Fault Diagnosis of Planetary Gear Based on Fuzzy Entropy of CEEMDAN and MLP Neural Network by Using Vibration Signal

Transcription

1 ITM Web of Conferences 11, 82 (217) DOI: 1.151/ itconf/ IST217 Fault Diagnosis of Planetary Gear Based on Fuzzy Entropy of CEEMDAN and MLP Neural Networ by Using Vibration Signal Xi-Hui CHEN, Gang CHENG a, Chang LIU and Yong LI School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou, , China Abstract. A ethod of planetary gear fault diagnosis based on the fuzzy entropy of coplete enseble epirical ode decoposition with adaptive noise (CEEMDAN) and ulti-layer perceptron (MLP) neural networ is proposed. The vibration signal is decoposed into ultiple intrinsic ode functions (IMFs) by CEEMDAN, and the fuzzy entropy that cobines the fuzzy function and saple entropy is proposed and used to extract the feature inforation contained in each IMF. The fuzzy entropies of each IMF are defined as the input of the MLP neural networ, and the planetary gear status can be recognized by the output. The experients prove the proposed ethod is effective. 1 Introduction Planetary gear often used in the ey parts of the transission syste of large-scale coplex equipent. However, it often suffered fro the influences of heavy-duty and hostile environent, leading faults to occur [1]. Therefore, it is of great significance to study the fault diagnosis of planetary gears. Due to the influence of its coplex structure, installation errors and operating environent, the vibration signal of planetary gear shows the characteristics with nonlinear and nonstationary [2]. Therefore, a fault feature extraction ethod that is suitable for processing the nonstationary vibration signal should be developed. The tie-frequency analysis ethod not only reflects the frequency characteristics of the signal but also shows the tie-varying characteristics, aing it is ore suitable for the analysis of nonstationary vibration signals. Epirical ode decoposition (EMD) is a typical adaptive tiefrequency analysis ethod, but it has a ajor drawbac of odal aliasing [3]. With the developent of research, enseble epirical ode decoposition (EEMD) is proposed to solve the proble of odal aliasing. However, the reconstructed signal after EEMD contains ore residual noise, and it is not a coplete decoposition process. CEEMDAN is an iproved EEMD algorith, and the liited adaptive white noise is added at each decoposition stage. Each IMF is obtained by calculating the only reaining part, and the reconstruction error is alost zero. Therefore, CEEMDAN can overcoe the odal aliasing phenoenon of EEMD, itigating the incopleteness of EEMD, and a set of high quality and effective intrinsic ode function (IMF) can be obtained [4, 5]. Saple entropy is now applied in the fault feature quantification to reflect the coplexity of the signal fro the perspective of their siilarity. However, in the calculation process of saple entropy, a Corresponding author: chenxh@cut.edu.cn The Authors, published by EDP Sciences. This is an open access article distributed under the ters of the Creative Coons Attribution License 4. (

2 ITM Web of Conferences 11, 82 (217) DOI: 1.151/ itconf/ IST217 the siilarity of the signal is reflected to a dichotoy, exhibiting both siilarity and dissiilarity, it is inaccurate to describe the siilarity. So the fuzzy entropy is proposed [6]. The fuzzy function is used to describe the signal siilarity, and a ore accurate calculation for the signal siilarity is achieved. The coplexity and stability of the signal are described ore reasonably and effectively. The recognition of planetary gear status is iportant after extracting the feature inforation, and soe intelligent classification technologies are widely used [7]. The MLP neural networ has great practical value in pattern recognition in any fields, and it is coposed of an input layer, an output layer and any hidden layers. MLP neural networ is a type of belong to ulti-layer feed-forward neural networ, and it realizes the data transforation of input features by the transfer functions of the hidden layers. MLP neural networ can be applied to recognize different planetary gear statuses, generating a structured networ to achieve highly coplex nonlinear apping by data self-learning [8]. Therefore, in this paper, a fault diagnosis ethod of planetary gear based on fuzzy entropy of CEEMDAN and MLP neural networ is established. 2. Model analysis 2.1 Coplete enseble epirical ode decoposition with adaptive noise EMD is originally proposed by Huang [3], but it has the drawbac of odal aliasing. EEMD is proposed to solve this proble, and the Gaussian white noise is added into the original signal to change the distribution of extree points. However, the reconstructed signal of the decoposition result of EEMD still contains ore residual noise, and EEMD is not a coplete decoposition process. Therefore, CEEMDAN is proposed, and the liited adaptive white noise is added at each decoposition stage. Each IMF is obtained by calculating the only reaining part, and the reconstruction error is zero. Therefore, CEEMDAN not only can overcoe the odal aliasing, but can also eliinate the incopleteness of EEMD. The reconstructed signal is identical to the original signal [9, 1]. The decoposition process of CEEMDAN can be described as follows: Step1: Assue E j () is defined as the first j IMF that is obtained by EMD [3], and () t is the white noise with a zero ean unit variance. For the signal xt ()+ () t, the first IMF that is expressed as IMF1(t) is obtained by EMD with M experients, and it is expressed as follows: 1 M 1 where is the aplitude coefficient of the white noise. Step2: The first reaining part can be described as follows: M 1 IMF() t E{ x() t ()} t (1) rt ()=() xt IMF() t (2) 1 1 Step3: The coputation process of the second IMF of the original signal xt () by CEEMDAN is expressed as follows: M 1 IMF ( t)= E{ r( t) E ( ( t))} (3) M 1 Step4: For the other stages, naely, 2,3,..., K, the calculation process of the first reaining part is sae as Step2 and Step3. The first +1 IMF is as follows: 2

