This chapter focuses on data-driven approach for detection, estimation and diagnosis of mechanical faults in electrical machines. Vibration monitoring (through accelerometers) is widely used in electrical rotating machines in order to monitor mechanical faults in the machines. The chapter presents the application of statistical feature extraction methods, namely principal component analysis (PCA) and linear discriminant analysis (LDA), along with the Kullback–Leibler divergence to perform vibration monitoring. A frequency domain analysis based on an adequate preprocessing and PCA or LDA will lead to high-level discriminative features extracted from vibration signals. A statistical spectral analysis is proposed in order to detect and identify small bearing faults. The main advantages of this approach are that prior knowledge of the characteristic frequencies is not necessary and besides few PCA/LDA-based features, specifically only two, will be sufficient to differentiate among different types of bearing faults and different fault severities.

Vibration analysis is a powerful tool for condition monitoring of rotating machinery. In the nonstationary case, this analysis often involves denoising and extraction of the time-varying harmonic components buried within the vibration signal. However, the complexity of many contemporary techniques-especially in relation to nonstationary signals-and their dependence on prior knowledge of the system kinematics in order to be effective is an inhibitor to autonomous fault detection and monitoring of nonstationary systems. In this article, a nonparametric, blind spectral preprocessing approach to simultaneously denoise and extract the harmonic content from nonstationary vibration signals is presented. The proposed approach utilizes mean shift clustering in conjunction with the short-time Fourier transform to separate time-varying harmonics from background noise within the frequency spectrum, without the need for a priori knowledge of the system. The technique is fully invertible, allowing the time signals corresponding to the separated time-varying harmonic and residual components to be reconstructed. The performance of the proposed technique is compared against existing preprocessing methods and validated using several industrial data sets: first, using vibration data obtained from a low-speed, nonstationary industrial automated people mover gearbox, next, using vibration data from an aircraft engine containing outer race faults, and finally, using nonstationary vibration data from a wind turbine containing frequent speed fluctuations.

Early detection of small and large leaks in water distribution pipes allows for proactive maintenance and corrective actions to take place in a timely manner, thus mitigating significant water loss and increasing the longevity of the network. Most of the acoustic leak detection methods today are geared toward inspections—focused on probing periodic short-term data acquired in the process of inspection—rather than dealing with large volumes of long-term data acquired from monitoring programs. The common challenge encountered in both the acoustic inspection methods and in long-term monitoring of acoustic signatures lies in delineating weak leak-induced signatures within the highly noisy and nonstationary acoustic environment typical of uncontrolled real-world operating water distribution systems. This paper focuses on addressing the problem of leak detection where long-term monitoring acoustic data is available to characterize the operating conditions, without relying on controlled experiments to acquire data or expert user knowledge. The key contribution of this paper is to present a new data-driven approach using association rules (ARs) to extract information from large volumes of monitored acoustic data which can enable identification of relatively small changes in the acoustic signatures due to leaks. ARs are employed to model and synthesize the information contained in long-term monitored acoustic data and associations between statistical features obtained from such measurements are identified and used to design a leak indicator that captures the deviation of leak-induced data from a reference leak-free model. It will be shown that the proposed indicator has a high detection rate, can detect relatively small leaks, and crucially, conducive to work in uncontrolled long-term monitoring situations.

Small leaks in buried water distribution pipelines run continuously for long periods of time without being detected. They do not produce any appreciable flow or pressure changes at the monitored locations. The non-stationarity of the monitoring data, background noise, and the uncertainties in interpreting sensory information adds complexity to detecting leaks. This paper explores the application of singular spectrum analysis (SSA) in extracting leak components from noisy measurements. SSA is a non-parametric and adaptive method, able to decompose a signal into interpretable components without making linearity or stationarity assumptions. When applied to noisy hydro-acoustic signals, it is shown that the leak signatures are extracted efficiently. A semi-supervised approach for leak detection is presented, in which the SSA decomposition of leak-free historical data is combined with ensemble one-class support vector machine. The results demonstrate the effectiveness of SSA for leak detection in water distribution pipelines.

Singular spectrum analysis (SSA) is a signal decomposition technique that aims at expanding signals into interpretable and physically meaningful components (e.g., sinusoids, noise, etc.). This paper presents new theoretical and practical results about the separability of the SSA and introduces a new method called sliding SSA. First, the SSA is combined with an unsupervised classification algorithm to provide a fully automatic data-driven component extraction method for which we investigate the limitations for components separation in a theoretical study. Second, the detailed automatic SSA method is used to design an approach based on a sliding analysis window, which provides better results than the classical SSA method when analyzing nonstationary signals with a time-varying number of components. Finally, the proposed sliding SSA method is compared to the empirical mode decomposition and to the synchrosqueezed short-time Fourier transform, applied on both synthetic and real-world signals.

