# Some Aspects of the Modelling of Dried Red Beets Rehydration Process
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model No.** & **Model Name** & **Variable** & **R\({}^{2}\)** & **Adjusted R\({}^{2}\)** & **RMSE** \\ \hline \multirow{4}{*}{(1)} & \multirow{4}{*}{[PERSON]} & mass gain & 0.7248–0.9926 & 0.7103–0.9922 & 0.1329–1.3085 \\  & & volume increase & 0.9175–0.9915 & 0.9131–0.9911 & 0.2194–1.1742 \\  & & dry matter loss & 0.9381–0.9948 & 0.9348–0.9945 & 0.0161–0.0610 \\  & & moisture content increase & 0.9076–0.9918 & 0.9027–0.9914 & 3.0062–18.0152 \\ \hline \multirow{4}{*}{(2)} & \multirow{4}{*}{Lewis (Newton)} & mass gain & 0.9185–0.9850 & 0.9142–0.9842 & 0.0418–0.1076 \\  & & volume increase & 0.8888–0.9758 & 0.8830–0.9745 & 0.0652–0.1466 \\  & & dry matter loss & 0.9104–0.9899 & 0.9057–0.9893 & 0.0435–0.1684 \\  & & moisture content increase & 0.9294–0.9907 & 0.9257–0.9902 & 0.0353–0.1015 \\ \hline \multirow{4}{*}{(3)} & \multirow{4}{*}{Henderson–Pabis} & mass gain & 0.9070–0.9834 & 0.9021–0.9797 & 0.0392–0.0956 \\  & & volume increase & 0.8556–0.9733 & 0.8480–0.9719 & 0.0564–0.1336 \\  & & dry matter loss & 0.8702–0.9883 & 0.8634–0.9877 & 0.0449–0.1754 \\  & & moisture content increase & 0.9400–0.9924 & 0.9368–0.9920 & 0.0350–0.1062 \\ \hline \multirow{4}{*}{(4)} & \multirow{4}{*}{Page} & mass gain & 0.7849–0.9962 & 0.7736–0.9960 & 0.0219–3.0943 \\  & & volume increase & 0.9113–0.9923 & 0.9066–0.9919 & 0.0365–0.8878 \\  & & dry matter loss & 0.9373–0.9963 & 0.9340–0.9961 & 0.0209–0.1474 \\  & & moisture content increase & 0.8327–0.9935 & 0.8239–0.9932 & 0.0282–1.4445 \\ \hline \multirow{4}{*}{(5)} & \multirow{4}{*}{Modified Page} & mass gain & 0.9647–0.9966 & 0.9628–0.9964 & 0.0236–0.0897 \\  & & volume increase & 0.9349–0.9948 & 0.9314–0.9945 & 0.0213–0.0972 \\  & & dry matter loss & 0.6522–0.9898 & 0.6339–0.9892 & 0.0463–0.2967 \\  & & moisture content increase & 0.9137–0.9919 & 0.9091–0.9915 & 0.0311–0.1913 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Summary of the results of statistical analyses on the modelling of \(m\), \(V\), \(m_{d,m}\), and \(M\) changes during the rehydration of dried red beets at models parameters expressed with equations presented in Tables 5–8. beets. The Peleg model gave, however, the best results (R\({}^{2}\) = 0.9381-0.9948, adjusted R\({}^{2}\) = 0.9348-0.9945, RMSE = 0.0161-0.0610). As far as the moisture content increase during the investigated process is concerned, it can be accepted that the [PERSON] (Newton), Henderson-Pabis, and modified Page models described the kinetics of the process in quite acceptable ways. The values of the considered statistical test criteria for the mentioned models fell within the range of 0.9137 to 0.9924 for R\({}^{2}\), 0.9091 to 0.9920 for adjusted R\({}^{2}\), and 0.0311 to 0.1913 for RMSE. Comparing the obtained results, it can be admitted that among the three indicated models, the Henderson-Pabis model gave slightly better results in describing the moisture content increase during the rehydration of dried red beets (R\({}^{2}\) = 0.9400-0.9924, adjusted R\({}^{2}\) = 0.9368-0.9920, RMSE = 0.0350-0.1062). The investigated models, namely, [PERSON] ([PERSON]), [PERSON], [PERSON], and modified Page, are empirical ones, but their constants have physical meaning because they give the information about the rate of the investigated process. It turned out, from research, that model constants depended on the parameters of drying and rehydration processes. Determined equations of the model constants (Tables 5-8) allowed us to calculate the values of these constants and to predict how the kinetics of the rehydration of dried red beets (mass gain, volume increase, dry matter loss, and moisture content increase) depends on drying and rehydration conditions, namely, on \(T_{d}\), \(v_{d}\), \(L\), and \(T_{r}\). Our results regarding the modelling of the rehydration process (model constants were calculated based on the parameters of the drying and rehydration conditions) were similar to those previously presented [75; 76]. Different ANN structures were tested (Table 10).