## 2 Parameter Selection and Data Reduction
### Parameter Selection  
Grinding process is the sequel of the ore crushing process, whose purpose is to produce useful components of the ore to reach all or most of the monomer separation, while avoiding an excessive wear phenomenon and achieving the particle size requirements for sorting operations. The typical two-stage closed-circuit wet-type mineral grinding process considered in this paper is shown in Figure 1. The coarse ore from the primary crusher is mixed in the ore bin and then fed into the ball mill together with water for wet grinding. By changing the frequency of the pendulum feeder, we can control the quantity entering the ball mill. The tumbling and crushing action with the grinding medium grinds the coarse ore to finer sizes. The slurry containing the fine product is discharged from the ball mill to the pump sump and then pumped to hydrocyclones for classification. The slurry is separated into two streams in the hydrocyclones: the underflow with the larger particles and the overflow with the finer particles. The underflow is recycled back to the ball mill with the new coarse ore for further regrinding. The overflow slurry flows to the next stage of the grinding system for finer particle grinding. The next stage of the grinding process is the same as the first stage, and the overflow flows into the subsequent beneficiation operation as the desired product.  
The grinding process is a complex controlled object that is influenced by many factors. PPS is the key operational index that dictate the product quality and is usually used as the controlled variable in the grinding process. The manipulated variables are listed as follows: the milling ore feed velocity (denoted by \(f_{1}\)), the water feed velocity of the two-stage hydrocyclones (denoted by \(w_{11}\), \(w_{12}\)), the pump water feed velocity of the two-stage sums (denoted by \(w_{21}\)\(w_{22}\)), and the frequency of the two-stage pumps (denoted by \(p_{1}\), \(p_{2}\)). Combined with the actual situation of a concentrator in northeast China, the fresh ore is mainly composed of hematite, magnetic ore, and carbonate iron ore. We use  
Figure 1: Flow chart of two-stage grinding process.  
the characteristics of the crushing ore size, ore grade, magnetic tube \(mFe\), magnetic tube recovery rate, raw ore \(FeO\) content, and raw ore \(mFe\) content to describe them in this paper.  
The calculation of adjusting all of the above-mentioned operating parameters, according to the nature of the ore, is too complex, and the construction on site has a large lag and uncertainty. So combined with the actual situation of a concentrator in northeast China, this paper simplifies as follows. (1) Long-term industrial tests showed that the grinding efficiency is highest when the underflow concentration of the two-stage cyclone are around 65% and 85%, respectively. When the amount of ore and water is well controlled so that the concentration of one stage of underflow is 65%, the concentration of the second-stage underflow is exactly 85% without adding water to the cyclone. So the water feed rate of the second-stage hydrocyclones is set to zero. (2) The main function of water feeding to the sums is to avoid slurry precipitation. So the water feed rate of the two-stage sumps is a fixed value that does not changes as the manipulated variable. (3) The frequency of the two-stage pumps is also fixed, based on long-term industrial trials. (4) Operators can adjust the amount of steel ball supplied according to complete real-time regulation. According to the above assumptions, this paper's operating parameters are simplified to the water feed velocity of the first-stage hydrocyclones and the milling ore feed velocity. These parameters need to be adjusted, according to the ore properties fluctuation and PPS requirements.