A predictive model was developed using Artificial Neural Network for the bulk density, WABS and pectin solubility of cowpea precooked using infrared heating. Three main factors that influence the response were fed into the neural network as the independent variables, the experimental data of the process was cleaned and processed using fitnet ANN model. The MSE, R and R2 of the training, validation, and testing datasets are presented in (Table 4). However, the overall R and R2 value was utilized in selecting the best predictive model for each of the response variable. Besides, scatter plots with coefficient of correlation are presented in (Fig. 2).
The plot of the best validation performance, together with the actual, predicted response and error (difference between the predicted and actual response) plot are presented in Fig. 3 and Fig. 4 respectively. From the evaluation result, for the bulk density, the overall R and R2 values are greater than 0.9, implying that ANN was efficient in developing a predictive model for the bulk density of cowpea prepared using infrared heating.
Specifically, the highest overall R and R2 values are 9.8740E-01 and 9.7496E-01 respectively with a validation MSE of 1.06E-05. This was compared with the R2 obtained using linear, 2FI and quadratic model (Table 5). Comparatively, the R2 of the predictive model generated using ANN was approximately higher by 21%, 13%, and 3% for linear, 2FI and quadratic model respectively.
For WABS, the overall R and R2 ranged between 0.5 and 0.9991. After repeated training, validation and testing, a significantly high R and R2 values were eventually obtained at the 5th iteration with R and R2 values of 9.9911E-01 and 9.9821E-01 respectively with a validation MSE of 3.75E + 00. Similar to the bulk density, the R2 value was compared with that obtained using linear, 2FI and quadratic model (Table 5). Comparatively, the R2 of the predictive model generated using ANN was approximately higher by 28%, 23%, and 11% for linear, 2FI and quadratic model respectively.
For Pectin solubility, the coefficient of regression for the linear, 2FI and quadratic model for pectin solubility are very low, ranging from 0.3–0.49, however, using ANN, a high R and R2 was obtained after training, validating, and testing the model using three different neurons (5,8 and 10 neurons). The three different neurons employed for pectin solubility were utilized to obtain a significant overall model performance indicator (R and R2). The best overall R and R2 values were obtained using 10 neurons and at the 5th run, with values of 0.938 and 0.88 respectively, and validation MSE of 245. Comparatively the R2 value of the model predicted using ANN was approximately higher by 64%, 54%, and 44% for linear, 2FI and quadratic model respectively. The predictive model developed using ANN are presented in equation.
The R2 value from this study is within the range to those reported as indicated in Table 1. The results of comparison between the actual and predicted values as shown in Fig. 5, indicated that the values of the parameters measured in this study (Bulk density, WABS and pectin solubility) are closely related. Reportedly, ANN has been utilized in various fields, nonetheless reports on using ANN for predicting the cooking properties of cowpea when moisture content, temperature and time are varied during infrared heating was not found. This study fills that gap by presenting a method of using Artificial intelligence technologies (specifically artificial neural network) for predicting the bulk density, WABS and pectin solubility of cowpea precooked via the use of infrared form of heating under varied independent parameters of moisture content, temperature, and time.
Table 4. MSE, R and R2 Values obtained from Model Training, Validation and Testing.
