计算机与应用化学
計算機與應用化學
계산궤여응용화학
COMPUTERS AND APPLIED CHEMISTRY
2014年
9期
1047-1050
,共4页
陈普敏%韩善鹏%李鸿英%张劲军%刘闯%刘丽云
陳普敏%韓善鵬%李鴻英%張勁軍%劉闖%劉麗雲
진보민%한선붕%리홍영%장경군%류틈%류려운
非线性拟合%Gauss-Newton法%分子扩散系数
非線性擬閤%Gauss-Newton法%分子擴散繫數
비선성의합%Gauss-Newton법%분자확산계수
nonlinear fitting%Gauss-Newton Method%molecular diffusion coefficient
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%。
在採用泰勒分散法測量多元體繫溶液的分子擴散繫數的實驗中,實驗過程的數理模型包含多箇待求參數,且需從多條符閤同一箇方程的實驗麯線中提取齣所需的實驗結果。這是一箇多麯線多參數的非線性擬閤問題。基于最小二乘法建立瞭求解模型,採用 Gauss-Newton 法對模型中的參數進行不斷逼近。通過2組(每組有5條麯線)由計算機生成的虛擬麯線對基于Gauss-Newton法的Matlab程序進行檢驗,結果錶明:在所得的8箇分子擴散繫數中,Gauss-Newton法處理結果與真實值的平均相對偏差為3.18%,最大相對偏差為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%.