Abstract: To improve the efficiency and accuracy of blade profile error evaluation,a PCA-improved ICP-improved Sequential Quadratic Programming (SQP) based non-reference profile evaluation method was proposed.According to the minimum coverage area principle,a blade profile evaluation model was established,and its profile error value was specified by the forward Hausdorff distance.Therefore,the calculation of the profile was to solve the optimization problem of minimizing the maximum distance between the measured point cloud data and the theoretical geometrical surface.PCA method was used for coarse registration,and the fine alignment was realized by an improved ICP method.The improved SQP used the division approximation method to obtain the distance between the points and the surface,and the grid division coefficient and the search interval coefficient of SQP algorithm were optimized adaptively and iteratively to meet the optimization objective of the minimum distance between the upper and lower envelope profiles of the measured surface.Experimental results showed that the proposed method could evaluate the blade surface more efficiently,which avoided the problem of local optima caused by inappropriate initial values in the traditional ICP method for 3D registration,meanwhile eliminating the systematic error of blade measurement.The reasonable optimization of the grid division coefficient and the accurate positioning of SQP algorithm's search interval shortened the iterative calculation time,and not only improved the accuracy of profile evaluation,but also improved the efficiency by 36.6% compared with the traditional algorithms.

Key words: surface profile of blade, minimum coverage area, forward Hausdorff distance, division-approach method, point cloud registration

摘要： 为了提高叶片轮廓误差评定的效率与精度,提出了一种无基准轮廓度组合评定方法:PCA-改进ICP-改进SQP。基于最小包容区域理论建立叶片轮廓度评定模型,以单向豪斯多夫距离定义轮廓误差值,将轮廓度的计算转化为曲面测量数据点云至理论型面的最大距离最小化寻优问题。采用PCA方法进行叶片采样点的粗配准;精配准则由改进ICP方法完成;改进SQP运用分割逼近法求解点面距,以被测曲面上下两包络面的距离最小为优化目标自适应迭代优化网格分割系数与SQP算法的搜索区间系数。叶片在机测量实验结果表明,所提出的方法能够更为高效的评定叶片表面轮廓误差,避免了传统ICP方法在三维配准中由于初始变换不合适导致陷入局部最优的问题,消除了叶片测量的系统误差;网格分割系数的合理优化与SQP算法搜索区间的准确定位缩短了迭代计算时间,相较于传统算法不仅提高了轮廓度评定的精度而且使效率提升了36.6%。

关键词: 叶片面轮廓度, 最小包容区域, 单向豪斯多夫距离, 分割逼近法, 点云配准