The idea of pattern recognition (PR) is adopted in many modern approaches to
damage identification. Generally speaking, a PR algorithm simply assigns a class label to a sample of measured data. The appropriate class labels would encode damage type, location and extent. In order to carry out the higher levels of identification using PR, it will almost certainly be necessary to construct examples of data corresponding to each class [4]. Each possible fault class should usually have a training set of measurement vectors that are associated uniquely with it. This type of learning algorithm in which the diagnostic is trained by showing it the desired label for each data set is called supervised learning.
The main drawback of supervised learning is that every possible damage situation should be known and data should be available, for training the algorithm with the class labels, from modelling or experiment. The complexity of systems may cause problems in modelling. Moreover, the damage itself may be difficult to model and it may also make the system dynamically nonlinear: a typical structural example is an opening-closing fatigue crack. For experiment, it is simply not possible to damage a real system for accumulating data from all possible damage configurations.
An alternative is unsupervised learning, which can only be applied for detection
(Level 1 of Section 1.1.3). The techniques are often referred to as novelty detection or anomaly detection methods [71, 72]. In this case, diagnostics is established by using only training data from the normal operating condition of the system. Any significant deviation from training class is identified as a departure from normal condition, i.e. as acquired damage. An important remark is that only significant deviations should be detected: some criteria must be applied in order to distinguish between statistical fluctuations in the data (for example, measurement noise) and a real deviation from normality. An appropriate approach is Statistical Pattern Recognition (SPR).
Another important observation is that there may be variations in the normal conditions that are not statistical: the characteristics of the system may vary with changing environmental conditions, and this must be considered when designing the monitoring system [4]. If the data used to characterise the normal operating condition does not span the whole range of operational and environmental conditions observed in practice, it is likely to signal novelty when a previously unseen condition occurs. A fault will incorrectly be diagnosed.
A technique for preventing this situation to occur, by taking into account all the practical conditions, is presented and applied in Chapters from 2 to 5: it is based on Principal Component Analysis.
Another pattern recognition technique that will be briefly described in Section 1.4.4 is quite different, since it is not based on vibrations. It is the Acoustic Emission method.
1.4.1. Component analysis
Component analysis is a technique of multivariate statistical analysis that can linearly or nonlinearly transform an original set of variables into a substantially smaller set of variables. It can be viewed as a classical method for dimensionality reduction. This technique has been widely applied to virtually every substantive area including cluster analysis, visualization of high-dimensionality data, regression, data compression and pattern recognition.
The Principal Component Analysis (PCA) technique is deeply investigated in Chapter 2, with a discussion (in Section 2.2.5) about other methods based on component analysis. A more detailed description of some extensions of PCA, such as the Kernel-PCA (KPCA) or Local-PCA, can be found in [13]. This reference also introduces a collection of time-domain and frequency-domain statistical features, which should effectively reflect the machine status. PCA is exploited in the first part of this work (Chapters from 2 to 5) for addressing the problem of machine fault diagnosis. However, this technique can be also applied in structural diagnostics, by adopting the identification methods presented in Chapters from 6 to 9 in order to estimate proper features such as the natural frequencies of a structure.
Several papers reported the success of applying component analysis to machine fault diagnosis, often in combination with other pattern recognition techniques. For example, in [73, 74] the combination of component and Support Vector Machine for induction motor fault diagnosis has successfully been implemented. Fault diagnosis of low speed bearings is presented in [12] using a pattern classification method based on Relevance Vector Machine: in this case component analysis was employed with the aim to support the data preparation process. Another class of detection techniques is based on subspace methods: for example, [13] explores subspace-based gearbox condition monitoring using
1.4.2. Vector machine
Vector machine methods are here briefly introduced for completeness, without getting into details.
