(87a) Application of Metamodeling Techniques to Calibrate DEM Models: What about Efficiency?

Parameter identification for material models is an extensive task, which is omnipresent in practical application of the discrete element method (DEM) for particle technology. Calibration of DEM parameters is necessary since micro-mechanical properties of granular materials can be challenging to measure or simulation parameters cannot be directly related to physically measurable characteristics; for example, parameters like rolling friction or the ones connected to wear and comminution. Hence, an iterative calibration process is required, during which DEM parameters are altered until the simulation results agree with physical measurements.

Recent research in DEM calibration has put emphasis on using metamodels and numerical optimization. However, no evaluation of the efficiency of such approaches has been done to date. This study compares four approaches -- three metamodels and a direct optimization (DIRECT) approach -- with regard to their outcome and efficiency for calibration of bulk density and angle of repose. Two of the metamodels are Kriging-based, while the third is an artificial neural network (ANN). A two-stage process serves as calibration framework, where in the first stage an optimized DEM parameter set is calibrated based on the respective metamodel and in the second stage this parameter set is used as starting value for further optimization with the DEM model.

Each of the four approaches led to satisfactory calibration outcome, but the calibrated DEM parameter sets' values varied. The metamodels' quantitative prediction quality is formidable for both the angle or repose and bulk density. Regarding the calibration process, the DIRECT approach required a total of 25 DEM model runs, while this number ranged from 14 to 48 runs for the metamodel-based approaches, including the initial datasets. These results demonstrate that using an increased number of datasets for metamodel parameterization is not reflected in achieving faster convergence during the second calibration stage. In fact, only for the smallest number of datasets in this study the metamodel approaches were able to outperform the DIRECT approach. Even though the Kriging and ANN metamodels showed similar quantitative prediction quality, the ANN model resulted in a considerably lower number of overall DEM model runs and therefore proved to be more efficient. The possible reason for this behavior is due to the use of a gradient-based optimization algorithm in the first calibration stage.

In summary, adapting metamodel-based optimization for DEM calibration has great potential to significantly outperform direct optimization, if applied correctly. Gradientless optimization algorithms should be preferred for metamodel-based calibration and further improvement of efficiency could be achieved by implementing more intricate methods, like efficient global optimization.