary to ensure good generalisation of the model. Recently, technologies have been developed that overcome this challenge, by extending SHM to populations of structures, such that valuable knowledge may be transferred between instances of structures that are sufficiently similar. This new approach is termed population-based structural heath monitoring (PBSHM). The current paper presents a formal representation of populations of structures, such that risk-based decision processes may be specified within them. The population-based representation is an extension to the hierarchical representation of a structure used within the probabilistic risk-based decision framework to define fault trees. The result is a series, consisting of systems of systems ranging from the individual component level up to an inventory of heterogeneous populations. The current paper considers an inventory of wind farms as a motivating example and highlights the inferences and decisions that can be made within the hierarchical representation.

On topological data analysis for SHM; an introduction to persistent homology

This paper aims to discuss a method of quantifying the 'shape' of data, via a methodology called topological data analysis. The main tool within topological data analysis is persistent homology; this is a means of measuring the shape of data, from the homology of a simplicial complex, calculated over a range of values. The required background theory and a method of computing persistent homology is presented here, with applications specific to structural health monitoring. These results allow for topological inference and the ability to deduce features in higher-dimensional data, that might otherwise be overlooked. A simplicial complex is constructed for data for a given distance parameter. This complex encodes information about the local proximity of data points. A singular homology value can be calculated from this simplicial complex. Extending this idea, the distance parameter is given for a range of values, and the homology is calculated over this range. The persistent homology is a representation of how the homological features of the data persist over this interval. The result is characteristic to the data. A method that allows for the comparison of the persistent homology for different data sets is also discussed.

On topological data analysis for structural dynamics: an introduction to persistent homology

Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be introduced. The main tool within topological data analysis (TDA) is persistent homology. Persistent homology is a method of quantifying the shape of data over a range of length scales. The required background and a method of computing persistent homology is briefly discussed in this work. Ideas from topological data analysis are then used for nonlinear dynamics to analyse some common attractors, by calculating their embedding dimension, and then to assess their general topologies. A method will also be proposed, that uses topological data analysis to determine the optimal delay for a time-delay embedding. TDA will also be applied to a Z24 Bridge case study in structural health monitoring, where it will be used to scrutinise different data partitions, classified by the conditions at which the data were collected. A metric, from topological data analysis, is used to compare data between the partitions. The results presented demonstrate that the presence of damage alters the manifold shape more significantly than the effects present from temperature.

Mitigating sampling bias in risk-based active learning via an EM algorithm

Risk-based active learning is an approach to developing statistical classifiers for online decision-support. In this approach, data-label querying is guided according to the expected value of perfect information for incipient data points. For SHM applications, the value of information is evaluated with respect to a maintenance decision process, and the data-label querying corresponds to the inspection of a structure to determine its health state. Sampling bias is a known issue within active-learning paradigms; this occurs when an active learning process over- or undersamples specific regions of a feature-space, thereby resulting in a training set that is not representative of the underlying distribution. This bias ultimately degrades decision-making performance, and as a consequence, results in unnecessary costs incurred. The current paper outlines a risk-based approach to active learning that utilises a semi-supervised Gaussian mixture model. The semi-supervised approach counteracts sampling bias by incorporating pseudo-labels for unlabelled data via an EM algorithm. The approach is demonstrated on a numerical example representative of the decision processes found in SHM.

A generalised form for a homogeneous population of structures using an overlapping mixture of Gaussian processes

Reductions in natural frequency are often used as a damage indicator for structural health monitoring (SHM) purposes. However, fluctuations in operational and environmental conditions, changes in boundary conditions, and slight differences among nominally-identical structures can also affect stiffness, producing frequency changes that mimic or mask damage. This variability has limited the practical implementation and generalisation of SHM technologies. The aim of this work is to investigate the effects of normal variation, and to identify methods that account for the resulting uncertainty. This work considers vibration data collected from a set of four healthy full-scale composite helicopter blades. The blades were nominally-identical but distinct, and slight differences in material properties and geometry among the blades caused significant variability in the frequency response functions, which presented as four separate trajectories across the input space. In this paper, an overlapping mixture of Gaussian processes (OMGP), was used to generate labels and quantify the uncertainty of normal-condition frequency response data from the helicopter blades. Using a population-based approach, the OMGP model provided a generic representation, called a form, to characterise the normal condition of the blades. Additional simulated data were then compared against the form and evaluated for damage using a marginal-likelihood novelty index.

Improving decision-making via risk-based active learning: Probabilistic discriminative classifiers

Gaining the ability to make informed decisions on operation and maintenance of structures provides motivation for the implementation of structural health monitoring (SHM) systems. However, descriptive labels for measured data corresponding to health-states of the monitored system are often unavailable. This issue limits the applicability of fully-supervised machine learning paradigms for the development of statistical classifiers to be used in decision-support in SHM systems. One approach to dealing with this problem is risk-based active learning. In such an approach, data-label querying is guided according to the expected value of perfect information for incipient data points. For risk-based active learning in SHM, the value of information is evaluated with respect to a maintenance decision process, and the data-label querying corresponds to the inspection of a structure to determine its health state. In the context of SHM, risk-based active learning has only been considered for generative classifiers. The current paper demonstrates several advantages of using an alternative type of classifier -- discriminative models. Using the Z24 Bridge dataset as a case study, it is shown that discriminative classifiers have benefits, in the context of SHM decision-support, including improved robustness to sampling bias, and reduced expenditure on structural inspections.