Environmental Engineering Reference
The structure of the NLRM is given below:
where O is the observed output, ʱ 1 , ʱ 2 , ʲ 1 , ʲ 2 … ʱ n , ʲ n are the regression coefficients
and H's are the hidden neuron outputs.
The structure of ANN model was found to be 7-2-1. Therefore, there are only
two hidden neurons and their output (H1, H2) are taken as input for NLRM. The
calibration data were used to determine the values of the regression coefficients.
Evaluation of Model Performance
Five different standard statistical performance evaluation criteria are used to evalu-
ate the performance of various models. These include Average Absolute Relative
Error (AARE), Coefficient of Correlation ( R ), Nash-Sutcliff Efficiency ( E ),
Normalized Root Mean Square Error (NRMSE), and Threshold Statistics ( TS ). The
lower AARE values, the higher TS x and R values close to 1.0 would indicate a suf-
ficient condition for a good model. The AARE, NRMSE and TS statistical measures
give the effectiveness of a model in terms of its ability to accurately predict data
from a calibrated model. The other statistic, such as R , quantifies the efficiency of
the model in capturing the complex, dynamic and non-linear nature of the physical
process being modelled.
Results and Discussion
The statistical results from the hybrid model are presented in Table 1 . The values of
E and R in excess of 0.97 were obtained during both training and testing sets for the
model, which is excellent. The performance in terms of TS and AARE statistics is
also very good. A major fraction of the computed groundwater level (90 %, for the
models, during testing) had ARE of less than 5 %.
The scatter plots during testing data set (unseen by the model during training) are
presented in Fig. 3 . The graphical performance indicator gives better results when
the data pairs are closing to 45° line and the good superposition between the
observed and calculated values in the testing phase. The results demonstrate that the
Table 1 Results of the various statistical measures