既有网壳结构几何缺陷分布反演算法

Inversion algorithm for the geometric imperfection distribution of existing reticulated structures

针对目前传统的抽样检测手段无法获得既有结构真实几何缺陷分布的问题,提出基于概率图模型的既有网壳结构的马尔可夫随机场理论模型.基于局部马尔可夫性的计算假定,提出网壳结构双节点团和三节点团的计算单元,推导出相应的几何状态函数表达式;引入马尔可夫随机场的联合概率分布函数,推导既有网壳结构几何缺陷分布的反演方程,利用迭代-极大似然方程推导出计算几何缺陷分布的反演迭代方程.设计制作了一个K6单层球面网壳试验模型,采用本文反演算法对该试验模型的几何缺陷分布模态进行交叉验证.分析表明,当已知测点数占比大于16.5%时,反演计算得到的结构几何缺陷模态与实际模态具有较好的相似度;当节点几何缺陷的实测值出现异常时,反演计算结果可识别异常区域.

A Markov Random Field（MRF）model of existing reticulated structures was proposed by leading into the probabilistic graph model in view of the fact that the traditional sampling method can hardly obtain the actual distribution of geometric imperfections of existing structures.The calculation unit of double-node and triple-node clique was proposed.The corresponding geometric state function was deducted based on the assumption of local Markov property.The inversion equation for the geometric imperfection distribution of existing reticulated structures were proposed by introducing the joint probability distribution function of MRF.Then,in order to determine the geometric imperfection distribution,the inversion iteration equation was deducted using iterative maximum likelihood method.An experimental model of K6 single-layer reticulated shell was designed to verify the inversion algorithm by calculating and comparing the mode of geometric imperfection distribution.When the ratio of the measured points is greater than 16.5%,the geometric imperfection mode from the inversion calculation has good similarity with the actual mode.The results can even identify the abnormal values of the measured points.