Computationally efficient approach for identification of fuzzy dynamic groundwater sampling network

In the present work, uncertainty-based dynamic sampling frameworks were tested for a sampling horizon with multiple time steps. Future concentration values were assumed as fuzzy numbers. Multiple realization–based simulations were used for generation of fuzzy numbers. The first framework considers fuzzy variance reduction. The second framework considers mass estimation error reduction with maximization of spatial coverage of the dynamic sampling network. It is a multi-objective optimization problem with a large number of objectives. In Dhar and Patil (2012), uncertainty-based optimal sampling design model was suggested using Nondominated Sorting Genetic Algorithm-II (NSGA-II) as its optimization algorithm. However, NSGA-II becomes computationally expensive while handling more than three objectives. We extend the previously suggested algorithm for multi-objective sampling network design problems based on NSGA-III framework. Two design frameworks were proposed: one incorporating a simulation model and a fuzzy covariance for minimizing the total contaminant-concentration variance and the other incorporating a simulation model and a fuzzy kriging model in conjunction with an optimization model to minimize the fuzzy mass estimation error and spatial coverage of spatiotemporal sampling locations. NSGA-III was used for solving the sampling network design model. Performances of the proposed frameworks were evaluated for two hypothetical illustrative examples. The results indicate that the proposed design frameworks perform satisfactorily under uncertain system conditions.

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