## 3 Results
### Statistical Analysis  
This section analyzes _WEC-Sim_, _Gazebo_, and MBARI-WEC field data measurements using statistical metrics (field measurements used in this analysis are available online at [[https://mhkdr.openei.org/submissions/530](https://mhkdr.openei.org/submissions/530)]([https://mhkdr.openei.org/submissions/530](https://mhkdr.openei.org/submissions/530))). As stated through Section 2.2, each numerical model used parameters based on the MBARI-WEC's operating state for each set of sea state conditions during field trials. During MBARI-WEC operation, the scale factor and status of the heave cone doors could change due to commands from shore or automated safeguards. Therefore, when selecting the time interval for observing field data used in these comparisons, cases examined in this study were chosen such that both of these variables remained constant to ensure accuracy in the comparison between field data and simulations. Time intervals varied between 30 to 60 min for all chosen field data cases.  
Figure 8 compares predictions from the _Gazebo_ and _WEC-Sim_ models with field data for the RMS piston velocity, RMS motor speed, and mean electric power based on 56 independent observations. In each plot, the field measurements are shown on the \(x\)-axis, and simulation data are shown on the \(y\)-axis; the gray line with a slope of unity represents perfect agreement between the models and field measurements. A linear regression model was also fit to the data produced by both numerical models, and the coefficient of determination (\(R^{2}\)) is provided to demonstrate the degree to which the linear model accurately represents the simulation data. Visually inspecting the data for each model and their linear fit lines in all three plots of Figure 8 revealed that both models generally overestimated system performance. Studying the slope of the linear fit equations provided more information on the behavior of the simulation data as the field data parameter increased.  
Figure 7: Electric power versus motor speed for both _Gazebo_ and _WEC-Sim_ models in a monochromatic wave with a height of 1 m and period of 6 s. Both models’ electric power show similar dependence on motor speed except for speeds around \(+/-300\) RPM. This deviation can be attributed to the utilization of PTO bench testing results [4] for power loss calculations or direct calculations using RMS current, which is dependent on speed.  
Figure 8: _Gazeeb_ and _WEC-Sim_ data vs. field data for (**a**) RMS piston velocity, (**b**) RMS motor speed, and (**c**) mean electric power. The gray line with unity slope represents perfect agreement between simulation and field data. Furthermore, linear regression models were fitted for both models.  
Notably, the results from _Gazebo_ trended away from the field observations as magnitude increased at a higher rate than _WEC-Sim_. Typically, larger values of velocity, speed, and power occurred during more energetic sea states. The trendlines throughout Figure 8 suggested that the _Gazebo_ model estimated system performance well for lower energy sea states and _WEC-Sim_ did so for higher energy sea states. The sea states corresponding to these data points can be viewed by the black dots in Figure 9. Figure 9 also depicts the difference between the mean electric power of simulation data and field data binned by significant wave height and peak period, where the value represented in each bin is the average for all observations within that bin. For example, the 240 W difference in the _Gazebo_ model's 0.9-1.1 m, 3.0-5.0 s bin is the average of the mean electric power differences for the two data points in that bin.