Life prediction method of rolling bearing based on CNN-LSTM-AM

2.1. CNN

Convolution neural network is a kind of artificial neural network based on the biological “receptive field” mechanism, which is essentially a mapping from input to output, and can deal with image, voice, text and other data. it is widely used in image recognition, speech processing and fault diagnosis [21].

Fig. 1Schematic diagram of CNN structure

As shown in Fig. 1 is a typical CNN model structure [22], which consists of an input layer, a number of convolution layers, pooling layers, a fully connected layer and an output layer, while the convolution layer with feature extraction function is the core of CNN. The convolution layer convolution the input data through a number of different convolution kernels, coupled with bias to extract local features, which can enhance the significant features of the original signal. The specific calculation model of convolution layer is as follows:

where $x_j^l$ is the $j$th characteristic of the output of the $l$th convolution layer, $x_j^{l-1}$ is the output of the previous convolution layer, $k_{ij}^l$ is the kernel matrix of the convolution layer, $b_j^l$ is the offset of the convolution of the $l$ layer; * represents the convolution operation; $f\left(.\right)$ is the activation function.

The function of the pooling layer is to reduce the dimension of the features extracted by the convolution layer, reducing the amount of data while retaining useful information. CNN has three sampling operations, the most common of which is maximum pooling. The mathematical formula is as follows:

where $y_i^{l+1}\left(j\right)$ is the output value of the pooled layer, $x_i^l\left(k\right)$ is the output value of the pooled layer, $D_j$ is the width of the pooled core region.

2.2. LSTM

When dealing with sequence data, cyclic neural network is the most commonly used, while RNN is easy to cause gradient disappearance or gradient explosion when the input sequence is too long.

Long-term memory network is a special kind of RNN, which can learn long-term dependence and effectively solve the gradient problem in RNN. LSTM realizes the information processing in RNN through the gate control unit, and uses the switching degree of the door to determine the importance of the information to read, write or erase. The schematic diagram of the cellular structure of LSTM neurons is shown in Fig. 2.

Fig. 2Unit structure diagram of LSTM

The function and calculation process of each door of LSTM are as follows:

– The function of the forgetting door is to filter the information output from the previous state, that is, to delete the unimportant information:

where $f_t$ is the output state of the $t$-moment amnesia gate, $\sigma \left(\bullet \right)$ is the Sigmoid activation function, $W_f$ is the weight matrix, $h_{t-1}$ is the output of the previous moment, $x_t$ is the input of the current moment, $b_f$ is the bias of the amnesia gate.

– The input gate determines whether the new information about the current state is useful and adds it to the cellular state:

where $i_t$ is the output value of the $t$-time input gate, $W_i$ is the weight matrix of the input gate, $b_i$ is the bias matrix of the input gate, ${\tilde{c}}_t$ is the cell state information of the input gate, $\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}\left(\bullet \right)$ is the activation function, $W_c$ is the weight of the cell state, $b_c$ is the bias of the cell state.

– To update the status is to calculate the state value of the memory unit at the current time:

where $c_t$, $c_{t-1}$ are the cell state information at t-time and the last time, respectively.

– Outputs choose important information from the current state as output:

where $o_t$ is the output value of t-moment, $W_o$ is the weight matrix of the output gate, $b_o$ is the bias matrix of the output gate, $h_t$ is the output information of the current hidden state.

2.3. Attention mechanism

Attention mechanism is originated from the study of human vision, was proposed and applied by Bahdanau et al. [23] in 2014. In the case of limited computing power, Attention Mechanism, as a resource allocation scheme, can highlight important information. When the neural network is used to process a large amount of information, only the key information input can be selected for processing, so as to improve the efficiency of the neural network. In essence, the Attention mechanism is the weighted summation of the value of the elements in the Source, while Query and Key are used to calculate the weight coefficients of the corresponding Value. The specific calculation process is as follows:

(1) Calculate the similarity or correlation between Query and Key.

(2) Normalize the score of step (1) by introducing Softmax, the original calculated score is sorted into a probability distribution in which the sum of the weights of all elements is 1, and the weights of important elements can be more highlighted.

(3) Weight and sum the Value according to the weight coefficient, and the calculation formula is as follows:

where $Q$, $K$ and $V$ are the matrices composed of query vector, key vector and value vector, respectively. $D_K$ is the vector dimension of $Q$, $\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{m}\mathrm{a}\mathrm{x}(.)$ is a normalized function.

4.1. IMS Bearing datasets

In order to verify the effectiveness of the proposed method, the rolling bearing life cycle degradation data set published by the University of Cincinnati in PHM data Challenge in 2012 was selected [24]. The data set is collected from the PRONOSTIA test rig, which is shown in Fig. 4 as the structure diagram of the test rig. The platform is composed of AC motor, hydraulic loading system and PCB353B33 acceleration sensor. The rotational speed of the motor is 2000 rpm and the test bearing type is Rexnord ZA-2115 double-row bearing. The two accelerometers collect the bearing vibration signals on the $X$-axis and $Y$-axis respectively. The sampling frequency of the sensor is 20 KHz, and each sampling time is 1 s. Each file contains 20480 data of sampling points.

The experimental platform collects the life cycle degradation data of 17 bearings under 3 working conditions, and the bearing data set under each working condition is described in Table 1. In this paper, the life data of rolling bearings under condition 1 are selected for experimental verification.

