# Comprehensive Analysis of Fault Diagnosis Methods for Aluminum Electrolytic Control System

Authors: Jie-jia Li; Xiao-yan Han; Peng Zhou; Xiao-yu Sun; Na Chang
Journal: Advances in Materials Science and Engineering
 (2014)

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## Abstract

This paper established the fault diagnosis system of aluminum electrolysis, according to the characteristics of the faults in aluminum electrolysis. This system includes two subsystems; one is process fault subsystem and the other is fault subsystem. Process fault subsystem includes the subneural network layer and decision fusion layer. Decision fusion neural network verifies the diagnosis result of the subneural network by the information transferring over the network and gives the decision of fault synthetically. EMD algorithm is used for data preprocessing of current signal in stator of the fault subsystem. Wavelet decomposition is used to extract feature on current signal in the stator; then, the system inputs the feature to the rough neural network for fault diagnosis and fault classification. The rough neural network gives the results of fault diagnosis. The simulation results verify the feasibility of the method.


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## Body

## 1. Introduction

Aluminum electrolysis process is a nonlinear, coupling, time-varying, and time-delay process. The working current in the aluminum electrolysis process is usually in tens or hundreds of thousands of amperes. The process of aluminum electrolysis is in strong electric field, strong magnetic field, and strong thermal field. There is mutual interference between the three fields. So the environment is very bad. In the process of aluminum electrolysis there are process fault and system fault. Process fault happened because of the destroyed balance; the balance includes material balance and energy balance in the electrolytic tank. System fault is caused by the actuator motor fault in the process of electrolysis. In view of the above situations, this paper uses an aluminum electrolysis fault diagnosis system. This system can not only detect fault of aluminum electrolysis process but also can be used to detect the system fault of aluminum electrolysis. The principle of the aluminum electrolysis fault diagnosis system is shown in Figure1.Figure 1
Aluminum electrolysis fault diagnosis system.As shown in Figure1, the system is divided into two subsystems: a process fault diagnosis system and a system fault diagnosis system. Process fault diagnosis subsystem is used to test the aluminum electrolysis anode effect and the rolling aluminum fault occurred in the process. System fault diagnosis system is used for detecting bearing fault and broken bar fault of the motor in the process of aluminum electrolysis.


## 2. Establishing the Fault Diagnosis Model

### 2.1. Process Fault Diagnosis Subsystem

The model of process aluminum electrolysis is composed of data acquisition module, data processing module, two subnetworks, and decision fusion neural network [1]. Two subnetworks are as follows: one is detecting anode effect and the other is rolling aluminum. The fault diagnosis principle is shown in Figure 2. In fault diagnosis, the processed data input two subnetworks according to the nature of the fault, and the correlation is between parameters and fault. In order to simplify the fault diagnosis network structure, the method of principal component analysis is used. It can determinate main components and reduce the variable input of the subnetwork. Fault information of each subnetwork is summarized by decision fusion network. Decision fusion network gives the final results of fault diagnosis. The use of decision fusion network will greatly improve the accuracy of fault diagnosis and can compound fault diagnosis effectively.Figure 2
The structure of anode effect subnetwork.


#### 2.1.1. Data Acquisition and Data Processing

Data acquisition and data processing have an important impact on learning speed and modeling accuracy of the network. They are essential to establish the network mode. The process could be divided into three parts: data acquisition and determining variable, data normalization, and inspection and elimination of false value [2].(
1)  Data Acquisition and
Determining
Variable. In the aluminum electrolysis fault diagnosis system, the fault type is bound up with many parameters of electrolyzer. In this paper, the parameters related to aluminum electrolysis fault are the electrolyte temperature at time k, series of current, voltage, cell resistance change rate at time K, k-1, and K-2. These parameters after being distributed can be used as the input of the subneural network.(
2)  Data Normalization. Because data parameters are collected in different units, there is a great difference between the sizes of the value. Larger value will greatly reduce the convergence speed of neural network [3]. Therefore, in order to improve the training speed of the model and the accuracy of the fault diagnosis model, the line current, voltage, electrolyte temperature, and other variables are normalized, the process uses the following method:
(1)xi=x-i-AiBi-Ai wherex-i is the actual value of the input in the network; Bi is the upper limit value; Ai is the lower limit value corresponding to input node; xi is the value of the sample.(
3)  Inspection and Elimination of False Value. The data will introduce some spurious values in the table. When data was collected by the computer automatically, these false values often deviate with the nearby value. False values cause the accuracy of the model to decrease and even led to a wrong conclusion. Therefore, before establishing the model, the filter processing for data is necessary. This paper uses the weighted average filtering method.


