A wavelet-outlier robust extreme learning machine for rainfall forecasting in Ardabil City, Iran

In this paper, the monthly long-term precipitation of the city of Ardabil from 1976 to 2020 is simulated by a modern hybrid learning machine. To this end, the Wavelet and Outlier Robust Extreme Learning Machine (ORELM) models are integrated to produce a hybrid model called "Wavelet-Outlier Robust Extreme Learning Machine (WORELM)". First, the observed data are normalized, and the best normalization coefficients for the study are acquired. About 70% of the observed data are employed to train the artificial intelligence models and the remaining (i.e., 30%) to test them. After that, the optimal mother wavelet and the best decomposition level of the wavelet model are computed. Then, the optimal number of the hidden layer neurons and the best activation function of the ORELM model is chosen by performing a trial and error procedure. In this study, the regularization parameter of the ORELM model is also optimized. Moreover, using the autocorrelation function (ACF), the most influencing lags of the time-series data are detected, and 14 WORELM models are developed. By analyzing the WORELM models, the best model and the effective lags of the time-series data are introduced. The outcomes of the hybrid WORELM model are finally compared with other machine learning (ML) algorithms to prove the superiority of the WORELM model.