using Bacterial Foraging Algorithm (BFO) to estimate the coefficients of uniformity of water distribution in sprinkler irrigation

One of the important parameters in agriculture, regarding to assessing irrigation systems, is water distribution uniformity coefficient (CU) in sprinkler irrigation. The first study of sprinkler irrigation uniformity was executed by Christiansen (1942) in California that led to introduce the Christiansen uniformity coefficient. Nowadays, it is very common to use Christiansen uniformity coefficient in sprinkler irrigation systems. Many researchers have investigated water distribution uniformity coefficient in solid set sprinkler systems. While, other researchers such as Hart and Reynolds (1965), Karmeli (1997), Vories and Bernuth (1986), Dabbous (1962), Heerman (1983), Keller and Bliesner (1990), Carrion et al. (2001), Montero et al. (2003) and Bavi et al. (2006) have investigated different aspects of water distribution uniformity coefficient. A sprinkler water distribution pattern depends on the system design parameters such as: the sprinkler spacing, operating pressure, nozzle diameter, as well as environmental variables such as: wind speed and direction. The sprinkler irrigation distribution patterns have been characterized by various statistical uniformity coefficients. Also, various coefficients of uniformity (CUs) have been developed over the past decades. CU amount of water sprinkler operating depends on different pressure heads (P), riser height (RH), distance between sprinklers on lateral pipes (Sl) and the distance between lateral pipes (Sm). The best combination of the above parameters for maximum CU is still unknown for applicators. Many researches, such as Hezar Jaribi et al. (2009), have been done to estimate various relationships using different algorithms. Different researchers have used various concepts to express the coefficients of uniformity; hence the equations lead to different results in the expression of the distributed water uniformity in the same fields. This paper evaluates different uniformity coefficients, using Bacterial Foraging Algorithm (BFO), to propose the best and optimized equation for CU. Generally, the task is to optimize certain properties of a system by pertinently choosing the system parameters. So, in this study, CU has been estimated by Bacterial Foraging Algorithm, and an equation was proposed with the optimized coefficients for CU. The field experiments were conducted on a farmland located in Hashem Abad Agricultural Research Station of Gorgan Cotton Research Institute, about 11 kilometers northwest from Gorgan, Iran. In this area, the lands were irrigated by solid set sprinkler irrigation systems. The sprinkler uniformity tests were conducted using rain-gauge for measuring uniformity coefficients. CU quantities of zb model sprinkler (made in Iran) were considered with three different pressure heads (2.5, 3 and 3.5 atm), two riser heads (60 and 100 cm) and seven sprinkler arrangements (Sl×Sm including: 9×12, 9×15, 12×12, 15×12, 12×18, 15×15, 15×18m). In this study nonlinear equation uniformity coefficients in sprinkler irrigation have been optimized by using Bacterial Foraging Algorithm (BFO). Typically, the BFO consists of four main mechanisms including chemotaxis, swarming, reproduction, and elimination-dispersal event. Totally, the algorithm was run more than 70 times for various conditions and obtained the best case. While optimizing CU Equation by Bacterial Foraging Algorithm (BFO), The best results obtained in S, Nc, Nre, Ned, and C(i) which were equal to 24, 500, 8, 8 and 0.01, respectively. The outcome of this optimization is the following equation which was derived to estimate the Christiansen uniformity coefficient (based on the specified working pressure of the sprinkler, sprinkler height, distance between sprinklers on the pipes side and distance between side pipes). To evaluate the proposed optimal equation, it was used to estimate Christiansen uniformity coefficient distribution of the 70% of the experimental data. Then, the model obtained from 70% of the data was verified with remaining 30% of the experimental data. The estimated Christiansen uniformity coefficient distribution (obtained from the equation) revealed high accuracy, compared with the 30% and 70% of the observed data. Result showed that the maximum absolute error between the outcomes of this algorithm with the measured values was less than 3%. This error was based on using 30% of the data. Also, the root-mean square error (RMSE) was equal to 2.13. Therefore, it is revealed that this algorithm has high accuracy in estimating water distribution uniformity coefficient. Generally, it can be said that Bacterial Foraging Algorithm is more acceptable for optimizing nonlinear functions, comparing with other algorithms such as genetic and differential evolution algorithm. Also, it has much higher rate of convergence, whereas does not make local optimal problems.