二次曲面拟合与拟合参数不确定度分析

由离散点进行二次曲面拟合问题可归结为存在约束条件的非线性优化问题,在总结了拟合参数初值计算和优化算法的基础上,研究了点位的坐标测量误差对拟合参数和曲面轮廓度评价的影响.给出了评价二者不确定度的解析方法和Monte-Carlo模拟方法,并指出,对于实际的测量数据,只有采用Monte-Carlo模拟方法进行拟合参数和轮廓度的不确定度评价才是可靠的.仿真实验和实物测量实验表明,给出的二次曲面拟合方法和不确定度估计方法是正确的. 

Quadratic surface fitting and uncertainty analysis of fitting parameters

The quadric surface fitting through cloud points was described as the constrained nonlinear optimization.The calculation of initial fitting parameters and optimization algorithm were summarized,and then the influence of point coordinate measurement error on fitting parameters and evaluation of surface contour was researched.The methods to assess their uncertainty through analysis and Monte-Carlo simulation were discussed.It was found that the uncertainty of fitting parameters and surface contour could be evaluated reliably only through Monte-Carlo simulation for measurement data from actual surfaces.The simulation and actual measurement experiments were conducted,which suggested that the methods of quadric surface fitting and uncertainty assessment presented be correct.