Support Vector Machine (SVM) is a kind of machine learning technique based on statistical learning theory. The basic idea of applying SVM to pattern classification can be stated as follows [12]: first, map the inputs vectors into one features space, possible in higher space, either linearly or nonlinearly, which is relevant with the kernel function. Then, within the feature space from the first step, seek an optimized linear division, that is, construct a hyperplane which separates two classes. However, this technique can also be extended to multi-class classification. SVM training seeks a global optimized solution and avoid over- fitting, so it has the ability to deal with a large number of features. A complete description about SVM is available in [75].
A more recent method is the Relevance Vector Machine (RVM), that uses Bayesian inference to obtain parsimonious solutions for regression and classification. The RVM has an identical functional form to the SVM, but provides probabilistic classification. Interested readers are suggested to refer to [76].
1.4.3. Subspace methods
Subspace methods can be exploited in different applications such as, in particular, diagnostics of machines and structures. These methods can be considered as part of the pattern recognition framework, since they are applied to condition-based maintenance consisting in the early detection of slight deviations with respect to a characterisation of the system in usual working conditions.
When applied to machine diagnostics, subspace methods have recently been more investigated by researchers and were effectively used in pattern recognition. Subspace methods have the good merits of combining feature extraction and pattern classification into one single step. In the method, data in the original pattern space are projected onto a low-dimensional feature subspace extracted by the redundancy reduction techniques, such as PCA, Independent Component Analysis (ICA) and KPCA. For example, in [13] the KPCA technique was chosen to construct the nonlinear subspace for gearbox condition monitoring.
When structures are considered, in many applications the problem of fault detection is solved by investigating changes in the eigenstructure of a linear dynamical system. Several fault detection algorithms, based on subspace-based identification methods and statistical process techniques, are described for example in [77, 78]. Extensions to damage localisation can be found in [79, 80]. Subspace methods are introduced in Chapter 6 and some new techniques are presented in Chapters from 7 to 9 (with an application in Chapter 10).
1.4.4. The acoustic emission method
The Acoustic Emission (AE) method is a high frequency analysis technique which was initially developed as a non-destructive testing (NDT) tool to detect crack growth in materials and structures. The AE technique can be found in a wide area of applications such as structural health monitoring, machine tool monitoring, tribological and wear process monitoring, gear defects monitoring and bearing fault monitoring.
For example, [81] overviews the modern applications of AE technique for monitoring damage in a variety of structures, and the new approaches that have enabled the successful application of the technique, leading to automated crack detection.
The utility of advanced signal processing algorithms and pattern recognition techniques for bearing acoustic emission to achieve early detection of bearing defects is established in [14]. During the bearing operation, bursts of acoustic emissions result from the passage of the defect through the roller and raceway contacts. Defects at different locations of a bearing will have characteristic frequencies at which bursts are generated. Therefore, the signal of a damaged bearing consists of periodic bursts of AE. The signal is usually considered to be amplitude modulated at the characteristic defect frequency. In the end, modulation of the AE by the characteristic defect frequency makes it possible to detect the presence of a defect and diagnose in what part of the bearing the defect appears. The AE method should have an earlier detection capability than is achieved with vibration; moreover, AE is also found to be a better signal than vibrations when the transducers have to be remotely placed from the bearing. A comprehensive and critical review on the application of Acoustic Emission Technology to condition monitoring and diagnostics of rotating machinery is given in [82].
Chapter 2
Principal Component Analysis
Principal Component Analysis (PCA) is one of the most valuable results from applied linear algebra, widely used in all forms of analysis because it is a simple, non-parametric method of extracting relevant information from confusing data sets. A simplified structure often underlies a complex data set: PCA provides a way for reducing it to a lower dimension to reveal this hidden structure, with simple computational issues.
The goal of this chapter is to provide both an intuitive feel for PCA and a thorough discussion of this topic. The mathematical concepts introduced in Sections 2.1 and 2.2 are taken from the excellent tutorial by Shlens [83]. In Section 2.3, particular attention is given on how PCA can be applied for damage detection.