既有空间结构位形推算的随机偏差方法

Stochastic Deviation Method of Reckoning Geometric Shapes of Existing Spatial Structures

摘要:

根据未测节点空间位置的不确定性和随机分布特性，提出了结构位形推算的随机偏差方法.结合空间结构特点，给出随机偏差方法的抽样测点选取原则和最小样本容量确定方法.基于概率论及数理统计理论，给出随机偏差方法的偏差分布推断方法.引入先验信息概念，基于贝叶斯统计理论，给出有先验信息条件下的参数推断方法.对实际网壳结构采用该随机偏差方法推算结构实际位形，并进行整体稳定性分析，结果表明基于随机偏差方法的鉴定分析结果更符合实际.

关键词:空间结构; 位形推算; 随机偏差; 分布推断; 先验信息

Abstract:

According to the uncertainty and the inherent randomness of unmeasured nodal positions, a stochastic deviation method (SDM) was proposed to reckon the geometric shapes of existing spatial structures. In a consideration of the characteristics of spatial structures, the sampling principle and the minimum sample size calculation approach in SDM were given. Based on the probability and the statistics theory, the procedure for inferring the random fields of nodal position deviations was built. In addition, the prior information concept was introduced into SDM, and approaches for inferring the stochastic parameters with prior information were put forward based on the Bayesian statistics theory. Finally, the proposed SDM was adopted to reckon the geometric shape of reticulated shell structures, and the nonlinear static stability analysis was carried out using SDMdetermined structural spatial positions. It is shown that SDM can give realistic results and be used for the appraisal of existing spatial structures.

Key words:spatial structures; geometric reckoning; stochastic deviation; distribution inference; prior information