摘要
建立了结构同时含有概率、模糊、凸集变量时的可靠性分析模型。首先对模糊变量取一截集水平α,得到与模糊变量向量相对应的区间向量,将问题化为仅含有随机变量和凸集变量的混合可靠性问题。其次根据随机和凸集两类变量的混合可靠性方法,得到截集水平α下,以凸集变量为自变量的可靠度的均值,即截集水平α下的结构混合可靠度值。然后,将结构混合可靠度在截集水平区间[0,1]内进行积分,得到三类变量混合的结构总体可靠度。对所定义可靠度指标的物理意义进行了解释,并以某典型功能函数为例,进行了公式推导。最后,给出了算例分析,方法的可行性及合理性得到了验证。算例还表明,当忽略模糊变量的模糊性质,或改变凸集变量的数学型式,都会引起可靠度结果的失真,因此在工程实际中,必须全面客观地处理各类不确定性变量,才能得到正确可信的可靠性分析结论。
A hybrid reliability model is built for structures with probabilistic,fuzzy and non-probabilistic convex variables are taken into account simultaneously.Firstly,theα-level cut sets can be made for the fuzzy variables,then the corresponding interval vector can be obtained and the original problem can be converted into the random-interval hybrid reliability problem.Secondly,according to the analysis method of random-interval reliability,the result underα-level,i.e.the mean value of the reliability with the interval variables as the independent variables,can be obtained.Thirdly,make the integration of the structural hybrid reliability in the interval of cut set level,i.e.[0,1],and the structural general reliability based on three types of mix variables is obtained.In current study,the physical significance of the proposed reliability index is explained and formula derivation is made for a typical limit-state-function as example.Finally,a numerical example is given and the feasibility and rationality of the proposed method are demonstrated.It is also shown that when the fuzziness of the fuzzy variables is neglected,i.e.only the core intervals of the fuzzy variables are used,the reliability analysis result obviously tends to be larger.Therefore,for practical engineering problems,all types of uncertain variables must be treated objectively and the right and authentic result of reliability analysis should be acquired thoroughly.
出处
《应用力学学报》
CSCD
北大核心
2017年第2期366-369,共4页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金(51509254)
海军工程大学青年基金(HGDQNJJ13013
HGDQNEQJJ15009)
关键词
结构可靠性
随机变量
模糊变量
凸集变量
混合可靠性
structural reliability
stochastic variable
fuzzy variable
convex variable
hybrid reliability
