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利用合成色素随pH变化的分布分数曲线和吸收光谱构成两维波谱信息，建立了灰色体系中色素的定量分析方法。约束背景双线性分解法（CBBL）结合数值遗传算法（NGA）用于两维矩阵的数据处理。推导了型体总数与两维矩阵的有效秩之间的关系。吸光度矩阵的主成分数根据残余矩阵的残差平方和与噪声水平相比较而确定，对标准样品及模拟灰色体系样品的研究表明该法确定的主成分数与理论值一致。对胭脂红、日落黄和柠檬黄的模拟灰色体系样品中各组分及市售饮料中的日落黄进行了测定，结果表明该方法具有较高的准确度。
Based on the two-dimensional spectral information of the distribution curve and the absorption spectrum of the synthetic pigment with the change of pH, a quantitative analysis method of the pigment in the gray system was established. Bounded background bilinear decomposition (CBBL) combined with numerical genetic algorithm (NGA) for two-dimensional matrix data processing. The relationship between the total number of shape and the effective rank of two-dimensional matrix is derived. The principal components of the absorbance matrix are determined from the square sum of residuals of the residual matrix and the noise level. Studies on the standard samples and the simulated gray system samples show that the principal components determined by this method are in agreement with the theoretical values. The compositions of the simulated gray system samples of carmine, sunset yellow and lemon yellow and the sunset yellow in commercial beverages were measured. The results show that the method has high accuracy.