Introduction

This section provides an overview of what Aspherix® Calibration can do.

What is Aspherix® Calibration

Aspherix® Calibration is a software module for calibrating DEM and CFD-DEM models used in Aspherix® and CFDEM®coupling. The main reason behind the development of Aspherix® Calibration is that the reliability and predictive qualities of DEM and CFD-DEM simulations depend on the choice of model parameters, which are often not known or not directly accessible through experiments.

Aspherix® Calibration implements the DIRECT (DIvision of RECTangles) algorithm, which is a direct search global optimization algorithm for bound-constrained problems. The DIRECT algorithm does not require gradients; therefore, it is well suited for calibration of simulation parameters. The algorithm maps the n target parameters to an n-dimensional unit hypercube, and then recursively divides the hypercube into hyper-rectangles until convergence is achieved. Subdivision is governed by evaluations of the objective function at the centers of the hyper-rectangles, which means that the hyper-rectangle with the best objective function gets subdivided further, and occasionally, other hyper-rectangles are checked as well to keep the algorithm global. A very thorough description of the algorithm can be found in Finkel.

One way to calibrate a DEM or CFD-DEM model is to define an experiment sensitive to one or more unknown model parameters, hereafter referred to as target parameters. Then, a simulation that mimicks the experiment as closely as possible is run with different values of the target parameters. The simulation output is compared to the experimental results through a quality function. Minimizing this quality function then yields the parameter values where experiment and simulation match best.

What happens during a Aspherix® Calibration run is straightforward: first, the calibration case is initialized. This can mean creation of a packing, scaling of geometries and creating a status from which each iteration of the optimization can be started. Then, the simulation is run for several iterations with different values of the target parameter. The optimizing algorithm controls the choice of the parameter values to be evaluated during the optimization run to find a global minimum for the quality function of the calibration case. Once this minimum is found, the result is written to a file calibrated_params.txt and Aspherix® Calibration exits.

Aspherix® Calibration requires Aspherix® and, for specific calibration cases, CFDEM®coupling. The installation directory is the same of Aspherix®.

Aspherix® Calibration features

  • runs on a single processor or in parallel

  • distributed-memory message-passing parallelism (MPI)

  • simultaneous or sequential calibration of the target parameters

  • highly-efficient algorithm for searching the quality function minimum

  • highly portable C++

  • runs from an input script

  • syntax for defining and using variables

  • several calibration templates

Licensing

Aspherix® Calibration is subject to commercial (proprietary) licence terms.

Literature

[1] D.E. Finkel, Global Optimization with the Direct Algorithm, North Carolina State University, 2005.