Identification the Location and Pumping Discharge of Unknown Wells Using the Learning Automata Algorithm

Document Type : Research Paper


1 Department of Civil Engineering, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran.

2 Department of Civil Engineering, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran,



The present article proposes a model using the inverse problem to find locations and pumping discharges of ‎‎unknown wells. The simulation is performed by using the two-dimensional groundwater flow equation, which is solved by ‎the finite difference numerical technique. The learning automata algorithm has been used as a tool for ‎optimization. ‎The simulation and the optimization models are linked to obtaining the final model. To identify the ‎location and discharge of the unknown wells, the proposed model changes the discharges of the wells and studies ‎the influence on the objective function which is the root mean square error of the calculated and observed ‎‎piezometric head. The wells which increase the objective function are deleted. After the completion of this ‎stage, the locations of the wells are moved to the vicinity in all directions and the locations which yield fewer ‎errors in terms of the objective function will result in the final locations. To check the efficiency of this ‎model, two hypothetical aquifers were used in ‎a steady and unsteady flow state, in which there are some ‎unknown wells. The prepared model showed the ‎ability to determine these wells' number, location, and flow rate ‎with the accuracy of the root mean square error of 0.061 meters in the first numerical example and 0.010 in the second numerical example.


Main Subjects

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