3 ITM Web of Conferences 11, 82 (217) DOI: 1.151/ itconf/ IST217 r() t r 1() t IMF() t M 1 IMF 1( t)= E1{ r( t) E( ( t))} M 1 (4) Step5: Step4 is continued until the reaining part of the signal can no longer be decoposed, and the criterion is that the nuber of extree points is not ore than two. The nuber of final IMFs is K, and the final reaining part is as follows: K Rt () xt () IMF() t (5) It can be seen fro the realization process of CEEMDAN that the decoposition process is coplete and can realize the reconstruction of the original signal. In each decoposition stage, the white noise can obtain an appropriate signal-to-noise ratio by adjusting the coefficient Fuzzy entropy The calculation process of fuzzy entropy is as follows[11]: Step1: Assuing IMF ( t ) { z (1), z (2),..., z ( n )}, a set of vectors that are used to calculate the fuzzy entropy is built, and they are expressed as follows: A { z( i), z( i 1),..., z( i 1)} u ( i) i 1,2,..., n 1 (6) i where is the length of the vector. u () i is the ean of each vector. Step2: The distances of each vector are calculated, and the distance between defined as follows: A and i A can be j d ( A, A ) ax( A( l) A ( l) ) l 1,2,..., n (7) ij i j i j Step3: The siilarity between each set of vectors is described using a fuzzy function. An exponential function [12] is used, and it is defined as follows: D ij n ( dij / r) e (8) where n is the boundary gradient of the exponential function, and r is the siilar tolerance. Step4: The representation function B is defined as follows: B 1 1 n n 1 n - n - Dij (9) i 1 j 1, j i Step5: Mae =+1 and repeat Step1-Step4, expressed as follows: 1 B can be obtained, and the fuzzy entropy can be FuzzyEn ln 1 ( B B ) (1) 2.3 Multi-Layer Perceptron Neural Networ The MLP neural networ is coposed of input layer, output layer and hidden layer, and the training process of the MLP neural networ [13, 14] is expressed as follows: 3

4 ITM Web of Conferences 11, 82 (217) DOI: 1.151/ itconf/ IST217 Step1: The connection weights of the MLP neural networ are initialized. The inputted features are sent to the hidden layer, and the calculation of each neuron of the hidden layer is expressed as follows: J sh f( xiw j jh h ) (11) j where xi is the j-th input feature, j W jh is the connection weight between input neuron j and hidden neuron h, is the bias of the h-th hidden neuron. f( ) is the activation function. h Step2: The calculation result of the hidden neuron is transitted to the output layer, and the calculation of each neuron of the output layer is expressed as follows: H yo g( shwh ) (12) h where s is the output of the h-th hidden neuron, h W is the connection weight between hidden h neuron h and output neuron, is the bias of the -th output neuron. Step3: Each output neuron has a target pattern corresponding to an input pattern t, and the error inforation of the output neuron is calculated as t yo. The error inforation of the hidden layer is then calculated as: K h ( Wh) sh 1 (13) Step4: The weight updating of the hidden neurons and the output neurons is expressed as follows: W ( t 1) W ( t) xi [ W ( t) W ( t 1)] jh jh h j jh jh W ( t 1) W ( t) s [ W ( t) W ( t 1)] h h h h h (14) where is the learning rate, and is a oentu factor. Step5: Deterine whether the syste eets the stop condition. 3 Test equipent and data acquisition The fault siulation experient of the planetary gear is carried out, and the basic layout of the experient is shown in Figure 1. In the experient, the otor speed is set to 4 Hz, and the load is set to 13.5 N. Five types of sun gears are siulated, and they are noral gear, broen gear, gear with one issing tooth, wear gear and gear with a tooth root crac. The sapling frequency is set to 128 Hz, and the vibration signals of the five types of gears are collected. 4

