# A Method for Identifying the Wear State of Grinding Wheels Based on VMD Denoising and AO-CNN-LSTM
## 3 Experiment
### Analysis of VMD Denoising and AO-CNN-LSTM Neural Network Model Recognition Results  
Under the experimental conditions outlined in Section 3.1, a total of 8 sets of grinding wheel experiments were conducted in this study. Each experiment involved the collection of 40 segments of AE signals. After initial preprocessing with the PXPA3 preamplifier filter, the signals underwent VMD denoising, resulting in a sample set consisting of 320 segments of AE signals. The grinding wheel wear experiments in this paper are segmented into 10 nodes, and noise-containing datasets are curated by selecting acoustic emission signals from each node. Initially, the Variational Mode Decomposition (VMD) algorithm is employed to denoise the dataset, yielding a sample set. Subsequently, the sample set is partitioned into training, testing, and validation sets. The training and validation sets are harnessed for model training, constituting 70% and 10% of the total sample set, respectively. The testing  
Figure 14: Typical AE signal of severe wear after VMD denoising. Figure 13: Typical AE signal of severe wear. set is deployed to assess the recognition accuracy of the neural network model for new sample data corresponding to the grinding wheel wear states, constituting 20% of the total sample set. Throughout the experiment, the grinding wheel undergoes three wear states, and one-hot encoding is implemented to assign three sample labels corresponding to the wear states: Initial Wear [1, 0, 0], Intermediate Wear [0, 1, 0], Severe Wear [0, 0, 1] [26]. The labeling and partitioning results of the sample set are presented in Table 2.  
To intuitively assess the overall performance of the proposed grinding wheel wear recognition model in this study, three metrics were employed: the loss curve, and the accuracy by using the confusion matrix to compare the true category and the predicted category. The loss function during training is illustrated in Figure 15. It can be observed that the loss function rapidly decreases in the early stages of training, and as the number of training iterations increases, the rate of decline gradually slows down, ultimately reaching a stable state. The trend indicates that the model training converges, demonstrating effective training results. Accuracy refers to the proportion of correctly classified samples among the total number of samples. The confusion matrix summarizes dataset records in a matrix form based on two criteria: the true category and the predicted category by the classification model. The rows of the matrix represent the true values, while the columns represent the predicted values [27]. The classification accuracy on the training set, validation set, and test set, along with the overall classification confusion matrix, is illustrated in Figures 16-19, where 1 represents Initial Wear, 2 represents Intermediate Wear, and 3 represents Severe Wear. In the confusion matrix, green represents correct classification, while red represents misclassification. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample Correspondences with Grinding Wheel Wear States** & **Initial Wear** & **Intermediate Wear** & **Severe Wear** \\ \hline Sample labels & [1, 0, 0] & [0, 1, 0] & [0, 0, 1] \\  & Training set & 99 & 75 & 50 \\ Sample quantities & Validation set & 14 & 11 & 7 \\  & Test set & 28 & 22 & 14 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Labeling and Partitioning of the Sample Set. Figure 15: The Loss function of Train set and Validation set during training. The confusion matrix clearly demonstrates the classification performance of the model proposed in this paper on the grinding wheel wear dataset. The overall precision and recall of the model are both above 95%, showing high comprehensive performance. The precision of the model for all three categories exceeds 95%, with the precision of initial wear and intermediate wear both exceeding 99%, resulting in an overall recognition accuracy of 98.8%.