It can be seen from Table 4.1 that based on the mse and R values during training, the performance of the ANN model improved when an additional hidden layer is included in the network and it is further improved when the training function of Bayesian regulation backpropagation is used. During testing, the data set includes forty five cases, which were not used during training. By applying the models to the testing dataset; the mse of 7.09876, 1.63661 and 3.18439 for Model 1, Model 2 and Model 3, were generated respectively. In contrast to the experience with the training set, using the Bayesian regulation back propagation algorithm did not give a better mse value.
A comparison of the three models was made. Although Model 2 provides a better mse than Model 3 during testing (1.6366 and 3.1844 respectively, as shown in Table 4.1), by comparing the average percentage error over all test cases (10.07 for Model 2 and 6.51 for Model 3), it can be seen that Model 3 gives a better performance and prediction. In comparing the worst and best cases, the worst case of Model 3 has an error of 21.51%, which is significantly lower than that of Model 1 (162.26%) and Model 2 (105.77%). The best case of Model 3 has an error of 0.50%, which is also lower than that of Model 1 (2.53%) and Model 2 (1.20%). The oil production curves of the best and worst case of Model 3 are shown in Fig. 4.1, and it can be seen the curves for predicted output and target output are closely approximating each other in both cases. Thus, it can be concluded that Model 3 gives the best performance and consequently, it was incorporated into the automated prediction system.
It can be seen from Table 4.1 that based on the mse and R values during training, the performance of the ANN model improved when an additional hidden layer is included in the network and it is further improved when the training function of Bayesian regulation backpropagation is used. During testing, the data set includes forty five cases, which were not used during training. By applying the models to the testing dataset; the mse of 7.09876, 1.63661 and 3.18439 for Model 1, Model 2 and Model 3, were generated respectively. In contrast to the experience with the training set, using the Bayesian regulation back propagation algorithm did not give a better mse value.A comparison of the three models was made. Although Model 2 provides a better mse than Model 3 during testing (1.6366 and 3.1844 respectively, as shown in Table 4.1), by comparing the average percentage error over all test cases (10.07 for Model 2 and 6.51 for Model 3), it can be seen that Model 3 gives a better performance and prediction. In comparing the worst and best cases, the worst case of Model 3 has an error of 21.51%, which is significantly lower than that of Model 1 (162.26%) and Model 2 (105.77%). The best case of Model 3 has an error of 0.50%, which is also lower than that of Model 1 (2.53%) and Model 2 (1.20%). The oil production curves of the best and worst case of Model 3 are shown in Fig. 4.1, and it can be seen the curves for predicted output and target output are closely approximating each other in both cases. Thus, it can be concluded that Model 3 gives the best performance and consequently, it was incorporated into the automated prediction system.
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