# An Extremely Close Vibration Frequency Signal Recognition Using Deep Neural Networks
## 4 Results and Discussion
### Comparison of Simulation and Experimental Motor Vibration Frequency  
The subsequent discussion explains the recognition using FBG experiment data and compares the simulation and experimental vibration frequency signal. In Figure 8, the  
Figure 7: The recognition probability for superposition frequency using simulation testing data.  
graph color order is the same as the previous graph in Figure 6. There are various ranges of recognition probability in this figure. The highest probability value is the green line representing frequency 50.02 Hz, with a recognition probability of 70.34%. Using the FBG experiment testing data has a lower recognition probability than simulation data. However, the proposed system correctly recognizes the vibration frequency.  
Figure 9 illustrates the comparison of simulation and experimental vibration signal data at a single frequency of 50.02 Hz using the proposed system. The \(x\)-axis represents frequency in Hz, and the \(y\)-axis represents the probability value from 0.5 to 1. Two lines on the graph, red and blue, represent the simulation and experiment results, respectively. Using simulation data, it recognized 50.02 Hz correctly, with the highest probability starting at 0.8893 until the lowest probability of 0.5792 at 50.50 Hz. Using experimental data, it recognized 50.00 Hz correctly, with the highest probability starting at 0.7034 until the lowest probability was 0.6761 at 50.50 Hz.  
Figure 8: The recognition probability for a single frequency using FBG experiment testing data.  
Figure 9: The probability comparison for a single frequency between simulation and experiment data.  
Based on Figure 9, the simulation data results have a more comprehensive range of probability than the experimental data in terms of recognizing the single frequency across the given range. The tendency for simulation data to exhibit more linearity than experimental data can be attributed to several factors. Simulations, often reliant on simplified models of intricate systems, tend to overlook the complexities inherent in real-world phenomena. These simplified models may impose constraints and assumptions that lead to more linear outcomes.  
Additionally, simulations typically operate in idealized conditions, free from measurement errors inherent in experimental setups. This absence of real-world disturbances can contribute to the perceived linearity of simulation data. Furthermore, the process of parameterization in simulations, wherein parameters are adjusted to fit specific conditions, may inadvertently introduce linearity into the results.  
The proposed system has yielded a DNN model trained using only single simulation data, yet it demonstrates the ability to recognize both single and superposition simulation signals, as well as single experimental signals. This capability significantly enhances the system's versatility, as it increases the likelihood of accurately identifying any combination of multiple or superposition signals, whether they originate from simulations or experimental measurements.  
Training the DNN model with the simulation data has effectively developed a robust framework capable of handling various signal compositions and complexities. This adaptability ensures the system's effectiveness in real-world scenarios, where signals may exhibit diverse characteristics and combinations. Overall, the proposed system's ability to recognize both single and superposition signals from simulations and experiments marks a significant advancement in signal recognition methodologies.