多元非线性回归在织物染色计算机配色中的研究

为使预测织物染色的染料质量浓度与实际的染料质量浓度误差最小,本文通过到工厂采集实际的测量数据并对其进行分析,建立了三刺激值C,M,y与染料质量浓度的数学模型,并在Excel中利用多元非线性回归分析方法,得到最小二乘估计点,同时结合多项式拟合,建立染料质量浓度与三刺激值C,M,y的多元非线性方程组,通过显著性F检验,验证所建数学模型的回归显著性效果,并利用牛顿迭代法反向求解该数学模型,得到对应的染料质量浓度.结果表明,采用多元非线性回归分析建立的数学模型,求得的结果与实际测量的数据误差非常小,该研究可以应用到实际染色配色中.

Research on Multiple Nonlinear Regression in Computer Color Matching for Textile Dyeing

A mathematical model for the three stimulus values C, M, Y and the dye weight concentrations has been established by collecting and analyzing the actual data from a factory in order to minimize the er- ror between the predicted textile dyeing recipe and the actual textile dyeing recipe. The multivariate non- linear equations of the dye weight concentrations and three stimulus values C, M, Y can be established by using the multiple nonlinear regression analysis method and getting the least squares estimation points, and combining with polynomial fitting in Excel. Then, the regression significant effects of mathematical model can be verified through the F Significant Test. Finally, the corresponding dye mass concentrations can be got by using the Newton iterative method to solve the mathematical model reversely. The error be- tween the experimental results, obtained from the mathematical model established by using multiple non- linear regression analysis method, and the actual values is very small. So the method can be used to actual dyeing applications.