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Mathematical Problems in Engineering
Volume 2015, Article ID 908027, 12 pages
Research Article

Circuit Tolerance Design Using Belief Rule Base

1Institute of System Science and Control Engineering, School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China
2Manchester Business School, The University of Manchester, Manchester M15 6PB, UK

Received 30 October 2014; Accepted 31 December 2014

Academic Editor: Gang Li

Copyright © 2015 Xiao-Bin Xu 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.


A belief rule-based (BRB) system provides a generic nonlinear modeling and inference mechanism. It is capable of modeling complex causal relationships by utilizing both quantitative information and qualitative knowledge. In this paper, a BRB system is firstly developed to model the highly nonlinear relationship between circuit component parameters and the performance of the circuit by utilizing available knowledge from circuit simulations and circuit designers. By using rule inference in the BRB system and clustering analysis, the acceptability regions of the component parameters can be separated from the value domains of the component parameters. Using the established nonlinear relationship represented by the BRB system, an optimization method is then proposed to seek the optimal feasibility region in the acceptability regions so that the volume of the tolerance region of the component parameters can be maximized. The effectiveness of the proposed methodology is demonstrated through two typical numerical examples of the nonlinear performance functions with nonconvex and disconnected acceptability regions and high-dimensional input parameters and a real-world application in the parameter design of a track circuit for Chinese high-speed railway.