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Confidence assessment and interval prediction for multi-input model via grey system theory

Haoliang Wang (School of Automation Science and Electrical Engineering, Beihang University, Beijing, China)
Xiwang Dong (School of Automation Science and Electrical Engineering, Beihang University, Beijing, China)
Qingdong Li (School of Automation Science and Electrical Engineering, Beihang University, Beijing, China)
Zhang Ren (School of Automation Science and Electrical Engineering, Beihang University, Beijing, China)

Grey Systems: Theory and Application

ISSN: 2043-9377

Article publication date: 5 February 2018

Abstract

Purpose

By using small reference samples, the calculation method of confidence value and prediction method of confidence interval for multi-input system are investigated. The purpose of this paper is to offer effective assessing methods of confidence value and confidence interval for the simulation models used in establishing guidance and control systems.

Design/methodology/approach

In this paper, first, an improved cluster estimation method is proposed to guide the selection of the small reference samples. Then, based on analytic hierarchy process method, the new calculation method of the weight of each reference sample is derived. By using the grey relation analysis method, new calculation methods of the correlation coefficient and confidence value are presented. Moreover, the confidence interval of the sample awaiting assessment is defined. A new prediction method is derived to obtain the confidence interval of the sample awaiting assessment which has no reference sample. Subsequently, by using the prediction method and original small reference samples, Bootstrap resampling method is used to obtain more correlation coefficients for the sample to reduce the probability of abandoning the true.

Findings

The grey relational analysis is used in assessing the confidence value and interval prediction. The numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

Originality/value

Based on the selected small reference samples, new calculation methods of the correlation coefficient and confidence value are presented to assess the confidence value of model awaiting assessment. The calculation methods of maximum confidence interval, expected confidence interval and other required confidence intervals are presented, which can be used in assessing the validities of controller and guidance system obtained from the model awaiting assessment.

Keywords

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants ******.

Citation

Wang, H., Dong, X., Li, Q. and Ren, Z. (2018), "Confidence assessment and interval prediction for multi-input model via grey system theory", Grey Systems: Theory and Application, Vol. 8 No. 1, pp. 69-83. https://doi.org/10.1108/GS-07-2017-0024

Publisher

:

Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited