Nature-inspired optimal tuning of input membership functions of fuzzy inference system for groundwater level prediction

Abstract

We present a novel regression algorithm that combines a Fuzzy Inference System (FIS) with a nature-inspired algorithm to predict variations in GroundWater Levels (GWLs). Initially, we considered several input features, including precipitation, temperature, evaporation, relative humidity, soil type, and GWL Lag. A feature importance analysis using regression tree ensemble learning reveals GWL lag as the most relevant feature and soil type as the least relevant. We eliminate features with low importance scores (soil type, temperature, and evaporation) to improve the computational efficiency. Our approach leverages Fuzzy C-Means (FCM) clustering to develop a Sugeno-type FIS with definite clusters. The dataset is clustered based on feature similarity, and Gaussian membership functions are assigned to each cluster. The mapping of each point is controlled by the range and standard deviation of the Gaussian membership functions. We train the model keeping 70% of the dataset, iteratively tuning the parameters of the Gaussian membership function for all clusters through the Invasive Weed Optimization (IWO) algorithm. The performance of the model is then evaluated using the remaining 30% of the datasets. The F-IWO-GWL model accurately predicts GWL fluctuations, achieving a high correlation coefficient (R = 0.89), low normalized root mean square error (nRMSE = 0.18), and minimal bias (bias = 0.08). A comparative analysis involving seventeen benchmark algorithms reveals the superior performance of our algorithm. To ensure a fair comparison, we calculated key metrics including Akaike’s Information Criterion (AIC), Bayesian Information Criterion (BIC), and Corrected AIC (AICc). The F-IWO-GWL algorithm exhibits the lowest values for AIC, BIC, and AICc among all tested algorithms, suggesting the best goodness-of-fit. This study provides a robust approach for predicting GWL fluctuation, applicable to various groundwater management scenarios. It offers valuable insights for policymakers and stakeholders involved in groundwater management, aiding informed decision-making.