PHM2012 rolling bearing data includes data in both horizontal and vertical directions. However, Singleton et al. [25] found that the horizontal vibration signal can provide more degradation information than the vertical vibration signal, so this paper only uses the rolling bearing vibration data collected in the horizontal direction for the test.

Fig. 4PRONOSTIA test rig

Taking bearing1-3 in the IMS data set as an example, the full life cycle time domain waveform of the vibration signal of bearing 1-3 in the horizontal direction is shown in Fig. 5. It can be seen from Fig. 5 that the amplitude of the time domain vibration signal of the rolling bearing 1-3 increases gradually with the passage of running time, which is beneficial to the extraction of health feature information with the trend of degradation. At the same time, the root mean square value (RMS) of bearing1-3 is extracted, and its degradation trend is shown in Fig. 6. By observing Fig. 6, we can see that the RMS value of bearing 1-3 increases slowly from 0, and then increases rapidly, which well reflects the degradation trend of bearing 1-3 in the process of operation. Therefore, this paper selects 14 time domain features, such as average, amplitude and peak, and 5 frequency domain features, such as root mean square frequency and average frequency, as the input of the life prediction model.

Fig. 5Bearing 1-3 full life cycle time domain waveform

Fig. 6Trend of root mean square of bearing 1-3

4.2. Performance degradation index

In order to quantitatively evaluate the effect of the model for bearing RUL prediction, this paper takes the root mean square error (RMSE) and Scoring function between the predicted value and the real value of rolling bearing remaining life as the evaluation index. Among them, RMSE can accurately reflect the average deviation between the predicted value and the real value. The smaller the RMSE, the better the performance of the model. The calculation formula is as follows:

where $N$ is the number of samples, $f\left(i\right)$ is the true value of the current sample, $\widehat{f}\left(i\right)$ is the predicted value of the model, $R_i$is the actual value of the remaining life of the bearing, ${\widehat{R}}_i$ is the predicted value of the remaining life of the bearing, ${Er}_i$ is the percentage error of the $I$th sample.

5.1. XJTU-SY Bearing datasets

In order to further illustrate the applicability of the proposed method, a control experiment was carried out by using the data set of XJTU-SY rolling bearing accelerated life test. The bearing accelerated life testing platform used in this test is designed by the joint laboratory and manufactured by Shenyang science and technology. The platform consists of an AC motor, a motor speed controller, a rotating shaft, a supporting bearing, a hydraulic loading system and a test bearing, as shown in Fig. 9.

Fig. 9Testbed of rolling element bearings

The adjustable working conditions of the test platform mainly include radial force and rotational speed, in which the radial force is generated by the hydraulic loading system, which acts on the bearing housing of the test bearing, and the rotational speed is set and adjusted by the speed controller of the AC motor. The test bearing is LDK UER204 rolling bearing, and its related parameters are shown in Table 3. A total of three types of working conditions are designed, as shown in Table 4, there are 5 bearings under each type of working conditions.

In order to obtain the vibration signal of the whole life cycle of the bearing, two unidirectional accelerometers are fixed on the horizontal and vertical direction of the test bearing through the magnetic seat, respectively. In the experiment, DT9837 portable dynamic signal collector is used to collect vibration signals. In the experiment, the sampling frequency is 25.6 kHz, the sampling interval is 1 min, and the sampling time is 1.28 s.

Because the load is applied in the horizontal direction, the vibration signal in this direction can contain more degradation information, so the horizontal vibration signal is selected for spectrum and envelope spectrum analysis. In the whole life cycle of bearing operation, the signal processing method is used to extract features from time domain and frequency domain respectively to reflect the degradation process from normal state to serious fault. Lei Yaguo, et al. [26] study found that with the passage of running time, the characteristic amplitude shows an increasing trend, which better reflects the degradation process of the bearing. Similarly, 14 time domain features and 5 frequency domain features are selected as the input of the life prediction model.

In order to evaluate the prediction effect of the proposed method, the prediction results of this method are compared with those of LSTM-AM, CNN-LSTM and CNN-BiLSTM algorithms. RMSE and Score are used to evaluate the performance of the model. The specific results are shown in Table 5.

It can be seen from Table 5 that compared with the other three methods, the prediction Score value of the proposed method is the lowest and the RMSE score is the highest. The comparison between CNN-LSTM- AM and CNN-LSTM algorithm shows that under the premise of increasing attention mechanism, the RMSE value of the proposed method is 13.8 % lower than that of CNN-LSTM algorithm, the score is 2.4 % higher, and the computing time of the model is 5.6 % faster. By assigning different attention weights to different stages of bearing degradation, the attention mechanism makes the model pay more attention to the important sequence information, which can improve the accuracy of RUL prediction and improve the computational efficiency.

Comparing the results of CNN-LSTM-AM and LSTM-AM prediction method, we can see that the RMSE value of the proposed method is 16.5 % lower than that of LSTM-AM algorithm, and the score is 4.7 % higher. The results prove that CNN-LSTM model can mine deep features and make full use of the context information of sequence data to complete the accurate prediction of bearing RUL. Comparing the prediction results of CNN-LSTM-AM and CNN-BiLSTM model, it can be concluded that the RMSE value of the proposed method is reduced by 7.9 %, and the score is increased by 1.5 %, which verifies the effectiveness of the proposed method in rolling bearing life prediction.