1. Introduction
In mineral processing, grinding is used to reduce the particle size of the ore so that the valuable mineral constituent is exposed and can be recovered in the subsequent beneficiation operation, such as flotation or magnetic separation. The product particle size (PPS) is the most crucial production index which is a required constant to ensure the quality of the subsequent product. However, grinding, which is a complex and time-variant process, is affected by a large number of operational parameters. What is more, the iron ore’s composition is unstable with the decrease in mineral resources [
1].
Because of these difficulties, the research on the grinding process has received much attention. Generally, the PPS needs to be controlled within the desired range suitable for the subsequent beneficiation process. With the development of new intelligent modeling and control methods, many intelligent modeling methods have been successfully implemented in the modeling process of grinding processing. Recently, the advanced control methods based on model predictive control [
2,
3,
4] or supervisory control [
5,
6] for the grinding process have been discussed. It is worth noting that the results mentioned above are stringently based on the mathematical models of the system. However, the grinding process is difficult to describe by mathematical models since the actual industrial process is essentially a multi-input–multi-output system (MIMO) with large inertia, nonlinearity, strong coupling, uncertainty, and interference factors [
7]. Moreover, due to the lack of online analyzers measuring the grinding particle size and the difficulty of obtaining transfer functions of the grinding process, many concentrators cannot realize optimal control by adopting the model-based control method proved to be effective in other plants [
8]. The distinct element method, finite element method, smooth particle hydrodynamics method and discrete element coupling algorithm were adapted to the grinding process, focusing on the media motion state, mechanism research, mill parameter optimization research, ball mill power consumption and energy distribution [
9,
10]. The coupling of various methods can realize the combination of advantages of various methods and simulate the actual working conditions of the ball mill more truly and comprehensively [
11,
12,
13]. However, due to the complex and unstable model, the uncertainty of ore properties, high technical experience requirement and high computational cost, the progress of the coupling method in the mill simulation is difficult to implement. With the development of science and technology, a hybrid intelligent optimal control method based on an expert system for the operation of the complex industrial process is proposed. CBR [
14,
15], rule-based reasoning (RBR) [
16,
17] and a fuzzy expert system [
18,
19,
20] are applied to provide potential solutions for such grinding problems. Among these methods, CBR is an approach to problem solving that utilizes previous cases and experiences that are similar to the current one. The advantage of this method is that it bypasses the unavailable parameters and makes full use of the available experience and data to obtain satisfactory results with little change in the process equipment. Compared with other intelligent algorithm, another important advantage of CBR is that it enables sustained learning by updating the case base after a problem has been solved.
Based on the previous research, the ball mill ore and water feeding intelligent optimization based on CBR are proposed. Historical production data are firstly switched into the form of the case, which include characteristics and characteristic solutions. The characteristics consist of the crushing ore size, ore taste, magnetic tube
content, magnetic tube recovery rate, raw ore
content, raw ore
content, and overflow particle size target value, while the characteristic solution is the ball mill ore feeding and water feeding. Then k-nearest neighbor (KNN) algorithm is applied to calculate the similarity between cases in cases retrieved with the Euclidean distance. The accuracy of CBR is mainly affected by the quantity, quality, and weight of cases. Considering that it is very difficult to obtain a large number of samples in industrial practice, this paper adopts the method of data expansion to increase the sample density. GAN, proposed by Goodfellow et al. in 2014, has been proved to be the most effective method of data augmentation in recent years [
21]. GAN is different from other data expansion methods, such as the synthetic minority oversampling technique (SMOTE) and variational auto encode, in that it pays more attention to learning the internal distribution of the original data rather than differentiating or adding noise to the original data. Through the zero-sum game, GAN can be trained to generate more realistic data. GANs have been successfully applied in generating realistic data in many fields. Shao et al. employed GAN to enrich fault samples to detect the faults in an induction motor [
22]. Wang et al. proposed a new model of fault diagnosis by combining GAN and stacked denoising autoencoders to recognize the planetary gearbox fault pattern. Mao et al. [
23] and Liu et al. adopted GAN to generate a large number of fault samples to obtain a balanced data set and then input it into a classifier to realize the fault diagnosis of the induction motor [
24]. Spyridon proposed an unsupervised fault detection scheme based on GAN in which the judgment on fault occurrence is made by the discriminator [
25].
