A novel prediction intervals method integrating an error & self-feedback extreme learning machine with particle swarm optimization for energy consumption robust prediction

Nowadays, petrochemical industries with many integrated units and equipment have characteristics of high uncertainty and nonlinearity. Therefore, it becomes more and more difficult to make reliable and accurate point measurement of energy modeling. To tackle this problem, a novel prediction intervals (PIs) method integrating error & self-feedback extreme learning machine (ESF-ELM) with particle swarm optimization (PSO) is proposed. For improving the energy modeling accuracy of extreme learning machine (ELM), the input weights are initialized using cosine similarity coefficients but not randomly initialized. In addition, an error-feedback layer and a self-feedback layer are added to the input layer and the hidden layer for enhancing generalization performance, respectively. Finally, PSO with a comprehensive measure is developed to evaluate the mean coverage probability and the mean width percentage of PIs. The proposed ESF-ELM with PSO is applied to constructing PIs of energy consumption for a Purified Terephthalic Acid production process. Simulation results show the proposed model can generate high-quality PIs with large coverage probability, narrow width, and superiority in adaptability and reliability, which provides guidance for decision makers to maximize benefits and give reasonable future plans.