arXiv subjects

K. Worden

Publications and source records attributed to K. Worden.

At least 19 recordsLinked to original sources

arXiv2026

Latent variable models for simultaneous EOV identification and removal in population-based SHM

The robust treatment of environmental and operational variability (EOV) is an open challenge in population-based structural health monitoring (PBSHM). The difficulty is compounded in the case that the EOV signals are unmeasured. A common approach in conventional SHM is to apply \emph{projection-based} methods that discard subspaces of healthy feature data, reasoning that the EOV signal dominates the variance of the measured features. However, a common pitfall of projection-based approaches is that when damage acts close to the same variance-dominant direction, damage sensitivity is removed along with the EOV. An alternative identifying assumption for the removal of particular unmeasured EOVs is slowness; the latent EOV process is characterised by its long temporal correlation. In this paper, the latent EOV is cast as a state-space Gaussian process, enabling tractable $\mathcal{O}(T)$ inference via a Kalman filter. A robust hierarchical Bayesian identification framework is developed that enables population-level identification of latent EOVs and EOV-free residual features, using a Laplace approximation. The approach is first validated on a single laboratory-scale benchmark structure from the literature, subject to thermal EOVs, demonstrating robust damage detection and EOV recovery. The method is then applied to a simulated nine-turbine offshore wind farm with staggered deployment and damage, where it delivers a substantial true-positive uplift over projection and cointegration-based baselines at matched false-positive rates.

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arXiv2026

Transfer learning via interpolating structures

Despite recent advances in population-based structural health monitoring (PBSHM), knowledge transfer between highly-disparate structures (i.e., heterogeneous populations) remains a challenge. The current work proposes that heterogeneous transfer may be accomplished via intermediate structures that bridge the gap in information between the structures of interest. A key aspect of the technique is the idea that by varying parameters such as material properties and geometry, one structure can be continuously morphed into another. The approach is demonstrated via a case study involving the parameterisation of (and transfer between) simulated heterogeneous bridge designs (Case 1). Transfer between simplified physical representations of a 'bridge' and 'aeroplane' is then demonstrated in Case 2, via a chain of finite-element models. The facetious question 'When is a bridge not an aeroplane?' has been previously asked in the context of predicting positive transfer based on structural similarity. While the obvious answer to this question is 'Always,' the results presented in the current paper show that, in some cases, positive transfer can indeed be achieved between highly-disparate systems.

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arXiv2025

Active transfer learning for structural health monitoring

Data for training structural health monitoring (SHM) systems are often expensive and/or impractical to obtain, particularly for labelled data. Population-based SHM (PBSHM) aims to address this limitation by leveraging data from multiple structures. However, data from different structures will follow distinct distributions, potentially leading to large generalisation errors for models learnt via conventional machine learning methods. To address this issue, transfer learning -- in the form of domain adaptation (DA) -- can be used to align the data distributions. Most previous approaches have only considered \emph{unsupervised} DA, where no labelled target data are available; they do not consider how to incorporate these technologies in an online framework -- updating as labels are obtained throughout the monitoring campaign. This paper proposes a Bayesian framework for DA in PBSHM, that can improve unsupervised DA mappings using a limited quantity of labelled target data. In addition, this model is integrated into an active sampling strategy to guide inspections to select the most informative observations to label -- leading to further reductions in the required labelled data to learn a target classifier. The effectiveness of this methodology is evaluated on a population of experimental bridges. Specifically, this population includes data corresponding to several damage states, as well as, a comprehensive set of environmental conditions. It is found that combining transfer learning and active learning can improve data efficiency when learning classification models in label-scarce scenarios. This result has implications for data-informed operation and maintenance of structures, suggesting a reduction in inspections over the operational lifetime of a structure -- and therefore a reduction in operational costs -- can be achieved.

