On robust regression analysis as a means of exploring environmental and operational conditions for SHM data

In the data-based approach to structural health monitoring (SHM), the absence of data from damaged structures in many cases forces a dependence on novelty detection as a means of diagnosis. Unfortunately, this means that benign variations in the operating or environmental conditions of the structure must be handled very carefully, lest they lead to false alarms. If novelty detection is implemented in terms of outlier detection, the outliers may arise in the data as the result of both benign and malign causes and it is important to understand their sources. Comparatively recent developments in the field of robust regression have the potential to provide ways of exploring and visualising SHM data as a means of shedding light on the different origins of outliers. The current paper will illustrate the use of robust regression for SHM data analysis through experimental data acquired from the Z24 and Tamar Bridges, although the methods are general and not restricted to SHM or civil infrastructure

Is it worth changing pattern recognition methods for structural health monitoring?

The key element of this work is to demonstrate alternative strategies for using pattern recognition algorithms whilst investigating structural health monitoring. This paper looks to determine if it makes any difference in choosing from a range of established classification techniques: from decision trees and support vector machines, to Gaussian processes. Classification algorithms are tested on adjustable synthetic data to establish performance metrics, then all techniques are applied to real SHM data. To aid the selection of training data, an informative chain of artificial intelligence tools is used to explore an active learning interaction between meaningful clusters of data

Simplifying transformations for nonlinear systems: Part II, statistical analysis of harmonic cancellation

The first paper in this short sequence described the idea of a simplifying transformation and applied the concept to a numerical optimisation-based variant of normal form analysis. The idea of the numerical normal form transformation was simply to eliminate or reduce the contribution of a pre-defined set of harmonics in the system response. It was shown that reducing the defined harmonics could lead to amplification of other components of the response. The idea of the current paper is to conduct a Monte Carlo worst-case analysis to investigate how badly unconstrained harmonics might be amplified by the optimisation

Robust methods for outlier detection and regression for SHM applications.

In this paper, robust statistical methods are presented for the data-based approach to structural health monitoring (SHM). The discussion initially focuses on the high level removal of the ‘masking effect’ of inclusive outliers. Multiple outliers commonly occur when novelty detection in the form of unsupervised learning is utilised as a means of damage diagnosis; then benign variations in the operating or environmental conditions of the structure must be handled very carefully, as it is possible that they can lead to false alarms. It is shown that recent developments in the field of robust regression can provide a means of exploring and visualising SHM data as a tool for exploring the different characteristics of outliers, and removing the effects of benign variations. The paper is not, in any sense, a survey; it is an overview and summary of recent work by the authors

On the usage of active learning for SHM

The key element of this work is to demonstrate a strategy for using pattern recognition algorithms to investigate correlations between feature variables for Structural Health Monitoring (SHM). The task will take advantage of data from a bridge. An informative chain of artificial intelligence tools will allow an active learning interaction between the unfolded shapes of the manifold of online data by characterising the physical shape between variables. In many data mining and machine learning applications, there is a significant supply of unlabelled data but an important undersupply of labelled data. Semi-supervised active learning, which combines both labelled and unlabelled data can offer serious access to useful information and may be the crucial element in successful decision making, regarding the health of structures

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

Model selection and parameter estimation in structural dynamics using approximate Bayesian computation

This paper will introduce the use of the approximate Bayesian computation (ABC) algorithm for model selection and parameter estimation in structural dynamics. ABC is a likelihood-free method typically used when the likelihood function is either intractable or cannot be approached in a closed form. To circumvent the evaluation of the likelihood function, simulation from a forward model is at the core of the ABC algorithm. The algorithm offers the possibility to use different metrics and summary statistics representative of the data to carry out Bayesian inference. The efficacy of the algorithm in structural dynamics is demonstrated through three different illustrative examples of nonlinear system identification: cubic and cubic-quintic models, the Bouc-Wen model and the Duffing oscillator. The obtained results suggest that ABC is a promising alternative to deal with model selection and parameter estimation issues, specifically for systems with complex behaviours

Outlier ensembles: A robust method for damage detection and unsupervised feature extraction from high-dimensional data

Outlier ensembles are shown to provide a robust method for damage detection and dimension reduction via a wholly unsupervised framework. Most interestingly, when utilised for feature extraction, the proposed heuristic defines features that enable near-equivalent classification performance (95.85%) when compared to the features found (in previous work) through supervised techniques (97.39%) — specifically, a genetic algorithm. This is significant for practical applications of structural health monitoring, where labelled data are rarely available during data mining. Ensemble analysis is applied to practical examples of problematic engineering data; two case studies are presented in this work. Case study I illustrates how outlier ensembles can be used to expose outliers hidden within a dataset. Case study II demonstrates how ensembles can be utilised as a tool for robust outlier analysis and feature extraction in a noisy, high-dimensional feature-space

A probabilistic risk-based decision framework for structural health monitoring

Obtaining the ability to make informed decisions regarding the operation and maintenance of structures, provides a major incentive for the implementation of structural health monitoring (SHM) systems. Probabilistic risk assessment (PRA) is an established methodology that allows engineers to make risk-informed decisions regarding the design and operation of safety-critical and high-value assets in industries such as nuclear and aerospace. The current paper aims to formulate a risk-based decision framework for structural health monitoring that combines elements of PRA with the existing SHM paradigm. As an apt tool for reasoning and decision-making under uncertainty, probabilistic graphical models serve as the foundation of the framework. The framework involves modelling failure modes of structures as Bayesian network representations of fault trees and then assigning costs or utilities to the failure events. The fault trees allow for information to pass from probabilistic classifiers to influence diagram representations of decision processes whilst also providing nodes within the graphical model that may be queried to obtain marginal probability distributions over local damage states within a structure. Optimal courses of action for structures are selected by determining the strategies that maximise expected utility. The risk-based framework is demonstrated on a realistic truss-like structure and supported by experimental data. Finally, a discussion of the risk-based approach is made and further challenges pertaining to decision-making processes in the context of SHM are identified

Foundations of population-based SHM, part III : heterogeneous populations – mapping and transfer

This is the third and final paper in a series laying foundations for a theory/methodology of Population-Based Structural Health Monitoring (PBSHM). PBSHM involves utilising knowledge from one set of structures in a population and applying it to a different set, such that predictions about the health states of each member in the population can be performed and improved. Central ideas behind PBSHM are those of knowledge transfer and mapping. In the context of PBSHM, knowledge transfer involves using information from a source domain structure, where labels are known for given feature sets, and mapping these onto the unlabelled feature space of a different, target domain structure. This mapping means a classifier trained on the transformed source domain data will generalise to the unlabelled target domain data; i.e. a classifier built on one structure will generalise to another, making Structural Heath Monitoring (SHM) cost-effective and applicable to a wide range of challenging industrial scenarios. This process of mapping features and labels across source and target domains is defined here via domain adaptation, a subcategory of transfer learning. A mathematical underpinning for when domain adaptation is possible in a structural dynamics context is provided, with reference to topology within a graphical representation of structures. Subsequently, a novel procedure for performing domain adaptation on topologically different structures is outlined