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Mathematical Problems in Engineering
Volume 2017, Article ID 5120704, 12 pages
Research Article

Prediction Interval Construction for Byproduct Gas Flow Forecasting Using Optimized Twin Extreme Learning Machine

1Department of Information Service and Intelligent Control, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China
2University of Chinese Academy of Sciences, Beijing 100049, China

Correspondence should be addressed to Jingtao Hu; nc.ais@oatgnijuh

Received 20 March 2017; Revised 28 May 2017; Accepted 27 July 2017; Published 23 August 2017

Academic Editor: Dan Simon

Copyright © 2017 Xueying Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Prediction of byproduct gas flow is of great significance to gas system scheduling in iron and steel plants. To quantify the associated prediction uncertainty, a two-step approach based on optimized twin extreme learning machine (ELM) is proposed to construct prediction intervals (PIs). In the first step, the connection weights of the twin ELM are pretrained using a pair of symmetric weighted objective functions. In the second step, output weights of the twin ELM are further optimized by particle swarm optimization (PSO). The objective function is designed to comprehensively evaluate PIs based on their coverage probability, width, and deviation. The capability of the proposed method is validated using four benchmark datasets and two real-world byproduct gas datasets. The results demonstrate that the proposed approach constructs higher quality prediction intervals than the other three conventional methods.