在采用泰勒分散法测量多元体系溶液的分子扩散系数的实验中,实验过程的数理模型包含多个待求参数,且需从多条符合同一个方程的实验曲线中提取出所需的实验结果。这是一个多曲线多参数的非线性拟合问题。基于最小二乘法建立了求解模型,采用Gauss-Newton法对模型中的参数进行不断逼近。通过2组(每组有5条曲线)由计算机生成的虚拟曲线对基于Gauss-Newton法的Matlab程序进行检验,结果表明:在所得的8个分子扩散系数中,Gauss-Newton法处理结果与真实值的平均相对偏差为3.18%,最大相对偏差为8.67%。 In the experiment of using Taylor scattering method to measure the molecular diffusion coefficient of multivariate solution, the mathematical model of the experimental process contains a number of parameters to be solved, and the experimental results needed to be extracted from the experimental curves conforming to the same equation. This is a multi-curve nonlinear multi-parameter fitting problem. Based on the least squares method, a solving model was established and the parameters in the model were continuously approximated by Gauss-Newton method. The Gauss-Newton-based Matlab program was tested by two groups of 5 curves (each with 5 curves). The results showed that the results of Gauss-Newton method and the real The average relative deviation of the values ​​was 3.18% and the maximum relative deviation was 8.67%.