## 4 Results and Discussion  
The aim of this study was to develop a Bayesian network model to predict the main particulars of a Z-Drive harbor tugboat equipped with azimuthing propulsors at the concept and preliminary design phases; the ballard pull (BP) and ship speed (V) were used as the input layer, and the length (LOA), beam (B), draft (T), draft-maximum (Tmax), and power (P) were used as the output layer with ten hidden layers.  
When analyzing the performance graph of the constructed Bayesian network, as visualized in Figure 10 and depicted in Figure 11, it becomes apparent that the optimal validation performance was achieved at epoch 754, with a mean squared error (MSE) calculated as 1184.1913. Moreover, the determination coefficients (R2) for the training, testing, and overall process of the Bayesian network were found to be 0.99977, 0.99651, and 0.99906, respectively, indicating a high level of consistency between the actual and expected values. These findings underscore the reliability of the model. In the case of the implemented power regressions group 1 and 2, the coefficients of determination were 0.4383 and 0.4626, 0.6891 and 0.2159, 0.6064 and 0.2129, 0.7527 and 0.2266, and 0.9368 and 0.2656 for LOA, B, T, Tmax, and P, respectively. Notably, although the coefficients of determination for the speed (V) parameter are relatively low, this can be attributed to the weaker correlation with speed (V) in the dataset used.  
When examining the actual and predicted values of the output parameters depicted in Figure 12, it becomes apparent that the actual values closely align with the predicted values. Furthermore, upon evaluating the mean absolute percentage error (MAPE) values presented in Figure 13, it is evident that the model yields results with a lower error rate, particularly within the range of 60 to 80 metric tons.  
Figure 14 illustrates the average mean absolute percentage errors (MAPEs) for the developed model. It can be observed that the MAPE values for all datasets were determined as 7.71%, 5.17%, 9.57%, 8.28%, and 2.14% for LOA, B, T, Tmax, and P in the Bayesian network, respectively. Meanwhile, for the power regressions group 1 and 2, the corresponding values were 9.38% and 8.77%, 4.16% and 6.89%, 6.47% and 9.43%, 4.69% and 8.77%, and 4.29% and 15.90% for LOA, B, T, Tmax, and P, respectively. The average of these values was calculated as 6.574% for the Bayesian network and 5.795% and 9.955% for power regressions groups 1 and 2, respectively. Notably, among the output parameters, the maximum mean error occurred at 71.81%, while the mean error for all datasets was  
Figure 14: Error histogram of the developed model—average of MAPEs.  
relatively acceptable. However, it is worth mentioning that power regression 2 exhibited a relatively high MAPE value, despite the overall error being within an acceptable range.  
In the context of power regression, the coefficient of determination (R-squared) is commonly computed by software to assess the goodness of fit of the model, similar to its application in linear regression. However, given that power regression entails a non-linear relationship between variables, the calculation of R-squared entails comparing the variation accounted for by the model to the total variation present in the dataset. Meanwhile, the MSE and MAPE results demonstrate that the developed Bayesian network model, along with the implemented power regression models, presents a promising approach for predicting the main characteristics of the azimuthing-propulsor-equipped Z-Drive harbor tugs during the initial stages of ship design.