Feng－yun XIE，San－mao XIE

School of Mechanical and Electronical Engineering，East China Jiaotong University，Nanchang 330013，China

Gear fault classification based on support vector machine*

Feng－yun XIE?，San－mao XIE

School of Mechanical and Electronical Engineering，East China Jiaotong University，Nanchang 330013，China

Gears are critical elements in rotating machinery.An approach is proposed based on support vectormachine(SVM)to solve classification ofm ultip le gear conditions.These conditions are divided into normal，wear，and broken teeth conditions.The rootmean square(RMS)and the wavelet packet energy at different scales of the vibration signals of gearbox casing are emp loyed in constructing the features of classifier.SVMis emp loyed for the classifier，and it has the abilities ofmu lti-class classification and good generalization.The experim ental results show that the proposed method is able to discrim inate the gear faults clearly.

Gear，Support vectormachine，F(xiàn)ault classification，Wavelet packet energy

*Project supported by Jiangxi Province Education Department Science Technology Project(GJJ14365)，and Jiangxi Province Nature Science Foundation (20132BAB201047，20114BAB206003)

? Feng－yun XIE，PhD.E－mail:xiefyun@163.com

Gear systems arewidely used in rotatingmachinery，and gear abnormity is a crucial reason for machine failure.It is significant to study the technique of gear fault classification for increasingmachine processing reliability.Early fault detection in gears has been the subject of intensive investigation and many methods based on vibration signal analysis have been developed.For instance，Mcfadden proposed an interpolation technique for time domain averaging of gear vibration［1］.Rafiee proposed a multi－layer perceptron neural network to recognize gears and bearings fault of a gearbox system［2］.As a powerful machine learning approach for classification problems，support vectormachine is known to have good generalization ability.SVMare introduced by Vapnik in the late 1960s on the foundation of statistical learning theory.In the early 1990s，The techniques used for SVM started emergingwith greater availability of computing power and used in numerous practical applications［3 －5］.

In this paper，an approach based on vibration signal processing techniques and SVMis proposed for solving the gear fault classification.For classifying gear fault，the piezoelectric accelerometer is used for data acquisition.The features of the classification by SVMare considered on a dataset composed of two sets of features:the first is from the RMS of time domain，the second consists of the wavelet packet energy calculated in the time－frequency.Two sets of features provide sensitive information for a classifier.The classifier is based on SVM method.The results show that the proposed method has a good classification capability.

1.Support vector machine theory

SVMincorporates the maximal margin strategy and the kernelmethod.The architecture of a classical SVMis shown in Figure 1.

Figure 1.Architecture of SVM

SVMis a supervised learning approach used for nonlinear classification which has also led to many other recent developments in kernel based learning methods in general.The authors in this study used the one－against－allmethod for SVM multiclass classification［6］.The“winner－takes－all”rule is used for the final decision，where thewinning class is the one corresponding to the SVM with the highest output.Thismethod constructs k SVM models where k is the number of classes.The ith SVMis trained with all of the examples in the ith classwith positive labels，and all other examples with negative labels.Given m training data(x1，y1)，，(xm，ym)，where xi∈ Rn，i=1，…，m and yi∈ {1，…，k}is the class of xi，the ith SVM solves the following problem:

Where the training data xiismapped to a higher dimensional space by the functionΦand the penalty parameter C.ξis a slack variable，ω is aweight，and b is a threshold.

After solving(1)，k decision functions are obtained here:

Where x is in the classwhich has the largest value of the decision function.Considering the problem of indivisible linear vectors，and selecting the relaxation factor，punishment parameter，and non－linear mapping core function，the sample can be mapped into a high dimension space and be transformed to a linear classification problem in attributive space.

2.Experiment setup and signal analysis

In order to research gear fault classification，a test bench of the gear fault simulation was set up.The experiment testing chart is shown in Figure 2.The vibration signals of machining process are obtained by piezoelectric accelerometer DH107.The vibration signals are amplified by charge amplifier5070 and simultaneously recorded by dynamic signal test and analysis system with 5 kHz sampling frequency.