#### 2.1.2. Designing Subnetwork Structure

Because of the complexity and big delay characteristics of the process of aluminum electrolysis, for each subnetwork, using the traditional model is hard to make an accurate diagnosis. So this paper uses the improved Elman neural network. Take the anode effect subnetwork for example; 3 is the number of input nodes of the network. The output of the network uses a single node output; it means the number of output layer nodes of the network is 1 [4]. The hidden layer and structure layer have 2 nodes; the structure of anode effect sub network is shown in Figure 2. By training the neural network, we determine the structure and parameters of neural network. The output value of the neural network is between 0 and 1. WhenR1 = 0 (approximately 0), it means electrolytic tank without the occurrence of anode effect; whenR1 = 1 (approximately 1), it means a cell anode effect.A mathematical model for the network algorithm is as follows:(2)xc(k)=αxc(k-1)+x(k-1),(3)x(k)=f(w1xc(k)+w2u(k)),(4)r(k)=g(w3x(k)).
The learning algorithm is briefly as follows.Let the actual network output of stepk be r(k), the target output of step k is rd(k) and error function is defined as
(5)E(k)=12(rd(k)-r(k))T(rd(k)-r(k))Calculate partial derivatives ofE(k) to connection power w1, w2, and w3, respectively. By the gradient descent method the Elman neural network learning algorithm can be improved [5]:
(6)Δwij1(k)=-η1σE(k)σwij1(k)=-η1σE(k)σri(k)σri(k)σxc(k)σxc(k)σx(k)σx(k)σwij1(k)=-η1(rid(k)-ri(k))gj(∙)fj(∙)xc(k),Δwij2(k)=-η2σE(k)σwij2(k)=-η2σE(k)σri(k)σri(k)σxc(k)σxc(k)σx(k)σx(k)σwij2(k)=-η2(rid(k)-ri(k))gj(∙)fj(∙)u(k),Δwij3(k)=-η3σE(k)σwij3(k)=-η3σE(k)σri(k)σri(k)σxc(k)σxc(k)σx(k)σx(k)σwij3(k)=-η3(rid(k)-ri(k))gj(∙)fj(∙)x(k).
In type w1, w2, and w3 are the learning rates, respectively, for η1, η2, and η3.


#### 2.1.3. Design Decision Fusion Network

Third neural network is decision fusion network. It uses the wavelet neural network structure. The output of the pre-subnetwork is the input of the third neural network [6]. The number of fault diagnosis network is 2, so the input number of decision fusion network is 2. In this paper, wavelet neural network is used for fault fusion in the aluminum electrolysis, and sample data for training and testing sample data are captured in the field data. The fault diagnosis of aluminum electrolysis, anode effect, rolling aluminum fault, rolling aluminum, and anode effect occur at the same time. The decision network has 4 output modes. Fault categories corresponding to the various outputs are given in Table 1.Table 1
The network fault model and the corresponding output value.
Fault classification
Output value
Y
2
Y
1
Normal system
0
0
Anode effect
1
0
Rolling aluminum fault
0
1
Rolling aluminum and anode effect
1
1Decision fusion network uses wavelet neural network structure. It is composed of input layer, hidden layer, and output layer. The principle is as follows: first, choose wavelet functions; then, the wavelet functions replace Sigmoid BP network in the hidden layer. The algorithm of the network still adopts the relevant algorithm of BP network. Finally linear superposition by wavelet basis function will be selected; thereby, we established a wavelet neural network.


### 2.2. System Fault Diagnosis Subsystem

#### 2.2.1. The Structure of Fault Diagnosis Model

When induction motor produces various faults, the waveforms of the air-gap flux will change, leading to the harmonic component of the current in stator to change. Different faults lead to different changes of the waveform and current in stator contains independent information under different status in the motor, so analysis of the current in stator can detect the faults in the induction motor. Analysis of the current in stator is a non-invasive method of fault detection. It only keeps watch on the current and does not interfere in the internal structure of the motor. So we put the current in stator as the research object and then detect the bearing fault and broken rotor bar fault. A major difficulty is the noise that is inescapable in the analysis of the current in stator; thus, eliminating effectively the interference of the noise is one of the key issues of induction motor fault diagnosis. The collected stator current signals are stationary signals generally with the traditional signal analysis methods such as Fourier transform that has some limitations. This paper adopts the EMD algorithm for data preprocessing on various stator current signals data preprocessing; it has high adaptive decomposition ability and good ability. It uses the wavelet analysis extract feature of the current which has been denied and then inputs the characteristics which have been extracted to the rough neural network fault diagnosis. Finally the fault diagnosis is given [7].


#### 2.2.2. Data Preprocessing

There is a difficulty in the fault diagnosis of induction motor using stator current signal. It is inevitable to the collected signals by different kinds of noise interference, and the presence of noise will directly affect the fault feature information extraction and thus affects the accuracy of fault diagnosis. Preprocessing current signal in stator will improve signal-to-noise ratio. It is important for fault detection. In this paper, the pretreatment of empirical mode decomposition method is applied to the current signal in stator to remove high frequency noise in the signal. First, we use the EMD method to decompose the fault signal; then, the Hilbert spectrum analysis should be used for each IMF component. Due to the high-frequency noise in the low voltage, distribution networks are mainly concentrated in more than 10 KHz. We remove the instantaneous frequency which is higher than 10 KHz IMF component, so as to achieve the purpose of removing high frequency noise. EMD decomposition process is shown in Figure3.Figure 3
EMD decomposition process.Hilbert transformation based on EMD aims to obtain the Hilbert spectrum of the signal for time-frequency analysis. If the basic modal components group for a signal is known, Hilbert transformation can be performed on each IMF. Then according to formula (1), we obtain the instantaneous frequency:
(7)ω(t)=dϕ(t)dt,x(t)=∑i=1nimfi(t)+rn(t),wherern(t) is the remainder, representing the average trend of the signal, and each IMF component, imf1(t), imf2(t), or imfn(t), includes different frequency components from high to low in signal, respectively.Hill transformation for each basic modal component is in formula (2):
(8)x(t)=rnRe∑i=1nai(t)ejϕ(t)=Re∑i=1nai(t)ei∫ωi(t)dt,
where Re is the real part and rn is omitted in the derivation. Signal amplitude may be expressed as a time function or a frequency function in the three-dimensional space by (3). This amplitude of the signal is called contour in the time frequency plane. This amplitude distribution is known as H(W,t) in Hilbert spectrum and is referred to as Hilbert spectrum. It is denoted as
(9)H(ω,t)=Re∑i=1nai(t)ei∫ωi(t)dt.Then, it can be defined as boundary spectrum:(10)h(ω)=∫0TH(ω,t)dt,
where T is the sampling duration of the signal. Boundary spectrum is the integral of the time axis. Its significance lies in the expression of the contribution of each frequency in the overall amplitude, and it reflects in a sense of probability amplitude over the entire time on the accumulation of amplitude. The square of frequency of the Hilbert spectrum can get the instantaneous energy density:
(11)IE(t)=∫H(ω,t)2dω,
where IE(T) represents the time fluctuation of energy. Empirical mode decomposition method is called Hilbert spectrum analysis of Hilbert-Huang transformation based on the above introduction.


