CAJ | 학술논문

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%。
재채용태륵분산법측량다원체계용액적분자확산계수적실험중，실험과정적수리모형포함다개대구삼수，차수종다조부합동일개방정적실험곡선중제취출소수적실험결과。저시일개다곡선다삼수적비선성의합문제。기우최소이승법건립료구해모형，채용 Gauss-Newton 법대모형중적삼수진행불단핍근。통과2조（매조유5조곡선）유계산궤생성적허의곡선대기우Gauss-Newton법적Matlab정서진행검험，결과표명：재소득적8개분자확산계수중，Gauss-Newton법처리결과여진실치적평균상대편차위3.18%，최대상대편차위8.67%。
In order to obtain the results of multi-component Taylor dispersion experiment, it needs to fit more than two measurement curves to the same function, in which contains the needed diffusion coefficients. It is a nonlinear fitting problem about multi-curves and multi-parameters. A mathematical model have been built based upon the least-square-method. The Gauss-Newton method has been used to gradually approach the parameters in the model. The reliability of the MATLAB code, based on the Gauss-Newton method, has been checked by three sets of simulation curves. Results show that, the fitting results adequately agreed with the simulation values, with the average relative error of 3.18%and the maximum relative error of 8.67%.