Figure 2.Schematic diagram of testing system

The gear conditions are divided into three categories:normal，wear，and broken teeth.The realtime processing signals under different conditions are shown as Figure 3.The fast Fourier transforms(FFT)processing results of the time domain signals are shown in Figure 4.

The time－frequency amplitude is different significantly in the three different conditions as shown in Figure 3 and Figure 4.

Figure 3.The time domain chart of vibration signals

Figure 4.The frequency domain chart of vibration signals

3.Feature extraction

According to the results of vibration signals analysis，feature extractionmethod in this paper is adopted in time and time－frequency domain analysis.It includes RMS and the energy of wavelet package of vibration signals.

RMS is a statisticalmeasure of themagnitude of a varying quantity that can reflect changes in the amplitude of time domain.Three group vibration signals are selected for experimental test.The RMS in the different conditions is calculated and the results of RMS are shown in Table 1.

Table 1.RMS of vibration signals in different conditions

The RMS of vibration signals in different gear conditions are denoted as feature T1.

Wavelet package decomposition(WPD)is a wavelet transform where the signal is passed through more filters than discrete wavelet transform.WPD can record the detailed information about the different frequency bands，and is a good time－frequency analysis tool［7 －8］.In this paper，the three－level wavelet packet decomposition with wavelet sym4 is carried out.The energy of the first and the second nodes in three different conditions are significantly different than that of other nodes.The energy summations of the first node and the second node in three different conditions are shown in Table 2.

Table 2.Energy summations of the first and second nodes

The energy summation of the first and second nodes in different gear conditions is denoted as feature T2.

4.Gear fault classification

In order tomake themulti－class gear fault classification，amulti－class classification system based on SVMis developed.The system is composed of three cascaded binary classifiers.The classification processing based on SVMis shown in Figure 5.

Figure 5.Flow chart of the gear fault classification

According to three gear conditions，two subclassifiers are designed.One distinguishes the normal and fault，the other distinguishes the fault typewhich iswear and broken teeth.

Define class 1 as normal condition，class 2 as gear wear condition，and class3 as broken teeth condition.Select the radial basis function as the kernel function，the width of the radial basis kernel function asσ2=σ2=5，and the error penalty parameter as γ=1.The result of gear fault classification based on SVMis shown in Figure 6，where x1is RMS，and x2is the energy ofWPD.It can be clearly seen that all experimental data are classified correctly by SVM method.

Figure 6.Results of gear fault classification based on SVM

The feature values of the group 1 and group 2 are used for training SVMand the feature values of the group 3 is used for classification.The result of recognition based on SVMis shown in Table 3.

Table 3.Result of classification based on SVM

It can be seen that the result of recognition based on SVMis correct in Table 3.

5.Conclusion

A procedure is proposed for classification of gear condition using SVM classifiers by feature exaction from time－domain vibration signals.The RMS and energy of WPD are selected as the inputs of SVM.The gear processing conditions are divided into normal，wear and broken teeth.The SVM successfully classifies the signals of normal，wear，and broken teeth，and which is very effective.In future works，the comparison with other classification methods are recommended.

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基于支持向量機(jī)的齒輪故障分類*

謝鋒云?，謝三毛

華東交通大學(xué)機(jī)電學(xué)院，南昌 330013

齒輪是旋轉(zhuǎn)機(jī)械中的關(guān)鍵元件。提出了一個(gè)基于支持向量機(jī)的齒輪多故障分類方法。齒輪狀態(tài)被劃分為正常、齒輪磨損和斷齒狀態(tài)。振動(dòng)信號(hào)的均方根和小波包能量被選作為分類器的特征參數(shù)。分類器選用支持向量機(jī)(SVM)。SVM具有良好的實(shí)用性及多分類能力。實(shí)驗(yàn)結(jié)果表明:提出的方法能很好地區(qū)分齒輪故障。

齒輪;支持向量機(jī);故障分類;小波包能量

TH 133;TP391

10.3969/j.issn.1001－3881.2014.18.010

2014－06－10