In this paper, we introduce the ASTRES* toolbox which offers a set of Matlab functions for non-stationary multi-component signal processing. The main purposes of this proposal is to offer efficient tools for analysis, synthesis and transformation of any signal made of physically meaningful components (e.g. sinusoid, trend or noise). The proposed techniques contain some recent and new contributions, which are now unified and theoretically strengthened. They can provide efficient time-frequency or time-scale representations and they allow elementary components extraction. Usage and description of each method are then detailed and numerically illustrated.

This paper is a contribution to the detection and characterisation of small cracks using Eddy Current Testing in the Non Destructive Evaluation framework. Small cracks are considered as incipient faults defined as gradual faults whose signature is weak and concealed by the noise. They are characterized by high signal to noise ratio and low fault to noise ratio. The detection and diagnosis of such faults is still an open challenge. For complex systems, model-based incipient fault detection and diagnosis (FDD) methods usually fail because of the inaccuracy of the model to describe all the phenomena and their interactions. Data-driven methods using statistical features are very promising as long as historical data are available. However in the case of incipient faults, there is not a significant variation of a single feature. The fault signature lies in the global variation of the signal properties. The proposed method relies on the Kullback-Leibler Divergence (KLD) as a nonparametric fault indicator. It measures the slight dissimilarities between the probability density functions of the current signal compared to the faultless or healthy one. Through experimental results, the KLD exhibits a higher sensitivity than the usual statistical features for the detection of small cracks (with dimensions in the order of 0.1 mm) realized in a nickel-based superalloy plate. Moreover, the detection is done with zero missed detection probability. Furthermore, the fault severity is assessed through the characteristics of the crack (surface, length, and depth). In the principal component analysis framework, the analysis of four statistical features (KLD, mean, variance, and maximum) dependency to the excitation frequency allows to discriminating among the cracks.

The Kullback–Leibler (KL) divergence is at the centre of Information Theory and change detection. It is characterized with a high sensitivity to incipient faults that cause unpredictable small changes in the process measurements. This work yields an analytical model based on the KL divergence to estimate the incipient fault magnitude in multivariate processes. In practice, the divergence has no closed form and it must be numerically approximated. In the particular case of incipient fault, the numerical approximation of the divergence causes many false alarms and missed detections because of the slight effect of the incipient fault. In this paper, the ability and relevance to estimate the incipient fault amplitude using the numerical divergence is studied. The divergence is approximated through the calculation of discrete probabilities for faultless and faulty signals. The estimation results that are obtained by simulation induce an error lower than 1% on the fault amplitude.

Most statistics for fault detection in engineering systems are designed to detect shifts in the process distribution parameters, such as mean or variance shifts. The incipient fault is, however, more likely to affect the probability distributions in an unpredictable (random) manner. It causes slight distortions along the distribution shape rather than a particular parametric change. In this paper, it will be shown that the detection of such a fault requires rather nonparametric informational distances, which measure the dissimilarity between two probability distributions. In particular, The Kullback-Leibler (KL) divergence is proposed to be a fault indicator. Once it has been applied to eddy-currents testing (ECT) signals, it is shown able to reveal the signature of minor cracks (0.01 mm2). The KL divergence, viewed as a global fault indicator, will be compared to the local statistical moments. It is going to show a higher sensitivity to the imperceptible changes, which are caused by minor cracks.

Conventionally, Singular Spectral Analysis (SSA) is seen as a technique of decomposition of a signal into periodic components, trend and noise. As a complement to the separability question that was recently addressed by Empirical Modal Decomposition (EMD) [1] and "synchrosqueezing" [2], this work is concerned with the case where the components may be non-stationary. A characterization of the components separability is first proposed through the spectral interpretation of the singular spectrum. A new clustering solution is then offered for an automatic selection of the singular values that allows obtaining these components.

This research deals with the discrimination between conditions of faults in rolling element bearings based on a global spectral analysis. This global spectral analysis allows to obtain spectral features with significant discriminatory power. These features are extracted from the envelope spectra of vibration signals without prior knowledge of the bearings specific parameters and the characteristic frequencies. These extracted spectral features will then be the global spectral signature produced by the bearing faults. Since the signature produced by the faults in bearing balls is very weak, and hard to be detected and identified, this paper proposes the linear discriminant analysis as part of the global spectral analysis method in order to improve the diagnosis of ball faults. The application on experimental vibration data acquired from bearings containing different types of faults with different small sizes shows the proficiency of the overall method. The Bhattacharyya distance is used to confirm the efficiency of the obtained results.

