Fault Early Warning Based on Improved Deep Neural Network of Auto-Encoder

Qilu University of Technology (Shandong Academy of Sciences), Shandong Computer Science Center (National Supercomputer Center in Jinan), Shandong Key Laboratory of Computer Networks, Jinan 250014, China School of Mechanical Engineering, Shandong University, Key Laboratory of High Efficiency and CleanMechanical Manufacture, Jinan 250100, China Beijing Institute of Petrochemical Technology, School of Information Engineering, Information Technology Teaching and Experiment Center, Beijing 102617, China


Introduction
Major accidents caused by mechanical equipment failures always alert people to ensure the safe and reliable operation of equipment. Especially, the equipment failure of the key production line will bring significant shutdown losses. It will not only cause huge economic losses but also endanger personal safety in serious cases. e fault diagnosis and prediction of mechanical equipment play an important role in improving equipment operation reliability and optimizing operation [1]. It is the premise to ensure the safe and stable operation of mechanical equipment, and it is very important for the maintenance of mechanical equipment.
Due to the large number of measuring points, monitoring parameters, and high sampling frequency of mechanical equipment, the complex condition of monitoring big data has been formed, which makes the fault diagnosis of mechanical equipment enter the era of big data [2][3][4][5][6]. e big data bring new opportunities and challenges to the health monitoring and fault diagnosis of mechanical equipment [7]. In recent years, deep learning has made a breakthrough in big data analysis in the fields of speech recognition and image recognition, and deep learning theory has been applied in the fields of mechanical fault diagnosis and health monitoring [8][9][10][11], but the diagnosis and identification of faults are still in the preliminary exploration stage [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. A deep neural network of auto-encoder (DAE) can extract fault features from noise signals and can be well combined with a sample enhancement method to deal with small sample problems [30][31][32][33][34][35][36][37]. Fault diagnosis methods based on deep learning are often realized through supervised learning of a large number of fault data, which requires a large number of fault marking data. However, in practical industrial applications, the monitoring data are a large amount of normal operation data, and the fault data under abnormal conditions are difficult to collect from the mechanical system. e lack of tag training data is a common problem. It is difficult to reconcile the contradiction between small fault samples and large sample training for deep learning. How to solve the contradiction between small sample fault state data in actual fault diagnosis and prediction and large training samples required by the deep network model is a difficult problem. In order to realize the rapid detection and early warning of faults, this study constructs a fault detection model based on the improved deep self-coding network based on the data in the normal operation state, which provides a solution for the lack of complete samples in the actual diagnosis.

DAE Model.
e DAE network is formed by stacking multiple automatic encoders (AE) [38,39] (shown in Figure 1). e input data in high-dimensional space are converted into the coding vector in low-dimensional space through the coding network, and the coding vector in lowdimensional space is reconstructed back to the original input data through the decoding network.

Fault Early Warning Model.
When the equipment is in a normal state, the input and output of DAE fit very well, the original structure and stable relationship between variables have been maintained, and the reconstruction error of corresponding DAE is in dynamic and stable change. When the equipment is abnormal, it will cause the change of relevant variables, and the internal correlation of feature space will be destroyed which will be reflected in the error trend of variables. e reconstruction error of the DAE model will deviate from the original stable state and increase accordingly. It means that the fault occurs. erefore, the abnormal change of reconstruction error on monitoring parameters is used as the index to detect the fault in this study.
e reconstruction error of the variable is obtained from the difference between the reconstructed value and the actual value, as shown in the following formula: where R e is the reconstruction error of sample, x is the actual value, and x ′ is the reconstruction value. e threshold is set according to the distribution of reconstruction error of training samples, and the fault detection criteria are shown in the following formula: 3. e Improved Model. CNN was originally used to realize image classification and played an important role in the field of image classification. e vibration signal is one-dimensional data. Some scholars choose to process a one-dimensional vibration signal into a time-frequency map and input it into CNN as a two-dimensional image to realize fault diagnosis, which has achieved certain success. However, the above operations make the data processing inconvenient. erefore, the one-dimensional CNN (1d-CNN) [40,41] is used to directly process the original vibration signal. With the increase in network depth, the training becomes more and more difficult. Some special weight initialization strategies and batch normalization (BN) methods have greatly improved this problem. However, when the model converges, the methods bring another problem: with the increase of network depth, the training error does not decrease, but increases. Residual network (ResNet) solves the problem of training difficulty caused by network depth, and the network performance (accuracy and accuracy) is far better than the traditional network model. e original vibration signal is used as the input of 1d-CNN, and a self-coding network model is constructed, as shown in Figure 2.

