Gear fault detection using artificial neural networks and support vector machines with genetic algorithms

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Abstract

A study is presented to compare the performance of gear fault detection using artificial neural networks (ANNs) and support vector machines (SMVs). The time-domain vibration signals of a rotating machine with normal and defective gears are processed for feature extraction. The extracted features from original and preprocessed signals are used as inputs to both classifiers based on ANNs and SVMs for two-class (normal or fault) recognition. The number of nodes in the hidden layer, in case of ANNs, and the radial basis function kernel parameter, in case of SVMs, along with the selection of input features are optimised using genetic algorithms (GAs). For each trial, the ANNs and SVMs are trained with a subset of the experimental data for known machine conditions. The trained ANNs and SVMs are tested using the remaining set of data. The procedure is illustrated using the experimental vibration data of a gearbox. The roles of different vibration signals, obtained under both normal and light loads, and at low and high sampling rates, are investigated. The results compare the effectiveness of both types of classifiers without and with GA-based selection of features and the classifier parameters. For most of the cases considered, the classification accuracy of SVM is better than ANN, without GA. With GA-based selection, the performance of both classifiers are comparable, in most cases, with three selected features. However, for SVMs with six features, 100% classification success is achieved in all test cases. The training time of SVMs is substantially less compared to ANNs in all cases considered. The present classification accuracy compares well with the results reported in a recent work, (Mech. Systems Signal Process. 16 (2002) 373), though the data and the feature sets are different.

Introduction

Condition monitoring of machines is gaining importance in industry because of the need to increase reliability and to decrease possible loss of production due to machine breakdown. The use of vibration and acoustic emission (AE) signals is quite common in the field of condition monitoring of rotating machinery. By comparing the signals of a machine running in normal and faulty conditions, detection of faults like mass unbalance, rotor rub, shaft misalignment, gear failures and bearing defects is possible. These signals can also be used to detect the incipient failures of the machine components, through the on-line monitoring system, reducing the possibility of catastrophic damage and the down time. Some of the recent works in the area are listed in [1], [2], [3], [4], [5], [6], [7], [8]. Although often the visual inspection of the frequency domain features of the measured signals is adequate to identify the faults, there is a need for a reliable, fast and automated procedure of diagnostics.

Artificial neural networks (ANNs) have been applied in automated detection and diagnosis of machine conditions [3], [7], [8], [9], [10] treating these as classification or generalisation problems based on learning pattern from examples or empirical data modelling. However, the traditional neural network approaches have limitations on generalisation giving rise to models that can overfit to the training data. This deficiency is due to the optimisation algorithms used in ANNs for selection of parameters and the statistical measures used to select the model. Recently, support vector machines (SVMs), based on statistical learning theory, are gaining applications in the areas of machine learning, computer vision and pattern recognition because of high accuracy and good generalisation capability [11], [12], [13], [14], [15]. The main difference between ANNs and SVMs is in the principle of risk minimisation (RM) [14]. In case of SVMs, structural risk minimisation (SRM) principle is used minimising an upper bound on the expected risk whereas in ANNs, traditional empirical risk minimisation (ERM) is used minimising the error on the training data. The difference in RM leads to better generalisation performance for SVMs than ANNs. The possibilities of using SVMs in machine condition monitoring applications are being considered only recently [3], [16], [17]. In [17], a procedure was presented for condition monitoring of rolling element bearings comparing the performance of two classifiers, ANNs and SVMs, with all calculated signal features and fixed parameters for the classifiers. In this, vibration signals were acquired under different operating speeds and bearing conditions. The spectral data and the statistical features of the signals, both original and with some preprocessing like differentiation and integration, low- and high-pass filtering were used for classification of bearing conditions.

However, there is a need to make the classification process faster and accurate using the minimum number of features which primarily characterise the system conditions with an optimised structure of ANNs and SVMs [3], [16]. Genetic algorithms (GAs) were used for automatic feature selection in machine condition monitoring [3], [16], [18], [19], [20]. In [19], the procedure of Jack and Nandi [17] was extended to introduce a GA-based approach for selection of input features and classifier parameters, like the number of neurons in the hidden layer in case of ANNs and the radial basis function (RBF) kernel parameter, width, in case of SVMs. The features were extracted from the entire signal under each condition and operating speed. In [20], some preliminary results of ANNs and GAs were presented for fault detection of gears using only the time-domain features of vibration signals. In this approach, the features were extracted from finite segments of two signals: one with normal condition and the other with defective gears.

