A robust integrated Bayesian multi-model uncertainty estimation framework (IBMUEF) for quantifying the uncertainty of hybrid meta-heuristic in global horizontal irradiation predictions

Abstract

Accurate and stable prediction of global horizontal irradiation (GHI) is vital for managing energy systems, irrigation planning, and also decision making for future investment. Existing artificial intelligence (AI) models for prediction GHI generally have high performance, but suffer from instability and uncertainty, especially in different climate areas. Therefore, the aim of this study is to implement an ensemble strategy based on the Integrated Bayesian Multi-model Uncertainty Estimation Framework (IBMUEF) for simultaneous input parameters and model structure uncertainty quantification in AIs. In this study, robust prediction techniques of meta-heuristic optimization algorithms (Multiverse optimization (MVO), Sine-cosine algorithm (SCA), Salp swarm algorithm (SSA)) are hybridized with machine learning models of Adaptive Neuro Fuzzy Inference System (ANFIS) and Extreme Learning Machine (ELM) for GHI predictions. The ensemble IBMUEF combines the advantages of developed models to improve the predicting performance. Comparing results of IBMUEF against the developed individual models show the predictive skill and strength of IBMUEF for four meteorological stations in two climate areas (arid and semi-arid) located in Iran. The results of developed individual models showed that all six hybrid models (ANFIS-MVO, ANFIS-SCA, ANFIS-SSA, ELM-MVO, ELM-SCA, ELM-SSA) performed well in four stations. The ranking of models carried out by Multi-Criteria Decision-Making (MCDM) method of Weighted Aggregated Sum Product Assessment (WASPAS). The ANFIS-MVO model with the highest rank was selected as the best model that R2, RMSE, MAE, and NSE values were ranged from 0.9929 to 0.9989, from 16.23 to 54.78 Wh/m2/day, from 4.21 to 10.39 Wh/m2/day, and from 0.993 to 0.999, respectively. The accuracy of ensemble IBMUEF based on the average RMSE was 23.7% and 32.2% better than the ANFIS-MVO model in arid and semi-arid climates, respectively. Evaluation results related to input parameters and model structure uncertainties proved the superiority of ensemble IBMUEF over the individual models, while 95% confidence interval covered almost 96% of observation data. The results highlighted the significance of combining individual models in IBMUEF for more accurate prediction of GHI with a suitable level of uncertainty. In conclusion, simultaneous considering of model input uncertainty and model parameter uncertainty is crucial for obtaining realistic and certain GHI predictions and correct quantification of the uncertainty bounds.