Expert Systems with Applications

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1 Expert Systems with Applications 38 (2011) Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: Application and comparison of an ANN-based feature selection method and the genetic algorithm in gearbox fault diagnosis A. Hajnayeb a, A. Ghasemloonia b, S.E. Khadem a,, M.H. Moradi c a Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran b Faculty of Engineering and Applied Science, Memorial University, St. John s, NL, Canada c Biomedical Engineering Department, Amirkabir University, Tehran, Iran article info abstract Keywords: Artificial neural network Diagnosis Vibration analysis Genetic Algorithm Feature selection In this paper, a system based on artificial neural networks (ANNs) was designed to diagnose different types of fault in a gearbox. An experimental set of data was used to verify the effectiveness and accuracy of the proposed method. The system was optimized by eliminating unimportant features using a feature selection method (UTA method). Consequently, the fault detection system operates faster while the classification error decreases or remains constant in some other cases. This method of feature selection is compared with Genetic Algorithm (GA) results. The findings verify that the results of the UTA method are as accurate as GA, despite its simple algorithm. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction The vibration monitoring of gears and gearboxes due to their importance in industry and their vibration signal characteristics has been an interesting topic for researchers in this field. Therefore, fault diagnostics and monitoring techniques for gearboxes have been improved in a short time frame. With the improvement of condition monitoring devices, the fault diagnosis systems tended toward the real-time fault detection methods. The real-time processing systems are mostly unable to process several vibration signal input features. Therefore, it was desired for the fault diagnosis systems to collaborate with feature selection algorithms to increase the efficiency of fault detection and decrease the human errors. The following section is comprised of an introduction to gearbox fault detection systems and feature selection techniques, based on artificial neural networks (ANNs), fuzzy systems and the genetic algorithm. Various types of signals used in gear vibration processing techniques can be grouped into five major categories: (1) raw signal, (2) time synchronous average signal, (3) residual signal, (4) difference signal and (5) band pass mesh signal. Gear faults are mostly initiated by localized defects such as fatigue fractures and cracks. These preprocessed signals are then processed with different signal processing techniques, such as statistical methods. Defects primarily alter the amplitude and phase of the gear vibration (Ma & Li, 1994). Three major methods have been used excessively in fault detection approaches for gearbox condition Corresponding author. Tel.: address: khadem@modares.ac.ir (S.E. Khadem). monitoring: frequency based cepstrum approach, time domain approach and joint time frequency approach. Since most of the faults have their own frequency characteristics in the frequency spectrum of a gearbox, the frequency domain approach is a traditional diagnostic technique. In this method the frequency spectra of a faulty gear is compared to the spectra of the same gear in the no-fault condition. One of the fault indicators in this method is the modulated sidebands around the gear meshing frequency and its harmonics, usually higher order harmonics. Cepstrum is the inverse Fourier transform of the power spectrum and indicates periodicity in the spectrum and faults can be recognized in this method due to the fact that faults occur periodically (Lebold, McClintic, Campbell, Byington, & Maynard, 2000). But in a gearbox with so many gears in mesh, it could be difficult to detect the fault, due to the presence of so many frequency components in the spectra. Simple frequency analysis, such as spectrum analysis, is generally unable to detect failure at early stages of fault generation. Therefore, time and time frequency domain methods become more applicable. In the time domain analysis, the time synchronous averaging (TSA) of the raw vibration signal removes periodic events related to the non-faulty gears and reduces noise effects. Advanced rapid fault detection can be conducted through the TSA tracing. Time averaging processing techniques, such as the extraction of the residual signal and the amplitude and the phase modulation of the tooth meshing harmonics, have been improved for early detection of gear damages (Ma & Li, 1995). In addition, the Kurtosis value of the phase modulation and the resonance demodulation technique can also be used. However, because of the impacts produced by local faults, the vibration signal of the faulty gearbox is considered as a non-stationary signal (Wang, 2001) /$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi: /j.eswa

