# Moisture Measurement in Paper and Cardboard Packaging Waste Bales for Recycling
## 3 Results and Discussion
### Calibration Equation  
As previously mentioned, a calibration equation was developed so that the equipment could be used with more accuracy as close as possible to the bales to be analyzed in the daily use of the equipment.  
A linear regression model was applied using voltage and oven moisture to develop the equation. However, a previous residuals study using the Cooks distance method was conducted to identify possible outliers, as displayed in Figure 3.  
Figure 3: Outliers’ identification with the R software boxplot and Cooks distance method. The outliers were the F2, Q2 and Q4 bales.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **R2** \\ \hline Moisture & 0.63 \\ Density & 0.23 \\ Weight & 0.11 \\ Compression density & 0.11 \\ Type of material & 0.01 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Coefficient of determination (R2) relating different variables and voltage measurements.  
Three outliers were identified in Figure 3. In particular, bales F2 and Q4 presented a lower voltage measurement with the high moisture content, and the opposite was true for bale Q2. Therefore, they were excluded so as not to interfere with the model. The calibration equation was calculated with a linear regression model as presented in Figure 4.  
A linear regression of the voltage and oven moisture values without outliers determined the calibration equation to be MC % = 17.131V + 1.635, with an R\({}^{2}\) of 0.655. This is a low correlation. However, cardboard is a rough material, and the standard deviation for the moisture content, measured by the oven drying method, was 1.349%. The comparison for the preinsert programs in the equipment (S4, S5 and S6) had shown lower coefficients of determination and higher standard deviations (Figure 5), thus demonstrating the calibration equation generating more accurate results for the purpose of measuring moisture in cardboard bales.  
Due to the lack of opportunity to test the calibration equation on bales after the conclusion of the project, to test the model, a K-fold cross validation with K = 10 was performed with R software. The obtained resampling results were RMSE = 1.333, R\({}^{2}\) = 0.764 and MAE = 1.112, with a mean squared error of 1.333, which is acceptable regarding the usage of the equipment in the real operational environment, and a higher R\({}^{2}\) of 0.764. Despite there not being a strong R\({}^{2}\), the results were better than the linear regression (R\({}^{2}\) of 0.655), suggesting that with further sampling, the model can be improved. The results are consistent with previous work using similar technology, despite differences in the studied materials. [PERSON] et al. [14] reported a maximum mean error of 2.16% when using a coplanar dielectric device to measure palmwood moisture content, and [PERSON] et al. [9] reported an RSME equal to 2.1% for a similar device.  
Figure 4: Linear regression of V and oven moisture (%). MC = 17.131V + 1.635, residual standard error: 1.366 at 43 degrees of freedom, multiple R\({}^{2}\) of 0.655, adjusted R\({}^{2}\) of 0.647, F-statistic of 81.79 on 1 and 43 DF; \(p\)-value of 1.663 \(\times\) 10\({}^{-11}\).  
Such error is explained by the amplitude of the results and the dispersion of the correlation between the oven moisture content and the voltage, especially in bales with higher moisture contents. This is consistent with the findings of [PERSON], et al. [14]. Therefore, it is necessary to collect further data to make the equation more robust. Nevertheless, it is useful to recommend the use of such equipment in bales that have faces with the fewest empty spaces possible and no contaminants, such as excess superficial moisture, metals or fats. Those limiting factors were identified in the file measurements and help to explain the variability of the measurements.