Balancing Results from AI-Based Geostatistics versus Fuzzy Inference by Game Theory Bargaining to Improve a Groundwater Monitoring Network

Abstract

An artificial intelligence-based geostatistical optimization algorithm was developed to upgrade a test Iranian aquifer’s existing groundwater monitoring network. For that aquifer, a preliminary study revealed that a Multi-Layer Perceptron Artificial Neural Network (MLP-ANN) more accurately determined temporally average water table elevations than geostatistical kriging, spline, and inverse distance weighting. Because kriging is usually used in that area for water table estimation, the developed algorithm used MLP-ANN to guide kriging, and Genetic Algorithm (GA) to determine locations for new monitoring well location(s). For possible annual fiscal budgets allowing 1–12 new wells, 12 sets of optimal new well locations are reported. Each set has the locations of new wells that would minimize the squared difference between the time-averaged heads developed by kriging versus MLP-ANN. Also, to simultaneously consider local expertise, the algorithm used fuzzy inference to quantify an expert’s satisfaction with the number of new wells. Then, the algorithm used symmetric bargaining (Nash, Kalai–Smorodinsky, and area monotonic) to present an upgradation strategy that balanced professional judgment and heuristic optimization. In essence, the algorithm demonstrates the systematic application of relatively new computational practices to a common situation worldwide.

Keywords

• bargaining theory
• fuzzy inference system
• groundwater monitoring
• geostatistics
• artificial neural network
• optimization