磨矿破碎过程粒度分布的分布式参数蒙特卡洛动力学模拟及加速方法

卢绍文; 蔚润琴; 崔玉洁

doi:10.16383/j.aas.c180020

磨矿破碎过程粒度分布的分布式参数蒙特卡洛动力学模拟及加速方法

doi: 10.16383/j.aas.c180020

1.
东北大学流程工业综合自动化国家重点实验室沈阳 110819
2.
东北大学信息科学与工程学院沈阳 110819
3.
东北大学秦皇岛分校控制工程学院秦皇岛 066004

基金项目:

国家自然科学基金 61833004

国家自然科学基金 61473071

详细信息

作者简介:
蔚润琴东北大学信息科学与工程学院硕士生, 2012年获太原理工大学自动化专业学士学位.主要研究方向为蒙特卡洛仿真.E-mail:18842300547@163.com

崔玉洁东北大学秦皇岛分校控制工程学院副教授.主要研究方向为机电一体化, 机器人技术.E-mail:cyjhjn@163.com

通讯作者:
卢绍文东北大学流程工业综合自动化国家重点实验室教授.于2006年获得伦敦大学皇后玛丽学院电子工程学博士学位.主要研究方向为多尺度随机建模方法, 模拟软件设计和数据可视化方法.本文通信作者.E-mail:lusw@mail.neu.edu.cn

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出版历程
- 收稿日期: 2018-01-10
- 录用日期: 2018-07-02
- 刊出日期: 2019-09-20

A Distributed Parameter Kinetic Monte Carlo Simulation Algorithm of Grinding Process and Its Acceleration

LU Shao-Wen^{1
, ,},
YU Run-Qin^2
,,
CUI Yu-Jie^3
,

1.
State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819
2.
College of Information Science and Engineering, Shenyang 110819
3.
School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004

Funds:

National Natural Science Foundation of China 61833004

National Natural Science Foundation of China 61473071

More Information

Author Bio:
Master student at Information Science and Engineering College, Northeastern University. She received her bachelor degree in automation from Taiyuan University of Technology in 2012. Her research interest covers Monte Carlo simulation methods

Associate professor at the Control Engineering College, Northeastern University at Qinhuangdao. Her research interest covers mechanical electronics and robotics

Corresponding author: LU Shao-Wen Professor at the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. He received his Ph. D. degree in electronic engineering from the Queen Mary University of London. His research interest covers multi-scale modeling, working with both stochastic simulation and visualization methods. Corresponding author of this paper

摘要

摘要: 本文针对磨矿破碎过程，提出一种分布式参数蒙特卡洛动力学方法的粒度分布预测模型和模拟算法.该算法采用了分段思想，将磨机沿着轴向分为若干个虚拟的子磨机；根据破裂、前向和后向移动三类微观事件定义了倾向函数和系统状态矩阵，并设计了分布式算法的调度策略.此外，针对蒙特卡洛动力学算法效率低的问题，提出了基于τ-leap的磨矿过程分布式参数蒙特卡洛模拟加速算法.为了解决分布式参数更新过程中状态不一致的问题，创新性地提出了一种基于缓冲区的同步方法.通过对仿真案例的分析表明，本文提出的分布式参数蒙特卡洛动力学算法具有较高的精度，提出的基于τ-leap的加速算法能够显著提高计算效率，同时保持较好的精度.
- 磨矿破碎过程 /
- 分布式参数模型 /
- 粒度分布 /
- 蒙特卡洛动力学模拟 /
- 模拟加速
Abstract: In this paper, we propose a prediction model for the particle size distribution of grinding process and a kinetic Monte Carlo simulation algorithm. The algorithm is based on the idea of dividing the mill into several virtual grinding machines along the axial direction. The preference function and the system state matrix are defined according to three kinds of microcosmic events, breakage, forward movement and back movement, and the scheduling strategy of distributed algorithm is designed. In addition, in view of the low efficiency of the kinetic Monte Carlo algorithm, a Monte Carlo simulation acceleration algorithm based on τ-leap is proposed. In order to solve the problem of inconsistent state when updating the distributed parameters, a new buffer based method is proposed. Case study based on simulation shows that the distributed parameter Monte Carlo dynamic algorithm proposed in this paper has high precision, and the proposed algorithm based on τ-leap can significantly improve the computational efficiency while maintaining good accuracy.
- Grinding process /
- distributed parameter model /
- particle size distribution /
- kinetic Monte Carlo simulation /
- simulation acceleration
注释:

