Groundwater Level Prediction Using a Multiple ObjectiveGenetic Algorithm-Grey Relational Analysis Based Weighted Ensemble of ANFIS Models

Predicting groundwater levels is critical for ensuring sustainable use of an aquifer’s limited groundwater reserves and developing a useful groundwater abstraction management strategy. The purpose of this study was to assess the predictive accuracy and estimation capability of various models based on the Adaptive Neuro Fuzzy Inference System (ANFIS). These models included Differential Evolution-ANFIS (DE-ANFIS), Particle Swarm Optimization-ANFIS (PSO-ANFIS), and traditional Hybrid Algorithm tuned ANFIS (HA-ANFIS) for the one- and multi-week forward forecast of groundwater levels at three observation wells. Model-independent partial autocorrelation functions followed by frequentist lasso regression-based feature selection approaches were used to recognize appropriate input variables for the prediction models. The performances of the ANFIS models were evaluated using various statistical performance evaluation indexes. The results revealed that the optimized ANFIS models performed equally well in predicting one-week-ahead groundwater levels at the observation wells when a set of various performance evaluation indexes were used. For improving prediction accuracy, a weighted-average ensemble of ANFIS models was proposed, in which weights for the individual ANFIS models were calculated using a Multiple Objective Genetic Algorithm (MOGA). The MOGA accounts for a set of benefits (higher values indicate better model performance) and cost (smaller values indicate better model performance) performance indexes calculated on the test dataset. Grey relational analysis was used to select the best solution from a set of feasible solutions produced by a MOGA. A MOGA-based individual model ranking revealed the superiority of DE-ANFIS (weight = 0.827), HA-ANFIS (weight = 0.524), and HA-ANFIS (weight = 0.697) at observation wells GT8194046, GT8194048, and GT8194049, respectively. Shannon’s entropy-based decision theory was utilized to rank the ensemble and individual ANFIS models using a set of performance indexes. The ranking result indicated that the ensemble model outperformed all individual models at all observation wells (ranking value = 0.987, 0.985, and 0.995 at observation wells GT8194046, GT8194048, and GT8194049, respectively). The worst performers were PSO-ANFIS (ranking value = 0.845), PSO-ANFIS (ranking value = 0.819), and DE-ANFIS (ranking value = 0.900) at observation wells GT8194046, GT8194048, and GT8194049, respectively. The generalization capability of the proposed ensemble modelling approach was evaluated for forecasting 2-, 4-, 6-, and 8-weeks ahead groundwater levels using data from GT8194046. The evaluation results confirmed the useability of the ensemble modelling for forecasting groundwater levels at higher forecasting horizons. The study demonstrated that the ensemble approach may be successfully used to predict multi-week-ahead groundwater levels, utilizing previous lagged groundwater levels as inputs.