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Non-probabilistic reliability analysis of active control system for structural vibration
LI Yunlong, WANG Xiaojun , HUANG Ren
School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
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

1 不确定结构振动主动控制方程

CD分别为输出矩阵和直接转移矩阵,一般情况下直接转移矩阵D=0,输出矩阵C可以根据要输出的物理量进行选取.由式(3)可以看出,如果系统的自由度n较大时,状态空间方程的维数就会很大,不便于进行控制器的设计和分析.

ωii分别为系统第i阶自然频率和模态阻尼比.

 图 1 系统动力响应穿过阈值的可能次数Fig. 1 Possible times of dynamic response across the threshold

 图 2 非概率可靠度计算示意图Fig. 2 Schematic diagram of non-probabilistic reliability calculating

 图 3 二自由度弹簧-质量-阻尼器振动系统 Fig. 3 Two-degrees of freedom mass-spring-damper vibration system

 图 4 控制前与控制后系统的响应输出Fig. 4 Comparison between responses of open-loop and closed-loop system
 图 5 区间闭环控制系统响应上下界Fig. 5 Interval bounds of interval closed-loop system

 方法 响应最大值的上界/m 名义值(均值)/m 响应最大值的下界/m 计算时间/s 可靠度/% 蒙特卡洛 0.104 4 0.208 2 0.351 4 177.553 99.9 非概率 0.053 2 0.203 95 0.354 7 0.147 98.4

 图 6 某型飞机弹舱振动与噪声主动控制模型Fig. 6 Active control of vibration and noise model of an aircraft bomb bay

 图 7 弹性板的前两阶振动模态Fig. 7 The first two vibration modal of elastic plate

 阶数 1 2 3 4 5 频率/Hz 83.2 90.8 99 110.5 126.4 阶数 6 7 8 9 10 频率/Hz 147.1 172.4 202.4 221.7 236.7

 图 8 弹性板控制前与控制后系统的响应输出Fig. 8 Open-loop and closed-loop system responses of elastic plate

 图 9 闭环控制系统响应上下界Fig. 9 Interval bounds of interval closed-loop system

 方法 响应绝对值的上界/mm 名义值(均值)/mm 响应绝对值的下界/mm 计算时间/s 可靠度/% 蒙特卡洛 4.039 4.450 5.051 27 424.7 98.1 非概率 3.473 4.288 5.108 16.439 93.0
5 结 论

1) 与传统概率方法(蒙特卡洛)相比,本文所提出的非概率可靠性分析方法,所需计算时间更短,计算结果更加保守,尤其适用于无法得到不确定量概率信息的复杂大型结构振动主动控制系统.

2) 本文基于非概率可靠性分析模型提出了一种解决结构动力学可靠性问题的方法,该方法可以适用于传统的开环动力学系统.

3) 本文的研究内容为基于可靠性的振动主动控制器设计提供了新的研究思路,为新型飞机设计过程中采用结构振动主动控制技术提供了理论依据与技术基础.

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#### 文章信息

LI Yunlong, WANG Xiaojun, HUANG Ren

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

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(2): 259-266.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0133