基于聚类状态主控边界点的单调多态关联系统可靠性分析

张永进; 孙有朝; 张燕军

doi:10.7527/S1000-6893.2017.220868

航空学报 >

2017 , Vol. 38 >Issue 8: 220868 - 220868

DOI: https://doi.org/10.7527/S1000-6893.2017.220868

固体力学与飞行器总体设计

基于聚类状态主控边界点的单调多态关联系统可靠性分析

张永进 ,
孙有朝 ,
张燕军

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1. 安徽工业大学数理科学与工程学院, 马鞍山 243002;
2. 南京航空航天大学民航学院, 南京 211106;
3. 扬州大学机械工程学院, 扬州 225127

收稿日期: 2016-10-19

修回日期: 2017-02-26

网络出版日期: 2017-04-19

基金资助

国家自然科学基金（U1333119，60979019，60572171，51605424，71601002）；中国民航局科技基金（MHRD201123，MHRD200908，MHRD0722）；江苏省自然科学基金（BK20150455）

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Reliability analysis for multi-state coherent system with monotonic components based on pivotal boundary points of clustering states

ZHANG Yongjin ,
SUN Youchao ,
ZHANG Yanjun

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1. School of Mathematics and Physics, Anhui University of Technology, Maanshan 243002, China;
2. College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;
3. College of Mechanical Engineering, Yangzhou University, Yangzhou 225127, China

Received date: 2016-10-19

Revised date: 2017-02-26

Online published: 2017-04-19

Supported by

National Natural Science Foundation of China (U1333119,60979019,60572171,51605424,71601002);CAAC Science and Technology Project (MHRD201123,MHRD200908,MHRD0722);Natural Science Foundation of Jiangsu Province (BK20150455)

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摘要

鉴于组成系统单元的多状态单调关联性特征，将多元离散函数理论引入描述系统状态结构函数，发展了控制状态等价类主导状态向量的状态等价类主控边界点的逻辑方法，推导了多态单调关联系统的状态结构函数、可靠性和期望状态表达式；面向顾客的需求偏好，将负效用函数嵌入系统平均性能效用模型；鉴于元件状态引起的计算复杂性，提出了集合运算的德摩根律法和新型的框图式算法，简化了系统可靠度的表达式。结合某型航空发动机的简化演算，验证了主导等价类向量方法和框图算法的合理性与有效性，为工程系统的可靠性设计和可靠性管理提供理论依据。

关键词： 主控边界点; 离散函数; 多状态关联系统; 单调性; 可靠性

本文引用格式

张永进 , 孙有朝 , 张燕军 . 基于聚类状态主控边界点的单调多态关联系统可靠性分析[J]. 航空学报, 2017 , 38(8) : 220868 -220868 . DOI: 10.7527/S1000-6893.2017.220868

Abstract

Considering the monotone and coherence of the multi-state system, the multiple discrete function theory is introduced to describe the structure function of system state. The logic approaches for the equivalence class of the component state which control the state vector of system are proposed, and the expressions for the state structure function, reliability and expected states are derived for the multi-state coherent system. To avoid the complexity of computation caused by the number of the state, the Demogen law and the new block diagram algorithm are developed to simplify the expression for the system reliability. An illustrative example of a certain type of aero engine verifies the effectiveness of the logic vector measure controlling the state equivalence class and the block diagram algorithm. It provides theoretical basis for reliability design and reliability management of system engineering.

Key words： pivotal boundary point; discrete function; multi-state coherent system; monotonicity; reliability

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