# Modeling and Test Results of an Innovative Gyroscope Wave Energy Converter
## 5 Performance Test
### Multiple Regression and Prediction  
Figure 14 shows the effect of changes in damping coefficient, pitch amplitude, wave period, and flywheel speed on output power. In order to observe the influence of the changes of the two parameters on the output power of the system, we kept the other two parameters at the rated values in each figure. The theoretical output power will increase with the decrease in the wave period, the raising of the pitch amplitude, and the increase in the flywheel speed, no matter how the parameters change. More importantly, an appropriate damping coefficient needs to be selected. In the case of A = 10\({}^{\circ}\) and \(\phi\) = 10,000 rpm, the maximum power of 46.06 W was achieved at T = 5 s and c\({}_{y}\) = 30 Nm-s/rad rather than c\({}_{y}\) = 25 or 35 Nm-s/rad, in Figure 14a. Figure 14b-d shows that the power changes slowly  
Figure 12: Effect of the wave period: (**a**) output power; (**b**) conversion efficiency; (**c**) flywheel precession angular displacement; (**d**) platform counter torque. The complete output formula of power is expressed in Figure 15a. Power = 70.15 \(-\) 0.4581 \(\times\) 1 + 0.006638X2 \(-\) 30.493X3 + 6.639X4 + 2.8507X3^2 + 0.05007X1 \(\times\) X3 \(-\) 0.000925X2 \(\times\) X3 + 0.000158X2 \(\times\) X4 \(-\) 0.9250X3 \(\times\) X4. R-sq is a measure of fit, which is defined as the ratio of regression model error to total error. The R-sq value of the model is 99.89% in Figure 15a, which indicates an excellent correlation between the experimental value and the fitted value. T contributed the most to the model, while c\({}_{y}\) contributed the least in Figure 15b. A low \(p\)-value (\(p\leq 0.1\)) implies that the relevant data source is statistically significant. The P-value is less than 0.001 in this regression, which also indicates the obtained model is considered statistically significant and desirable in Figure 15c. Differently from R-sq, when the added variables in the model are not statistically significant, R-sq (adj) will decrease, so R-sq (adj) is one of the important indicators to measure the quality of the model built. The larger the R-sq (adj), the better the model fits. Among the variables, the R-sq (adj) of the minimum value X3 is greater than 80%, indicating the system has high goodness of fit in Figure 15d. Figure 15e,f shows the interaction of the variables and the effect of every single variable on the output. Intersecting lines are used to indicate significant interactions; however, there are no two important interactions in Figure 15e. There is even no mutual influence between c\({}_{y}\) and Rev or A. Among the individual effects of the four variables on the output, T has the largest impact on the power in Figure 15f, while other variables have less impact on the output in a small range of changes, which is the same as the simulation conclusion. Figure 15: Multiple regression analysis and power prediction: (**a**) R-sq report; (**b**) contribution of each parameter in R-sq; (**c**) P value; (**d**) R-sq (adj) report; (**e**) parameter interactive analysis; (**f**) influence of parameters on output; (**g**) residual analysis; (**h**) prediction and optimization report. Residual plots for power are shown in Figure 15g. The residual is the difference between the actual observation value and that fitted from the regression. When the points on the plot fall near the straight line, it indicates the data are normally distributed. It can be clearly seen from the figure that the experimental points are all near the straight line, which verifies the data are normally distributed. By comparing 81 sets of simulation results with multiple linear regression data, we get an average power error of 0.0375, and a variance of 0.0245, which also verifies the effectiveness of the model. The prediction and optimization report in Figure 15h provides an ideal output scheme for pursuing maximum power goals.