<
Bulk Density
|
|
1st RUN
|
2ND RUN
|
3RD RUN
|
4TH RUN
|
5TH RUN
|
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
Training
|
8.77E-06
|
9.9048E-01
|
9.8105E-01
|
9.87E-06
|
9.8995E-01
|
9.8000E-01
|
5.58E-06
|
9.9193E-01
|
9.8392E-01
|
5.36E-06
|
9.9387E-01
|
9.8777E-01
|
2.35E-05
|
9.7855E-01
|
9.5756E-01
|
Validation
|
1.29E-05
|
9.9035E-01
|
9.8080E-01
|
1.06E-05
|
9.8114E-01
|
9.6263E-01
|
5.32E-05
|
9.7521E-01
|
9.5104E-01
|
6.76E-05
|
9.5105E-01
|
9.0449E-01
|
1.49E-05
|
9.8897E-01
|
9.7807E-01
|
Testing
|
3.66E-05
|
9.5684E-01
|
9.1555E-01
|
2.38E-05
|
9.7778E-01
|
9.5606E-01
|
3.87E-05
|
9.6548E-01
|
9.3215E-01
|
4.93E-05
|
8.1903E-01
|
6.7082E-01
|
5.08E-05
|
9.7085E-01
|
9.4256E-01
|
Overall
|
|
9.8573E-01
|
9.7166E-01
|
|
9.8740E-01
|
9.7496E-01
|
|
9.8133E-01
|
9.6301E-01
|
|
9.6262E-01
|
9.2664E-01
|
|
9.7802E-01
|
9.5652E-01
|
WABS
|
|
1st RUN
|
2ND RUN
|
3RD RUN
|
4TH RUN
|
5TH RUN
|
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
Training
|
4.18E+01
|
8.3982E-01
|
7.0529E-01
|
1.67E+00
|
9.9395E-01
|
9.8793E-01
|
1.64E+00
|
9.9415E-01
|
9.8834E-01
|
2.53E+00
|
9.9024E-01
|
9.8057E-01
|
2.34E+00
|
9.9173E-01
|
9.8352E-01
|
Validation
|
1.03E+02
|
9.0581E-01
|
8.2048E-01
|
9.79E+00
|
9.7925E-01
|
9.5892E-01
|
6.37E+00
|
9.7162E-01
|
9.4405E-01
|
6.55E+00
|
9.8165E-01
|
9.6363E-01
|
3.75E+00
|
9.8802E-01
|
9.7619E-01
|
Testing
|
2.51E+02
|
7.2171E-01
|
5.2086E-01
|
3.24E+00
|
9.9270E-01
|
9.8545E-01
|
3.91E+00
|
9.9089E-01
|
9.8187E-01
|
7.43E+00
|
9.8121E-01
|
9.6276E-01
|
2.67E+00
|
9.9437E-01
|
9.8876E-01
|
Overall
|
|
7.5224E-01
|
5.6587E-01
|
|
9.8927E-01
|
9.7866E-01
|
|
9.9057E-01
|
9.8123E-01
|
|
9.8668E-01
|
9.7354E-01
|
|
9.9911E-01
|
9.9821E-01
|
Pectin Solubility (70 15 15 5 neurons)
|
|
1st RUN
|
2ND RUN
|
3RD RUN
|
4TH RUN
|
5TH RUN
|
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
Training
|
1.08E+02
|
9.0191E-01
|
8.1344E-01
|
8.65E+01
|
9.3759E-01
|
8.7907E-01
|
6.19E+01
|
9.6242E-01
|
9.2625E-01
|
1.81E+02
|
8.7271E-01
|
7.6162E-01
|
8.45E+01
|
9.4470E-01
|
8.9245E-01
|
Validation
|
9.94E+00
|
9.9988E-01
|
9.9976E-01
|
1.42E+01
|
9.9102E-01
|
9.8212E-01
|
2.74E+02
|
9.3218E-01
|
8.6896E-01
|
5.38E+01
|
8.7556E-01
|
7.6661E-01
|
8.11E+01
|
9.5924E-01
|
9.2013E-01
|
Testing
|
1.34E+02
|
9.1965E-01
|
8.4575E-01
|
1.98E+02
|
8.1991E-01
|
6.7225E-01
|
6.70E+01
|
6.7995E-01
|
4.6233E-01
|
1.97E+02
|
9.8189E-01
|
9.6410E-01
|
1.19E+02
|
