# Towards a Digital Twin for Open-Frame Underwater Vehicles Using Evolutionary Algorithms
## 4 BlueROV2 Case
### Analysis of the Results  
Once the algorithm reached a solution, it was analyzed to verify that it was adequate and realistic. Some of this work was completed by setting an adequate range that avoided completely unrealistic solutions. The final values obtained are shown in Table 5.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Stage** & **Description** & **Parameter Values** \\ \hline \multirow{3}{*}{Initialization} & Custom initialization for the first generation; standard initialization for subsequent generations & Specific parameter values; random parameter values within predefined ranges Population size: 60 \\ \hline \multirow{3}{*}{Fitness Function} & Sum of absolute differences between ground truth and simulated data & - \\ \hline Selection & Tournament selection strategy & Tournament size: 5 \\ \hline Crossover & Two-point crossover strategy & Cross rate: 0.5 \\ \hline Mutation & Gaussian mutation operator & Mutation rate: 0.25 \\ \hline Termination & Maximum number of generations & Generations: 30 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Summary of genetic algorithm settings.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Initial Value** & **Optimized Value** & **Difference (\%)** \\ \hline \(I_{XX}\) & 0.344 & 0.371 & 7.85 \\ \hline \(I_{YY}\) & 0.316 & 0.352 & 11.39 \\ \hline \(I_{ZZ}\) & 0.389 & 0.426 & 9.51 \\ \hline \(X_{ii}\) & 13.272 & 15.63  
The inertia values are very close to the initial estimations using the CAD model within a range of around 10%; however, the real values are slightly larger. This difference may well be caused by small elements that are not included in the CAD model, such as screws, cables, or similar objects. The added mass for the linear movements seems to be relatively close to the initial estimations but less accurate than the previous one, with a \(\pm\)25% variation. Initial estimations for these values were intended to be only a general guide, so these results seem adequate. Regarding the physical meaning, results for the linear movements seem correct as the sway and heave movements that have a bigger surface area and tend to move more water with them show higher values of added mass. The rotational movements also seem correct, with values a little bit smaller than the initial estimations, but with a very similar relation between them.  
The linear and quadratic damping coefficients for the displacements show very small variations within a \(\pm\)5 range, which also confirms that the initial estimations with the load cell tests were accurate. Regarding the rotations, both linear and quadratic damping coefficients for the rotations show a higher difference in percentage, with the quadratic ones much closer to the estimations. It is important to consider that the values of these coefficients are small, so even small deviations from the original values are translated into big percentages. These results confirm that the hydrodynamic properties of the vehicle were kept after the optimization process and should improve the model's behavior compared to the original one.