基于部分最大可满足性问题的动态系统中最小故障检测隔离集求解方法  

Approach for generating minimal fault detectability and isolability set in dynamic system based on partial maximum satisfiability problem

作　　者：欧阳丹彤[1,2] 孙睿 田新亮 张立明[1,2] 刘萍萍[1,2] OUYANG Dan-tong;SUN Rui;TIAN Xin-liang;ZHANG Li-ming;LIU Ping-ping(College of Computer Science and Technology,Jilin University,Changchun 130012,China;Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education,Jilin University,Changchun 130012,China;College of Software,Jilin University,Changchun 130012,China)

机构地区：[1]吉林大学计算机科学与技术学院,长春130012 [2]吉林大学符号计算与知识工程教育部重点实验室,长春130012 [3]吉林大学软件学院,长春130012

出　　处：《吉林大学学报（工学版）》2023年第4期1163-1173,共11页Journal of Jilin University:Engineering and Technology Edition

基　　金：国家自然科学基金项目(62076108,61872159,61672261);吉林省教育厅科学研究项目(JJKH20211106KJ,JJKH20211103KJ);吉林省自然科学基金项目(20200201283JC)。

摘　　要：选择一组能够检测并隔离所有故障的故障检测隔离集(FDIS)是动态系统基于模型故障检测与隔离(FDI)的重要步骤,该步骤通常要求FDIS的基数最小,即求解最小故障检测隔离集(MFDIS),MFDIS的求解时间随着问题规模增大呈指数级增长。BILP(Binary integer linear programming)完备方法是现行动态系统中通用和最高效的MFDIS求解方法,但该方法的求解效率有待提高。本文首次提出了基于部分最大可满足性问题(PMS)的MFDIS求解方法。提出极小超定方程集(MSO)的概念,将部分MSO集合用MSO等价集表示,以缩减问题规模。将MFDIS求解问题转化为PMS问题,进而提高求解效率。实验结果表明,本文方法将问题规模平均约简至原来的8.22%;与BILP方法相比,本文方法的求解效率提高了4.18~9.5倍。Selecting fault detectability and isolability set(FDIS)that can detect and isolate all faults is an important step in model-based fault detection and isolation of dynamic systems.This step usually requires the minimal cardinality of FDIS,that is,generating minimal fault detectability and isolability set(MFDIS).The solution time of MFDIS increases exponentially with the increase of the scale of the problem.BILP complete method is the most common and efficient method to generate MFDIS in dynamic systems,but the efficiency of this method needs to be improved,and the complete solution of large-scale cases can’t be obtained in an acceptable time.In this paper,an approach for generating MFDIS based on partial maximum satisfiability problem(PMS)is proposed for the first time.The concept of MSO equivalent set is proposed,and some MSO sets are represented by MSO equivalent set to reduce the size of the problem.Then,the MFDIS genarating problem is transformed to PMS problem to improve the solving efficiency.The experimental results show that the proposed reduction method reduces the problem size to 8.22%of the original size on average;compared with BILP method,the efficiency of the proposed method is increased by 4.72 times on average.

关 键 词：基于模型诊断 最小故障检测隔离集 故障检测与隔离 最小型超定方程集 部分最大可满足性问题 

分 类 号：TP306[自动化与计算机技术—计算机系统结构]