Comprehensive Analysis of Fault Diagnosis Methods for Aluminum Electrolytic Control System

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.


Introduction
Aluminum electrolysis process is a nonlinear, coupling, timevarying, 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 Figure 1.
As shown in Figure 1, 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.

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.
The structure of anode effect subnetwork.
network will greatly improve the accuracy of fault diagnosis and can compound fault diagnosis effectively.

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 , series of current, voltage, cell resistance change rate at time ,  − 1, and  − 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: where   is the actual value of the input in the network;   is the upper limit value;   is the lower limit value corresponding to input node;   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.When R1 = 0 (approximately 0), it means electrolytic tank without the occurrence of anode effect; when R1 = 1 (approximately 1), it means a cell anode effect.A mathematical model for the network algorithm is as follows: The learning algorithm is briefly as follows.
Let the actual network output of step  be (), the target output of step  is   () and error function is defined as Calculate partial derivatives of () to connection power  1 ,  2 , and  3 , respectively.By the gradient descent Advances in Materials Science and Engineering 3 method the Elman neural network learning algorithm can be improved [5]: In type  1 ,  2 , and  3 are the learning rates, respectively, for  1 ,  2 , and  3 .1. Decision 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.

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 highfrequency 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 Figure 3. 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. and minima of x(t) and find Whether R is a Then according to formula (1), we obtain the instantaneous frequency: where   () is the remainder, representing the average trend of the signal, and each IMF component, imf 1 (), imf 2 (), or imf n (), includes different frequency components from high to low in signal, respectively.Hill transformation for each basic modal component is in formula (2): where Re is the real part and   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 (, ) in Hilbert spectrum and is referred to as Hilbert spectrum.It is denoted as Then, it can be defined as boundary spectrum: where  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: where IE() represents the time fluctuation of energy.Empirical mode decomposition method is called Hilbert spectrum analysis of Hilbert-Huang transformation based on the above introduction.

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 As shown in formula (12), wavelet transform coefficient   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 threelayer decomposition diagram of wavelet packet is shown in Figure 4.   is the signal reconstruction of the first  band in  layer and   is the energy of signal   ; then, we have where  is the wavelet packet decomposition level; decomposition band number  is  = 0, 1, 2, . . ., 2 − 1;  is a signal reconstruction discrete of the first  band in  layer;   is the amplitude of discrete point which is belongs to   ;  is the data length.The total energy signal   is equal to the energy of each frequency band: After the energy normalization for feature factor in formula (14), we can get the fault feature vectors that extracted by wavelet packet decomposition In the process of extraction of fault features, we should select an appropriate value of .If the  value is too small, we cannot extract fault feature effectively, and if the  value is too large, the dimension of  is large and it will affect the diagnostic rate.This paper adopts the motor vibration signal decomposed by wavelet packet and  (0)  0 is the signal for each frequency band energy of the reconstructed signal.After energy normalization, fault feature vector  by wavelet packet decomposition is obtained.

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.Table 2 shows the various outputs corresponding to the fault mode.
In 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 is .The output of the rough neuron  is the rough membership The output layer only contains one fuzzy neuron, and its output  as input feature vector belongs to the degree of classification type in rough neural network: where   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   ,   , and   : where  is the desired output for the rough neural network;  is the acute output;  and , respectively, are the number of neurons in input layer and hidden layer.From (19) we know that the error  of output in the rough neural network where  is the learning efficiency and  is the number of iterations.

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 outputs y1 y2 of the network for anode effect that occurs are shown in Figure 5.
From the simulation curve in Figure 5, it can be seen that the value of the outputs Y1 and Y2 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 output Y2 is larger than 0.5 and it can be considered that cold trough fault may occur.After 25 minutes, the value of output Y2 is larger than 0.9 and is close to 1.It can be considered that anode effect occurs.
The outputs of the network Y1 and the network Y2 during rolling aluminum are shown in Figure 6: about 12 minutes ago, the output of the neural network of Y1 and Y2 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 output Y1 is larger than 0.9 and is close to 1.It can be seen that electrolytic tank has rolling aluminum fault.

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.
2.2.1.The Structure of Fault Diagnosis Model.When induction motor produces various faults, the waveforms of the airgap flux will change, leading to the harmonic component
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 2 Advances in Materials Science and Engineering

Table 1 :
[7] network fault model and the corresponding output value. 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].