1) 本文责任编委吴立刚

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图 1 离散径向分布参数磨机模型示意图

Fig. 1 Illustration of the distributed parameter grinding mill model

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图 2 分段子磨机缓冲区示意图

Fig. 2 The buffer zones for sub-grinding mill

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图 3 分布参数MC算法(图中简称MC)和$\tau $-leap加速算法计算得到的平均粒径随时间变化趋势

Fig. 3 The averaged particle size over simulation time for distributed parameter MC algorithm and the $\tau$-leap accelerated algorithm

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图 4 各子磨机系统的输入和输出物料的累积粒度分布曲线对比

Fig. 4 The cumulative particle size distribution of the input and output of each sub-mill

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图 5 不同$\epsilon$值所对应的$M_p $值随时间变化图

Fig. 5 The values of $M_p $ during the simulation under different $\epsilon$

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图 6 基于$\tau$-leap的加速算法在不同$\epsilon$取值下的WSCV与分布式参数MC算法相对误差

Fig. 6 The relative difference of WSCV of the $\tau$-leap acceleration algorithm comparing with the MC algorithm

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图 7 基于$\tau$-leap的加速算法相对于分布式参数MC算法的TSS加速倍数

Fig. 7 The magnitude of speedup achieved by $\tau$-leap over the MC algorithm

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表 1 离散差分数值算法和$\tau$-leap方法相对于分布参数MC算法的相对误差比较

Table 1 The relative errors of the discrete numerical algorithm and the $\tau$-leap algorithm with the MC algorithm

	子磨机编号	1	2	3	4	5	6	7	8	9	10
第1组	最大误差	8.6	3.8	4.9	7.2	8.6	7.2	5.8	6.7	5.4	5.7
$(\times 10^{-3})$	平均误差	2.2	0.7	1.0	2.1	2.9	1.2	2.2	2.7	1.9	2.7
%第2组	最大误差	4.4	3.3	7.3	7.2	1.1	7.5	6.4	1.1	9.5	6.7
$(\times 10^{-3} )$	平均误差	1.0	1.2	1.7	1.8	3.1	2.2	2.6	2.9	1.4	1.8

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表 2 基于$\tau$-leap的加速算法在不同$\epsilon$取值下与分布式参数MC算法的$M_p $的相对误差($\%$)

Table 2 The relative difference of $M_p $ ($\%$) of the $\tau$-leap acceleration algorithm comparing with the MC algorithm

$t$ (min)	0$\sim$0.1	0.1$\sim$0.2	0.2$\sim$0.3	0.3$\sim$0.4	0.4$\sim$0.5	0.5$\sim$0.6	0.6$\sim$0.7	0.7$\sim$0.8	0.8$\sim$0.9	0.9$\sim$1.0
$M_p $ ($\epsilon$ = 1$\times10^4$)	0.0125	0.0077	0.0038	0.0034	0.0037	0.0029	0.0025	0.0019	0.0023	0.0026
$M_p $ ($\epsilon$ = 1$\times10^3$)	0.2654	0.1426	0.0802	0.0738	0.0665	0.0738	0.0671	0.0533	0.0516	0.0532
$M_p $ ($\epsilon$ = 1$\times10^2$)	0.4565	0.3605	0.1825	0.0770	0.1720	0.1649	0.1071	0.0819	0.0809	0.0426
$t$ (min)	1.0$\sim$1.1	1.1$\sim$1.2	1.2$\sim$1.3	1.3$\sim$1.4	1.4$\sim$1.5	1.5$\sim$1.6	1.6$\sim$1.7	1.7$\sim$1.8	1.8$\sim$1.9	1.9$\sim$2.0
$M_p $ ($\epsilon$ = 1$\times10^4$)	0.0019	0.0035	0.0044	0.0044	0.0035	0.0035	0.0027	0.0026	0.0028	0.0023
$M_p $ ($\epsilon$ = 1$\times10^3$)	0.0471	0.0580	0.0328	0.0420	0.0448	0.0337	0.0369	0.0488	0.0528	0.0445
$M_p $ ($\epsilon$ = 1$\times10^2$)	0.0447	0.0586	0.0495	0.0504	0.0524	0.0574	0.0534	0.0559	0.0872	0.1015

