Two-stage parameter estimation applied to ordinary differential equation models

• An efficient two-stage (TS) parameter estimation method for ODE models was developed.
• The TS method is simple, easy to implement, and robust in estimating the unknown parameters.
• Three examples were examined, and the results confirmed the utility of the developed TS method.

A two-stage (TS) parameter estimation method for identifying ordinary differential equation (ODE) models, which minimizes the squared residuals between the derivatives of the fitted values of available measurements and the rate changes of the states, is presented. The model is an alternative to the traditional method, in which the measured squared residuals and measurements of state are used to obtain near-optimal estimated parameters for ODEs in the first stage of the TS method. Therefore, the problem of ill-conditioning, encountered in integrating the system equations, can be ignored. The second stage of the TS method minimizes the squared residuals in the model's traditional integrated form by using the estimated parameter values from the first stage as initial guesses. Three examples were examined, and the results confirmed the utility of the developed TS parameter estimation method for easy programming and low computation time. The first example is a semi-batch reactor model of toluene hydrogenation, while a continuous stirred-tank reactor model is used for the second example. Finally, a batch-process model focused on the synthesis of glycerol ether synthesis from glycerol and tert-butyl alcohol is examined.

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