Statistical Parameters
Statistics is the technique used to discover patterns in the large amounts of data. These are the prominent statistical parameters used in the thermal modeling of the dryer.
Root Mean Square Deviation/Root Mean Square Error
The root mean square deviation (RMSD) is also known as the root mean square error. It measures the difference between predicted and experimental values. It is expressed mathematically as:
Coefficient of Correlation (r)
The coefficient of correlation develops the relationship between experimental and predicted values. It is denoted by Y and its value varies between -1 and 1.
Coefficient of Determination
The coefficient of determination is denoted by R^{2}. It indicates how well the data fit the trendline curve. It is a tool that is used in validating the prediction model or hypotheses based on other related information.
Sum of Squared Errors
The sum of squared errors (SSE) is the difference between the experimental and predicted values of the model.
n
SSE = ^(Х„,_{/}-Х_{рт},_{/})^{2} (5.53)
j=i
Mean Percentage Error (MPE)
The MPE is the average percentage error between predicted values and experimental values.
Mean Square Error (MSE)
The mean square error is one of the statistical tools that quantify the difference between predicted value and actual value. It is the average of the sum squared error. This is calculated as
5.5.8 Adjusted R^{2} (R^{2})
The Adjusted R^{2} (R^{2}) is used to assess the nature and value of R^{2} automatically, and errors increase when extra variables are included in the model. However, the values of R^{2} and adjusted R^{2} will give similar results for a large sample of data.
Adjusted R2 (R̅2)
Chauhan and Kumar (2018) have carried out thermal modelling of a north- wall-insulated greenhouse dryer under both active and passive modes (as shown in Figure 5.4) for the drying of Indian gooseberries (amla).
The gooseberries are small in size, so are dried whole. Therefore they take longer to dry than other agricultural produce. The drying time for goosber- ries was five days in both dryers. The three most sensitive parameters were selected to be predicted by thermal modeling, namely crop temperature,
hgd
(b)
FIGURE 5.4
Schematic diagram of the greenhouse dryer with thermal energy flow for (a) passive mode, and (b) active mode of the insulated north wall greenhouse dryer.
FIGURE 5.5
Experimental observ'ation and predicted outcome for gooseberries under the passive mode of greenhouse dryer.
greenhouse room temperature, and crop weight. Figures 5.5 and 5.6 present the experimental data along with the predicted data on an hourly basis for the whole five days.
To validate the predicted data from the thermal modeling, two main statistical tools were applied in both modes of operation, namely root mean square of percentage deviation, and the coefficient of correlation. A detailed presentation of all the statistical analysis is presented in Table 5.4. The study showed that the predicted and experimental values agree with a high level of accuracy.
FIGURE 5.6
Experimental observation and predicted outcome for gooseberries under the active mode of greenhouse dryer.
TABLE 5.4
Statistical Analysis of Thermal Modelling of the North-Wall-Insulated Greenhouse Dryer in (a) Passive Mode, and (b) Active Mode
S.No |
Drying Day |
E, (%) |
E„ (%) |
E,„ (%) |
R_{c} |
R„ |
R,„ |
2 |
2nd |
16.02 |
7.61 |
7.77 |
0.99 |
0.99 |
1.00 |
3 |
3^{rd} |
16.36 |
6.23 |
6.44 |
0.99 |
0.99 |
0.98 |
4 |
4th |
12.31 |
4.96 |
5.92 |
0.98 |
0.96 |
0.99 |
5 |
5^{th} |
11.48 |
4.58 |
6.43 |
097 |
0.96 |
0.99 |
2 |
2nd |
12.16 |
9.29 |
4.84 |
0.96 |
0.94 |
0.99 |
3 |
3^{rd} |
12.24 |
5.52 |
5.13 |
0.95 |
0.98 |
0.99 |
4 |
4th |
11.72 |
3.61 |
5.82 |
0.98 |
0.98 |
0.98 |
5 |
5^{th} |
9.42 |
4.81 |
5.13 |
0.97 |
0.96 |
0.99 |