#### 2.2.3. Feature Extraction

How to extract feature information of the fault signal on the motor effectively is one of the most critical problems in motor fault diagnosis. This problem is the bottleneck of motor fault detection and it influences the accuracy of fault detection directly. Wavelet analysis has good performance in time-frequency localization signal, so it has become a powerful tool for fault feature extraction of signals. Wavelet packet analysis is a type of improved wavelet analysis. Wavelet packet analysis can divide the frequency band of the signal accurately, and it can make multilayer division for the frequency band of the fault signal. The wavelet analysis can choose the corresponding band adaptively on the basis of the characteristics of signal analysis. According to wavelet transform formula and the Parseval energy integral equation, we have(12)∫R|f(x)|2dx=∑f|cni|2.
As shown in formula (12), wavelet transform coefficient Cni is the dimension with energy. Because the signal decomposed into each frequency band has certain energy, the signal energy in each frequency band can be used as the feature vector to represent the running state of the machine. The three-layer decomposition diagram of wavelet packet is shown in Figure 4.Figure 4
Three-layer decomposition diagram of wavelet packet.S
n
i is the signal reconstruction of the first i band in n layer and Eni is the energy of signal Sni; then, we have
(13)Eni=∑p=1qxip,
where N is the wavelet packet decomposition level; decomposition band number i is i=0,1,2,…,2k-1; P is a signal reconstruction discrete of the first i band in n layer; xip is the amplitude of discrete point which is belongs to Sni; q is the data length. The total energy signal En is equal to the energy of each frequency band:
(14)Ek=∑i=0nEni.
After the energy normalization for feature factor in formula (14), we can get the fault feature vectors that extracted by wavelet packet decomposition
(15)T=[En0,En1,En2,…,Enm]Ek.In the process of extraction of fault features, we should select an appropriate value ofn. If the n value is too small, we cannot extract fault feature effectively, and if the n value is too large, the dimension of T is large and it will affect the diagnostic rate. This paper adopts the motor vibration signal decomposed by wavelet packet and U0(0) is the signal for each frequency band energy of the reconstructed signal. After energy normalization, fault feature vector T by wavelet packet decomposition is obtained.


#### 2.2.4. The Model of Fault Classification

In order to improve the accuracy of fault diagnosis and fault classification, this paper uses the rough neural network structure. The input of the rough neural network is the characteristic which is extracted by wavelet. There are four forms of the output: normal system, bearing fault, rotor broken bar fault, and bearing fault and rotor broken bar fault which occur simultaneously. Table2 shows the various outputs corresponding to the fault mode.Table 2
The network fault model and the corresponding output value.
Fault classification
Output
Y
2
Y
1
Normal system
0
0
Bearing fault
1
0
Broken rotor bar fault
0
1
Bearing fault and broken rotor bar fault
1
1In order to improve the convergence speed of neural network, the input layer rough neural network uses rough neurons, while the hidden layer and the output layer neurons are fuzzy neurons.The number of the rough neurons in input layer isn. The output of the rough neuron i is the rough membership degree mri of the input xi. The number of fuzzy neuron in hidden layer is m, each pair neurons between the hidden layer and input layer have two connection weights rij and ωij (i=1,2,...,n;j=1,2,...,m). The input neuron j of the hidden layers is the outputs and connection weights of the input layer
(16)hj=ti=1n[(rij⟶mri)sωij]=∏i=1n(rij⟶mri)sωij,
where t is operator t, s is operator s, and → is connect operator
(17)rij⟶mri={min⁡(1,mririj),rij≥mri,1,others,(rij⟶mri)sωij=(rij-mri)+ωij-(rij⟶mri)ωij.
The output layer only contains one fuzzy neuron, and its output O as input feature vector belongs to the degree of classification type in rough neural network:
(18)O=sj=1m[hjuj],
where uj is the connection weight and connection weight is between hidden layer neuron and the output neuron. Rough neural network uses the back propagation learning training, respectively, to adjust the connection weights of rij, wij, and uij:
(19)e=(y-o)2={y-sj=1m[ti=1n((rij⟶mri)sωij)uj]}2=F(rij,ωij,uj),
where y is the desired output for the rough neural network; O is the acute output; n and m, respectively, are the number of neurons in input layer and hidden layer. From (19) we know that the error e of output in the rough neural network is a function f of the connection weights; therefore, the adjustment formula weights can be expressed as
(20)uj(t+1)=uj(t)+α(∂e∂uj),rij(t+1)=rij(t)+α(∂e∂rij),ωij(t+1)=ωij(t)+α(∂e∂ωij),
where α is the learning efficiency and t is the number of iterations.


## 2.1. Process Fault Diagnosis Subsystem

The model of process aluminum electrolysis is composed of data acquisition module, data processing module, two subnetworks, and decision fusion neural network [1]. Two subnetworks are as follows: one is detecting anode effect and the other is rolling aluminum. The fault diagnosis principle is shown in Figure 2. In fault diagnosis, the processed data input two subnetworks according to the nature of the fault, and the correlation is between parameters and fault. In order to simplify the fault diagnosis network structure, the method of principal component analysis is used. It can determinate main components and reduce the variable input of the subnetwork. Fault information of each subnetwork is summarized by decision fusion network. Decision fusion network gives the final results of fault diagnosis. The use of decision fusion network will greatly improve the accuracy of fault diagnosis and can compound fault diagnosis effectively.Figure 2
The structure of anode effect subnetwork.


