Industrial Prediction Intervals with Data Uncertainty

  • Jun Zhao
  • Wei Wang
  • Chunyang Sheng
Part of the Information Fusion and Data Science book series (IFDS)


Prediction intervals (PIs) construction is a comprehensive prediction technique that provides not only the point estimates of the industrial variables, but also the reliability of the prediction results indicated by an interval. Reviewing the conventional PIs construction methods (e.g., delta method, mean and variance-based estimation method, Bayesian method, and bootstrap technique), we provide some recently developed approaches in this chapter. Here, a bootstrapping-based ESN ensemble (BESNE) model is specially proposed to produce reliable PIs for industrial time series, in which a simultaneous training method based on Bayesian linear regression is developed. Besides, to cope with the error accumulation caused by the traditional iterative mode of time series prediction, a non-iterative granular ESN is also reported for PIs construction, where the network connections are represented by the interval-valued information granules. In addition, we present a mixed Gaussian kernel-based regression model to construct PIs, in which a gradient descent algorithm is derived to optimize the hyper-parameters of the mixed Gaussian kernel. In order to tackle the incomplete testing input problem, a kernel-based high order dynamic Bayesian network (DBN) model for industrial time series is then proposed, which directly deals with the missing points involved in the inputs. Finally, we provide some case studies to verify the effectiveness of these approaches.


Prediction intervals Time series Reliability Uncertainty Delta method Mean and variance-based estimation Bootstrap technique ESNs ensemble Bayesian estimation Non-iterative prediction Interval-weighted Gamma test Mixed Gaussian kernel Noisy inputs ANNs Missing input DBNs Approximate inference 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Jun Zhao
    • 1
  • Wei Wang
    • 1
  • Chunyang Sheng
    • 2
  1. 1.Dalian University of TechnologyDalianChina
  2. 2.Shandong University of Science and TechnologyQingdaoChina

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