By its very nature, the distribution of attribute weights also influences the process of similarity assessment. Considering that the operating parameters of the grinding process are not single, it means all case solutions should be considered when weighting the case description. However the commonly used CBR assigns weights through expert experience, which is generally qualitative rather than quantitative. To address the above issues, this paper used NSGA-II which has been used in industrial production [
26,
27,
28] for multi-objective optimization of weights based on historical cases.
The main contributions of this paper can be summarized as follows. (1) The CBR-based grinding parameter optimization algorithm is proposed to maximize the use of available data and expert experience for plants with changing ore properties and incomplete monitoring equipment. (2) The operational parameters and observation data are simplified by combining the process and actual field conditions, and the GAN algorithm is used to realize the expansion of data. (3) The paper introduces an allocation method of the attribute weights, based on NSGA-II, to make it efficacious and precise to multiple case solutions. (4) The method proposed in this paper was experimented in a dressing plant and achieved satisfactory results, which provides experience for subsequent studies.
The paper is organized as follows:
Section 2 presents background information about the ball mill grinding process and the data augmentation method.
Section 3 introduces CBR and optimizes the weight of each characteristic by NSGA-II. This is followed by
Section 4, which presents the simulation results of the optimization, comparing them with the other algorithms.
Section 5 presents the application results in a Chinese ore dressing mill. The last part gives the conclusion.
2. Parameter Selection and Data Reduction
In this section, two-stage closed-circuit mineral grinding processes are first introduced. Combined with the actual situation, some key parameters are selected to optimize the grinding processes. Then, the collected data are expanded by the data augmentation method to make the data-driven model more precise.
2.1. 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 ), the water feed velocity of the two-stage hydrocyclones (denoted by , ), the pump water feed velocity of the two-stage sumps (denoted by ), and the frequency of the two-stage pumps (denoted by , ). 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 the characteristics of the crushing ore size, ore grade, magnetic tube , magnetic tube recovery rate, raw ore content, and raw ore 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 and , respectively. When the amount of ore and water is well controlled so that the concentration of one stage of underflow is , the concentration of the second-stage underflow is exactly 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 sumps 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.
2.2. Data Augmentation
Limited by the upgrading of technology and the backwardness of modern equipment on the industrial site, there are not enough data for parameter optimization and calculation. The primary purpose of the method in this section is to generate a large amount of data so as to provide sufficient samples for data-driven methods to calculate.
The GAN was proposed by Goodfellow et al. in 2014, and consists of two essential components, namely, the generator and the discriminator. Through the zero-sum game, GANs can be trained to generate more realistic data. GAN is widely used in image generation and recognition, speech generation and recognition, data generation, and other fields. The main thought behind GAN is using adversarial networks to improve the quality of generated data. The generator learns the probability distribution of the original data and generates artificial samples that mimic the pattern, using random noises. The discriminator discriminates the artificially generated data from the actual data and prompts the generator to produce better quality data in the next iteration. The general semantics flow chart of GAN is depicted in
Figure 2.
The GANs framework is equivalent to a minimax two-player game, which can be described by the following function [
21]:
where
x is a real datum with a distribution, and
and
z is a random vector.
z is made to be an input of
G through which the generated datum
can be obtained.
is denoted as the distribution of
. Then,
D represents the probability that
x comes from
, rather than from
. Ideally,
if
and
if
.
D is trained to maximize the probability of assigning the correct label to both the real datum
x and the generated datum
.
In this paper, GAN is used to generate grinding industry data. The data include the crushing ore size, ore grade, magnetic tube , magnetic tube recovery rate, raw ore content, raw ore content, the water feed rate, and the fresh ore feed rate. After the actual field investigation records, 182 sets of data were used as the original sample.
