基于灵敏度矩阵特征值的索杆张力结构主动张拉索优选方法

An approach for choosing optimal actively-stretched cables of cable-strut tensile structures based on eigenvalue of sensitivity matrix

施工时合理选择主动张拉索是控制索杆张力结构预张力偏差的主要措施。以单元的预张力偏差平方和作为评价整体结构预张力偏差的指标,通过对反映单元预张力偏差与索长误差关系的灵敏度矩阵进行谱分解,将该指标表示为索长误差与灵敏度矩阵的特征值和特征向量的解析关系式,理论上解释了选择不同主动张拉索会使灵敏度矩阵特征值发生变化,从而直接影响到对结构预张力偏差的控制效果。由于灵敏度矩阵特征值具有衰减迅速的特点,故采用其一阶特征值和特征向量可有效估计结构的最不利预张力偏差。进一步以灵敏度矩阵的一阶特征值为评价指标,基于遗传算法提出了一种主动张拉索的优选方法。以一实际索杆张力结构为例,进行不同条件下的主动张拉索优选分析,其结果验证了优选方法的有效性。

An appropriate choice of actively-stretched cables is the main measure to control the pretension deviation during the construction of cable-strut tensile structure. The quadratic sum of elemental pretension deviations is adopted as an index to evaluate the pretension deviation of the whole structure. By means of the spectral decomposition of the sensitivity matrix,which reflects the relationship between cable length errors and pretension deviations,this index can be expressed as an analytical form relating to the cable length errors,the eigenvalues of the sensitivity matrix as well as its eigenvectors. Theoretically,the different choice of actively-stretched cables is expounded to lead to change of the eigenvalues of sensitivity matrix,and directly impact on the control effect of structural pretension deviation. Due to the rapid attenuation of the eigenvalues of sensitivity matrix,the unfavorable structural pretension deviation can be effectively estimated by only using its first-order eigenvalue and eigenvector. Adopting the first-order eigenvalue of sensitivity matrix as the evaluating indicator,an optimization algorithm for choosing actively-stretched cables is put forward based on the Genetic Algorithm. The optimal actively-stretched cables of a practical cable-strut tensile structure are analyzed under different conditions. The results reveal the validity of the method put forward in this paper.