# A Size-Controlled AFGAN Model for Ship Acoustic Fault Expansion
## 4 Experimental Setup
### Sample Expansion Performance on Other Machine Learning Algorithms  
To test the generalization of the expanded samples generated by the size-controlled AFGAN, some models are built on different machine learning algorithms, and their classification performance before and after expansion at the optimum sample size are compared. The algorithms used in this task \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{4}{c}{**Sample Size per**} \\  & \multicolumn{4}{c}{**Typical Fault Source**} & \multirow{2}{*}{**Accuracy**} \\  & **90 Hz** & **296 Hz** & **360 Hz** & \\ \hline E\({}_{1}\): the optimum size & 831 & 538 & 282 & 83.00\% \\ E\({}_{2}\): half the optimum size & 416 & 269 & 141 & 82.67\% \\ E\({}_{3}\): double the optimum size & 1000 & 1000 & 564 & 81.67\% \\ E\({}_{4}\): all 1000 samples & 1000 & 1000 & 1000 & 83.00\% \\ E\({}_{5}\): none & 0 & 0 & 0 & 61.76\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Accuracies of different expanded sample sizes. Figure 3: The accuracies as the sample size variation for different arrangement schemes. contain the most common machine learning algorithm like MLP neural network, passive aggressive classifier (PAC) [23], ridge classifier [24], extreme gradient boosting classifier (Xgboost) [25], random forest (RF) [26], and gradient boosting decision tree (GBDT) [27]. To eliminate the uncertainty, 11 different seeds (0, 50,..., 500) are set for the different learning process to obtain different models. Therefore, there are a total of 46 models developed for validating the generalization of the expanded data, where the data shuffle process does not influence Xgboost and ridge classifier. To demonstrate the performances' differences based on data before and after expansion, the absolute accuracy increase (AAI) and relative error reduction (RER) are calculated. RER is used to eliminate the original performance of the model, which means when the original model has already achieved high accuracy, the AAI must be smaller than the one with lower accuracy, so the RER is calculated to eliminate this influence. RER is calculated with  
\[RER=\frac{Acc_{ae}-Acc_{be}}{Acc_{be}}. \tag{8}\]  
Figure 4 presents the AAIs of different models versus different algorithms and Figure 4 presents the RERs. Different colours represent different shuffle seeds. The average AAI and RER are 11.6% and 33.0%, and there are 93.5% (i.e., 43/46) models improved their accuracies. Table 2 summarized the average performances of the models from each algorithm. Most of the models have improved their performance after sample expansion. Figure 4: The accuracies (**a**) increase and (**b**) relatively error reduction under different machine learning algorithms and shuffle seeds. To present the details of the models, the recognition accuracies of 11 GBDT models and MLP before and after sample expansion are given in Figure 5. The average AAI of GBDT before expansion is 84.2%, and, after using the expanded samples, the average recognition accuracy increases to 91.0%. As for the models built on MLP, average accuracy before expansion is 55.7%, after using the expanded samples, the average recognition accuracy increases to 75.1%. For these two nonlinear algorithms, the performances have obtained significant improvement even if the parameters were not specially tuned. The best model even achieved 92% detection accuracy, which is comparable with the previous studies even with different fault conditions [5; 6]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & \
\begin{tabular}{c} **Mean Absolute** \\ **Accuracy Increase** \\ \end{tabular} &
\begin{tabular}{c} **Improved Models** \\ **Percentage** \\ \end{tabular} \\ \hline MLP & 19.4\% (43.8\%) & 100\% \\ Passive Aggressive Classifier & 12.2\% (26.6\%) & 100\% \\ Ridge Classifier & 14.3\% (31.2\%) & 100\% \\ Extreme Gradient Boosting Classifier & 17.3\% (74.3\%) & 100\% \\ Random Forest & 7.1\% (15.2\%) & 72.7\% \\ Gradient Boosting Decision Tree & 6.8\% (42.8\%) & 100\% \\ \hline \hline \end{tabular}
\end{table}