2 10206 A. Hajnayeb et al. / Expert Systems with Applications 38 (2011) In the late 1990s, time frequency techniques were widely used for gear fault detection, which were applied to deal with nonstationary signals. Faults change the energy and frequency content of the gear vibration signal through local modulation. For localized defects, the resulting energy and frequency variation are local in time. As the fluctuation in energy and frequency increases, they will eventually become noticeable in the spectrum in the form of sidebands. Additionally, a spectrum can neither differentiate sidebands from other spontaneous stationary frequency components, nor tell when a local fluctuation occurred. On the other hand, time frequency analysis is an ideal tool for the analysis of signal components with time and spatial locality. Different kinds of time frequency distribution methods such as wavelet transform, Wigner Ville distribution, Pseudo Wigner Ville distribution were applied by Cohen (1989), Forrester (1989a),Forrester (1989b), Staszewski (1994), Yesilyurt (2003), Wang and McFadden (1993). Interests in automating the fault detection and diagnosis of machinery and reducing human errors have encouraged researchers to use soft computing methods. Artificial neural networks (ANNs) and fuzzy logic are used for identifying the machinery condition, while the genetic algorithm is used to optimize the monitoring system parameters. Fuzzy logic-based condition monitoring systems require expert s information of machinery faults and their symptoms. Wu and Hsu (2009) designed a fuzzy logic-based fault diagnosis system for a gearbox system. However, these systems are fast and close to human inference rules and qualitative measurement techniques. On the other hand, monitoring systems based on ANNs do not require any background on the machinery characteristics and can be trained using a data set of machinery vibrations in different fault conditions. Samanta (2004) used an ANN for two-class (normal or faulty) recognition of a gearbox. Rafiee, Arvani, Harifi, and Sadeghi (2007) used a multiple-layer perceptron ANN to classify three different fault conditions and one no-fault condition of a gearbox. The genetic algorithm has been used as an effective tool for evolving monitoring systems and boosting their accuracy and speed of fault diagnosis (Samanta, 2004; Wu & Hsu, 2009). Saxena and Saad (2007) prepared an ANN for fault diagnosis of ball bearings and applied the genetic algorithm to find the best subset of the ANN input features and the number of neurons in the hidden layer of the ANN and improved the accuracy of fault diagnosis. The major drawback of the genetic algorithm however, is its heavy burden of computations. In the present study, a multiple layer perceptron ANN was designed to classify four different conditions of a gearbox using its vibration signals. To increase the accuracy and speed of the designed system, a subset of input features was selected. For this reason, two methods were used for feature selection and the results were compared, namely the UTA algorithm and the genetic algorithm. The UTA algorithm is simpler and faster than the GA, but not as efficient as the GA. The methods are implemented using experimental vibration data of a gearbox. 2. Theory of ANNs An artificial neural network (ANN) is a nonlinear mapping tool that relates a set of inputs to a set of outputs. It can learn this mapping using a set of training data and then generalize the obtained knowledge to a new set of data. Today, ANNs have a variety of applications. As a classifier, one of the most commonly used ANNs is the Multi-Layer Perceptron (MLP) network. There are three types of layers in any MLP: the output layer, the input layer and the hidden layer. Each layer is comprised of n nodes (n P 1) and each node in any layer is connected to all the nodes in the neighboring layers. Each node can also be connected to a constant number which is called bias. These connections have their individual weights which are called synaptic weights and are multiplied to the node values of the previous layer. Input and output data dimensions of the ANN determine the number of nodes in the input and output layers, respectively, but the number of hidden layers and their nodes is determined heuristically. The number of hidden layers and nodes in an MLP is proportional to its classification power. However, there is an optimum number of hidden layers and nodes for each case and considering more than those amounts leads to over fitting of the classifier and made the computations substantially increased. The value of any node can be computed through Eq. (1): a lþ1 ¼ sigðf lþ1 ðw lþ1 a l þ b lþ1 ÞÞ where a l, b l and l are output vector, bias vector and layer number, respectively. W is the synaptic weights matrix of the MLP. f l is the Activation function of the lth layer and can be used to create nonlinear boundaries for the classifier. sig is the activation function which can be used to bound the node values between 0 and 1. After setting the