(45e) Self Starting and Globally Convergent Parameters Estimation Method for Aggregation-Breakage Population Balance Model Using Genetic Algorithm

Some of the main challenges to the estimation of parameters for the aggregation-breakage population equation from experimental data include the determination of a good initial point to ensure the convergence of the numerical procedure and also ensuring the procedure converges to the global optimum not some local minima. The initial point is usually determined using short time processing of mono-size feed or by trial and error. This method is very time consuming and convergence to the global minimum is not guaranteed. In this write-up, a procedure is proposed for choosing good initial points for the optimisation using Genetic Algorithm and then employing a gradient searching optimisation method to speed-up convergence to the minimum point. The methodology employs a multi-start approach to ensure the PB parameters obtained correspond to the global optimum not some local minimum. In the present study, the objective function is defined as the Euclidean norm of the difference between the experimental and simulated cumulative volume fraction. The aggregation-breakage population balance equation is solved using the discretised population balance (DPB) method with number and volume conservation. The procedure is then tested using simulated data with and without errors and experimental data from a wet milling process with satisfactory outcomes.