Geometric imperfection is one of the most disadvantageous factors that impair mechanical behaviors of existing reticulated shell structures. However, the available consistent mode methods and statistical methods which usually applied in designing structures can hardly estimate the actual geometric imperfection distribution for existing structures, because these methods use the assumed imperfections. In this paper, a Markov Random Field (MRF) theoretical model of existing reticulated shells is established by introducing the theory of probabilistic graphical model. The unit of graphic model named node clique are proposed to deduct the geometric state function of reticulated shells, based on the local Markov property. Then the inversion function along with its iterative equation is established to predict geometric imperfection distribution of existing reticulated shells. The MRF method makes the predicted distribution of the numerical model as consistent as possible with its corresponding actual structure, and only a few measurement nodes are needed as known conditions. An experimental structure of K6 single-layer reticulated shell is built to verify the proposed theory by comparing the calculated geometric imperfection distribution results with the actual measured data. Meanwhile, the significance level of the calculated results between MRF and traditional stochastic method is analyzed, which shows MRF method can effectively predict the geometric imperfections of single layer reticulated shells.

几何缺陷是削弱现有网状壳结构机械性能的最不利因素之一。但是，通常用于设计结构的可用一致模式方法和统计方法几乎无法估计现有结构的实际几何缺陷分布，因为这些方法使用了假定的缺陷。通过引入概率图形模型理论，建立了现有网壳的马尔可夫随机场理论模型。提出了基于节点马尔可夫的图形模型单元来推导网状壳的几何状态函数。然后建立反演函数及其迭代方程，以预测现有网状壳的几何缺陷分布。MRF方法使数值模型的预测分布与其相应的实际结构尽可能一致，并且作为已知条件仅需要几个测量节点。通过将计算出的几何缺陷分布结果与实际测量数据进行比较，建立了K6单层网状壳的实验结构，以验证所提出的理论。同时，分析了MRF方法和传统随机方法之间计算结果的显着性水平，表明MRF方法可以有效地预测单层网壳的几何缺陷。MRF方法使数值模型的预测分布与其相应的实际结构尽可能一致，并且作为已知条件仅需要几个测量节点。通过将计算出的几何缺陷分布结果与实际测量数据进行比较，建立了K6单层网状壳的实验结构，以验证所提出的理论。同时，分析了MRF方法和传统随机方法之间计算结果的显着性水平，表明MRF方法可以有效地预测单层网壳的几何缺陷。MRF方法使数值模型的预测分布与其相应的实际结构尽可能一致，并且作为已知条件仅需要几个测量节点。通过将计算出的几何缺陷分布结果与实际测量数据进行比较，建立了K6单层网状壳的实验结构，以验证所提出的理论。同时，分析了MRF方法与传统随机方法之间计算结果的显着性水平，表明MRF方法可以有效预测单层网壳的几何缺陷。通过将计算出的几何缺陷分布结果与实际测量数据进行比较，建立了K6单层网状壳的实验结构，以验证所提出的理论。同时，分析了MRF方法与传统随机方法之间计算结果的显着性水平，表明MRF方法可以有效预测单层网壳的几何缺陷。通过将计算出的几何缺陷分布结果与实际测量数据进行比较，建立了K6单层网状壳的实验结构，以验证所提出的理论。同时，分析了MRF方法与传统随机方法之间计算结果的显着性水平，表明MRF方法可以有效预测单层网壳的几何缺陷。