structure of the MLP ANN, it should be trained. Training an ANN means adjusting the synaptic weights in a way that any particular input leads to the desired output. It can be conducted by different algorithms. One of the most commonly used learning algorithms is resilient back propagation, which is used in this paper. For any learning algorithm, a limit should be defined to stop the learning process, which is called Stopping Criterion and usually consists of the following rules, or all of them simultaneously: (a) The error root mean square in an epoch becomes less than a predefined value. (b) Error gradient becomes less than a predefined value. (c) The number of epochs reaches a predefined number. The error vector for an MLP is defined as the difference between the network output vector and the desired output vector. Selecting an appropriate structure, initial weights, training algorithm for an MLP and supplying it with enough training datasets, enables the MLP to operate as a powerful classifier. In this study, it classifies the gearbox condition into three faulty (three types of fault will be created on a gear) and one healthy condition, according to the symptoms extracted from the measured vibration signals. 3. Feature selection algorithms In this section, two methods for feature selections are discussed. The first one is the UTA algorithm and the second one is the genetic algorithm. The UTA algorithm is based on the substitution of the mean value of one input feature for its values in the feature vectors. The selection algorithm is explained in the following concise steps (Utans, Moody, & Rehfuss, 1995): 1. Select a suitable ANN for the problem. Train the network and test it. 2. Replace the ith feature by its mean value in all dataset and test the previous ANN, which has been trained in step1. 3. Subtract the previous the mean square error (MSE) value of the ANN from its new value for each feature set. 4. Eliminate the feature which causes negative difference in the MSE value or the smallest positive difference in the MSE value (if all of them are positive values). ð1þ

3 A. Hajnayeb et al. / Expert Systems with Applications 38 (2011) Prune the initial feature set until the classification performance decreases significantly or diminishes to a value lower than a desired margin. The merit of this algorithm is that it is not necessary to train the ANN again. Therefore the selection algorithm becomes faster, especially in cases where the ANN has a large number of hidden layers or hidden nodes. As mentioned before, the second algorithm, which is used in this paper for feature selection, is the genetic algorithm (GA). GA is a search algorithm based on the idea inspired by genetics in nature. It starts with generating an initial population, randomly comprising a certain number of chromosomes, which are in fact, possible solutions to the problem. Then, a predefined fitness function is evaluated. In the next step, a new generation of chromosomes is created, using the previous generation. Three methods could be implemented for this purpose selection, crossover and mutation. Their effectiveness in the next generation should be evaluated. The number of chromosomes in the next generation remains constant. The mentioned steps are usually continued until a terminating condition is reached. 4. ANN classifier for Gearbox fault diagnosis An MLP artificial neural network, which has only one hidden layer, is used as a classifier in the present study. Two binary neurons in the output layer are used, which are capable of presenting four output classes including three different defective conditions and one no-fault condition of the gearbox. The number of input features is 12. An MLP with (12:20:2) structure is found to be suitable for this problem, using trial and error for finding the optimum number of hidden layer neurons. The MLP creation, training, and simulation are implemented in MATLAB s Ò neural network toolbox. The LOGSIG activation function is used for both of the hidden and output layers. The resilient back propagation (Trainrp) learning function is selected for training the back propagation MLP. Resilient back propagation is one of the most efficient algorithms for pattern recognition problems (MathWorks Inc., 2005). The stopping criterion in the training process of the MLP is the maximum training epochs of 2000, the minimum MSE value of 10 30, or minimum gradient of In each training and testing process, nearly half of the dataset is used for training and the rest is used for testing the network. The results of each section are calculated by averaging 100 MLP networks results. These 100 MLPs are the same, except for their initial weight values. The averaging eliminates the dependency of the classification results to initial weights. 