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arXiv2025

Physics-informed transfer learning for SHM via feature selection

Data used for training structural health monitoring (SHM) systems are expensive and often impractical to obtain, particularly labelled data. Population-based SHM presents a potential solution to this issue by considering the available data across a population of structures. However, differences between structures will mean the training and testing distributions will differ; thus, conventional machine learning methods cannot be expected to generalise between structures. To address this issue, transfer learning (TL), can be used to leverage information across related domains. An important consideration is that the lack of labels in the target domain limits data-based metrics to quantifying the discrepancy between the marginal distributions. Thus, a prerequisite for the application of typical unsupervised TL methods is to identify suitable source structures (domains), and a set of features, for which the conditional distributions are related to the target structure. Generally, the selection of domains and features is reliant on domain expertise; however, for complex mechanisms, such as the influence of damage on the dynamic response of a structure, this task is not trivial. In this paper, knowledge of physics is leveraged to select more similar features, the modal assurance criterion (MAC) is used to quantify the correspondence between the modes of healthy structures. The MAC is shown to have high correspondence with a supervised metric that measures joint-distribution similarity, which is the primary indicator of whether a classifier will generalise between domains. The MAC is proposed as a measure for selecting a set of features that behave consistently across domains when subjected to damage, i.e. features with invariance in the conditional distributions. This approach is demonstrated on numerical and experimental case studies to verify its effectiveness in various applications.

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arXiv2025

On the use of Statistical Learning Theory for model selection in Structural Health Monitoring

Whenever data-based systems are employed in engineering applications, defining an optimal statistical representation is subject to the problem of model selection. This paper focusses on how well models can generalise in Structural Health Monitoring (SHM). Although statistical model validation in this field is often performed heuristically, it is possible to estimate generalisation more rigorously using the bounds provided by Statistical Learning Theory (SLT). Therefore, this paper explores the selection process of a kernel smoother for modelling the impulse response of a linear oscillator from the perspective of SLT. It is demonstrated that incorporating domain knowledge into the regression problem yields a lower guaranteed risk, thereby enhancing generalisation.

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arXiv2024

Anomaly Detection in Offshore Wind Turbine Structures using Hierarchical Bayesian Modelling

Population-based structural health monitoring (PBSHM), aims to share information between members of a population. An offshore wind (OW) farm could be considered as a population of nominally-identical wind-turbine structures. However, benign variations exist among members, such as geometry, sea-bed conditions and temperature differences. These factors could influence structural properties and therefore the dynamic response, making it more difficult to detect structural problems via traditional SHM techniques. This paper explores the use of a hierarchical Bayesian model to infer expected soil stiffness distributions at both population and local levels, as a basis to perform anomaly detection, in the form of scour, for new and existing turbines. To do this, observations of natural frequency will be generated as though they are from a small population of wind turbines. Differences between individual observations will be introduced by postulating distributions over the soil stiffness and measurement noise, as well as reducing soil depth (to represent scour), in the case of anomaly detection.

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arXiv2023

Population-based wind farm monitoring based on a spatial autoregressive approach

An important challenge faced by wind farm operators is to reduce operation and maintenance cost. Structural health monitoring provides a means of cost reduction through minimising unnecessary maintenance trips as well as prolonging turbine service life. Population-based structural health monitoring can further reduce the cost of health monitoring systems by implementing one system for multiple structures (i.e.~turbines). At the same time, shared data within a population of structures may improve the predictions of structural behaviour. To monitor turbine performance at a population/farm level, an important initial step is to construct a model that describes the behaviour of all turbines under normal conditions. This paper proposes a population-level model that explicitly captures the spatial and temporal correlations (between turbines) induced by the wake effect. The proposed model is a Gaussian process-based spatial autoregressive model, named here a GP-SPARX model. This approach is developed since (a) it reflects our physical understanding of the wake effect, and (b) it benefits from a stochastic data-based learner. A case study is provided to demonstrate the capability of the GP-SPARX model in capturing spatial and temporal variations as well as its potential applicability in a health monitoring system.