Ce papier traite de la detection et du diagnostic de defauts mecaniques et plus particulierement ceux que l'on retrouve dans les roulements a billes pouvant equiper une machine electrique. Generalement les defauts dans les roulements sont diagnostiques grâce a la recherche des frequences caracteristiques associees aux elements constitutifs du roulement. Ces frequences sont supposees connues a priori ou estimees. Ce papier propose de faire la discrimination entre les defauts de roulements en fonction de la localisation et la severite du defaut, tout en s'affranchissant de la connaissance a priori des frequences caracteristiques. La methode repose sur l'extraction des parametres frequentiels representatifs de la signature frequentielle globale des defauts afin de faire la classification. Pour notre approche, l'analyse des resultats experimentaux montre que l'Analyse en Composantes Principales appliquee sur ces parametres permet de discriminer avec precision les differents types de defauts. L'Analyse Discriminante Lineaire est ensuite proposee afin d'ameliorer la qualite de la discrimination entre des defauts de billes de severite differente.

Informative features having important discriminatory power, also called high-level features, for classification of bearings faults can be automatically extracted from the spectrum of the vibration signal envelope without the a prior knowledge of the characteristic bearing frequencies. It was shown in a previous work that the Principal Component Analysis (PCA), when applied on a specific spectral matrix based on these spectral features, allows discriminating accurately between different faults conditions of bearings. Healthy and faulty bearings with faults on the outer-race, the inner-race and the balls are separated into distinct classes irrespective of the system operating point. The classification does not need any complex classifier like neural networks or support vector machines. There are still some difficulties, however, to discriminate between different levels of severity related to the faults in the bearing balls. The present work uses Linear Discriminant Analysis (LDA) to improve the classification of faults on balls according to their severity level, while only relying on the information carried out by the already used spectral features. Experimental results show that the LDA, besides its simplicity, extracts from the spectral features new variables having more discriminatory power than the principal components. The accuracy of the discrimination into the PCA and LDA spaces is evaluated using Bhattacharyya distance, a well-known measure of class separability. The linear discriminant axes allow for a good discrimination between different sizes of faults in bearing balls. The obtained results validate the contribution of the LDA space to the diagnosis of faults in bearings elements based on the proposed spectral features.

Fault Detection and Isolation (FDI) based on Principal Component Analysis (PCA) is achieved through the construction of control charts. Control charts differ, primarily, by the subspace into which they were defined, namely, the principle and the residual subspaces. Abnormalities are detected in the plotted monitoring chart if the confidence limit is violated. Often, the Hotelling's T-2 control chart, defined in the principal subspace, is applied for process monitoring. But to detect a fault with the T-2 chart, it must cause significant changes in the principal subspace, because little disturbances may be hidden by the large amount of variabilities present in the principal subspace.In this paper, we propose to use the Kullback-Leibler divergence, a probabilistic measure taken from information theory, as a diagnosis criterion. We show the efficiency of this criterion for which we find that small faults which might not be detected by the Hostelling test, become detectable without ambiguity. The simulation results show a significant improvement in the fault detection.

Process-history based methods are very commonly used for fault diagnosis and detection. However their efficiency is closely related to the quality of the measured data. In noisy environments, they usually fail particularly for incipient faults. This paper is an attempt to determine an analytical model allowing to estimate a theoretical threshold for fault detection based on the Fault to Noise Ratio (FNR). This model is developed using the Kullback-Leibler Divergence (KLD). For feature extraction, the used data are previously processed through Principal Component Analysis (PCA). The model is validated with simulated data and the results are so far very encouraging.

The limitations of statistical approaches used for Fault Detection and Diagnosis (FDD) of processes, are related to the local character of used statistics. For the sake of enhancing the detectability of incipient faults and assessing efficiently the fault level, that is the quality of operation, one should investigate the benefits a 'global' fault detection approach may provide. The Kullback-Leibler Divergence is proposed under the discipline of Statistical Process Control (SPC). A theoretical analysis is conducted to establish an analytical model relating the divergence to the fault severity amplitude. The model, when applied to a numerical example, provides an upper bound of the fault amplitude. While the usual statistics are not able to estimate the fault level, an upper bound is always necessary to guarantee a safety margin for the process.

Usually, bearing faults are diagnosed by the search of bearing characteristic frequencies in the spectrum of current or vibration signals. This local approach, even efficient, has the drawback of requiring the a prior knowledge of these frequencies. Moreover, characteristic bearing frequencies are only a part of the global spectral signature induced by natural bearing damages. In real situations, a fault on a particular bearing element may not produce the corresponding characteristic frequency. Several multiple harmonics of this frequency and sidebands related to their modulations by rotational frequencies can be quite dominant. An effective diagnosis should rather consider the global fault signature. Based on the fact that the global information encoded in the frequency domain is usually descriptive enough to diagnose and classify bearing faults, the present work proposes a classification scheme for bearing conditions which does not require the characteristic frequencies to be known or estimated. The method combines the envelope analysis, the sliding Fast Fourier Transform (FFT) technique and Principal Component Analysis (PCA). The application on experimental data shows that bearing faults can be diagnosed and classified accurately and without overlapping, irrespective of the system operating point. The extracted spectral features are informative enough to discriminate between different conditions of bearing.