随机和认知不确定性量化的置信区域法
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摘要
针对非线性机械系统中混合不确定性量化的问题,提出了随机和认知不确定性量化的置信区域法。首先,分别用概率论方法和区间方法来处理混合不确定性中的随机不确定性和认知不确定性,得到混合不确定性的置信区域;然后,为了在时间域内对不确定性进行传播,对传统双层循环蒙特卡罗抽样方法进行了改进;最后,以非线性质量-弹簧-阻尼系统为例讨论了基于混合不确定性分析方法的有效性。结果表明,同时考虑随机不确定性和认知不确定性,有利于提高系统设计的可靠性,为非线性机械系统的设计与精度分析提供了理论依据。
Focusing on the quantification of mixed-uncertainty in nonlinear mechanical systems,a confidence region method for the quantification of aleatory and epistemic uncertainty is presented.In this method,interval analysis is used to represent epistemic uncertainty while probability theory is used to represent aleatory uncertainty,in order to obtain the confidence region of mixed uncertainties.Then,the traditional double-loop Monte Carlo sampling approach is improved to propagate uncertainties during the entire time domain.Finally,a nonlinear mass-spring-damper system is simulated to discuss the validity of the analysis method based on mixed-uncertainty.The results show that it can improve the reliability of the system′s design when both aleatory and epistemic uncertainties of the parameters are considered,and can set a theoretical foundation for the dynamic design and precision analysis of nonlinear mechanical systems.
Focusing on the quantification of mixed-uncertainty in nonlinear mechanical systems,a confidence region method for the quantification of aleatory and epistemic uncertainty is presented.In this method,interval analysis is used to represent epistemic uncertainty while probability theory is used to represent aleatory uncertainty,in order to obtain the confidence region of mixed uncertainties.Then,the traditional double-loop Monte Carlo sampling approach is improved to propagate uncertainties during the entire time domain.Finally,a nonlinear mass-spring-damper system is simulated to discuss the validity of the analysis method based on mixed-uncertainty.The results show that it can improve the reliability of the system′s design when both aleatory and epistemic uncertainties of the parameters are considered,and can set a theoretical foundation for the dynamic design and precision analysis of nonlinear mechanical systems.
引文
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[2]Li L,Sandu C.On the impact of cargo weight,vehicle parameters,and terrain characteristics on the prediction of traction for off-road vehicles[J].Journal of Terramechanics,2007,44(3):221-238.
[3]Sandu A,Sandu C,Ahmadian M.Modeling multibody systems with uncertainties.Part I:theoretical and computational aspects[J].Multibody System Dynamics,2006,15(4):373-395.
[4]Sandu C,Sandu A,Ahmadian M.Modeling multibody systems with uncertainties.Part II,numerical applications[J].Multibody System Dynamics,2006,15(3):241-262.
[5]An D,Choi J,Schmitz T L,et al.In situ monitoring and prediction of progressive joint wear using Bayesian statistics[J].Wear,2011,270(11):828-838.
[6]Hofer E,Kloos M,Krzykacz-Hausmann B,et al.An approximate epistemic uncertainty analysis approach in the presence of epistemic and aleatory uncertainties[J].Reliability Engineering&System Safety,2002,77(3):229-238.
[7]Huang Hongzhong,Zhang Xudong.Design optimization with discrete and continuous variables of aleatory and epistemic uncertainties[J].ASME Journal of Mechanical Design,2009,131(3):310061-310068.
[8]张保强,陈国平,郭勤涛.不确定性热弹耦合梁的固有振动分析[J].振动与冲击,2012,31(19):160-164.Zhang Baoqiang,Chen Guoping,Guo Qintao.Free vibration analysis of a thermoelastic coupled beam with material uncertainty[J].Journal of Vibration and Shock,2012,31(19):160-164.(in Chinese)
[9]赵宽,陈建军,阎彬,等.含随机参数的多体系统动力学分析[J].力学学报,2012,44(4):802-806.Zhao Kuan,Chen Jianjun,Yan Bin,et al.Dynamic analysis of multibody systems with probabilistic parameters[J].Chinese Journal of Theoretical and Applied Mechanics,2012,44(4):802-806.(in Chinese)
[10]曾开春,向锦武.高超声速飞行器飞行动力学特性不确定分析[J].航空学报,2012,33(4):1-11.Zeng Kaichun,Xiang Jinwu.Flight dynamic characteristics of hypersonic vehicles with uncertain parameters[J].Acta Aeronautica et Astronautica Sinica,2012,33(4):1-11.(in Chinese)
[11]Nilsson N J.Probabilistic logic[J].Artificial Intelligence,1986,28(1):71-87.
[12]Oberkampf W L,Helton J C,Joslyn C A,et al.Challenge problems:uncertainty in system response given uncertain parameters[J].Reliability Engineering&System Safety,2004,85(1):11-19.
[13]Ross T J.Fuzzy logic with engineering applications[M].2nd ed.New York:Wiley,2004:6-20.
[14]Merlet J P.Solving the forward kinematics of a Gough-type parallel manipulator with interval analysis[J].The International Journal of Robotics Research,2004,23(3):221-235.
[15]杜永峰,李万润,李慧.基于测量数据不确定性的结构参数识别[J].振动、测试与诊断,2012,32(4):629-633.Du Yongfeng,Li Wanrun,Li Hui.Structural parameters identification based on uncertainty of measurement data[J].Journal of Vibration,Measurement&Diagnosis,2012,32(4):629-633.(in Chinese)
[16]Beynon M,Curry B,Morgan P.The Dempster-Shafer theory of evidence:an alternative approach to multicriteria decision modelling[J].Omega,2000,28(1):37-50.
[17]Dubois D.Possibility theory and statistical reasoning[J].Computational Statistics&Data Analysis,2006,51(1):47-69.
[18]Helton J C,Johnson J D,Oberkampf W L,et al.Representation of analysis results involving aleatory and epistemic uncertainty[J].International Journal of General Systems,2010,39(6):605-646.
[19]Sentz K,Ferson S.Probabilistic bounding analysis in the quantification of margins and uncertainties[J].Reliability Engineering&System Safety,2011,96(9):1126-1136.
[20]Helton J C.Quantification of margins and uncertainties:conceptual and computational basis[J].Reliability Engineering&System Safety,2011,96(9):976-1013.
[21]Oberkampf W L,Roy C J.Verification and validation in scientific computing[M].New York:Cambridge University Press,2010:606-610.
[22]胡海岩.应用非线性动力学[M].北京:航空工业出版社,2000:68-72.