The Process of Fault Early Warning Method
R e fluctuates within the threshold range under normal conditions. When R e exceeds the threshold and remains above the threshold, it can be determined that the equipment has failed. e fault prediction method based on DAE mainly includes offline model training, reconstruction error construction, and online fault detection, as shown in Figure 3.

Offline Model Training.
e vibration signal in normal conditions collected by the sensor is normalized as samples x i (i � 1, 2, . . . , n). e samples are divided into training set and test set. e training of the DAE model is shown in Figure 4. e calculation between hidden layers is shown in the following formula:  Security and Communication Networks where x l i,j is the i-th characteristic value of the j-th feature vector value in the L-th layer of DAE, w l−1 i,j is weight coefficient, L is the convolution kernel size, F is the activation function, and b is the deviation value.
Add an output layer after the last hidden layer, the output of DAE is shown in the following formula: where x i ′ is the i-th output value of DAE, x i,j is the i-th characteristic value of the j-th feature vector in the last hidden layer of DAE, w i,j is weight coefficient, L is the convolution kernel size, F is the activation function, and b is the deviation value. e error between output and expected value is calculated by the following formula: where x i is the i-th true value of the sample, and x i ′ is i-th output value of the DAE.

Online Fault Detection.
e vibration signal f of the equipment is collected in real time by the acquisition device, and the samples are normalized to obtain the data x i . Input x i into the trained DAE model to obtain the corresponding reconstruction error R i e , and R i e is compared with evaluating the equipment status.

Determination of Adaptive Threshold
In the fault prediction, it is commonly used to set the fixed threshold of the reconstruction error. However, due to the influence of environment, modeling error, and other factors, the reconstruction error in a normal state may fluctuate. So, if a fixed threshold is set for state evaluation, it is easy to cause a false alarm. erefore, the adaptive reconstruction error is set for fault detection and early warning in this study.
According to the principle of statistics, the mean and variance of residuals are calculated as follows: where R j is the reconstruction error corresponding to different times. e confidence interval of the mean value (the confidence is 1 − α) can be expressed as the following formula: where α is the confidence level, and z is the correlation coefficient of the confidence level. In practical application, the confidence is usually set to be 95%-99%. If the confidence is 95%, then z is 1.96, and the threshold can be obtained from the following formula: Take R thl as the threshold. When the residual exceeds this threshold and remains above the threshold, it indicates that the system is abnormal and in the early stage of fault. Figure 5, the data are collected from the two-stage gearbox. e gear speed change is controlled by a motor. e torque is provided by the magnetic brake and can be adjusted by changing the input voltage. e pinion with 32 teeth and 80 teeth is installed on the first-stage input shaft. e second stage consists of a 48 teeth pinion and a 64 teeth pinion. e input shaft speed is measured by the tachometer, and the gear vibration signal is measured by the accelerometer. e vibration signals of normal and fault samples used in this study are shown in Figure 6 and Figure 7.

Model Parameter of Improved DAE.
A seven-layer DAE model is constructed in this study. e network structure parameter is shown in Table 1, and the parameter of the model is shown in Table 2.

DAE Model Test of Gearbox under Normal Condition.
After the model is trained, the data of the gearbox under normal state are tested. e adaptive threshold is calculated by (9). e change trend of R e obtained from DAE is shown  Security and Communication Networks 5 in Figure 8. It can be seen that R e of the gearbox is always within the adaptive threshold range under normal conditions.

DAE Model Test of Gearbox under Normal Condition.
e data before and after the fault are used to verify the fault detection effect of the model. When the model is used in the  gearbox fault state, calculate R e ., e trend of R e is shown in Figure 9. It can be seen that R e exceeds the threshold at 2200, and the value is basically above the threshold. e gearbox fault can be determined, and the early warning of fault can be carried out.

Conclusion
is study presents a fault detection method based on normal operation data, which solves the contradiction between small sample fault data and large training samples required by the deep network model. e main conclusions are as follows: (1) An improved DAE network is designed, which directly uses the original vibration data for fault detection, and the data in the normal state are used for unsupervised pretraining and supervised fine-tuning of the network. In this method, the reconstruction error is selected as the fault state parameter. In order to reduce the misjudgment caused by environmental factors, the adaptive threshold of reconstruction error is introduced as the decision-making basis of fault early warning.  Security and Communication Networks monitoring data, advanced deep learning algorithm and comprehensive high-precision prediction model of multiple environmental factors outside the gearbox will be the next focus of this study.
Data Availability e data set used in this article can be obtained from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest regarding this work.