基于节点位置相关性分析的结构位形推算方法

A New Approach to Calculating Structural Geometric Shape Based on the Correlation Analysis of Nodal Positions

既有空间结构鉴定计算应按结构实际位形建立几何模型.根据空间结构几何构造特性,采用节点位置偏差相关系数的函数模型分析节点位置相关性并给出模型参数确定方法;基于节点位置相关性分析,提出根据抽样测量节点位置推算结构几何位形的方法,以条件概率分布期望作为未测节点实际位置偏差的期望估计值,以交叉验证的方差置信上限作为偏差的方差估计值,由此确定偏差分布,得到结构实际几何位形,建立结构鉴定计算的不确定模型.对实际网壳结构根据抽样测量节点位置推算结构实际几何位形,并进行整体稳定性分析.研究结果表明,基于节点位置相关性分析的推算方法结果更符合实际.

In both the analysis and appraisal of existing spatial structures,structures should be modeled in accordance with the actual geometric shapes. A function of correlation coefficient was recommended to model the correlated deviation of nodal positions according to the geometric characteristics of the existing spatial structures,and the approach to calculating model parameters was given. Based on the correlation analysis of nodal positional deviations,a new method of reckoning the structural geometric shapes by sampling nodal positions was proposed. In the proposed method, the deviation distributions of unmeasured nodal positions can be inferred from sampling data where expectations should be calculated by conditional distributions and variances would be estimated as upper limits of the confidence intervals from the cross validation. Then, using the calculated deviation distributions,uncertain geometric models can be established to analyze and assess the existing spatial structures. Through calculating the shell shape by sampling the nodes and analyzing its overall stability, it concludes that the method based on nodal positions correlation analysis meets the actual case. The proposed method was applied to reckoning the geometric shape of a reticulated shell structure,and the nonlinear static stability analysis was carried out. It is shown that the proposed method can give reliable results and apply to the appraisal of existing spatial structures.