# A Method for Identifying the Wear State of Grinding Wheels Based on VMD Denoising and AO-CNN-LSTM
## 2 Grinding Wheel Wear State Recognition Based on VMD Denoising and AO-CNN-LSTM
### VMD Algorithm for Denoising AE Signals
#### 2.2.2 CNN-LSTM  
CNN is a type of deep feedforward neural network that relies on convolutional operations, encompassing an input layer, convolutional layer, pooling layer, fully connected layer, and output layer [20]. In this study, the acoustic emission signal's sample point data is segmented into a one-dimensional dataset, serving as the input data for CNN. Consequently, the convolutional layer utilizes one-dimensional convolution (Conv1D) for computation [21]. Feature extraction in CNN hinges on the convolutional kernels within the convolutional layer. These kernels scan the one-dimensional input data through stepwise translation, performing convolution operations as defined in Equation (16):  
\[y_{i}=f(k_{i}\times x+b_{i}) \tag{16}\]  
In Equation (16), \(x\) represents the input layer data; \(k_{i}\) is the \(i\)-th convolutional kernel, \(b_{i}\) is the bias of the \(i\)-th convolutional kernel; \({}^{*}\) denotes the convolution operation; and \(f()\) is the activation function. In this study, ReLU function was chosen as the activation function, as shown in Equation (17):  
\[ReLU(x)=\max(0,x)=\left\{ \begin{aligned} & 0& x<0\\ & x\geq 0\end{aligned} \right. \tag{17}\]  
LSTM, a refinement of RNN in deep learning, proves to be effective in overcoming the challenge of vanishing gradients encountered in the training process of conventional models. Particularly suited for the analysis and prediction of long-time sequences, LSTM enhances the learning capacity of the network. In contrast to the standard RNN, LSTM introduces a memory state unit in the hidden layer neural nodes to retain past information. It employs three gating structures--namely, the input gate, forget gate, and output gate--to regulate the retention and updating of historical information [22]. Figure 3 illustrates the fundamental unit of LSTM. The combined prediction model proposed in this paper, CNN-LSTM, is illustrated in Figure 4. In this architecture, CNN performs feature extraction on the aforementioned input layer of AE data, employing two alternating layers of convolutional and pooling layers. The resulting feature vector, denoted as \(x_{t}\), serves as the input for the LSTM layer. The state memory unit, \(C_{t-1}\), is responsible for preserving the motion state information from the preceding time step, while the hidden unit, \(h_{t-1}\), records the prediction of the grinding wheel wear state from the previous time step. These three components collectively influence the forget gate, determining which information is to be forgotten. The inputs \(x_{t}\) and \(h_{t-1}\) undergo transformations through the sigmoid function and tanh function, respectively, jointly influencing the state memory unit to decide which information should be retained. The output gate, \(h_{t}\), is determined by the updated state memory unit \(C_{t-1}\) and the output \(o_{t}\). CNN-LSTM amalgamates the strengths of CNN in capturing local features and LSTM in handling sequential information, rendering it well-suited for processing acoustic emission data. In this study, MSE was selected as the loss function, which is represented as  
\[L_{LOSS}=\frac{1}{n}\sum_{i=1}^{n}(x_{i}-\hat{x}_{i})^{2} \tag{18}\]  
where \(n\) denotes the number of samples, \(x_{i}\) represents the ground truth, and \(\hat{x}_{i}\) denotes the corresponding predicted value. In the recognition of grinding wheel wear states, AE signals typically exhibit temporal patterns, and conventional neural network structures struggle to capture this temporal information. CNN can assist in identifying frequency domain features associated with  
Figure 4: The structure of the CNN-LSTM model. Figure 3: Basic unit of LSTM. different states during the grinding wheel wear process, capturing detailed information related to wear. LSTM aids in analyzing the temporal aspects of acoustic emission signals. By combining CNN and LSTM, CNN-LSTM can better handle sequential data, possessing stronger spatiotemporal modeling capabilities [23].