# DDTree: A Hybrid Deep Learning Model for Real-Time Waterway Depth Prediction and Smart Navigation
## 4 Performance Analysis
### Analysis of Results Using Residual Analys  
In order to verify the prediction accuracy of the hybrid DDTree model and the prediction ability of the model, the residual values of different models were obtained by calculating the prediction time and the actual value. The smaller the residual value, the stronger the prediction ability of the model, and the model fully learns the characteristics of the data from the training dataset. The residual analysis plots were created from the two models. Figure 10(a),b shows the distribution plots of residuals and the residual histograms. In Figure 10(a), the waterway depth residual error value fluctuates around 0, which means that it is consistent with the actual prediction results and shows no bias. It can be seen from the results of two experiments that there are significant differences in the prediction of waterway depth results in the areas with small depths, such as near islands and shoal edges. The residual depth difference of this part is also significantly higher than other areas. In other deep-water navigation areas, the waterway depth predicted by the DDTree model is closer to the actual waterway depth, so the residual value of this part of the prediction of waterway depth result is smaller. In addition, in Figures 7 and 9, there are also obvious differences at the edges of the navigation areas at different depths where the residual value is large. The waterway depth information of this part of the channel tends to fluctuate greatly, and it is affected by the hydrological and meteorological conditions. Therefore, the prediction results using the DDTree model can show a certain degree of error. Figure 10(b) shows the sample distribution of the residual values. Most of the residual values are around 0. The residuals of the overall prediction of waterway depth are in accordance with the normal distribution, so the DDTree model can predict the waterway depth information of the waterway channel without bias. Figure 12 shows a difference plot between the ground truth depth map and predicted depth map for Nantong Port (Figure 11(a)) and Fangcheng Port (Figure 11(b)), respectively. One can note that the errors mostly concentrate on the boundaries of different seafloor depth zones. However, there are two areas with notable depth errors, which may be explained by the lack of AIS data in these areas. We also compared and analyzed the traditional DNN model and decision tree model. Table 3 shows the prediction results of the model using different parameters. After the evaluation of the model, we chose the mean square error (MSE) as an indicator to calculate the deviation of the predicted value from the actual value, and reflect the prediction ability of the model. Table 3 shows a comparative analysis of the performance of the two models on the actual bathymetry data. Figure 11: Residual analysis of the prediction results of the hybrid DDTree model: (**a**) the plot of residuals, (**b**) the residual histogram. In predictive analysis, the confusion matrix is a table composed of false positives, false negatives, true positives, and true negatives. The confusion matrix function evaluates accuracy by computing the confusion matrix with each row corresponding to the true class. In Equation (8), \(\mathbf{P}\) indicates the precision; \(R\) is the recall; and \(F\) is used to measure the value of precision and recall--it is the harmonic mean of precision and recall values. When \(\mathbf{\alpha}=1\), \(\mathbf{F_{1}}\) score is calculated for performance evaluation. \[F=\frac{\left(1+\alpha^{2}\right)\!PR}{\alpha^{2}(P+R)}, \tag{8}\]  
In Table 3, MSE and the coefficient of determination (\(\mathbf{R}^{2}\)) are used to demonstrate the performance of the model; MSE is used to measure the prediction error of the model and \(\mathbf{R}^{2}\) is used to measure the accuracy of the prediction. We can see that the MSE value of the DDTree model is small and the \(\mathbf{R}^{2}\) value is close to 1.