Jinane Harmouche

Incipient fault detection and diagnosis based on Kullback-Leibler divergence using principal component analysis

Most of fault indicators are devoted to detect deviations related to specific features but they fail to detect and estimate unpredictable slight distortions often caused by incipient faults. The Kullback-Leibler divergence is characterised with a high sensitivity to incipient faults that cause unpredictable small changes in the process measurements. This work has two main objectives: first estimate the amplitude of incipient faults in multivariate processes based on the divergence and second evaluate, through detection error probabilities, the performance of the divergence in the detection of incipient faults in noisy environments.Throughout all the paper, the Fault-to-Noise Ratio (FNR) has been referred to as a comparative criterion between the fault level and noise; particularly the region around 0 dB of FNR is of interest in the evaluation. A theoretical study is developed to derive an analytical model of the divergence that considers the presence of Gaussian noise and allows obtaining a theoretical estimate of the fault amplitude. After application on a simulated AR process, the fault amplitude estimate turns out to be an overestimation of the actual amplitude, therefore guaranteeing a safety margin for monitoring. Accurate fault severity estimation for an eddy currents application shows the effectiveness of this approach. HighlightsWe propose to enhance the fault detection approach based on the KLD modelling with the introduction of the noise.Based on the aforementioned model an estimator of the fault amplitude is developed and validated.The performances of the detection are studied in a noisy environment with the introduction of the Fault to Noise Ratio (FNR).The robustness of the proposed method is evaluated with the computation of the miss-detection and false alarms probabilities.A performed validation of this approach with a simulated AR model is given.

Improved Fault Diagnosis of Ball Bearings Based on the Global Spectrum of Vibration Signals

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.

Faults diagnosis and detection using principal component analysis and Kullback-Leibler divergence

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 Hotellings T2 control chart, defined in the principal subspace, is applied for process monitoring. But to detect a fault with the T2 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.

Statistical Approach for Nondestructive Incipient Crack Detection and Characterization Using Kullback-Leibler Divergence

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.

Linear discriminant analysis for the discrimination of faults in bearing balls by using spectral features

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.

A global approach for the classification of bearing faults conditions using spectral features

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.

The ASTRES toolbox for mode extraction of non-stationary multicomponent 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.

Capability evaluation of incipient fault detection in noisy environment: A theoretical Kullback-Leibler Divergence-based approach for diagnosis

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.