引入模糊参数的结构Info-Gap可靠性模型
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摘要
基于Info-Gap理论,在Minkowski范数中引入模糊参数,建立了一种具有模糊属性的Minkowski范数Info-Gap模型.进一步将其应用于Info-Gap可靠性分析,提出了二态失效假设情况下的结构模糊Info-Gap可靠性模型.应用模糊集理论,研究了可靠性指标的计算方法.新方法有效融合了区间凸集模型和椭球凸集模型,调和了在进行结构非概率可靠性分析中两种凸集模型产生的差异.算例分析验证了新方法的适用性和合理性.
A fuzzy Minkowski norm Info-Gap model was proposed by introducing a fuzzy parameter in Minkowski norm based on Info-Gap theory.Then the model was applied to Info-Gap reliability analysis,and the fuzzy Info-Gap reliability model for structures was proposed based on binary failure assumption.The calculation method of the reliability index was also studied by utilizing fuzzy sets theory.The new fuzzy Info-Gap model integrated the interval convex model and ellipsoidal convex model.The new reliability model fixed inconsistencies between the both convex models in non-probabilistic structural reliability analysis.Numerical example verified the rationality and applicability of the proposed method.
A fuzzy Minkowski norm Info-Gap model was proposed by introducing a fuzzy parameter in Minkowski norm based on Info-Gap theory.Then the model was applied to Info-Gap reliability analysis,and the fuzzy Info-Gap reliability model for structures was proposed based on binary failure assumption.The calculation method of the reliability index was also studied by utilizing fuzzy sets theory.The new fuzzy Info-Gap model integrated the interval convex model and ellipsoidal convex model.The new reliability model fixed inconsistencies between the both convex models in non-probabilistic structural reliability analysis.Numerical example verified the rationality and applicability of the proposed method.
引文
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[7] KANG Z,LUO Y J.Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models[J]. Computer Methods in Applied Mechanics&Engineering,2009,198(41/44):3228-3238.
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[9] KANG Z,ZHANG W.Construction and application of an ellipsoidal convex model using a semi-definite programing formulation from measured data[J].Computer Methods in Applied Mechanics&Engineering,2016,300:461-489.
[10]王晓军,邱志平,武哲.结构非概率集合可靠性模型[J].力学学报,2007,39(5):641-646.
[11] HU J X,QIU Z P.Non-probabilistic convex models and interval analysis method for dynamic response of a beam with bounded uncertainty[J].Applied Mathematical Modeling,2010,34(3):725-734.
[12]李昆锋,杨自春.基于Info-Gap理论的结构非概率可靠性方法研究[J].机械强度,2013,35(2):174-178.
[13]王新刚,张义民,王宝艳,等.凸方法和区间法在可靠性设计中的对比分析[J].东北大学学报,2008,29(10):1467-1469.
[14] QIU Z P.Convex models and interval analysis method to predict the effect of uncertain-but-bounded parameters on the buckling of composite structures[J]. Computer Methods in Applied Mechanics&Engineering,2005,194:2175-2189.
[2]刘成立,吕震宙,罗志清,等.一种通用的稳健可靠性指标[J].机械工程学报,2011,47(10):192-198.
[3]李昆锋,杨自春,孙文彩.结构非概率-模糊混合可靠性分析方法[J].华中科技大学学报:自然科学版,2012,40(8):67-71.
[4] YANG Z,ZHANG Y,MENG W,et al.A convex model approach for structure non-probabilistic reliability analysis[J].Journal of Risk&Reliability,2017,231(10):1-8.
[5] JIANG C,BI R G,LU G Y,et al.Structural reliability analysis using non-probabilistic convex model[J].Computer Methods in Applied Mechanics&Engineering,2013,254:83-98.
[6]郭书祥,吕震宙,冯元生.基于区间分析的结构非概率可靠性模型[J].计算力学学报,2001,18(1):56-60.
[7] KANG Z,LUO Y J.Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models[J]. Computer Methods in Applied Mechanics&Engineering,2009,198(41/44):3228-3238.
[8] KANG Z, LUO Y J, ALEX L. On non-probabilistic reliability-based design optimization of structures with uncertain-but-bounded parameters[J].Structural Safety,2011,33(3):196-205.
[9] KANG Z,ZHANG W.Construction and application of an ellipsoidal convex model using a semi-definite programing formulation from measured data[J].Computer Methods in Applied Mechanics&Engineering,2016,300:461-489.
[10]王晓军,邱志平,武哲.结构非概率集合可靠性模型[J].力学学报,2007,39(5):641-646.
[11] HU J X,QIU Z P.Non-probabilistic convex models and interval analysis method for dynamic response of a beam with bounded uncertainty[J].Applied Mathematical Modeling,2010,34(3):725-734.
[12]李昆锋,杨自春.基于Info-Gap理论的结构非概率可靠性方法研究[J].机械强度,2013,35(2):174-178.
[13]王新刚,张义民,王宝艳,等.凸方法和区间法在可靠性设计中的对比分析[J].东北大学学报,2008,29(10):1467-1469.
[14] QIU Z P.Convex models and interval analysis method to predict the effect of uncertain-but-bounded parameters on the buckling of composite structures[J]. Computer Methods in Applied Mechanics&Engineering,2005,194:2175-2189.