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arXiv2023

Towards a population-informed approach to the definition of data-driven models for structural dynamics

Machine learning has affected the way in which many phenomena for various domains are modelled, one of these domains being that of structural dynamics. However, because machine-learning algorithms are problem-specific, they often fail to perform efficiently in cases of data scarcity. To deal with such issues, combination of physics-based approaches and machine learning algorithms have been developed. Although such methods are effective, they also require the analyser's understanding of the underlying physics of the problem. The current work is aimed at motivating the use of models which learn such relationships from a population of phenomena, whose underlying physics are similar. The development of such models is motivated by the way that physics-based models, and more specifically finite element models, work. Such models are considered transferrable, explainable and trustworthy, attributes which are not trivially imposed or achieved for machine-learning models. For this reason, machine-learning approaches are less trusted by industry and often considered more difficult to form validated models. To achieve such data-driven models, a population-based scheme is followed here and two different machine-learning algorithms from the meta-learning domain are used. The two algorithms are the model-agnostic meta-learning (MAML) algorithm and the conditional neural processes (CNP) model. The algorithms seem to perform as intended and outperform a traditional machine-learning algorithm at approximating the quantities of interest. Moreover, they exhibit behaviour similar to traditional machine learning algorithms (e.g. neural networks or Gaussian processes), concerning their performance as a function of the available structures in the training population.

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arXiv2023

On the hierarchical Bayesian modelling of frequency response functions

For situations that may benefit from information sharing among datasets, e.g., population-based SHM of similar structures, the hierarchical Bayesian approach provides a useful modelling structure. Hierarchical Bayesian models learn statistical distributions at the population (or parent) and the domain levels simultaneously, to bolster statistical strength among the parameters. As a result, variance is reduced among the parameter estimates, particularly when data are limited. In this paper, a combined probabilistic FRF model is developed for a small population of nominally-identical helicopter blades, using a hierarchical Bayesian structure, to support information transfer in the context of sparse data. The modelling approach is also demonstrated in a traditional SHM context, for a single helicopter blade exposed to varying temperatures, to show how the inclusion of physics-based knowledge can improve generalisation beyond the training data, in the context of scarce data. These models address critical challenges in SHM, by accommodating benign variations that present as differences in the underlying dynamics, while also considering (and utilising), the similarities among the domains.

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arXiv2023

A probabilistic approach for acoustic emission based monitoring techniques: with application to structural health monitoring

It has been demonstrated that acoustic-emission (AE), inspection of structures can offer advantages over other types of monitoring techniques in the detection of damage; namely, an increased sensitivity to damage, as well as an ability to localise its source. There are, however, numerous challenges associated with the analysis of AE data. One issue is the high sampling frequencies required to capture AE activity. In just a few seconds, a recording can generate very high volumes of data, of which a significant portion may be of little interest for analysis. Identifying the individual AE events in a recorded time-series is therefore a necessary procedure to reduce the size of the dataset. Another challenge that is also generally encountered in practice, is determining the sources of AE, which is an important exercise if one wishes to enhance the quality of the diagnostic scheme. In this paper, a state-of-the-art technique is presented that can automatically identify AE events, and simultaneously help in their characterisation from a probabilistic perspective. A nonparametric Bayesian approach, based on the Dirichlet process (DP), is employed to overcome some of the challenges associated with these tasks. Two main sets of AE data are considered in this work: (1) from a journal bearing in operation, and (2) from an Airbus A320 main landing gear subjected to fatigue testing.

stat.AP↗

arXiv2023

Better Together: Using Multi-task Learning to Improve Feature Selection within Structural Datasets

There have been recent efforts to move to population-based structural health monitoring (PBSHM) systems. One area of PBSHM which has been recognised for potential development is the use of multi-task learning (MTL); algorithms which differ from traditional independent learning algorithms. Presented here is the use of the MTL, ''Joint Feature Selection with LASSO'', to provide automatic feature selection for a structural dataset. The classification task is to differentiate between the port and starboard side of a tailplane, for samples from two aircraft of the same model. The independent learner produced perfect F1 scores but had poor engineering insight; whereas the MTL results were interpretable, highlighting structural differences as opposed to differences in experimental set-up.