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表 3 基于$\tau$-leap的加速算法在不同$\epsilon$取值下与分布式参数MC算法的$M_p $的相对误差($\%$)

Table 3 The relative difference of $M_p $ ($\%$) of the $\tau$-leap acceleration algorithm comparing with the MC algorithm

$t$ (min)	0$\sim$0.1	0.1$\sim$0.2	0.2$\sim$0.3	0.3$\sim$0.4	0.4$\sim$0.5	0.5$\sim$0.6	0.6$\sim$0.7	0.7$\sim$0.8	0.8$\sim$0.9	0.9$\sim$1.0
WSCV ($\epsilon$ = 1$\times10^4$)	27.6599	16.4219	5.5694	6.4539	6.3902	2.0711	1.6268	0.8461	1.4014	2.8565
WSCV ($\epsilon$ = 1$\times10^3$)	29.3654	19.5643	12.4057	14.1440	8.9499	9.0685	7.7018	5.3212	4.5702	4.0914
WSCV ($\epsilon$ = 1$\times10^2$)	30.5564	20.5641	15.235	16.2165	8.9873	8.1839	8.4892	6.1973	5.0565	5.9391
$t$ (min)	1.0$\sim$1.1	1.1$\sim$1.2	1.2$\sim$1.3	1.3$\sim$1.4	1.4$\sim$1.5	1.5$\sim$1.6	1.6$\sim$1.7	1.7$\sim$1.8	1.8$\sim$1.9	1.9$\sim$2.0
WSCV ($\epsilon$ = 1$\times10^4$)	2.2858	2.6192	3.0302	3.5939	3.3510	5.3169	2.5186	2.1569	1.7443	1.1591
WSCV ($\epsilon$ = 1$\times10^3$)	6.6934	6.8302	6.3439	6.9364	1.6810	2.7825	3.3907	4.0133	5.6812	3.2316
WSCV ($\epsilon$ = 1$\times10^2$)	7.2165	7.6127	7.3752	7.9085	2.3725	2.6708	4.3917	5.4931	6.3914	3.9081

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表 4 基于$\tau$-leap的加速算法相对于分布式参数MC算法的TSS加速倍数

Table 4 The magnitude of speedup achieved by $\tau$-leap over the MC algorithm

$t$ (min)	0$\sim$0.1	0.1$\sim$0.2	0.2$\sim$0.3	0.3$\sim$0.4	0.4$\sim$0.5	0.5$\sim$0.6	0.6$\sim$0.7	0.7$\sim$0.8	0.8$\sim$0.9	0.9$\sim$1.0
TSS ($\epsilon$ = 1$\times10^4$)	1.2654	1.0361	1.0256	0.8022	0.8122	0.8222	0.8322	0.8461	0.8522	0.9578
TSS ($\epsilon$ = 1$\times10^3$)	3.0340	3.2120	3.6136	4.1904	4.7486	6.0206	7.1760	10.1046	12.0586	13.5427
TSS ($\epsilon$ = 1$\times10^2$)	30.5564	33.6722	42.8775	50.7719	59.0955	77.1530	94.5627	106.1508	115.3813	120.9510
$t$ (min)	1.0$\sim$1.1	1.1$\sim$1.2	1.2$\sim$1.3	1.3$\sim$1.4	1.4$\sim$1.5	1.5$\sim$1.6	1.6$\sim$1.7	1.7$\sim$1.8	1.8$\sim$1.9	1.9$\sim$2.0
TSS ($\epsilon$ = 1$\times10^4$)	1.0695	1.1649	1.2973	1.3904	1.5310	1.6498	1.7270	1.8265	1.9938	2.3590
TSS ($\epsilon$ = 1$\times10^3$)	14.8307	15.9210	17.4453	18.5544	20.0657	21.9578	22.8312	24.1852	27.2161	30.1375
TSS ($\epsilon$ = 1$\times10^2$)	129.0026	140.3950	147.3712	161.3876	175.1282	180.8352	184.7492	191.9528	226.3620	227.326

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