5. Feature extraction method In this section, the signal features (input features of the ANN) are explained. The first seven features in the input features vector of the classifier are the same features that were used by Matsuura (2004). In summary, the features which were used in this study for classification are as shown in Table 1: (Futter, 1995; McFadden, 1989; Samuel & Darryll, 2005). Each feature value is divided into its maximum value to keep the input values of the ANN between [0, 1]. This normalization of the features boosts the performance of the ANN. 6. Experimental test rig and data acquisition The gearbox, which is under examination in this study, is a 4- stage motorcycle gearbox comprised of spur gears of pitch module of 2.5 and the contact ratio of 1.4. A 380 W electric motor drives the gearbox with the nominal speed of 1420 rpm through a rigid coupling, instead of belt transformation, to avoid the trembling effect. For the sake of data acquisition, a Pulse Ò multi-analyzer along with a 3D accelerometer and a tachometer was used. The accelerometer was mounted on the gearbox casing and close to one of its bearings. The tachometer was located in front of the coupling to store the rotary speed for data preprocessing. The mesh frequency according to the speed and the number of teeth in the mating gears is f mesh ¼ 29 :1420 ¼ 686:33 Hz. Major peaks of vibration signal are up to the 9th harmonic, which is 6176 Hz. According 60 to the Nyquist sampling theorem, in order to avoid aliasing effect, the sampling frequency was set to 16 khz, which was more than twice of the highest frequency component under the study. A complete schematic of the gearbox with the data acquisition system is shown in Fig. 1. Two common types of fault were created on one of the gears, which had 29 teeth and were in mesh with another gear with 24 teeth. First, the crest of one of the teeth was removed by 5% to Table 1 Features and their definitions. Feature Equation Definition Characteristics Maximum max{ x i } Max value of the signal in the time domain Detection of severe faults value qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi RMS value P 1 N N i¼1 x2 i Root mean square of the signal Detection of unbalanced parts in the system Mean square value f 3 ¼ 1 N i¼1 x2 i Mean square of the signal Indicates the average power of the signal P Variance 1 N N 1 i¼1 ðx i f 3 Þ 2 Variance of the signal Spreading out of random values Kurtosis N N i¼1 i xþ 4 Fourth normalized moment of the signal Detection of worn or broken tooth and Gaussian noise factor 2 ðx i¼1 i xþ 2 Crest factor X peak RMS Ratio of maximum amplitude to RMS Detection of broken tooth or outer ring failure in bearings Clearance PeakValue pffiffiffiffiffi 2 Ratio of maximum amplitude to the mean value Detection of faults which cause high amplitude pulses factor ð1=nþ jx i¼1 ij without increasing mean value RMS_BP FIR (Equiripple) RMS value of band-pass filtered signal 1500 Hz < f < 7200 Hz RMS_HP FIR (Equiripple) RMS value of high-pass filtered signal 7200 Hz < f FM0 PPPA n i¼1 iþ Peak to peak value of the time signal to summation of amplitudes at harmonic frequencies Detection of significant worn in a tooth NA4 N i¼1 i rþ 4 P m variance Detection of continuing growth of the fault 1 m j¼1 NA4 1 N i¼1 ðr i rþ 4 ð M2Þ 2 i¼1 ðr ij r jþ 2 Normalized fourth moment of the signal with time signal variance Detection of repeatable errors

4 10208 A. Hajnayeb et al. / Expert Systems with Applications 38 (2011) Fig. 1. Test rig and the data acquisition system (Chitsaz, 2005). Fig. 2. The results of genetic algorithm for 20 generations. generate 5% fault signal. Then, the crest was removed up to 20% and the vibration data was stored in a PC. Finally, the tooth was removed completely to generate the signal for broken tooth state of the fault. All the vibration data was stored to conduct further analysis. It should be mentioned that the vibration signal for the nofault state was acquired before generating any fault and stored in the PC for comparative studies. 7. Results In this section the implementation of the two mentioned methods (UTA and GA), on the problem of gearbox fault diagnosis will be explained. First, the results of each method are shown, and at the end, a comparative study will be conducted. In the first step of UTA implementation, 12 input features are sorted, according to the change of mse values (Table 2). The initial performance of the system before algorithm implementation was 100% for no-fault state and 100%, 91.7% and 99.8% for 5% fault state, 20% fault state and broken tooth respectively. The total performance of the system was 97.2% which is the percentage of gear condition classification success. According to Table 2, the most ineffective feature is the 6th feature which is the Crest factor. Eliminating the 6th parameter and running the algorithm again with the remaining 11 parameters, the total performance of 97.7 was achieved. It indicates that eliminating the 6th parameter does not make a significant change in the total performance of the system. The classification success of the gear states were 99%, 100%, 95.7% and 99.8% for no-fault, 5% fault, 20% fault and broken tooth respectively. By implementing the algorithm again on the diagnosis system with the remaining 11 features, the 5th