5 ITM Web of Conferences 11, 82 (217) DOI: 1.151/ itconf/ IST217 Motor Acceleration sensors Fixed-axis gearbox Planetary gearbox Data acquisition syste Load syste Figure 1. Fault experient for the planetary gear 4 Experient signal analysis The five types of vibration signals for different gears are collected and shown in Figure Noral Broen One issing tooth Wear Tooth root crac Tie/s Figure 2. Five types of vibration signals for different gears It can be seen fro Figure 2 that five types of vibration signals for different gears have no obvious difference. It is not able to distinguish the gear status by coparing the tie doain vibration signals, next, they are processed by the proposed ethod to verify the effectiveness of the ethod. The vibration signals are decoposed by CEEMDAN, and due to the liitation of space, the vibration signal of the broen gear is selected as an exaple to show the CEEMDAN process. To prove that the perforance of CEEMDAN is superior to that of EEMD, the decoposition results using EEMD and CEEMDAN for broen gear are shown in Figure 3. It can be seen fro Figure 3 that the vibration signal is decoposed into 12 IMFs and a residual signal, and for convenience of expression, the residual signal is called IMF13. IMF1-IMF13 are arranged fro high frequency to low frequency. The decoposition result of EEMD still exhibits a serious odal aliasing phenoenon, as shown in IMF6, IMF7, IMF8 and IMF9. Meanwhile, soe of the even are the illusive coponents, such as in IMF7 and IMF8. In the decoposition result using CEEMDAN, the quality of the obtained IMFs is greatly iproved, and the odal aliasing phenoenon is further suppressed. 5

6 ITM Web of Conferences 11, 82 (217) DOI: 1.151/ itconf/ IST217 IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 IMF8 IMF9 IMF1 IMF11 IMF12 IMF Tie/s (a) EEMD IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 IMF8 IMF9 IMF1 IMF11 IMF12 IMF Tie/s (b) CEEMDAN Figure 3. Decoposition result using EEMD and CEEMDAN for broen gear Fuzzy entropy cobining a fuzzy function and saple entropy is used to quantize the feature inforation contained in IMFs, and the fuzzy function is used to describe the siilarity of each vector. The exponential function D ij n ( dij / r) e is selected, in which there are soe paraeters that need to be deterined: the siilar tolerance r, boundary gradient n and length of the copared vectors. r is usually set by the standard deviation of the signal, and in this paper, r=.15sd. n is usually recoended to tae a saller integer value, so in this paper, n is set as 2. is deterined as 7 after soe experients. To prove that fuzzy entropy has a better perforance than saple entropy, the saple entropy and fuzzy entropy of each IMF are shown in Figure 4, respectively Noral Broen One issing tooth Wear Tooth root crac Noral Broen One issing tooth Wear Tooth root crac 2 2 Saple entropy 1.5 Fuzzy entropy IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 IMF8 IMF9 IMF1 IMF11 IMF12 IMF13 IMFs (a) Saple entropy IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 IMF8 IMF9 IMF1 IMF11 IMF12 IMF13 IMFs (b) Fuzzy entropy Figure 4. Saple entropy and fuzzy entropy of each IMF 6

7 ITM Web of Conferences 11, 82 (217) DOI: 1.151/ itconf/ IST217 It can be seen fro Figure 4(a) that the coplexity and stability of each IMF are described by the saple entropy. The saple entropies of the five types of gears are scattered in soe IMFs, for exaple, IMF2 and IMF1, but in ost of the IMFs, the saple entropies of soe gears overlap together, for exaple, IMF3 and IMF4, etc. Especially in IMF5, the saple entropies of the five types of gears even coincide at a point, and those situations will interfere with the identification of five types of gears. In the calculation process of the saple entropy, the siilarity description of the copared vectors is dichotoous, that causes the siilarity of the copared vectors can not be described accurately, and the tiny differences aong the signals can not be reflected effectively. The Fuzzy entropy is proposed, and the fuzzy function is used to calculate the siilarity of the copared vectors in the calculation process. It can be seen fro Figure 4(b) that the fuzzy entropies of the five types of gears are scattered in ost of the IMFs. Only in IMF11 and IMF12, the overlap phenoenon is appear, but the overlap phenoenon is relatively inor. It can be found that the fuzzy entropy ore easily distinguishes between the five types of gears, and it is thus superior to the saple entropy in the aspect of feature extraction. Recognizing the planetary gear status is the ost iportant step after extracting the feature inforation. Next, the fault diagnosis of the planetary gear is accurately achieved by applying a MLP neural networ. The training saple set is prepared, and each planetary gear status has 3 saples, for a total of 15 saples. The fuzzy entropies of each IMF decoposed by CEEMDAN are defined as the input of MLP neural networ, so that the input layer of MLP neural networ has 13 input neurons. Because the training saples are divided into five types, so the output layer of MLP neural networ has 5 output neurons. To train MLP neural networ, different planetary gear statuses are denoted with different labels in the output layer: the noral gear is denoted as [1 ], the broen gear is denoted as [ 1 ], the gear with one issing tooth is denoted as [ 1 ], the wear gear is denoted as [ 1 ] and the gear with tooth root crac is denoted as [ 1]. The neuron nuber of the hidden layer is usually deterined by trial-and-error. The learning rate of MLP neural networ is set as.5, and the training step is set as 8. The ean squared error is used to evaluate the training perforance of MLP neural networ when the training process is copleted. The changes in the ean squared error of the training process with different nubers of hidden neurons are shown in Figure 5(a). A testing saple set that includes different planetary gear status saples is prepared, and each planetary gear status has 4 saples, for a total of 2 saples. They are decoposed by CEEMDAN, and the fuzzy entropies of each IMF are inputted into the trained MLP neural networ for use in verifying the recognition perforance of the trained MLP neural networ. The overall recognition rate for planetary gear with different nubers of hidden neurons is shown in Figure 5(b)..6 9 Mean squared error Nuber of training steps Nuber of hidden neurons Overall recognition rate (%) Nuber of training steps Nuber of hidden neurons (a) Mean squared error (b) Overall recognition rate Figure 5. Mean squared error and overall recognition rate with different nubers of hidden neurons It can be seen fro Figure 5(a) that the ean squared error declines with the increase of the training steps, and it tends to stabilize when the training step is between 65 and 8, indicating that the training process of MLP neural networ is copleted. The final ean squared error has a iniu 7