### 2.1.1. Data Acquisition and Data Processing

Data acquisition and data processing have an important impact on learning speed and modeling accuracy of the network. They are essential to establish the network mode. The process could be divided into three parts: data acquisition and determining variable, data normalization, and inspection and elimination of false value [2].(
1)  Data Acquisition and
Determining
Variable. In the aluminum electrolysis fault diagnosis system, the fault type is bound up with many parameters of electrolyzer. In this paper, the parameters related to aluminum electrolysis fault are the electrolyte temperature at time k, series of current, voltage, cell resistance change rate at time K, k-1, and K-2. These parameters after being distributed can be used as the input of the subneural network.(
2)  Data Normalization. Because data parameters are collected in different units, there is a great difference between the sizes of the value. Larger value will greatly reduce the convergence speed of neural network [3]. Therefore, in order to improve the training speed of the model and the accuracy of the fault diagnosis model, the line current, voltage, electrolyte temperature, and other variables are normalized, the process uses the following method:
(1)xi=x-i-AiBi-Ai wherex-i is the actual value of the input in the network; Bi is the upper limit value; Ai is the lower limit value corresponding to input node; xi is the value of the sample.(
3)  Inspection and Elimination of False Value. The data will introduce some spurious values in the table. When data was collected by the computer automatically, these false values often deviate with the nearby value. False values cause the accuracy of the model to decrease and even led to a wrong conclusion. Therefore, before establishing the model, the filter processing for data is necessary. This paper uses the weighted average filtering method.


### 2.1.2. Designing Subnetwork Structure

Because of the complexity and big delay characteristics of the process of aluminum electrolysis, for each subnetwork, using the traditional model is hard to make an accurate diagnosis. So this paper uses the improved Elman neural network. Take the anode effect subnetwork for example; 3 is the number of input nodes of the network. The output of the network uses a single node output; it means the number of output layer nodes of the network is 1 [4]. The hidden layer and structure layer have 2 nodes; the structure of anode effect sub network is shown in Figure 2. By training the neural network, we determine the structure and parameters of neural network. The output value of the neural network is between 0 and 1. WhenR1 = 0 (approximately 0), it means electrolytic tank without the occurrence of anode effect; whenR1 = 1 (approximately 1), it means a cell anode effect.A mathematical model for the network algorithm is as follows:(2)xc(k)=αxc(k-1)+x(k-1),(3)x(k)=f(w1xc(k)+w2u(k)),(4)r(k)=g(w3x(k)).
The learning algorithm is briefly as follows.Let the actual network output of stepk be r(k), the target output of step k is rd(k) and error function is defined as
(5)E(k)=12(rd(k)-r(k))T(rd(k)-r(k))Calculate partial derivatives ofE(k) to connection power w1, w2, and w3, respectively. By the gradient descent method the Elman neural network learning algorithm can be improved [5]:
(6)Δwij1(k)=-η1σE(k)σwij1(k)=-η1σE(k)σri(k)σri(k)σxc(k)σxc(k)σx(k)σx(k)σwij1(k)=-η1(rid(k)-ri(k))gj(∙)fj(∙)xc(k),Δwij2(k)=-η2σE(k)σwij2(k)=-η2σE(k)σri(k)σri(k)σxc(k)σxc(k)σx(k)σx(k)σwij2(k)=-η2(rid(k)-ri(k))gj(∙)fj(∙)u(k),Δwij3(k)=-η3σE(k)σwij3(k)=-η3σE(k)σri(k)σri(k)σxc(k)σxc(k)σx(k)σx(k)σwij3(k)=-η3(rid(k)-ri(k))gj(∙)fj(∙)x(k).
In type w1, w2, and w3 are the learning rates, respectively, for η1, η2, and η3.


### 2.1.3. Design Decision Fusion Network

Third neural network is decision fusion network. It uses the wavelet neural network structure. The output of the pre-subnetwork is the input of the third neural network [6]. The number of fault diagnosis network is 2, so the input number of decision fusion network is 2. In this paper, wavelet neural network is used for fault fusion in the aluminum electrolysis, and sample data for training and testing sample data are captured in the field data. The fault diagnosis of aluminum electrolysis, anode effect, rolling aluminum fault, rolling aluminum, and anode effect occur at the same time. The decision network has 4 output modes. Fault categories corresponding to the various outputs are given in Table 1.Table 1
The network fault model and the corresponding output value.
Fault classification
Output value
Y
2
Y
1
Normal system
0
0
Anode effect
1
0
Rolling aluminum fault
0
1
Rolling aluminum and anode effect
1
1Decision fusion network uses wavelet neural network structure. It is composed of input layer, hidden layer, and output layer. The principle is as follows: first, choose wavelet functions; then, the wavelet functions replace Sigmoid BP network in the hidden layer. The algorithm of the network still adopts the relevant algorithm of BP network. Finally linear superposition by wavelet basis function will be selected; thereby, we established a wavelet neural network.