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arXiv2023

A Meta-Learning Approach to Population-Based Modelling of Structures

A major problem of machine-learning approaches in structural dynamics is the frequent lack of structural data. Inspired by the recently-emerging field of population-based structural health monitoring (PBSHM), and the use of transfer learning in this novel field, the current work attempts to create models that are able to transfer knowledge within populations of structures. The approach followed here is meta-learning, which is developed with a view to creating neural network models which are able to exploit knowledge from a population of various tasks to perform well in newly-presented tasks, with minimal training and a small number of data samples from the new task. Essentially, the method attempts to perform transfer learning in an automatic manner within the population of tasks. For the purposes of population-based structural modelling, the different tasks refer to different structures. The method is applied here to a population of simulated structures with a view to predicting their responses as a function of some environmental parameters. The meta-learning approach, which is used herein is the model-agnostic meta-learning (MAML) approach; it is compared to a traditional data-driven modelling approach, that of Gaussian processes, which is a quite effective alternative when few data samples are available for a problem. It is observed that the models trained using meta-learning approaches, are able to outperform conventional machine learning methods regarding inference about structures of the population, for which only a small number of samples are available. Moreover, the models prove to learn part of the physics of the problem, making them more robust than plain machine-learning algorithms. Another advantage of the methods is that the structures do not need to be parametrised in order for the knowledge transfer to be performed.

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arXiv2022

On an Application of Generative Adversarial Networks on Remaining Lifetime Estimation

A major problem of structural health monitoring (SHM) has been the prognosis of damage and the definition of the remaining useful life of a structure. Both tasks depend on many parameters, many of which are often uncertain. Many models have been developed for the aforementioned tasks but they have been either deterministic or stochastic with the ability to take into account only a restricted amount of past states of the structure. In the current work, a generative model is proposed in order to make predictions about the damage evolution of structures. The model is able to perform in a population-based SHM (PBSHM) framework, to take into account many past states of the damaged structure, to incorporate uncertainties in the modelling process and to generate potential damage evolution outcomes according to data acquired from a structure. The algorithm is tested on a simulated damage evolution example and the results reveal that it is able to provide quite confident predictions about the remaining useful life of structures within a population.

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arXiv2022

On generative models as the basis for digital twins

A framework is proposed for generative models as a basis for digital twins or mirrors of structures. The proposal is based on the premise that deterministic models cannot account for the uncertainty present in most structural modelling applications. Two different types of generative models are considered here. The first is a physics-based model based on the stochastic finite element (SFE) method, which is widely used when modelling structures that have material and loading uncertainties imposed. Such models can be calibrated according to data from the structure and would be expected to outperform any other model if the modelling accurately captures the true underlying physics of the structure. The potential use of SFE models as digital mirrors is illustrated via application to a linear structure with stochastic material properties. For situations where the physical formulation of such models does not suffice, a data-driven framework is proposed, using machine learning and conditional generative adversarial networks (cGANs). The latter algorithm is used to learn the distribution of the quantity of interest in a structure with material nonlinearities and uncertainties. For the examples considered in this work, the data-driven cGANs model outperform the physics-based approach. Finally, an example is shown where the two methods are coupled such that a hybrid model approach is demonstrated.

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arXiv2022

On partitioning of an SHM problem and parallels with transfer learning

In the current work, a problem-splitting approach and a scheme motivated by transfer learning is applied to a structural health monitoring problem. The specific problem in this case is that of localising damage on an aircraft wing. The original experiment is described, together with the initial approach, in which a neural network was trained to localise damage. The results were not ideal, partly because of a scarcity of training data, and partly because of the difficulty in resolving two of the damage cases. In the current paper, the problem is split into two sub-problems and an increase in classification accuracy is obtained. The sub-problems are obtained by separating out the most difficult-to-classify damage cases. A second approach to the problem is considered by adopting ideas from transfer learning (usually applied in much deeper) networks to see if a network trained on the simpler damage cases can help with feature extraction in the more difficult cases. The transfer of a fixed trained batch of layers between the networks is found to improve classification by making the classes more separable in the feature space and to speed up convergence.

