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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.
Therefore, it is very difficult to establish an accurate prediction model to analyze the error by error sources.This paper takes the three-dimensional coordinates of spatial measurement location and computer direct control DCC) parameters, including the moving speed, approach distance and touch velocity as the original independent variable of the CMM dynamic measurement error model, and obtain the nonlinear relationship function between the original independent variable and the dynamic measurement error by 3B spline transformation, and then use the orthogonal Projection method deduces the components of explanatory matrix which have nothing to do with the dependent variable to obtain a new interpretation matrix and then use the partial least squares (PLS) regression for dimensionality reduction and parameter estimation to obtain CMM dynamic measurement error model, that is based on 3B spline - Orthogonal projection partial least squares (3BS-OPPLS) model.This not only avoids the analysis of intricate error sources and their mutual influence, but also captures the non-linear influence of each variable on the dynamic measurement error and overcomes Multi-collinearity problems.The experimental results show that the established 3BS-OPPLS model is better than the 3B spline without orthogonal projection - Partial Least Squares (3BS-PLS) model, the prediction accuracy of the model has been significantly improved.