Development of a Two-Stage Parameter Estimation Method in Ordinary Differential Equation Models

• Main Authors: Wei-ling Liu, 劉韋伶
• Other Authors: Jyh-shyong Chang
• Format: Others
• Language: zh-TW
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/a8ks7x

碩士 === 大同大學 === 化學工程學系(所) === 102 === The proposed two-stage (TS) parameter estimation method in ordinary differential equation (ODE) model minimizes the squared residuals in the differential form of the model instead of the traditional integrated form of the model to obtain near-optimal estimated parameters for ODEs in the first stage of TS method. The squared residuals use the fitted values and the derivatives of the fitted values of available measurements. Therefore, the problem of ill-conditioning encountered in integrating the system equations can be immune.The second stage of the TS method minimizes the squared residuals in the traditional integrated form of the model using the estimated parameters of the first stage as the initial guesses. Three examples were considered to demonstrate the capabilities of the propose TS parameter estimation method. A batch-wise toluene hydrogenation reaction was the first example. A continuous stirred-tank reactor model was the second example and the last was a batch-wise glycerol ethers synthesis from glycerol etherification with tert-butyl alcohol.