Surrogate model for Bayesian optimal experimental design for adsorption isotherm parameters in chromatography

We applied Bayesian Optimal Experimental Design (B-OED) in the estimation of parameters involved in the Equilibrium Dispersive Model for chromatography with two components with the Langmuir adsorption isotherm. The parameters estimated were Henry's coefficients, the total absorption capacity and the number of theoretical plates, while the design variables were the injection time and the initial concentration of all components. The B-OED algorithm is based on Monte Carlo estimation, which becomes computationally challenging. This complication was relaxed by introducing a surrogate model based on Piecewise Sparse Linear Interpolation. Using the surrogate model reduces significantly the simulation time, by a factor of 4500, while the true solution is approximated with high degree of accuracy. The estimation of the parameters over the optimized design points minimizes the uncertainty in the estimation of parameters. Moreover, the B-OED methodology shows that there is no improvement of results after certain threshold values of the design factors. Quantitative estimates of the improved accuracy and the threshold values are given.