Aquifer parameter and zone structure estimation using kernel-based fuzzy c-means clustering and genetic algorithm

Abstract

Summary In this study, we propose an inverse solution algorithm through which both the aquifer parameters and the zone structure of these parameters can be determined based on a given set of observations on piezometric heads. In the zone structure identification problem, kernel-based fuzzy c-means (KFCM) clustering method is used. The association of the zone structure with the transmissivity distribution is accomplished through a coupled simulation–optimization model. In the optimization model, genetic algorithm (GA) is used due to its efficiency in finding global or near global optimum solutions. Since the solution is based on the GA procedures, the optimization process starts with a randomly generated initial solution. Thus, there is no need to define an initial estimate of the solution. This is an advantage when compared to other studies reported in the literature. Further, the objective function used in the optimization model does not include a reference to field transmissivity data, which is another advantage of the proposed methodology. Numerical examples are provided to demonstrate the performance of the proposed algorithm. In the first example, transmissivity values and zone structures are determined for a known number of zones in the solution domain. In the second example, optimum number of zones as well as the transmissivity values and the zone structures are determined iteratively. A sensitivity analysis is also performed to test the performance of the proposed solution algorithm based on the number of observation data necessary to solve the problem accurately. Numerical results indicate that the proposed algorithm is effective and efficient and may be used in the inverse parameter estimation problems when both parameter values and zone structure are unknown.