## 4 Simulation
### Simulation of the MERM  
For the dataset used in training, 500 speech data samples for emotion analysis were referenced from AI-Hub [23], and 2000 environmental sound samples (.wav) were referenced from ESC-50: Dataset for Environmental Sound Classification [24]. Speech data for emotion analysis and environmental sound data were randomly extracted and synthesized to generate 2000 noisy sound samples (.wav). Since the generator and discriminator are CNN-based models designed for image processing in deep learning, the audio data were converted into spectrograms (.png, 196 \(\times\) 128) and used as images. The performance evaluation of MERM is conducted using three metrics: error compared to the original data, training time, and the discriminator's loss function.  
1. Error Compared to the Original Data: This metric is calculated by inputting 10 samples of data generated by the generator, which incorporates noise into the original data, and predicting the data. The evaluation measures the sum of squared differences between the predicted data and the original data. A lower value indicates that the model outputs data more like the original data.
2. Training Time: This metric represents the time required for the model to complete training for 40 epochs. A shorter training time indicates a faster model.
3. Discriminator's Loss Function: This value reflects the discriminator's ability to detect the generator's forgery. A lower value indicates that the discriminator effectively identifies forged data. Conversely, a higher value suggests that the generator is more successful at deceiving the discriminator or that the discriminator has been enhanced. The evaluation involves using the generator to predict 50 test samples and calculating the discriminator's loss function value.  
Table 1 presents the evaluation of noise reduction performance for each model, where MCycleGAN(2) exhibits the lowest error of 14.781. This indicates that MCycleGAN(2)  
Figure 8: The F1 scores for each model.  
effectively handles noise while maintaining similarity to the original data compared to other models. In terms of training time, CycleGAN has the shortest duration at 2037 s, whereas MCycleGAN has the longest at 7590 s. The longer training time for MCycleGAN is attributed to its use of multiple cycles, making it relatively slower than other models.  
Regarding the discriminator's loss function, CycleGAN has a relatively high value of 11.2139 compared to other models. In contrast, MCycleGAN shows minimal differences based on the number of cycles: 0.2813 for two cycles and 0.2409 for four cycles. This suggests that CycleGAN's generator does not adequately deceive the discriminator. When comparing MCycleGAN with two cycles versus four cycles, it is observed that four cycles require approximately twice as much training time as two cycles, though the performance improvement is marginal. Consequently, the model with two cycles is deemed to offer better training time efficiency compared to the model with four cycles.  
Figure 9 show the loss of the generator and the loss of the discriminator during the training of each model over 40 epochs. During the same epoch, it can be observed that the MCycle GAN model moves in a direction where the generator's loss function decreases. While at epoch 0 it performs worse compared to Cycle GAN, from epoch 5 onward, it shows better performance than Cycle GAN. However, in the case of Cycle GAN, it was observed that the generator's loss function tends to increase during training. Therefore, it is predicted that more epochs may be needed for Cycle GAN.  
As for the loss function of the discriminator, at the 40 th epoch, \(D_{clean}\) shows the following values: MCycle GAN(4) = 0.1051, MCycle GAN(2) = 0.1100, Cycle GAN = 0.0714, indicating that the discriminator of MCycle GAN makes more errors. Although Cycle GAN's \(D_{clean}\) is smaller, the larger \(G_{L}\) suggests that the generator is not yet proficient in creating realistic fake data.