磨矿粒度动态过程的一种快速Monte Carlo仿真方法

A Fast Monte Carlo Algorithm for Dynamic Simulation of Particle Size Distribution of Grinding Processes

磨矿是降低矿物粒度的工业过程,产品粒度是磨矿过程的关键质量指标.由于磨矿粒度难以在线检测且磨矿生产过程具有综合复杂特性,难以采用传统控制方法实现磨矿粒度的控制.因此,建立磨矿粒度和关键工艺参数的动态模型对于磨矿运行控制和优化具有重要意义.采用总量平衡原理获得磨矿粒度的微分方程模型多数情况下无法获得解析解.而基于Monte Carlo(MC)方法的磨矿粒度模型能够精确模拟磨矿粒度分布的动态变化,但是其仿真效率低难以实用.本文针对这一问题提出一种新的MC仿真方法:在定总量方法的基础上引入新的颗粒移除机制,在移除过程中动态地分配各个粒级颗粒数目并保持破裂前后各个粒级颗粒所占总颗粒数的百分比不变,避免颗粒移除过程中由于粒级差异导致的抽样误差,且避免MC仿真速度随着仿真推进下降的问题.仿真实验验证表明,本方法能够在保证一定精度前提下显著提高磨矿粒度MC仿真的计算速度.最后,通过一个实例介绍了本文仿真模型在磨矿优化控制中的应用.

Grinding is an industrial process of reducing the particle size of ore, and the product particle size distribution （PSD） is the key quality index of the grinding process. Due to the difficulty of measuring PSD online and the comprehensive complexity of the grinding process, a PSD of the grinding process is difficult to control with traditional control methods. It is therefore important to establish the PSD model of grinding process to facilitate the optimization of its operation and control. Traditionally, the population balance principle is used to establish the PSD model, but it cannot arrive at an analytical solution in most cases. A Monte Carlo （MC） based model can accurately simulate the PSD dynamics, however it is too inefficient for practical use. In view of this problem, this paper proposes a new MC method which is developed based on the constant number MC （CNMC） method. This method develops a new particle removal mechanism to reduce the sampling noise caused by the CNMC removal operation. This can avoid the problem that the simulation speed decreases sharply with the simulation time. The simulation results validate that the proposed method can speed up the simulation while maintaining good accuracy. In the last, an application of the proposed model to the simulation of optimal control for a grinding process is introduced as an example.