8.8885E-01
|
7.9006E-01
|
Overall
|
|
9.3126E-01
|
8.6725E-01
|
|
9.3451E-01
|
8.7331E-01
|
|
9.33E-01
|
8.6993E-01
|
|
9.0123E-01
|
8.1222E-01
|
|
9.3685E-01
|
8.7769E-01
|
Pectin Solubility (70 15 15 8 neurons)
|
|
1st RUN
|
2ND RUN
|
3RD RUN
|
4TH RUN
|
5TH RUN
|
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
Training
|
1.32E+02
|
9.0341E-01
|
8.1615E-01
|
1.16E+02
|
9.1034E-01
|
8.2872E-01
|
8.25E+01
|
9.3505E-01
|
8.7431E-01
|
9.54E+01
|
9.2787E-01
|
8.6095E-01
|
1.14E+02
|
9.3029E-01
|
8.6544E-01
|
Validation
|
7.40E+01
|
9.5608E-01
|
9.1409E-01
|
1.41E+01
|
9.9875E-01
|
9.9750E-01
|
1.00E+02
|
9.6600E-01
|
9.3315E-01
|
1.38E+02
|
9.4704E-01
|
8.9688E-01
|
1.79E+02
|
9.1097E-01
|
8.2986E-01
|
Testing
|
2.16E+02
|
8.6983E-01
|
7.5660E-01
|
4.83E+01
|
7.3384E-01
|
5.3851E-01
|
9.97E+01
|
9.3803E-01
|
8.7990E-01
|
2.92E+01
|
9.7816E-01
|
9.5680E-01
|
5.32E+01
|
9.5776E-01
|
9.1731E-01
|
Overall
|
|
9.0392E-01
|
8.1707E-01
|
|
9.3699E-01
|
8.7795E-01
|
|
9.3786E-01
|
8.7958E-01
|
|
9.3547E-01
|
8.7510E-01
|
|
9.1876E-01
|
8.4412E-01
|
Pectin Solubility (70 15 15 10 neurons)
|
|
1st RUN
|
2ND RUN
|
3RD RUN
|
4TH RUN
|
5TH RUN
|
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
MSE
|
R
|
R2
|
Training
|
6.21E+01
|
9.5473E-01
|
9.1150E-01
|
1.53E+02
|
8.8425E-01
|
7.8190E-01
|
5.17E+01
|
9.5468E-01
|
9.1141E-01
|
1.04E+02
|
9.2294E-01
|
8.5182E-01
|
4.79E+01
|
9.6429E-01
|
9.2985E-01
|
Validation
|
2.04E+02
|
8.4422E-01
|
7.1270E-01
|
1.28E+02
|
9.1687E-01
|
8.4065E-01
|
1.75E+02
|
9.2084E-01
|
8.4794E-01
|
1.01E+01
|
9.5736E-01
|
9.1653E-01
|
2.45E+02
|
8.9312E-01
|
7.9767E-01
|
Testing
|
2.16E+02
|
9.0902E-01
|
8.2631E-01
|
3.27E+02
|
8.5306E-01
|
7.2772E-01
|
1.71E+02
|
7.8957E-01
|
6.2343E-01
|
1.05E+02
|
9.6088E-01
|
9.2329E-01
|
1.07E+02
|
8.3117E-01
|
6.9084E-01
|
Overall
|
|
9.2629E-01
|
8.5801E-01
|
|
8.7398E-01
|
7.6384E-01
|
|
9.3689E-01
|
8.7776E-01
|
|
9.3695E-01
|
8.7788E-01
|
|
9.3804E-01
|
8.7992E-01
|
Table 5
R and R2 Values of Conventional and ANN models in the present study.
Response
|
Bulk density
|
WABS
|
Pectin solubility
|
Variables
|
M,T,t
|
M,T,t
|
M,T,t
|
Predictive Models
|
Present Work
|
Present Work
|
Present Work
|
Linear[R2]
|
0.7700
|
0.7143
|
0.3140
|
2FI[R2]
|
0.8511
|
0.7653
|
0.4034
|
Quadratic[R2]
|
0.9477
|
0.8864
|
0.4904
|
ANN [R]
|
0.9874
|
0.9991
|
0.9380
|
ANN[R2]
|
0.9750
|
0.9982
|
0.8777
|
M: Moisture, T: Temperature, t: time |