Balancing AI-Based Geostatistical Optimization and Fuzzy Inference by Game Theory Bargaining to Improve a Groundwater Monitoring Network

An artificial intelligence-based geostatistical optimization model is developed for upgrading a test aquifer's existing groundwater monitoring network. A preliminary study of the aquifer revealed that a Multi-Layer Perceptron Artificial Neural Network (MLP-ANN) could more accurately determine aquifer water table elevations than geostatistical kriging, spline functions, and inverse distance weighting. Because kriging has been standardly used in that area for water surface estimation, the demonstrated model uses a deep learning ANN to guide kriging and Simple Genetic Algorithm (SGA) optimization to determine the candidate locations of new monitoring wells that will most improve the accuracy of kriged basin-scale water table estimates. To enhance utility of proposed network change(s) the model incorporates a monitoring network expert’s judgement via fuzzy inference. The model’s first phase has two parallel processes: a) for a range of new well numbers, the SGA determines the location of new wells that would minimize the squared difference between the kriged, and MLP-ANN estimated heads; b) a FIS describes a monitoring network expert's satisfaction with the number of new wells and the assumed unit well installation costs of the new wells. The second phase employs symmetric bargaining (Nash, Kalai-Smorodinsky, and area monotonic) and presents an upgrade strategy that reflects the best combination of professional judgment and heuristic optimization. The results showed that by adding three wells to the network in optimal locations, both accuracy and Satisfaction Of the Expert are equally achieved.