Approximating probability distribution of circuit performance function for parametric yield estimation using transferable belief model  

作　　者：XU XiaoBin ZHOU DongHua JI YinDong WEN ChengLin 

机构地区：[1]School of Automation and Institute of Systems Science and Control Engineering,Hangzhou Dianzi University [2]Department of Automation and Tsinghua National Laboratory for Information Science and Technology,Tsinghua University [3]Research Institute of Information Technology (RIIT), Tsinghua University

出　　处：《Science China(Information Sciences)》2013年第11期102-120,共19页中国科学（信息科学）（英文版）

基　　金：supported by National Key Technologies R&D Program of China(Grant No.2009BAG12A08);National Natural Science Foundation of China(Grant Nos.61004070,60934009,61034006,61104019);Commonweal Technology Application Research Project of Zhejiang Province(Grant No.2012C21025)

摘　　要：This paper applies the transferable belief model （TBM） interpretation of the Dempster-Shafer theory of evidence to approximate distribution of circuit performance function for parametric yield estimation. Treating input parameters of performance function as credal variables defined on a continuous frame of real numbers, the suggested approach constructs a random set-type evidence for these parameters. The corresponding random set of the function output is obtained by extension principle of random set. Within the TBM framework, the random set of the function output in the credal state can be transformed to a pignistic state where it is represented by the pignistic cumulative distribution. As an approximation to the actual cumulative distribution, it can be used to estimate yield according to circuit response specifications. The advantage of the proposed method over Monte Carlo （MC） methods lies in its ability to implement just once simulation process to obtain an available approximate value of yield which has a deterministic estimation error. Given the same error, the new method needs less number of calculations than MC methods. A track circuit of high-speed railway and a numerical eight-dimensional quadratic function examples are included to demonstrate the efficiency of this technique.This paper applies the transferable belief model （TBM） interpretation of the Dempster-Shafer theory of evidence to approximate distribution of circuit performance function for parametric yield estimation. Treating input parameters of performance function as credal variables defined on a continuous frame of real numbers, the suggested approach constructs a random set-type evidence for these parameters. The corresponding random set of the function output is obtained by extension principle of random set. Within the TBM framework, the random set of the function output in the credal state can be transformed to a pignistic state where it is represented by the pignistic cumulative distribution. As an approximation to the actual cumulative distribution, it can be used to estimate yield according to circuit response specifications. The advantage of the proposed method over Monte Carlo （MC） methods lies in its ability to implement just once simulation process to obtain an available approximate value of yield which has a deterministic estimation error. Given the same error, the new method needs less number of calculations than MC methods. A track circuit of high-speed railway and a numerical eight-dimensional quadratic function examples are included to demonstrate the efficiency of this technique.

关 键 词：Dempster-Shafer theory of evidence Monte Carlo methods parametric yield random set trans- ferable belief model 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术] TN710[自动化与计算机技术—计算机科学与技术]