Elizabeth J. Cross

Cointegration: a novel approach for the removal of environmental trends in structural health monitoring data

Before structural health monitoring (SHM) technologies can be reliably implemented on structures outside laboratory conditions, the problem of environmental variability in monitored features must be first addressed. Structures that are subjected to changing environmental or operational conditions will often exhibit inherently non-stationary dynamic and quasi-static responses, which can mask any changes caused by the occurrence of damage. The current work introduces the concept of cointegration, a tool for the analysis of non-stationary time series, as a promising new approach for dealing with the problem of environmental variation in monitored features. If two or more monitored variables from an SHM system are cointegrated, then some linear combination of them will be a stationary residual purged of the common trends in the original dataset. The stationary residual created from the cointegration procedure can be used as a damage-sensitive feature that is independent of the normal environmental and operational conditions.

Features for damage detection with insensitivity to environmental and operational variations

This paper explores and compares the application of three different approaches to the data normalization problem in structural health monitoring (SHM), which concerns the removal of confounding trends induced by varying operational conditions from a measured structural response that correlates with damage. The methodologies for singling out or creating damage-sensitive features that are insensitive to environmental influences explored here include cointegration, outlier analysis and an approach relying on principal component analysis. The application of cointegration is a new idea for SHM from the field of econometrics, and this is the first work in which it has been comprehensively applied to an SHM problem. Results when applying cointegration are compared with results from the more familiar outlier analysis and an approach that uses minor principal components. The ability of these methods for removing the effects of environmental/operational variations from damage-sensitive features is demonstrated and compared with benchmark data from the Brite-Euram project DAMASCOS (BE97 4213), which was collected from a Lamb-wave inspection of a composite panel subject to temperature variations in an environmental chamber.

Approaches to nonlinear cointegration with a view towards applications in SHM

One of the major problems confronting the application of Structural Health Monitoring (SHM) to real structures is that of divorcing the effect of environmental changes from those imposed by damage. A recent development in this area is the import of the technique of cointegration from the field of econometrics. While cointegration is a mature technology within economics, its development has been largely concerned with linear time-series analysis and this places a severe constraint on its application - particularly in the new context of SHM where damage can often make a given structure nonlinear. The objective of the current paper is to introduce two possible approaches to nonlinear cointegration: the first is an optimisation-based method; the second is a variation of the established Johansen procedure based on the use of an augmented basis. Finally, the ideas of nonlinear cointegration will be explored through application to real SHM data from the benchmark project on the Z24 Highway Bridge.

Cointegration and why it works for SHM

One of the most fundamental problems in Structural Health Monitoring (SHM) is that of projecting out operational and environmental variations from measured feature data. The reason for this is that algorithms used for SHM to detect changes in structural condition should not raise alarms if the structure of interest changes because of benign operational or environmental variations. This is sometimes called the data normalisation problem. Many solutions to this problem have been proposed over the years, but a new approach that uses cointegration, a concept from the field of econometrics, appears to provide a very promising solution. The theory of cointegration is mathematically complex and its use is based on the holding of a number of assumptions on the time series to which it is applied. An interesting observation that has emerged from its applications to SHM data is that the approach works very well even though the aforementioned assumptions do not hold in general. The objective of the current paper is to discuss how the cointegration assumptions break down individually in the context of SHM and to explain why this does not invalidate the application of the algorithm.

A nonlinear cointegration approach with applications to structural health monitoring

One major obstacle to the implementation of structural health monitoring (SHM) is the effect of operational and environmental variabilities, which may corrupt the signal of structural degradation. Recently, an approach inspired from the community of econometrics, called cointegration, has been employed to eliminate the adverse influence from operational and environmental changes and still maintain sensitivity to structural damage. However, the linear nature of cointegration may limit its application when confronting nonlinear relations between system responses. This paper proposes a nonlinear cointegration method based on Gaussian process regression (GPR); the method is constructed under the Engle-Granger framework, and tests for unit root processes are conducted both before and after the GPR is applied. The proposed approach is examined with real engineering data from the monitoring of the Z24 Bridge.

Switching Response Surface Models for Structural Health Monitoring of Bridges

Structural health monitoring (SHM) is the discipline of diagnosing damage and estimating safe remaining life for structures and systems. Often SHM is accomplished by detecting changes in measured quantities from the structure of interest; if there are no competing explanations for the changes, one infers that they are the result of damage. If the structure of interest is subject to changes in its environmental or operational conditions, one must understand the effects of these changes in order that one does not falsely claim that damage has occurred when one observes measurement changes. This problem—the problem of confounding influences—is particularly pressing for civil infrastructure where the given structure is usually openly exposed to the weather and may be subject to strongly varying operational conditions. One approach to understanding confounding influences is to construct a data-based response surface model that can represent measurement variations as a function of environmental and operational variables. The models can then be used to remove environmental and operational variations so that change detection algorithms signal the occurrence of damage alone. The current chapter is concerned with such response surface models in the case of SHM of bridges. In particular, classes of response surface models that can switch discontinuously between regimes are discussed.

