风洞模型变形单相机测量误差分析与补偿算法

Error analysis of single-camera model deformation measurement in wind tunnel and compensation algorithm

从描述像空间坐标与物体空间坐标之间几何关系的共线方程出发,推导了风洞模型变形单相机测量试验中展向坐标不变假设诱导的物体空间坐标计算误差的公式。针对2m量级风洞试验段,分析了相机位于不同安装位置对坐标计算误差的影响。基于弹性变形中大展弦比风洞模型剖面近似保持刚性的物理特性,提出了一种展向位移补偿算法,用于减小或消除展向坐标不变假设诱导的空间坐标计算误差。最后,采用数学仿真方法对提出的展向位移补偿算法进行了评估,数据结果表明:在模型表面RX/RY和RZ/RY存在奇性、空间坐标计算结果误差较大需要修正的情况下,该补偿算法可以得到比较准确的展向位移计算结果,从而将空间坐标计算误差控制在比较合理的范围内。

Expressions of coordinates＇ calculation errors in object space induced by the hypothesis that spanwise coordinate is constant in single-camera model deformation measurement experiments, are derived from the collinearity equations describing the relationship between 2D coordinates in image plane and 3D coordinates in object space. Then the effect of fixing camera at different positions on coordinates＇ calculation errors is analyzed for a 2 m scale wind tunnel test section. A spanwise displacement compensation algorithm is presented based on the nearly rigid section characteristics of high respect-ratio wind tunnel model in elastic deformation, to reduce or eliminate the coordinates＇ calculation errors induced by the hypothesis of constant spanwise coordinate. Finally, the compensation algorithm for spanwise displacement is evaluated by a numerical simulation method. The data results show that the compensation algorithm can give relatively exact spanwise displacement and bound the coordinates＇ calculation errors in a reasonable range when there is singularity of RX/RY or RZ/RY, and large errors of space coordinates calculation results need modification.