基于随机和认知不确定性分离的PBX构件可靠性分析
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摘要
由概率或概率盒方法量化高聚物粘结炸药(PBX)构件几何尺寸、材料属性、所受载荷等参数的不确定性,通过嵌套抽样法进行了不确定性传播分析,以分离随机和认知不确定性的影响。定量叠加了数值误差和模型形式误差,最终获得结构关心响应量的不确定性和炸药件的可靠度区间,与传统确定性的强度校核方法以及经典概率方法的可靠性分析结果进行了比较。结果表明,考虑不确定性的可靠性评估比传统确定性强度校核降低了工程应用的风险,而本方法给出的可靠度区间包含了经典概率方法计算的可靠度,在认知不确定性影响严重时仍然适用,并随着认知不确定性的缩减收敛于真实可靠度。
The uncertainties of model parameters,structural geometry,material property,and external force of the polymer bonder explosive,were quantified with probability box and propagated with nested sampling method in order to separate the different effect of aleatory uncertainty and epistemic uncertainty on response of interest. Moreover,numerical error and model form error were also quantitatively superposed to acquire the response uncertainty and the reliability interval of the polymer bonder explosive( PBX) structure consequently. In addition,the results of proposed method in this paper were compared with the determinate checking method and the probabilistic reliability method. It is indicated that the reliability assessment with the consideration of uncertainty can reduce the engineering risk than the determinate method.Furthermore,the reliability interval obtained by the proposed method covers the reliability calculated by probabilistic method,and can narrow down to the true reliability as the epistemic uncertainty decreases.
The uncertainties of model parameters,structural geometry,material property,and external force of the polymer bonder explosive,were quantified with probability box and propagated with nested sampling method in order to separate the different effect of aleatory uncertainty and epistemic uncertainty on response of interest. Moreover,numerical error and model form error were also quantitatively superposed to acquire the response uncertainty and the reliability interval of the polymer bonder explosive( PBX) structure consequently. In addition,the results of proposed method in this paper were compared with the determinate checking method and the probabilistic reliability method. It is indicated that the reliability assessment with the consideration of uncertainty can reduce the engineering risk than the determinate method.Furthermore,the reliability interval obtained by the proposed method covers the reliability calculated by probabilistic method,and can narrow down to the true reliability as the epistemic uncertainty decreases.
引文
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[2]Helton J C,Johnson J D.Quantification of margins and uncertainties:Alternative representations of epistemic uncertainty[J].Reliability Engineering and System Safety,2011,96(9):1034-1052.
[3]刘鸿文.材料力学[M].第4版.北京:高等教育出版社,2004:212-251.LIU Hong-wen.Material mechanics[M].4th edition.Beijing:Higher Education Publishing,2004:212-251.
[4]Svetlitsky V A.Statistical dynamics and reliability theory for mechanical structures[M].Berlin:Springer-Verlag Publishing,2003:313-348.
[5]Helton J C.Quantification of margins and uncertainties:Conceptual and computational basis[J].Reliability Engineering and System Safety,2011,96(9):976-1013.
[6]Shah H,Hosder S,Winter T.A mixed uncertainty quantification approach using evidence theory and stochastic expansions[J].International Journal for Uncertainty Quantification,2015,5(1):21-48.
[7]Hamada M,Martz H F,Reese C S,et al.A fully Bayesian approach for combining multilevel failure information in fault tree quantification and optimal follow-on resource allocation[J].Reliability Engineering and System Safety,2004,86(3):297-305.
[8]Sentz K,Ferson S.Probabilistic bounding analysis in the quantification of margins and uncertainties[J].Reliability Engineering and System Safety,2011,96(9):1126-1136.
[9]Jiang C,Han X,Lu G Y,et al.Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique[J].Computer Methods in Applied Mechanics and Engineering,2011,200(33-36):2528-2546.
[10]姜潮,郑静,韩旭,等.一种考虑相关性的概率-区间混合不确定模型及结构可靠性分析[J].力学学报,2014,46(4):591-600.JIANG Chao,ZHENG Jing,HAN Xu,et al.A probability and interval hybrid structural reliability analysis method considering parameters'correlation[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(4):591-600.
[11]吴丹清,吕震宙,程蕾.正态相关变量主客观不确定性分离和参数影响分析[J].力学学报,2014,46(5):794-801.WU Dang-qing,LZhen-zhou,CHENG Lei.An separation of the aleatory and epistemic uncertainties with correlated normal variables and analysis of the influence of parameters[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(5):794-801.
[12]Richards S A.CompletedRichardson Extrapolation in Space and Time[J].Communications in Numerical Methods in Engineering,1997,13(7):573-582.
[13]Roache P J.Verification and validation in computational scienceand engineering[M].Albuquerque:Hermosa Publishers,1998:15-180.
[14]Oberkampf W L,Roy C J.Verification and validation in scientific computing[M].Cambridge:Cambridge University Press,2010:315-326.
[15]Ferson S,Oberkampf W L,Ginzburg L.Model validation and predictive capability for the thermal challenge problem[J].Computer Methods in Applied Mechanics and Engineering,2008,197(29-32):2408-2430.
[16]Helton J C,Johnson J D,Sallaberry C J,et al.Survey of samplingbased methods for uncertainty and sensitivity analysis[J].Reliability Engineering and System Safety,2006,91(10-11):1175-1209.
[17]Williamson R C,Downs T.Probabilistic arithmetic I:numerical methods for calculating convolutions and dependency bounds[J].International Journal of Approximate Reasoning,1990,4:89-158.