基于改进偏最小二乘的CMM动态误差混合建模分析

Hybrid Modeling of CMM Dynamic Error Based on Improved Partial Least Squares

三坐标测量机(CMM)动态误差源错综复杂,并且相互影响,因此很难建立一个通过误差源分析误差的准确预测模型.本文以空间测量位置的三维坐标值和测量机测量时的计算机直接控制(DCC)参数,包括移动速度、逼近距离和触测速度作为CMM动态测量误差模型的原始自变量,并通过3B样条变换获得各原始自变量与动态测量误差的非线性关系函数,再利用正交投影法把解释矩阵中与因变量无关的成分扣除掉,得到新的解释矩阵后再用偏最小二乘(PLS)回归进行降维和参数估计,从而得到CMM动态测量误差模型,即基于3B样条-正交投影偏最小二乘(3BS-OPPLS)模型.这样既避免了分析错综复杂的误差源及其相互影响,又能够捕捉各自变量对动态测量误差的非线性影响,并能克服因解释变量过多而产生的多重共线性问题.实验结果表明建立的3BS-OPPLS模型的预测效果优于未经正交投影的3B样条-偏最小二乘(3BS-PLS)模型,模型的预测精度得到显著提高.

The error sources and their mutual influences on the dynamic measurement errors of coordinate measurement maehine（C1V/M） are complicated, and it is hard to build an accurate model to forecast the dynamic measurement errors by analyzing error sources. A dynamic measurement error model was built based on 3B spline-orthogonal projection partial least squares （3BS-OPPLS） model, which took three-dimensional coordinates and direct computer control（DCC） parameters including positioning velocity, approximate distance and contact velocity as the original independent variables of the model, and obtained the nonlinear function between the original independent variables and the CMM dynamic measurement errors by the 3B spline transform. Then the method of orthogonal projection was used to deduct the components which are unrelated to the dependent variable in the explanatory matrix and a new explanatory matrix was achieved. Finally, the partial least squares（PLS）regression was used to reduce dimensionality and estimate parameters of the model. The model not only avoids the analysis of the error sources and their mutual influences, but also captures the nonlinear effects of the independent variables on the dynamic measurement errors, and overcomes the multi-collinearity problems caused by too many explanatory variables. The experimental results show that the prediction effect of 3BS-OPPLS model is better than 3B spline-partial least squares （3BS-PLS） model without the orthogonal projection, and the prediction accuracy of the model is significantly improved.