# A Review on Data-Driven Condition Monitoring of Industrial Equipment
## 2 Data-Driven Condition Monitoring of Industrial Equipment
### Fault Diagnosis and Prediction
#### 2.2.2 Method Based on Deep Learning
For sequence training the loss function is:  
\[\mathrm{E}(y,\hat{y})=\sum_{t=0}^{T}\mathrm{E}_{t}(y_{t},\hat{y}_{t})=-\sum_{t=0 }^{T}y_{t}\log\hat{y}_{t} \tag{42}\]  
where \(y_{t}\) and \(\hat{y}_{t}\) are the true output value and the model prediction at moment t respectively, is and \(\mathrm{E}_{t}\) is the cross-entropy at moment t.  
In recent years, there has been increasing interest in the use of RNNs for equipment condition monitoring [163; 164; 165; 166; 167]. [PERSON] et al. [168] have implemented RNN successfully to the detection and classification of motor bearing faults. Using discrete wavelet transforms, fault features are extracted from the current and vibration signals of induction motors. Using orthogonal fuzzy neighborhood discriminant analysis (OFDNA), these characteristics are decreased further. OFDNA is then applied to acquire the most effective fault classification features. The RNN classifier uses these features as training and test sets to provide fault detection and diagnosis. The results shows that the RNN-based fault diagnosis approach can detect and classify induction motor bearing faults under various operating conditions. [PERSON] et al. predict the deterioration trend of rolling bearings by integrating RNN and reinforcement learning in [169]. The singular spectral entropy of the vibration signal is utilized to characterize the deterioration condition of the bearing, and the degradation trend is split into several stages by moving average noise reduction. The training and testing set for the RNN model is comprised of these phases. Then, reinforcement learning is employed at each stage to optimize the parameters of the RNN's hidden layer. By comparing RNN with reinforcement learning to ELM, SVM, and the original RNN model, the results indicate that RNN with reinforcement learning surpasses the other approaches in terms of prediction accuracy and convergence speed. As seen in the previous paragraph, RNNs have already made progress in the application of equipment condition monitoring. In practice, however, RNNs still have limits, most notably the disappearance or expansion of gradients when dealing with lengthy sequence issues. To solve this problem, a long short-term memory (LSTM) network structure containing memory units is proposed in [170]. A typical LSTM neural network cell is shown in Figure 8. Both LSTM and RNN are trained with similar parameters on the neural network structure, with the main difference being on the recurrent neuron nodes. Figure 6:0 LSTM cell architecture. In Figure 8, ht is the hidden state, which represents short-term memory, and Ct is the cell state, which represents long-term memory. Compared to the RNN basic recurrent neurons, the LSTM has an additional state or memory for long-term storage and another for short-term storage. The long-term state is updated slowly and mostly maintains long-term dependent information, whereas the short-term state is updated more often and varies more depending on the neuron's current state. The LSTM additionally has three gated cyclic units to regulate the updating and forgetting of memories, ensuring that vital information is constantly remembered, and less significant information is discarded, hence permitting the storage and flow of memories in the hidden layer units. In the recent decade, LSTM has received a great deal of interest in the field of equipment condition monitoring since it overcomes the limitations of RNNs in processing long sequences [81; 171; 172; 173; 174; 175; 176; 177; 178; 179; 180; 181; 182]. Regarding fault detection and diagnosis, [PERSON] et al. [183] implemented fault detection for permanent magnet synchronous motor using LSTM. To train the LSTM model, the three-phase current values and rotor position data at the moment of continuous sampling are utilized as inputs, and the current value at the next sampling moment is used as the desired output. Detection of faults is then accomplished by monitoring the model's prediction error. In [184], [PERSON] et al.