In the present work, the procedure of Samanta et al. [20] is extended to the diagnosis of gear condition using vibration signals of longer duration and larger feature space. Comparisons are made between the performance of ANNs and SVMs, both without and with automatic selection of features and classifier parameters. The main difference between the present work and the work of Jack and Nandi [19] is in the process of feature extraction from the time-domain signal. Fig. 1 shows the flow diagram of the proposed procedure. The selection of input features and the classifier parameters are optimised using a GA-based approach. These features, namely, mean, root mean square (rms), variance, skewness, kurtosis and normalised higher order (up to ninth) central moments are used to distinguish between normal and defective gears. Moments of order higher than nine are not considered in the present work to keep the input vector within a reasonable size without sacrificing the accuracy of diagnosis. The roles of different vibration signals, obtained under both normal and light loads and at low and high sampling rates, are investigated. The results show the effectiveness of the extracted features from the acquired and preprocessed signals in diagnosis of the machine condition. The procedure is illustrated using the vibration data of an experimental setup with normal and defective gears [21].

Section snippets

Vibration data

In Ref. [21], vibration signals measured from seven accelerometers on a pump driven by an electrical motor through a two-stage gear reduction unit were presented. The first two accelerometers (1 and 2) were radially mounted near the driving shaft, with an angle of 90° between the two, the third accelerometer was used to measure the axial vibration near the driving shaft. The remaining four accelerometers (4–7) were radially mounted on the machine casing, on both sides of the second gear pair.

Signal statistical characteristics

One set of experimental data each with normal and defective gears was presented in [21]. For each set, 7 vibration signals consisting of 77824 samples (yi) were obtained using accelerometers to monitor the machine condition. In the present work, these samples were divided into 38 bins of 2048 (n) samples each. Each of these bins was further processed to extract the following features (1–9): mean (μ), root mean square (rms), variance (σ2), skewness (normalised 3rd central moment, γ3), kurtosis

Artificial neural networks

ANNs have been developed in the form of parallel distributed network models based on biological learning process of the human brain. There are numerous applications of ANNs in data analysis, pattern recognition and control [22], [23]. Among different types of ANNs, multilayer perceptron (MLP) neural networks are quite popular and used for the present work. In this paper, the terms ANN and MLP have been used interchangeably in absence of other types of neural networks. Here a brief introduction

Support vector machines

SVMs were introduced by Vapnik in the late 1960s on the foundation of statistical learning theory [15]. However, since the middle of 1990s, the algorithms used for SVMs started emerging with greater availability of computing power, paving the way for numerous practical applications [11], [12], [13], [14], [15], [24]. The basic SVM deals with two-class problems—in which the data are separated by a hyperplane defined by a number of support vectors. A brief introduction of SVM is presented here

Genetic algorithms

GAs have been considered with increasing interest in a wide variety of applications [28], [29], [30]. These algorithms are used to search the solution space through simulated evolution of ‘survival of the fittest’. These are used to solve linear and non-linear problems by exploring all regions of state space and exploiting potential areas through mutation, crossover and selection operations applied to individuals in the population [28], [29]. The use of genetic algorithm needs consideration of

Simulation results

The data set (45×266×2×2×2) consisting of forty-five normalised features for each of the seven signals (7) split in form of 38 bins of 2048 samples each, two load conditions and two sampling rates with two gear conditions were divided into two subsets. The first 20 bins of each signal was used for training the ANNs and SVMs giving a training set of 45×140×2×2×2 and the rest (45×126×2×2×2) was used for validation. In ANNs, the target values of the two output nodes were assigned as one (1) and

Conclusions

A procedure is presented for detection of gear condition using two classifiers, namely, ANNs and SVMs with GA-based feature selection from time-domain vibration signals. The selection of input features and the appropriate classifier parameters have been optimised using a GA-based approach. The roles of different vibration signals, obtained under both normal and light loads and at low and high sampling rates, have been investigated. The classification accuracy of SVMs was better than of ANNs,

Acknowledgements

The data set was acquired in the Delft “Machine diagnostics by neural network” project with help from TechnoFysica B.V., The Netherlands and can be downloaded freely at web-address: http://www.ph.tn.tudelft.nl/∼ypma/mechanical.html. The authors thank Dr. Alexander Ypma of Delft Technical University for making the data set available and providing useful clarifications.

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