Optimal experimental design for parameter estimation of the Peleg model

•Optimal experimental design for a water absorption process has been carried out and compared to equidistant measurement points in ordinary and logarithmic time scale.•Depending on the rough estimation error of the parameter the best experimental design method is identified.•The optimal experimental design was carried out different optimization criteria.•Depending on the optimization criterion an exact or approximation function has been determined to simplify the optimal experimental design.

In this work an optimal experimental design is applied to determine the parameters of the Peleg model for water absorption kinetics as precisely as possible. The parameter estimation errors were calculated using equidistant measurements in time as well as equidistant measurements on a logarithmic time scale. They were then compared to the optimal design results calculated, using multiple optimality criteria, constant measurement errors and the error of the initial rough parameter estimates. It is demonstrated that the optimal experimental design is beneficial for the parameter error estimation for at least one of the two parameters of the Peleg model equation. The parameter estimation errors could be reduced by up to 62% compared to an equidistant experimental design.Furthermore an approximation function for the optimal design process is developed. Depending on the used optimality criterion, with this function optimal measuring points for the Peleg model can be calculated directly and therefore much faster than the optimization procedure for the optimal experimental design. In case of the very commonly used D-optimality criterion, this function is even an exact solution. The deviation of the parameter estimation errors from the approximation function are mostly around 0.01% and therefore negligible.