The data from the actual production process have some incorrect data. Some of the values are 0, while others are either unreasonably big or small. To get rid of the abnormal data, Formula (2) is used firstly for data screening.
where
is the
ith parameter value;
is the average of the values of the set of parameters. When one of the parameter values is greater than
times, the standard deviation, the sample should be deleted.
After data screening, 164 sets of data are left to generate samples. In the generator, the input is composed of the noise input, which contains 80-dimensional data, randomly generated by Gaussian distribution. There are two hidden layers, followed by the rectified linear unit (ReLU) as an activation function, and the kernel sizes are 120 and 240. The output of the generator is a one-dimensional data sample, using Sigmoid as the activation function. As for the discriminator, the input layer is with eight kernels, using LeakyReLU as an activation function, and the kernel size is 120. Another layer with 240 kernels using LeakyReLU is added and followed by dropout with the probability of 0.5. Finally, the model layer is flattened and linked to one fully connected layer with 0.5 dropouts.
GAN generates 886 samples. To verify the accuracy of the generated samples, the back-propagation neural network (BP), support vector machines (SVM), and extreme learning machine (ELM) are used to compare the original data and the generated data. We used of the original samples as test samples.
The mean absolute error(MAE), mean absolute percentage error(MAPE) and root mean square error(RMSE) of the generated data and the original data under different algorithms are shown in
Table 1 and
Table 2.
As can be seen from the tables, the generated samples can better improve each algorithm’s accuracy. The reason is that the original data volume is relatively small and the data interval is large, which makes it difficult to fit the data well. GAN can supplement the data to simulate some working conditions that are not in the original data but may occur, so that the database contains more working conditions. Although the generated data may not definitely have a positive effect on the optimization, the validity of the generated data can be proven after several generation experiments when all different classification methods show that the expanded data fit better than the original data.
5. Industrial Application Experiments
After testing and comparison with the actual industrial data, the proposed approach was applied to the dressing mill to verify the effectiveness. The average grade of the processed iron ore is
. The algorithm is programmed by MATLAB, and the human–computer surface (as shown in
Figure 9) is designed by Visual Basic. The surface is a simple version, and the actual application version’s language is Chinese with some additional features, such as querying historical data curves, setting parameters, and so on.
Figure 10 is a typical flowsheet of the optimal-setting system running manually. The auto-run indicates that the soft-sensor system carries out estimation operations in accordance with a specified time interval.
When a new set of ore characteristics or new overflow particle size target are obtained, the operator firstly judges whether to update the feature weights or not, then presses “calculate” to run the system. When they get the feedback of the actual overflow particle size, they need to input the data to the system, and the entire group of data saves in the host in the format of EXCEL. After two months of successful operation, a part of the data is shown in
Table 5.
to
in the table represent the ore properties retrieval conditions and
represents the target particle size requirement.
and
are the optimized feeding values and
O represents the actual PPS achieved with the optimized feeding values.
Figure 11 shows the target and the actual value of the overflow particle size. The mean absolute error (MAE) of the target and the actual value is 1.1289. This error is within the allowable range. What is more, the curve of the actual value and the target value are basically consistent. The algorithm can quickly and accurately calculate the set value of the ore and water feeding, according to the ore characteristics and the target of the overflow particle size compared with the traditional manual method. However, when the target value is less than 72 or greater than 80, the error is large. This is due to the following factors: (1) The cases in the case base are not enough, especially beyond 72–80. The cases cannot contain all the characteristics of the ore. (2) The target value beyond 72–80 means that the ore is much better or worse than the normal state. The other operating parameters of the grinding process are not adjusted according to the ore properties. In industrial applications, some error, such as human error and equipment error, makes the algorithm have some deviation, and some special cases also affect the accuracy of the system. As the optimization system is used for a long time, a large number of cases covering various situations are stored in the case base and the algorithm will be more accurate.