Aggregation of Pi-based forecast to enhance prediction accuracy

In contrast to point forecast, prediction interval-based neural network offers itself as an effective tool to quantify the uncertainty and disturbances that associated with process data. However, single best neural network (NN) does not always guarantee to predict better quality of forecast for different data sets or a whole range of data set. Literature reported that ensemble of NNs using forecast combination produces stable and consistence forecast than single best NN. In this work, a NNs ensemble procedure is introduced to construct better quality of Pis. Weighted averaging forecasts combination mechanism is employed to combine the Pi-based forecast. As the key contribution of this paper, a new Pi-based cost function is proposed to optimize the individual weights for NN in combination process. An optimization algorithm, named simulated annealing (SA) is used to minimize the PI-based cost function. Finally, the proposed method is examined in two different case studies and compared the results with the individual best NNs and available simple averaging Pis aggregating method. Simulation results demonstrated that the proposed method improved the quality of Pis than individual best NNs and simple averaging ensemble method.