Online Sequential Learning of Neural Networks in Solar Radiation Modeling Using Hybrid Bayesian Hierarchical Approach

Traditional learning process in solar radiation modeling usually requires historical data to perform regularization using training and cross-validation approaches. However, in applications where no historical data are available, regularization cannot be performed using traditional techniques. This paper presents a hierarchical Bayesian framework with the extended Kalman filter (Bayesian-EKF) to perform regularization in sequential learning of the artificial neural network (ANN) for solar radiation modeling. A highly stochastic time series for daily solar radiation, the global horizontal irradiance (GHI), is modeled based on different meteorological variables including temperature (T), relative humidity (RH), wind speed (WS), and sunshine duration (SSD). A comparison is made with well-known methods including the ANN-based nonlinear autoregressive with exogenous inputs neural network (NARX-NN) and Wiener filter-based multivariate linear regression (MLR). The method is validated on test data using coefficient of determination (R²) and root mean squared error (RMSE). The proposed technique effectively estimates the noise components in the data and achieves superior performance as compared to the traditional learning processes of NARX-NN and MLR. Moreover, it is more robust to statistical outliers in the data and does not require prior history for training and cross-validation. In the presence of the outliers, the performance of the NARX-NN degrades from R²= 94.73% to R²= 85.85% but there is virtually no difference in the case of Bayesian-EKF. Over and above, MLR performs better than NARX-NN but worse than Bayesian-EKF.