Modelling environmental effects on the dynamic characteristics of the Tamar suspension bridge

For structural health monitoring purposes, it has become extremely important to understand, model, and compensate for the effect of environmental variations on the dynamic characteristics of structures under their ambient operating conditions. In this paper, acceleration measurement data from the Tamar Suspension Bridge, UK, processed by the data-driven stochastic subspace identification method is investigated, and the environmental variations in the natural frequencies modelled with respect to the temperature and the wind loadings. Two different approaches are considered; 1) Principal Component Analysis (PCA) which effectively identifies a linear variation pattern induced by environmental effects and 2) meta-modelling, a purely mathematical way to find an input-output relationship of a system based on various combinations of polynomial functions. This study found that the temperature was the biggest contributor to the environmental variations of the bridge’s natural frequencies.

Exploring Environmental and Operational Variations in SHM Data Using Heteroscedastic Gaussian Processes

The higher levels of Structural Health Monitoring (SHM)—localisation, classification, severity assessment—are only accessible using supervised learning in the data-based approach. Unfortunately, one does not often have data from damaged structures; this forces a dependence on unsupervised learning i.e. novelty detection. This means that detection is sensitive to benign environmental and operational variations (EOVs) in or around the structure. In this paper a two-stage procedure is presented: identify EOVs in training data using a nonlinear manifold approach and remove EOVs by utilising the interesting tool of heteroscedastic Gaussian processes (GPs). In Classical GPs models, the data noise is assumed to have constant variance throughout the input space. This assumption is a drawback most of the time, and a more robust Bayesian regression tool where GP inference is tractable is needed. In this work a combination of data projection and a non-standard heteroscedastic GP is presented as means of visualising and exploring SHM data.

Some Recent Developments in SHM Based on Nonstationary Time Series Analysis

Many of the algorithms used for structural health monitoring (SHM) are based on, or motivated by, time series analysis. Quite often, detection methods are variants of approaches developed within the statistical process control (SPC) community. Many of the algorithms used represent mature theory and have a rigorous probabilistic or mathematical basis. However, one of the main issues facing SHM practitioners is that the structures of interest rarely respect the assumptions inherent in deriving algorithms. In the case of time series data, SPC-based approaches usually require the data to be stationary and, unfortunately, SHM data are often nonstationary because of benign variations in the environment of the structure of interest, or because of deliberate operational changes in the use of the structure. This nonstationarity can manifest itself as slowly varying trends on the data or in abrupt switches between regimes. Recent work in nonstationary time series methods for SHM has made considerable progress in accommodating nonstationarity and some of that work is discussed within this paper: in terms of understanding slowly varying trends, the cointegration algorithm from econometrics is presented; for understanding abrupt switches, Bayesian mixtures of experts are presented. Another issue in time series analysis is indirectly related to the assumption of linear behavior of structures and the impact of this assumption is briefly considered in terms of its effects on detection thresholds in SPC-like methods; again, progress has been made recently. Some issues still remain, and these are discussed also.

Prediction of landing gear loads using machine learning techniques

This article investigates the feasibility of using machine learning algorithms to predict the loads experienced by a landing gear during landing. For this purpose, the results on drop test data and flight test data will be examined. This article will focus on the use of Gaussian process regression for the prediction of loads on the components of a landing gear. For the learning task, comprehensive measurement data from drop tests are available. These include measurements of strains at key locations, such as on the side-stay and torque link, as well as acceleration measurements of the drop carriage and the gear itself, measurements of shock absorber travel, tyre closure, shock absorber pressure and wheel speed. Ground-to-tyre loads are also available through measurements made with a drop test ground reaction platform. The aim is to train the Gaussian process to predict load at a particular location from other available measurements, such as accelerations, or measurements of the shock absorber. If models can be successfully trained, then future load patterns may be predicted using only these measurements. The ultimate aim is to produce an accurate model that can predict the load at a number of locations across the landing gear using measurements that are readily available or may be measured more easily than directly measuring strain on the gear itself (for example, these may be measurements already available on the aircraft, or from a small number of sensors attached to the gear). The drop test data models provide a positive feasibility test which is the basis for moving on to the critical task of prediction on flight test data. For this, a wide range of available flight test measurements are considered for potential model inputs (excluding strain measurements themselves), before attempting to refine the model or use a smaller number of measurements for the prediction.