## 4 Results and Discussion  
The analyses were performed accounting the metrics of accuracy and recall for diagnostic testing. Accuracy is reported in Equation (12), whereas Equation (13) formalizes the \begin{table}
\begin{tabular}{c c} \hline \hline Epochs & 4 \\ Mini-batch size & 32 \\ Optimizer & Momentum \\ Initial learning rate & \(10^{-4}\) \\ L2 regularization & \(10^{-4}\) \\ Momentum factor & 0.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Fine-tuning hyperparameters for CNNs-based fault diagnosis. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Speeds (rpm)** & **Data Distributions** & **MMD** & **FID** \\ \hline \multirow{2}{*}{607} & Real—Simulated & 0.187 & 265.717 \\  & Real—Generated & 0.106 & 78.270 \\ \hline \multirow{2}{*}{877} & Real—Simulated & 0.218 & 317.714 \\  & Real—Generated & 0.069 & 47.888 \\ \hline \multirow{2}{*}{997} & Real—Simulated & 0.202 & 278.152 \\  & Real—Generated & 0.073 & 48.607 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: MMD and FID measuring the distance from real machine data for different operating conditions. concept of recall. In the equations, the variable \(TP\) represents the number of true positives, which identifies the accurate identification of damages. Variable \(TN\) represents the number of true negatives, which refers to accurately identified healthy data. \(FP\) represents the number of false positives, which refers to misclassified normal data as damaged. \(FN\) represents the count of false negatives, which indicates misclassified damaged data as normal. Hence, the recall rate serves as a metric to quantify the proportion of the fault samples that are correctly classified as such by the diagnosis model. \[Accuracy=\frac{TP+TN}{TP+TN+FP+FN}, \tag{12}\]  
\[Recall=\frac{TP}{TP+FN}. \tag{13}\]  
The test results for the three diagnostic models were produced using real experimental data and are presented in Figure 7. The figure presents the performance results in the case of training using real, simulated, and synthetic damaged data. The performance was measured in terms of mean and standard deviation, which were derived from five separate tests. It is evident that all models exhibit high accuracy when trained using real damaged data, but they fail in identifying damage (as shown in Figure 7b) when trained using simulated data. One notable finding is that two of the utilized models, specifically AlexNet and VGG16, reveal noteworthy diagnosis metrics when trained with synthetic data. The metrics derived from the use of synthetic IR data for training purposes exhibit a level of similarity to the high metrics produced from the utilization of real data. This implies that synthetic data have the potential to effectively replace actual data in the training of diagnostic algorithms. The training times are reported in Figure 7c. The AlexNet model is noted for its superior performance, whereas there are no notable distinctions identified among the real, simulated, and synthetic datasets in terms of training times. The findings indicate that the cycleGAN generative model successfully produces data that closely resemble the real data obtained from the test rig. In the specific scenario under investigation, this assertion was corroborated for a particular operational state (877 rpm) that underwent explicit training in the generative model. The aforementioned outcome can be observed in diverse manifestations within the literature. It is frequently employed to enhance the quality of training data by rectifying imbalances in datasets that may be, for instance, disadvantaged with respect to fault data. The findings reported in this study demonstrate that by the implementation of a suitable pre-processing approach and the integration of a cycleGAN generative model, it becomes feasible to generate data for operational scenarios that may not have been included in the experimental procedures, setting up as a zero-shot generative learning approach.