以機器學習方式預測粒子於滾動鼓中偏析軌跡

Abstract

離散元素法基於計算粒子之間的交互作用力，進而能準確地模擬出滾動鼓中粒子之大小顆粒粒子運動的偏析行為，但卻也需要龐大的計算成本。在本研究中，我們以三維(3D)與二維(2D)滾動鼓中，以離散元素法所得出的顆粒運動模擬數據作為機器學習的資料庫，以單顆粒子輸入與多顆粒子輸入至ANN、RNN、CNN三種不同的機器學習模型進行訓練。 在單顆顆粒運動訓練上，本研究以3D滾動鼓中的顆粒軌跡進行ANN模型訓練。在粒子徑向移動軌跡的時間外插預測上，得到決定係數0.93的運動預測；於軸向方向大小粒子軌跡預測上，得到決定係數0.65的運動預測。以2D滾動鼓中的顆粒軌跡進行RNN模型訓練，在移動軌跡的時間外插預測使用多對多模型，當參考點達30步時間步時，模型的外插預測能力會開始下降；而在移動軌跡的時間外插預測使用多對一模型時，當參考點增加時，模型的外插能力也跟著增加。 在多顆顆粒運動訓練上，本研究以多顆顆粒時間維度與空間維度上進行了ANN、RNN、CNN等模型之訓練，並以粒子重疊次數作為物理不一致性的比較標準，比較各模型於短時間與長時間的外插預測比較。在外插時間5秒後，ANN模型於物理不一致性上高出RNN與CNN模型分別有8倍與10倍大的誤差量，而RNN模型在30秒外插時間後誤差量也超出CNN模型2倍之多。若要在物理一致性上有更好的表現，需要多加考慮到模型學習空間維度上資訊能力，才可以有較好的預測表現。

Binary particle interaction based Discrete Element Method (DEM) simulations can accurately predict particle size segregation in a rotating drum. Although DEM simulations are accurate and reliable, they are computational expensive. In this study, we use DEM simulation predicted particle trajectories in a rotating drum as the database for Machine Learning (ML) particle trajectory forecasting training and validation. With single particle information as the input data, we used ANN model and RNN model to learn and predict particle trajectories in a 3D rotating drum and in a 2D rotating drum, respectively. We also used ANN, RNN and CNN machine learning models to learn and predict particle segregation trajectories in a 2D rotating drum by using whole particle information in the drum a the input data. Using the single particle training, the ANN model predicts the trajectories of 5 representative particles with the coefficient of determination R2 of 0.93 in the radial direction and 0.65 in the axial direction in the 5 sec extrapolation time. The RNN model shows that the accuracy of the MtM model design prediction is decreasing when the number of time steps is over 30; for MtO model design, the more number of time steps, the more accrual the model is. Using the whole particles training, because the ANN model doesn’t consider the temporal and spatial information, ANN has more than 8 times over RNN’s number of overlapping, and 10 times of CNN’s at 5 sec extrapolation time. As the extrapolation time increasing, number of particle overlapping increasing. For 30 sec extrapolation time, RNN has more than twice over CNN’s number of overlapping. To improve the model performances, the models should have the ability in learning spatial information when predicting particle size segregation trajectories in 2D rotating drum.