北京航空航天大学学报 ›› 2015, Vol. 41 ›› Issue (2): 259-266.doi: 10.13700/j.bh.1001-5965.2014.0133

• 论文 • 上一篇    下一篇

结构振动主动控制系统的非概率可靠性分析

李云龙, 王晓军, 黄仁   

  1. 北京航空航天大学 航空科学与工程学院, 北京 100191
  • 收稿日期:2014-03-20 出版日期:2015-02-20 发布日期:2015-03-12
  • 通讯作者: 王晓军(1978—), 男, 陕西岐山人, 教授, xjwang@buaa.edu.cn, 主要研究方向为结构力学、计算固体力学、结构可靠性. E-mail:xjwang@buaa.edu.cn
  • 作者简介:李云龙(1988—), 男, 山东滨州人, 博士生, lylsdust@163.com
  • 基金资助:

    中央高校基本科研业务费资助项目(YWF-14-HKXY-027); 国家自然科学基金资助项目(11372025); 航空科学基金资助项目(A2012ZA51010); 高等学校学科创新引智计划资助项目(B07009)

Non-probabilistic reliability analysis of active control system for structural vibration

LI Yunlong, WANG Xiaojun, HUANG Ren   

  1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2014-03-20 Online:2015-02-20 Published:2015-03-12

摘要:

为了解决结构主动振动控制系统的可靠性问题,考虑结构参数的不确定性,研究了结构振动主动控制系统可靠性分析的非概率方法.对不确定变量用区间数或区间向量进行描述,基于区间数学,提出了含区间不确定参数的闭环控制系统响应的计算方法,在此基础之上结合非概率可靠性分析方法,建立了适用于振动控制系统的非概率可靠性分析方法.该方法无需不确定量的概率信息,只需明确参数所在区间范围即可,对开环系统和闭环控制系统的可靠性分析与基于可靠性的控制器设计具有一定的理论意义.通过数值算例,将非概率可靠性分析方法与蒙特卡洛方法进行了比较,结果表明了本文所提方法的有效性和对复杂结构振动主动控制系统的适用性.

关键词: 非概率可靠性, 主动控制, 振动控制, 不确定性, 区间分析

Abstract:

To solve the reliability problem of active control system of structural vibration, considering the uncertainties in controlled structure, reliability analysis of the active control system for structural vibration based on non-probabilistic reliability model was studied. The uncertain parameters were expressed in the form of interval number or vector. Calculation method of responses of the closed-loop system with interval parameters was proposed based on interval mathematics. Combined with the non-probabilistic reliability model, non-probabilistic reliability analysis method, which requires the bounds of the uncertainties rather than the probability density function, was established for active vibration control systems. This reliability analysis approach had certain theoretical significance for reliability analysis of open-loop system, closed-loop control system and reliability-based controller design. The results of numerical examples demonstrate the effectiveness of the proposed method and the applicability for complex structures compared with the Monte Carlo method that can be taken as the benchmark of accuracy for judgment.

Key words: non-probabilistic reliability, active control, vibration control, uncertainty, interval analysis

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