Artificial Neural Networks versus Multiple Linear Regressions to Predict the Christiansen Uniformity Coefficient in Sprinkler Irrigation

Abstract

The Christiansen Uniformity Coefficient (CUC) describes the distribution of water in a sprinkler system. In this study, two types of models were developed to predict the Christiansen Uniformity Coefficient (CUC) of sprinkler irrigation systems: Artificial Neural Network (ANN), specifically the feed-forward neural networks, and multiple linear regression (MLR) models. The models were trained on a dataset of published research on the CUC of sprinkler irrigation systems, which included data on a variety of design, operating, and meteorological condition variables. In order to build the predictive model of CUC, 10 input parameters were used including sprinkler height (H), working pressure (P), nozzle diameter (D and da), sprinkler line spacing (SL), sprinkler spacing (SS), wind speed (WS), wind direction (WD), temperature (T), and relative humidity (RH). Fifty percent (50%) of the data was used to train ANN models and the remaining data for cross-validation (25%) and for testing (25%). Multiple linear regression models were built using the training data. Four statistical criteria were used to evaluate the model’s predictive quality: the correlation coefficient (R), the index of agreement (d), the root mean square error (RMSE), and the mean absolute error (MAE). Statistical analysis demonstrated that the best predictive ability was obtained when the models (ANN and MLR) utilized all the input variables. The results demonstrated that the accuracy of ANN models, predicting the CUC of sprinkler irrigation systems, is higher than that of the MLR ones. During the training stage, the ANN models were more accurate in predicting CUC than MLR, with higher R (0.999) and d (0.999) values and lower MAE (0.167) and RMSE (0.456) values. The R values of the MLR model fluctuated between 0.226 and 0.960, the d values oscillated from 0.174 to 0.979, the MAE values were in the range of 2.458% and 10.792%, and the RMSE values fluctuated from 2.923% to 13.393%. Furthermore, the study revealed that WS and WD are the most influential climatic parameters. The ANN model can be used to develop more accurate tools for predicting the CUC of sprinkler irrigation systems. This can help farmers to design and operate their irrigation systems more efficiently, which can save them time and money.