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arXiv2022

On generating parametrised structural data using conditional generative adversarial networks

A powerful approach, and one of the most common ones in structural health monitoring (SHM), is to use data-driven models to make predictions and inferences about structures and their condition. Such methods almost exclusively rely on the quality of the data. Within the SHM discipline, data do not always suffice to build models with satisfactory accuracy for given tasks. Even worse, data may be completely missing from one's dataset, regarding the behaviour of a structure under different environmental conditions. In the current work, with a view to confronting such issues, the generation of artificial data using a variation of the generative adversarial network (GAN) algorithm, is used. The aforementioned variation is that of the conditional GAN or cGAN. The algorithm is not only used to generate artificial data, but also to learn transformations of manifolds according to some known parameters. Assuming that the structure's response is represented by points in a manifold, part of the space will be formed due to variations in external conditions affecting the structure. This idea proves efficient in SHM, as it is exploited to generate structural data for specific values of environmental coefficients. The scheme is applied here on a simulated structure which operates under different temperature and humidity conditions. The cGAN is trained on data for some discrete values of the temperature within some range, and is able to generate data for every temperature in this range with satisfactory accuracy. The novelty, compared to classic regression in similar problems, is that the cGAN allows unknown environmental parameters to affect the structure and can generate whole manifolds of data for every value of the known parameters, while the unknown ones vary within the generated manifolds.

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arXiv2022

On an application of graph neural networks in population based SHM

Attempts have been made recently in the field of population-based structural health monitoring (PBSHM), to transfer knowledge between SHM models of different structures. The attempts have been focussed on homogeneous and heterogeneous populations. A more general approach to transferring knowledge between structures, is by considering all plausible structures as points on a multidimensional base manifold and building a fibre bundle. The idea is quite powerful, since, a mapping between points in the base manifold and their fibres, the potential states of any arbitrary structure, can be learnt. A smaller scale problem, but still useful, is that of learning a specific point of every fibre, i.e. that corresponding to the undamaged state of structures within a population. Under the framework of PBSHM, a data-driven approach to the aforementioned problem is developed. Structures are converted into graphs and inference is attempted within a population, using a graph neural network (GNN) algorithm. The algorithm solves a major problem existing in such applications. Structures comprise different sizes and are defined as abstract objects, thus attempting to perform inference within a heterogeneous population is not trivial. The proposed approach is tested in a simulated population of trusses. The goal of the application is to predict the first natural frequency of trusses of different sizes, across different environmental temperatures and having different bar member types. After training the GNN using part of the total population, it was tested on trusses that were not included in the training dataset. Results show that the accuracy of the regression is satisfactory even in structures with higher number of nodes and members than those used to train it.

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arXiv2022

On the application of generative adversarial networks for nonlinear modal analysis

Linear modal analysis is a useful and effective tool for the design and analysis of structures. However, a comprehensive basis for nonlinear modal analysis remains to be developed. In the current work, a machine learning scheme is proposed with a view to performing nonlinear modal analysis. The scheme is focussed on defining a one-to-one mapping from a latent `modal' space to the natural coordinate space, whilst also imposing orthogonality of the mode shapes. The mapping is achieved via the use of the recently-developed cycle-consistent generative adversarial network (cycle-GAN) and an assembly of neural networks targeted on maintaining the desired orthogonality. The method is tested on simulated data from structures with cubic nonlinearities and different numbers of degrees of freedom, and also on data from an experimental three-degree-of-freedom set-up with a column-bumper nonlinearity. The results reveal the method's efficiency in separating the `modes'. The method also provides a nonlinear superposition function, which in most cases has very good accuracy.

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