An artificial neural network (ANN) based on particle swarm optimization (PSO) was developed for the time series prediction. The hybrid ANN+PSO algorithm was applied on Mackey-Glass chaotic time series in the short-term x(t + 6). The performance prediction was evaluated and compared with other studies available in the literature. Also, we presented properties of the dynamical system via the study of chaotic behaviour obtained from the predicted time series. Next, the hybrid ANN+PSO algorithm was complemented with a Gaussian stochastic procedure (called stochastic hybrid ANN+PSO) in order to obtain a new estimator of the predictions, which also allowed us to compute the uncertainties of predictions for noisy Mackey-Glass chaotic time series. Thus, we studied the impact of noise for several cases with a white noise level (σ
N) from 0.01 to 0.1.
In this study, different hybridized techniques that combine an artificial neural network (ANN) with bio‐inspired optimization algorithms such as particle swarm optimization (PSO), genetic algorithm (GA), and a hybridized PSO+GA were applied to update the ANN connection weights and so forecast the disturbance storm time (Dst) index. The past values of Dst index time series were used as input parameters to forecast its variation from 1 to 6 hours ahead. The database collected considers 233,760 hourly data from 01 January 1990 to 31 August 2016, containing storms and quiet period, grouped into three data sets: learning set (116,880 hourly data points), validation set (58,440 data points), and testing set (58,440 data points). Several ANN configurations were studied and optimized during the training process by evaluating the root mean square error (RMSE) and the correlation coefficient (R). An analysis of the predictive capability of each method was made year per year, and according to the levels of the geomagnetic storm. Also, an additional test was applied to the proposed method using 17 intense geomagnetic storms reported during solar cycle 24, including the St. Patrick's Day storm of 2015. Results show that the hybridized ANN+PSO method can forecast the Dst index quite accurately from 1 to 3 h in advance (with RMSE≤5 nT and R≥0.9), while the ANN+PSO+GA method can forecast the Dst index quite accurately from 4 to 6 h ahead (RMSE≤7 nT and R≥0.8)
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