## 2.1.1. Data Acquisition and Data Processing

Data acquisition and data processing have an important impact on learning speed and modeling accuracy of the network. They are essential to establish the network mode. The process could be divided into three parts: data acquisition and determining variable, data normalization, and inspection and elimination of false value [2].(
1)  Data Acquisition and
Determining
Variable. In the aluminum electrolysis fault diagnosis system, the fault type is bound up with many parameters of electrolyzer. In this paper, the parameters related to aluminum electrolysis fault are the electrolyte temperature at time k, series of current, voltage, cell resistance change rate at time K, k-1, and K-2. These parameters after being distributed can be used as the input of the subneural network.(
2)  Data Normalization. Because data parameters are collected in different units, there is a great difference between the sizes of the value. Larger value will greatly reduce the convergence speed of neural network [3]. Therefore, in order to improve the training speed of the model and the accuracy of the fault diagnosis model, the line current, voltage, electrolyte temperature, and other variables are normalized, the process uses the following method:
(1)xi=x-i-AiBi-Ai wherex-i is the actual value of the input in the network; Bi is the upper limit value; Ai is the lower limit value corresponding to input node; xi is the value of the sample.(
3)  Inspection and Elimination of False Value. The data will introduce some spurious values in the table. When data was collected by the computer automatically, these false values often deviate with the nearby value. False values cause the accuracy of the model to decrease and even led to a wrong conclusion. Therefore, before establishing the model, the filter processing for data is necessary. This paper uses the weighted average filtering method.


## 2.1.2. Designing Subnetwork Structure

Because of the complexity and big delay characteristics of the process of aluminum electrolysis, for each subnetwork, using the traditional model is hard to make an accurate diagnosis. So this paper uses the improved Elman neural network. Take the anode effect subnetwork for example; 3 is the number of input nodes of the network. The output of the network uses a single node output; it means the number of output layer nodes of the network is 1 [4]. The hidden layer and structure layer have 2 nodes; the structure of anode effect sub network is shown in Figure 2. By training the neural network, we determine the structure and parameters of neural network. The output value of the neural network is between 0 and 1. WhenR1 = 0 (approximately 0), it means electrolytic tank without the occurrence of anode effect; whenR1 = 1 (approximately 1), it means a cell anode effect.A mathematical model for the network algorithm is as follows:(2)xc(k)=αxc(k-1)+x(k-1),(3)x(k)=f(w1xc(k)+w2u(k)),(4)r(k)=g(w3x(k)).
The learning algorithm is briefly as follows.Let the actual network output of stepk be r(k), the target output of step k is rd(k) and error function is defined as
(5)E(k)=12(rd(k)-r(k))T(rd(k)-r(k))Calculate partial derivatives ofE(k) to connection power w1, w2, and w3, respectively. By the gradient descent method the Elman neural network learning algorithm can be improved [5]:
(6)Δwij1(k)=-η1σE(k)σwij1(k)=-η1σE(k)σri(k)σri(k)σxc(k)σxc(k)σx(k)σx(k)σwij1(k)=-η1(rid(k)-ri(k))gj(∙)fj(∙)xc(k),Δwij2(k)=-η2σE(k)σwij2(k)=-η2σE(k)σri(k)σri(k)σxc(k)σxc(k)σx(k)σx(k)σwij2(k)=-η2(rid(k)-ri(k))gj(∙)fj(∙)u(k),Δwij3(k)=-η3σE(k)σwij3(k)=-η3σE(k)σri(k)σri(k)σxc(k)σxc(k)σx(k)σx(k)σwij3(k)=-η3(rid(k)-ri(k))gj(∙)fj(∙)x(k).
In type w1, w2, and w3 are the learning rates, respectively, for η1, η2, and η3.


## 2.1.3. Design Decision Fusion Network

Third neural network is decision fusion network. It uses the wavelet neural network structure. The output of the pre-subnetwork is the input of the third neural network [6]. The number of fault diagnosis network is 2, so the input number of decision fusion network is 2. In this paper, wavelet neural network is used for fault fusion in the aluminum electrolysis, and sample data for training and testing sample data are captured in the field data. The fault diagnosis of aluminum electrolysis, anode effect, rolling aluminum fault, rolling aluminum, and anode effect occur at the same time. The decision network has 4 output modes. Fault categories corresponding to the various outputs are given in Table 1.Table 1
The network fault model and the corresponding output value.
Fault classification
Output value
Y
2
Y
1
Normal system
0
0
Anode effect
1
0
Rolling aluminum fault
0
1
Rolling aluminum and anode effect
1
1Decision fusion network uses wavelet neural network structure. It is composed of input layer, hidden layer, and output layer. The principle is as follows: first, choose wavelet functions; then, the wavelet functions replace Sigmoid BP network in the hidden layer. The algorithm of the network still adopts the relevant algorithm of BP network. Finally linear superposition by wavelet basis function will be selected; thereby, we established a wavelet neural network.


## 2.2. System Fault Diagnosis Subsystem

### 2.2.1. The Structure of Fault Diagnosis Model

When induction motor produces various faults, the waveforms of the air-gap flux will change, leading to the harmonic component of the current in stator to change. Different faults lead to different changes of the waveform and current in stator contains independent information under different status in the motor, so analysis of the current in stator can detect the faults in the induction motor. Analysis of the current in stator is a non-invasive method of fault detection. It only keeps watch on the current and does not interfere in the internal structure of the motor. So we put the current in stator as the research object and then detect the bearing fault and broken rotor bar fault. A major difficulty is the noise that is inescapable in the analysis of the current in stator; thus, eliminating effectively the interference of the noise is one of the key issues of induction motor fault diagnosis. The collected stator current signals are stationary signals generally with the traditional signal analysis methods such as Fourier transform that has some limitations. This paper adopts the EMD algorithm for data preprocessing on various stator current signals data preprocessing; it has high adaptive decomposition ability and good ability. It uses the wavelet analysis extract feature of the current which has been denied and then inputs the characteristics which have been extracted to the rough neural network fault diagnosis. Finally the fault diagnosis is given [7].