8 ITM Web of Conferences 11, 82 (217) DOI: 1.151/ itconf/ IST217 value when the MLP neural networ has 11 hidden neurons, and it is.35. It can be seen fro Figure 5(b) that the overall recognition rate with different nubers of hidden neurons increases with the nuber of training steps, but the final overall recognition rate has a difference for different nubers of hidden neurons. The overall recognition rate for the planetary gear has a axiu value when the MLP neural networ has 11 hidden neurons, and it reaches 91%. Hence, the MLP neural networ with 11 hidden neurons has the best perforance for the fault diagnosis of the planetary gear, and the detailed recognition rates of the MLP neural networ with 11 hidden neurons for the different planetary gears are shown in Table 1. Table 1. Detailed recognition rates of the MLP neural networ with 11 hidden neurons Noral gear Broen gear Gear with Gear with Wear gear one issing tooth tooth root crac Recognition rate 92.5% 95% 9% 87.5% 9% Overall recognition rate 91% It can be seen fro Table 1 that the overall recognition rate of the MLP neural networ with 11 hidden neurons reaches 91%. Of different planetary gear statuses, the broen gear has the highest recognition rate, and it reaches 95%. While the wear gear has the lowest recognition rate, and it reaches 87.5%. The recognition rates of the noral gear, gear with one issing tooth and gear with tooth root crac are 92.5%, 9% and 9%, respectively. The experients prove the planetary gear faults can be recognized by the proposed ethod based on the fuzzy entropy of CEEMDAN and MLP neural networ, aing it an effective fault diagnosis ethod for planetary gears. Conclusions A ethod of planetary gear fault diagnosis based on the fuzzy entropy of CEEMDAN and MLP neural networ is proposed. CEEMDAN is used to decopose the vibration signal into ultiple IMFs, the quality of the obtained IMFs and the copleteness of the decoposition process are greatly iproved. Fuzzy entropy cobining a fuzzy function and saple entropy is used to quantize the feature inforation contained in the IMFs, and it can be found fro data analysis that the fuzzy saple has a better perforance than that of saple entropy, aing it ore suitable for extracting the feature inforation. The fuzzy entropies of each IMF are defined as the input of MLP neural networ, and the ean squared error is selected as a criterion to train MLP neural networ. The testing saple set is used to verify the recognition perforance of the trained MLP neural networ, and the overall recognition rate with different nubers of hidden neurons is calculated. The overall recognition rate for planetary gear has a axiu value when the MLP neural networ has 11 hidden neurons, and it reaches 91%. The recognition rate of the broen gear reaches 95%, and followed by noral gear, gear with one issing tooth, gear with tooth root crac and wear gear. These results show that the proposed fault diagnosis ethod based on the fuzzy entropy of CEEMDAN and MLP neural networ has a better recognition perforance for planetary gear, aing it an effective fault diagnosis ethod for planetary gears. Acnowledgent This wor was supported by a Project Funded by the Priority Acadeic Progra Developent of Jiangsu Higher Education Institutions, the Natural Science Foundation of Jiangsu Province (grant nuber BK ) and Fundaental Research Funds for the Central Universities (grant nuber 214ZDPY31); this support is gratefully acnowledged. 8

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