Rainfall-runoff (R-R) modelling is used to study the runoff generation of a catchment. The quantity or rate of change measure of the hydrological variable, called runoff, is important for environmental scientists to accomplish water-related planning and design. This paper proposes (i) an integrated model namely EO-ELM (an integration of equilibrium optimizer (EO) and extreme learning machine (ELM)) and (ii) a deep neural network (DNN) for one day-ahead R-R modelling. The proposed R-R models are validated at two different benchmark stations of the catchments, namely river Teifi at Glanteifi and river Fal at Tregony in the UK. Firstly, a partial autocorrelation function (PACF) is used for optimal number of lag inputs to deploy the proposed models. Six other well-known machine learning models, called ELM, kernel ELM (KELM), and particle swarm optimization-based ELM (PSO-ELM), support vector regression (SVR), artificial neural network (ANN) and gradient boosting machine (GBM) are utilized to validate the two proposed models in terms of prediction efficiency. Furthermore, to increase the performance of the proposed models, paper utilizes a discrete wavelet-based data pre-processing technique is applied in rainfall and runoff data. The performance of wavelet-based EO-ELM and DNN are compared with wavelet-based ELM (WELM), KELM (WKELM), PSO-ELM (WPSO-ELM), SVR (WSVR), ANN (WANN) and GBM (WGBM). An uncertainty analysis and two-tailed t-test are carried out to ensure the trustworthiness and efficacy of the proposed models. The experimental results for two different time series datasets show that the EO-ELM performs better in an optimal number of lags than the others. In the case of wavelet-based daily R-R modelling, proposed models performed better and showed robustness compared to other models used. Therefore, this paper shows the efficient applicability of EO-ELM and DNN in R-R modelling that may be used in the hydrological modelling field.

Blasting is essential for breaking hard rock in opencast mines and tunneling projects. It creates an adverse impact on flyrock. Thus, it is essential to forecast flyrock to minimize the environmental effects. The objective of this study is to forecast/estimate the amount of flyrock produced during blasting by applying three creative composite intelligent models: equilibrium optimizer-coupled extreme learning machine (EO-ELM), particle swarm optimization-based extreme learning machine (PSO-ELM), and particle swarm optimization-artificial neural network (PSO-ANN). To obtain a successful conclusion, we considered 114 blasting data parameters consisting of eight inputs (hole diameter, burden, stemming length, rock density, charge-per-meter, powder factor (PF), blastability index (BI), and weathering index), and one output parameter (flyrock distance). We then compared the results of different models using seven different performance indices. Every predictive model accomplished the results comparable with the measured values of flyrock. To show the effectiveness of the developed EO-ELM, the result from each model run 10-times is compared. The average result shows that the EO-ELM model in testing (R2 = 0.97, RMSE = 32.14, MAE = 19.78, MAPE = 20.37, NSE = 0.93, VAF = 93.97, A20 = 0.57) achieved a better performance as compared to the PSO-ANN model (R2 = 0.87, RMSE = 64.44, MAE = 36.02, MAPE = 29.96, NSE = 0.72, VAF = 74.72, A20 = 0.33) and PSO-ELM model (R2 = 0.88, RMSE = 48.55, MAE = 26.97, MAPE = 26.71, NSE = 0.84, VAF = 84.84, A20 = 0.51). Further, a non-parametric test is performed to assess the performance of these three models developed. It shows that the EO-ELM performed better in the prediction of flyrock compared to PSO-ELM and PSO-ANN. We did sensitivity analysis by introducing a new parameter, WI. Input parameters, PF and BI, showed the highest sensitivity with 0.98 each.