### 2.2.2. Data Preprocessing

There is a difficulty in the fault diagnosis of induction motor using stator current signal. It is inevitable to the collected signals by different kinds of noise interference, and the presence of noise will directly affect the fault feature information extraction and thus affects the accuracy of fault diagnosis. Preprocessing current signal in stator will improve signal-to-noise ratio. It is important for fault detection. In this paper, the pretreatment of empirical mode decomposition method is applied to the current signal in stator to remove high frequency noise in the signal. First, we use the EMD method to decompose the fault signal; then, the Hilbert spectrum analysis should be used for each IMF component. Due to the high-frequency noise in the low voltage, distribution networks are mainly concentrated in more than 10 KHz. We remove the instantaneous frequency which is higher than 10 KHz IMF component, so as to achieve the purpose of removing high frequency noise. EMD decomposition process is shown in Figure3.Figure 3
EMD decomposition process.Hilbert transformation based on EMD aims to obtain the Hilbert spectrum of the signal for time-frequency analysis. If the basic modal components group for a signal is known, Hilbert transformation can be performed on each IMF. Then according to formula (1), we obtain the instantaneous frequency:
(7)ω(t)=dϕ(t)dt,x(t)=∑i=1nimfi(t)+rn(t),wherern(t) is the remainder, representing the average trend of the signal, and each IMF component, imf1(t), imf2(t), or imfn(t), includes different frequency components from high to low in signal, respectively.Hill transformation for each basic modal component is in formula (2):
(8)x(t)=rnRe∑i=1nai(t)ejϕ(t)=Re∑i=1nai(t)ei∫ωi(t)dt,
where Re is the real part and rn is omitted in the derivation. Signal amplitude may be expressed as a time function or a frequency function in the three-dimensional space by (3). This amplitude of the signal is called contour in the time frequency plane. This amplitude distribution is known as H(W,t) in Hilbert spectrum and is referred to as Hilbert spectrum. It is denoted as
(9)H(ω,t)=Re∑i=1nai(t)ei∫ωi(t)dt.Then, it can be defined as boundary spectrum:(10)h(ω)=∫0TH(ω,t)dt,
where T is the sampling duration of the signal. Boundary spectrum is the integral of the time axis. Its significance lies in the expression of the contribution of each frequency in the overall amplitude, and it reflects in a sense of probability amplitude over the entire time on the accumulation of amplitude. The square of frequency of the Hilbert spectrum can get the instantaneous energy density:
(11)IE(t)=∫H(ω,t)2dω,
where IE(T) represents the time fluctuation of energy. Empirical mode decomposition method is called Hilbert spectrum analysis of Hilbert-Huang transformation based on the above introduction.


### 2.2.3. Feature Extraction

How to extract feature information of the fault signal on the motor effectively is one of the most critical problems in motor fault diagnosis. This problem is the bottleneck of motor fault detection and it influences the accuracy of fault detection directly. Wavelet analysis has good performance in time-frequency localization signal, so it has become a powerful tool for fault feature extraction of signals. Wavelet packet analysis is a type of improved wavelet analysis. Wavelet packet analysis can divide the frequency band of the signal accurately, and it can make multilayer division for the frequency band of the fault signal. The wavelet analysis can choose the corresponding band adaptively on the basis of the characteristics of signal analysis. According to wavelet transform formula and the Parseval energy integral equation, we have(12)∫R|f(x)|2dx=∑f|cni|2.
As shown in formula (12), wavelet transform coefficient Cni is the dimension with energy. Because the signal decomposed into each frequency band has certain energy, the signal energy in each frequency band can be used as the feature vector to represent the running state of the machine. The three-layer decomposition diagram of wavelet packet is shown in Figure 4.Figure 4
Three-layer decomposition diagram of wavelet packet.S
n
i is the signal reconstruction of the first i band in n layer and Eni is the energy of signal Sni; then, we have
(13)Eni=∑p=1qxip,
where N is the wavelet packet decomposition level; decomposition band number i is i=0,1,2,…,2k-1; P is a signal reconstruction discrete of the first i band in n layer; xip is the amplitude of discrete point which is belongs to Sni; q is the data length. The total energy signal En is equal to the energy of each frequency band:
(14)Ek=∑i=0nEni.
After the energy normalization for feature factor in formula (14), we can get the fault feature vectors that extracted by wavelet packet decomposition
(15)T=[En0,En1,En2,…,Enm]Ek.In the process of extraction of fault features, we should select an appropriate value ofn. If the n value is too small, we cannot extract fault feature effectively, and if the n value is too large, the dimension of T is large and it will affect the diagnostic rate. This paper adopts the motor vibration signal decomposed by wavelet packet and U0(0) is the signal for each frequency band energy of the reconstructed signal. After energy normalization, fault feature vector T by wavelet packet decomposition is obtained.


