Lake Water-Level fluctuations forecasting using Minimax Probability Machine Regression, Relevance Vector Machine, Gaussian Process Regression, and Extreme Learning Machine

Forecasting freshwater lake levels is vital information for water resource management, including water supply management, shoreline management, hydropower generation optimization, and flood management. This study presents a novel application of four advanced artificial intelligence models namely the Minimax Probability Machine Regression (MPMR), Relevance Vector Machine (RVM), Gaussian Process Regression (GPR) and Extreme Learning Machine (ELM) for forecasting lake level fluctuation in Lake Huron utilizing historical datasets. The MPMR is a probabilistic framework that employed Mercer Kernels to achieve nonlinear regression models. The GPR, which is a probabilistic technique used tractable Bayesian framework for generalization of multivariate distribution of input samples to vast dimensional space. The ELM is a capable algorithm-based model for the implementation of the single-layer feed-forward neural network. The RVM demonstrate depends on the specification of the Bayesian method on a linear model with proper preceding that results in demonstration of sparse. The recommended techniques were tested to evaluate the current lake water-level trend monthly from the historical datasets at four previous time steps. The Lake Huron levels from 1918 to 1993 was managed for the training phase, and the rest of data (from 1994 to 2013) was used for testing. Considering the monthly and annually previous time steps, six models were introduced and found that the best results are achieved for a model with (t-1, t-2, t-3, t-12) as input combinations. The results show that all models can forecast the lake levels precisely. The results of this research study exhibit that the MPMR model (R2 = 0.984; MAE = 0.035; RMSE = 0.044; ENS = 0.984; DRefined = 0.995; ELM = 0.874) found to be more precise in lake level forecasting. The MPMR can be utilized as a practical computational tool on current and future planning with sustainable management of water resource of Lake Michigan-Huron.

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