# Design of Capacitive Paddy Moisture Sensor Based on Electrical Impedance Spectroscopy Analysis
## 3 Results and Discussion
### Regression Analysis  
The relationship between capacitance and moisture at 2 kHz with different temperatures is shown in Figure 4. It can be seen clearly that the capacitance increased with increasing moisture and the paddy capacitance was greater at a high temperature.  
When the temperature was low, the relaxation time was very large and the molecular thermal motion was very weak, so the relaxation polarization related to thermal motion was established very slowly, almost in the \"frozen\" state, which causes that relaxation polarization lags far behind the change of the electric field [32; 33; 34]. However, with the increase of temperature, the relaxation time shortens and relaxation polarization increases [32; 33; 34]. Therefore, the paddy capacitance increases with the increase of temperature, as shown in the Figure 4.  
Figure 4: Moisture dependence of capacitance at a temperature range of 40 to 80 \({}^{\circ}\)C at 2 kHz.  
Figure 3: The change rate of capacitance at a temperature range of 40 to 80 \({}^{\circ}\)C.  
The capacitance and temperature at 2 kHz were normalized and two-thirds of the experimental data points (i.e., 55 experimental points) were selected evenly. Then, these experimental data points were analyzed by multivariate nonlinear regression analysis using SPSS to establish paddy regression models that acquire the paddy moisture content by paddy capacitance and temperature. The remaining third of the experimental data points (i.e., 28 experiments points) were used to evaluate the paddy moisture detection models.  
In the process of regression analysis, if the standardized residual of any experimental measurement point falls outside the interval (\(-\)2, 2), it will be determined as an abnormal experimental point with a 95% confidence level and will not participate in the fitting of the regression model. Repeated screening and fitting were carried out until there were no abnormal experimental points in the model. After removing the abnormal experimental points, the remaining 51 experimental points were used for fitting. The results observed allow the use of the following regression model to predict paddy moisture by the paddy capacitance and temperature:  
\[\begin{array}{ll}\textbf{{M}=f(C,T)=}&\textbf{{0.422}-0.093C+1.176 CT-0.86C^{ 2}-0.514T^{2}+0.622C^{2}T^{2}}\\ &-\textbf{{1.029}CT^{3}+0.233C^{4}+0.283T^{4}+0.018 lnC+0.076 lnT}\end{array} \tag{3}\]  
where \(\textbf{{C}}\) is the normalized paddy capacitance and \(T\) is the normalized temperature.  
The R\({}^{2}\) of the paddy moisture detection models at 2 kHz is 0.933 and the adjusted R\({}^{2}\) is 0.917. It can be seen clearly that the regression standardized residuals of these models were distributed evenly, as shown in Figure 5.  
The remaining 28 test points were used to evaluate the fit of the model. The standard deviation in the fitting test was 1.14% and the standardized residuals are shown in Figure 6.  
Figure 5: Regression standardized residuals of model at 2 kHz.  
Figure 6: Standardized residuals in the fitting test at 2 kHz.