### 2.2.4. The Model of Fault Classification

In order to improve the accuracy of fault diagnosis and fault classification, this paper uses the rough neural network structure. The input of the rough neural network is the characteristic which is extracted by wavelet. There are four forms of the output: normal system, bearing fault, rotor broken bar fault, and bearing fault and rotor broken bar fault which occur simultaneously. Table2 shows the various outputs corresponding to the fault mode.Table 2
The network fault model and the corresponding output value.
Fault classification
Output
Y
2
Y
1
Normal system
0
0
Bearing fault
1
0
Broken rotor bar fault
0
1
Bearing fault and broken rotor bar fault
1
1In order to improve the convergence speed of neural network, the input layer rough neural network uses rough neurons, while the hidden layer and the output layer neurons are fuzzy neurons.The number of the rough neurons in input layer isn. The output of the rough neuron i is the rough membership degree mri of the input xi. The number of fuzzy neuron in hidden layer is m, each pair neurons between the hidden layer and input layer have two connection weights rij and ωij (i=1,2,...,n;j=1,2,...,m). The input neuron j of the hidden layers is the outputs and connection weights of the input layer
(16)hj=ti=1n[(rij⟶mri)sωij]=∏i=1n(rij⟶mri)sωij,
where t is operator t, s is operator s, and → is connect operator
(17)rij⟶mri={min⁡(1,mririj),rij≥mri,1,others,(rij⟶mri)sωij=(rij-mri)+ωij-(rij⟶mri)ωij.
The output layer only contains one fuzzy neuron, and its output O as input feature vector belongs to the degree of classification type in rough neural network:
(18)O=sj=1m[hjuj],
where uj is the connection weight and connection weight is between hidden layer neuron and the output neuron. Rough neural network uses the back propagation learning training, respectively, to adjust the connection weights of rij, wij, and uij:
(19)e=(y-o)2={y-sj=1m[ti=1n((rij⟶mri)sωij)uj]}2=F(rij,ωij,uj),
where y is the desired output for the rough neural network; O is the acute output; n and m, respectively, are the number of neurons in input layer and hidden layer. From (19) we know that the error e of output in the rough neural network is a function f of the connection weights; therefore, the adjustment formula weights can be expressed as
(20)uj(t+1)=uj(t)+α(∂e∂uj),rij(t+1)=rij(t)+α(∂e∂rij),ωij(t+1)=ωij(t)+α(∂e∂ωij),
where α is the learning efficiency and t is the number of iterations.


## 2.2.1. The Structure of Fault Diagnosis Model

When induction motor produces various faults, the waveforms of the air-gap flux will change, leading to the harmonic component of the current in stator to change. Different faults lead to different changes of the waveform and current in stator contains independent information under different status in the motor, so analysis of the current in stator can detect the faults in the induction motor. Analysis of the current in stator is a non-invasive method of fault detection. It only keeps watch on the current and does not interfere in the internal structure of the motor. So we put the current in stator as the research object and then detect the bearing fault and broken rotor bar fault. A major difficulty is the noise that is inescapable in the analysis of the current in stator; thus, eliminating effectively the interference of the noise is one of the key issues of induction motor fault diagnosis. The collected stator current signals are stationary signals generally with the traditional signal analysis methods such as Fourier transform that has some limitations. This paper adopts the EMD algorithm for data preprocessing on various stator current signals data preprocessing; it has high adaptive decomposition ability and good ability. It uses the wavelet analysis extract feature of the current which has been denied and then inputs the characteristics which have been extracted to the rough neural network fault diagnosis. Finally the fault diagnosis is given [7].


## 2.2.2. Data Preprocessing

There is a difficulty in the fault diagnosis of induction motor using stator current signal. It is inevitable to the collected signals by different kinds of noise interference, and the presence of noise will directly affect the fault feature information extraction and thus affects the accuracy of fault diagnosis. Preprocessing current signal in stator will improve signal-to-noise ratio. It is important for fault detection. In this paper, the pretreatment of empirical mode decomposition method is applied to the current signal in stator to remove high frequency noise in the signal. First, we use the EMD method to decompose the fault signal; then, the Hilbert spectrum analysis should be used for each IMF component. Due to the high-frequency noise in the low voltage, distribution networks are mainly concentrated in more than 10 KHz. We remove the instantaneous frequency which is higher than 10 KHz IMF component, so as to achieve the purpose of removing high frequency noise. EMD decomposition process is shown in Figure3.Figure 3
EMD decomposition process.Hilbert transformation based on EMD aims to obtain the Hilbert spectrum of the signal for time-frequency analysis. If the basic modal components group for a signal is known, Hilbert transformation can be performed on each IMF. Then according to formula (1), we obtain the instantaneous frequency:
(7)ω(t)=dϕ(t)dt,x(t)=∑i=1nimfi(t)+rn(t),wherern(t) is the remainder, representing the average trend of the signal, and each IMF component, imf1(t), imf2(t), or imfn(t), includes different frequency components from high to low in signal, respectively.Hill transformation for each basic modal component is in formula (2):
(8)x(t)=rnRe∑i=1nai(t)ejϕ(t)=Re∑i=1nai(t)ei∫ωi(t)dt,
where Re is the real part and rn is omitted in the derivation. Signal amplitude may be expressed as a time function or a frequency function in the three-dimensional space by (3). This amplitude of the signal is called contour in the time frequency plane. This amplitude distribution is known as H(W,t) in Hilbert spectrum and is referred to as Hilbert spectrum. It is denoted as
(9)H(ω,t)=Re∑i=1nai(t)ei∫ωi(t)dt.Then, it can be defined as boundary spectrum:(10)h(ω)=∫0TH(ω,t)dt,
where T is the sampling duration of the signal. Boundary spectrum is the integral of the time axis. Its significance lies in the expression of the contribution of each frequency in the overall amplitude, and it reflects in a sense of probability amplitude over the entire time on the accumulation of amplitude. The square of frequency of the Hilbert spectrum can get the instantaneous energy density:
(11)IE(t)=∫H(ω,t)2dω,
where IE(T) represents the time fluctuation of energy. Empirical mode decomposition method is called Hilbert spectrum analysis of Hilbert-Huang transformation based on the above introduction.


