Parallel optimization for model calibration of large scale particle systems
Examensarbete för masterexamen
Engineering mathematics and computational science (MPENM), MSc
In this thesis we present an optimization framework for model calibration of Discrete Element Method (DEM) simulations. The DEM is a method for simulating large scale particle systems. Numerical complexity makes calibration of models computa tionally expensive and time consuming. We approach the procedure by viewing it as a black box optimization problem and apply a parallel optimization algorithm to perform calibration. The algorithm is a surrogate optimization method using Radial Basis Functions. We first sample the objective function with a Symmetric Latin Hypercube serving as a design of experiments. In the iterative part of the algorithm we implement the Metric Stochastic Response surface method proposed by Regis and Shoemaker. We choose new evaluation points based on a weighted score of the expected objective value of the point and its distance from previously evaluated points. The weight decides whether to focus on exploitation by trying to minimize the objective value of the next point, or exploration by evaluating points in areas of the sample space where we have less information. To reduce the wall time required in finding a solution the framework allows for asynchronous parallelism by simply evaluating many points at the same time. We also implement a method for early termination. The algorithm is applied to two DEM optimization problems. The first one is a calibration problem involving a device used to calibrate the friction of a material. The second one is an industrial optimization case where the position of a funnel is adjusted to achieve an even split of material flow. In both cases, the algorithm con verges to a solution in less than 40 evaluations. Furthermore the early termination and parallel strategies are shown to reduce the time required to solve the calibration case. We finish by discussing and comparing our results, giving some advantages and disadvantages found with the early termination functionality.
DEM, Discrete element method, Calibration, Optimization, Surrogate, Black-box, Parallelism