基于测量数据的不确定性结构分析的模糊理论

针对不确定性结构力学问题,提出了基于测量数据的模糊分析方法.该方法利用差值因子构造了不确定参数的隶属度函数,对不确定参数的有限个分散数据进行不确定性描述和定量化处理,估计出其真值估计和区间估计,将其运用到不确定性结构力学问题的模糊有限元分析中,以求得结构的不确定性响应.最后以十杆桁架结构为例,运用该方法对结构的不确定响应进行了分析,仿真结果验证了该方法的有效性.

Fuzzy theory for uncertain structural analysis based on measurement data

Based on the measurement data,a fuzzy analysis method was proposed to deal with the problems of uncertain structural mechanics. A new membership function of the uncertain parameters was constructed by utilizing the difference coefficient, and then a finite number of scattered data points of the uncertain parameters were described as fuzzy parameters and quantified by this method. The true values and the probable intervals for them were estimated, which were applied into the fuzzy finite element analysis of structural mechanics to obtain the uncertain response of the structure.A 10-bar truss structure with parametric uncertainties was used to analyze the uncertain response by the presented method.Numerical results illustrate its feasibility and validity.