# An Extremely Close Vibration Frequency Signal Recognition Using Deep Neural Networks
## 4 Results and Discussion  
This section demonstrates the results of the image-based vibration signal recognizing training loss and accuracy value, as well as the accuracy of the DNN model for single and superposition frequency. The accuracy comparison of using simulation and experiment data for a single frequency is also discussed.  
As mentioned in the previous section, the vibration signal neglects the signal noise level. Thus, the simulation of motor vibration, represented using a time-domain sinusoidal waveform, was carried out in MATLAB 2023b with various single-signal frequencies. Without any signal analysis method, these time-domain data must be converted into 2D images before training. The training dataset demonstrates notable performance, attaining high accuracy in image-based vibration signal recognition. Figure 5a-c illustrate the loss and accuracy of the training throughout the DNN model training epochs, which are applied in various frequency ranges such as 50 Hz, 100 Hz, and 500 Hz, respectively.  
Three different frequency ranges are chosen based on the electric motor's fundamental (50 or 60 Hz) and harmonic frequencies (odd multiple of the motor's fundamental frequency). These harmonic frequencies indirectly impact the motor's performance. Notably, the presence of harmonics within the motor drive system can adversely affect the power quality of electrical power supplied, potentially leading to severe consequences [39]. The accuracy of both datasets notably improves with DNN model training, signifying the proposed method's effectiveness in enhancing the model's generalization capability. The \(x\)-axis represents the epoch ranging from 0 to 100, the number of times the model has gone through the entire training dataset. The right \(y\)-axis represents the loss value, and the left \(y\)-axis represents the accuracy value, which varies from 0 to 1. The blue line represents the loss of the model. The red line represents the accuracy of the model.  
Among various evaluation metrics, accuracy, precision, recall, and F1 score are commonly employed to assess the performance of DNN models. These metrics were utilized to scrutinize the effectiveness of the proposed method during model training. Accuracy assesses the overall correctness of predictions, representing the proportion of correctly classified samples. The accuracy value of different frequency ranges is 95.16% for 50 Hz, 94.2% for 100 Hz, and 93.52% for 500 Hz.  
Precision gauges the precision of positive predictions, indicating the proportion of correctly predicted positive samples among all positive predictions. All the precision values have numbers above 90%, as shown in Figure 5a-c. Recall, also referred to as the true positive rate, quantifies the ability to correctly identify positive samples, evaluating the detection capability for true positive samples. The highest recall value is  
Overall, the simulation results of the proposed model underscore its promise, demonstrating the capability to recognize a single frequency below \(1\) Hz with a noteworthy accuracy across diverse frequency ranges.