feature was found as the next feature to be eliminated due to the minimum mse change. The process was continued until a significant change in the classifier performance occurred. As shown in Table 2, the total performance of the system in the 10th stage of the algorithm was 96.8, which was the classification success for the classifier system with three features. In the 11th implementation of the algorithm with the two remaining features, a significant change (about 20%) of total performance occurred. Therefore, it was concluded that the classifier s performance can still remain high with only three features in the classification process. Repeating the algorithm and eliminating one of these three parameters will lead to the reduction of the total performance of the system. In order to apply the GA algorithm to the gear vibrations feature selection study, the genetic Algorithm toolbox of Matlab is used. The percentage of wrong detection is considered as the problem fitness function, which will be minimized. The population is customized in a form that each individual (genome) has five variables. This number of variables equals the number of features, which are required to be selected out of 12 features. ANNs with the same structure, i.e. MLPs with (5:20:2) structure are used again. The number of hidden layers and their size are selected arbitrarily in this study, but their optimum values can also be found through another appropriate GA code. Each variable number is the label of a feature and is an integer value between 1 to 12. The population size of 6 is considered for each generation. No time limit was applied to the optimization process and it was performed for 20 generations. The values of StallGenLimit and StallTimeLimit have been set to 5 and 1000 (in order to allocate sufficient time for the GA to optimize the system) as the options of the genetic algorithm toolbox of Matlab Ò. These parameters stop the process if the change in the results is not significant during a specific number of generations or time interval. The final results of the GA method verify a 1.5% incorrect detection, which is equal to the 98.5% correct detection of gear condition. This result is better than those emerged through the UTA method. The selected features vector, that produces those results, is [3, 8, 7, 1, 10]. This set of features results in an accuracy of 100% for the diagnosis of no-fault, 5% worn and broken tooth conditions, while 20% worn condition is diagnosed by the 95.5% of accuracy. The process of the genetic algorithm is shown in Fig. 2 for all the generations from the beginning to the end of the process. It indicates that for this case study, after a few generations, the optimal results can be obtained. The reason of this fast convergence to the optimal results can be the small number of input features. For more complicated cases, the genetic algorithm takes a longer time to be executed. Table 2 Sorted features of the diagnosis system according to UTA algorithm. Step No No-fault % fault % fault Broken tooth fault Total Eliminated feature None

5 A. Hajnayeb et al. / Expert Systems with Applications 38 (2011) Both methods show promising results in feature selection of the gearbox diagnosis system. Although applying the GA algorithm to the problem is more complicated, it allows the inclusion of more parameters, such as the number of hidden layers, in the optimization process. The more optimizing parameters are used, the more efficient classification system is available. On the other hand, the UTA algorithm has a simpler procedure and is easy to implement. As mentioned before, for this problem, the GA converges in a few steps, but it can take a longer time for problems with more input features and larger networks. Because the optimum number of input features is unknown in the UTA algorithm, the algorithm has to be repeated for each step in order to detect the significant decrease in the performance. If the number of features in the final subset is known, the UTA presents promising results even in a single step. Therefore, if the number of features is unknown, the GA presents more accurate results in a shorter time interval. 8. Conclusions An ANN-based fault diagnosis system has been designed for a gearbox, using a number of vibrations features. The system diagnosis process has been optimized through selecting the best subset of features, using the UTA and the Genetic Algorithm (GA). Eliminating some features out of the input features resulted in faster, and in some cases, more accurate diagnosis systems. Comparing these two algorithms clarifies that the UTA gives a rough estimate in the first step, but it is faster than the GA. On the other hand, the GA has a heavier burden of computation, especially for a higher number of features. An advantage of using the GA is that the parameters of the diagnosis system can be optimized simultaneously if they are included in the GA process. This idea leads to more accurate results and faster processing. 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