## 2.2.3. Feature Extraction

How to extract feature information of the fault signal on the motor effectively is one of the most critical problems in motor fault diagnosis. This problem is the bottleneck of motor fault detection and it influences the accuracy of fault detection directly. Wavelet analysis has good performance in time-frequency localization signal, so it has become a powerful tool for fault feature extraction of signals. Wavelet packet analysis is a type of improved wavelet analysis. Wavelet packet analysis can divide the frequency band of the signal accurately, and it can make multilayer division for the frequency band of the fault signal. The wavelet analysis can choose the corresponding band adaptively on the basis of the characteristics of signal analysis. According to wavelet transform formula and the Parseval energy integral equation, we have(12)∫R|f(x)|2dx=∑f|cni|2.
As shown in formula (12), wavelet transform coefficient Cni is the dimension with energy. Because the signal decomposed into each frequency band has certain energy, the signal energy in each frequency band can be used as the feature vector to represent the running state of the machine. The three-layer decomposition diagram of wavelet packet is shown in Figure 4.Figure 4
Three-layer decomposition diagram of wavelet packet.S
n
i is the signal reconstruction of the first i band in n layer and Eni is the energy of signal Sni; then, we have
(13)Eni=∑p=1qxip,
where N is the wavelet packet decomposition level; decomposition band number i is i=0,1,2,…,2k-1; P is a signal reconstruction discrete of the first i band in n layer; xip is the amplitude of discrete point which is belongs to Sni; q is the data length. The total energy signal En is equal to the energy of each frequency band:
(14)Ek=∑i=0nEni.
After the energy normalization for feature factor in formula (14), we can get the fault feature vectors that extracted by wavelet packet decomposition
(15)T=[En0,En1,En2,…,Enm]Ek.In the process of extraction of fault features, we should select an appropriate value ofn. If the n value is too small, we cannot extract fault feature effectively, and if the n value is too large, the dimension of T is large and it will affect the diagnostic rate. This paper adopts the motor vibration signal decomposed by wavelet packet and U0(0) is the signal for each frequency band energy of the reconstructed signal. After energy normalization, fault feature vector T by wavelet packet decomposition is obtained.


## 2.2.4. The Model of Fault Classification

In order to improve the accuracy of fault diagnosis and fault classification, this paper uses the rough neural network structure. The input of the rough neural network is the characteristic which is extracted by wavelet. There are four forms of the output: normal system, bearing fault, rotor broken bar fault, and bearing fault and rotor broken bar fault which occur simultaneously. Table2 shows the various outputs corresponding to the fault mode.Table 2
The network fault model and the corresponding output value.
Fault classification
Output
Y
2
Y
1
Normal system
0
0
Bearing fault
1
0
Broken rotor bar fault
0
1
Bearing fault and broken rotor bar fault
1
1In order to improve the convergence speed of neural network, the input layer rough neural network uses rough neurons, while the hidden layer and the output layer neurons are fuzzy neurons.The number of the rough neurons in input layer isn. The output of the rough neuron i is the rough membership degree mri of the input xi. The number of fuzzy neuron in hidden layer is m, each pair neurons between the hidden layer and input layer have two connection weights rij and ωij (i=1,2,...,n;j=1,2,...,m). The input neuron j of the hidden layers is the outputs and connection weights of the input layer
(16)hj=ti=1n[(rij⟶mri)sωij]=∏i=1n(rij⟶mri)sωij,
where t is operator t, s is operator s, and → is connect operator
(17)rij⟶mri={min⁡(1,mririj),rij≥mri,1,others,(rij⟶mri)sωij=(rij-mri)+ωij-(rij⟶mri)ωij.
The output layer only contains one fuzzy neuron, and its output O as input feature vector belongs to the degree of classification type in rough neural network:
(18)O=sj=1m[hjuj],
where uj is the connection weight and connection weight is between hidden layer neuron and the output neuron. Rough neural network uses the back propagation learning training, respectively, to adjust the connection weights of rij, wij, and uij:
(19)e=(y-o)2={y-sj=1m[ti=1n((rij⟶mri)sωij)uj]}2=F(rij,ωij,uj),
where y is the desired output for the rough neural network; O is the acute output; n and m, respectively, are the number of neurons in input layer and hidden layer. From (19) we know that the error e of output in the rough neural network is a function f of the connection weights; therefore, the adjustment formula weights can be expressed as
(20)uj(t+1)=uj(t)+α(∂e∂uj),rij(t+1)=rij(t)+α(∂e∂rij),ωij(t+1)=ωij(t)+α(∂e∂ωij),
where α is the learning efficiency and t is the number of iterations.


## 3. The Simulation Study

In this paper, based on aluminum electrolysis factory, we provide test data for simulation of fault diagnosis and these data include failure data before and after the occurrence of fault. As an example, considering the anode effect and rolling aluminum fault, we choose the data which are obtained before and after the occurrence of fault in 30 minutes. The outputsy1 andy2 of the network for anode effect that occurs are shown in Figure 5.Figure 5
Anode effect fault diagnosis.From the simulation curve in Figure5, it can be seen that the value of the outputsY1 andY2 is 0~0.2 in about 10 minutes ago and there is no obvious change. As a result, it can be considered that the output of the neural network is 0. After 16 minutes, the value of the outputY2 is larger than 0.5 and it can be considered that cold trough fault may occur. After 25 minutes, the value of outputY2 is larger than 0.9 and is close to 1. It can be considered that anode effect occurs.The outputs of the networkY1 and the networkY2 during rolling aluminum are shown in Figure 6: about 12 minutes ago, the output of the neural network ofY1 andY2 is about 0~0.2, and there is no obvious change. It can be ignored and electrolytic cell is in a normal state. 26 minutes later, the value of the outputY1 is larger than 0.9 and is close to 1. It can be seen that electrolytic tank has rolling aluminum fault.Figure 6
Rolling aluminum fault diagnosis.


## 4. Conclusion

In this paper, starting from the actual engineering diagnosis, aluminum electrolysis fault diagnosis system is established. This system includes aluminum electrolytic process fault subsystem and aluminum electrolytic system fault subsystem. The simulation results show that the system has a good diagnosis effect. In addition, the results verify the feasibility and effectiveness of the fault diagnosis method.



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*Source: 975317-2014-07-21.xml*