The grinding process is a typical complex nonlinear multivariable process with strongly coupling and large time delays. Based on the datadriven modeling theory, the integrated modeling and intelligent control method of grinding process is carried out in the paper, which includes the softsensor model of economic and technique indexes, the optimized setpoint model utilizing casebased reasoning, and the selftuning PID decoupling controller. For forecasting the key technology indicators (grinding granularity and mill discharge rate of grinding process), an adaptive softsensor modeling method based on wavelet neural network optimized by the improved shuffled frog leaping algorithm (ISFLA) is proposed. Then, a set point optimization control strategy of grinding process based on casebased reasoning (CBR) method is adopted to obtain the optimized velocity setpoint of ore feed and pump water feed in the grinding process controlled loops. Finally, a selftuning PID decoupling controller optimized is used to control the grinding process. Simulation results and industrial application experiments clearly show the feasibility and effectiveness of control methods and satisfy the realtime control requirements of the grinding process.
Grinding process has complex production technique and many influencing factors, such as the characteristics of the ore fed into the circuit (ore hardness, particle size distribution, mineral composition, or flow velocity), the flow velocity of water fed into the loops, and the changes of the cyclone feed ore. Grinding process is a serious nonlinear, strong coupling, and large time delay industrial production process. Obtaining the optimal control results by the traditional control method is difficult. Scholars at home and abroad have carried out many advanced control strategies for the grinding process, such as fuzzy control [
Because of the limitations of the industrial field conditions and a lack of mature detectors, the internal parameters (particle size and grinding mills discharging rate) of the grinding process is difficult to obtain the realtime quality closedloop control directly. The softsensing technology can effectively solve the predictive problem of the online measurement of the quality indices. Therefore, the softsensor model according to the auxiliary variables can be set up in order to achieve the particle size and grinding mills discharging rate for the realtime forecasting and monitoring, which has great significance on improving the grinding process stability and energy conservation. Domestic scholars have proposed many softsensor models, such as neural network model [
Aiming at the grinding industrial process, the integrated automation control system is proposed, which includes the economic and technical indices soft sensor model, the setpoint optimized model based on the casebased reasoning method, and the selftuning PID decoupling controller. Simulation and experimental results show the feasibility and effectiveness of the proposed control method for meeting the realtime control requirements of the grinding production process. The paper is organized as follows. In Section
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 excessive wear phenomenon and achieving the particle size requirements for sorting operations. A typical grinding and classification process is shown in Figure
Technique flowchart of grinding process.
Grinding process is a complex controlled object. There are many factors to influence this process, such as the milling discharge ratio
The block diagram of the datadriven integrated modeling and intelligent control strategy of the grinding process is shown in Figure
System configuration of the integrated modeling and intelligent control methods of grinding process.
The integrated modeling and intelligent control system of grinding process includes the adaptive wavelet neural network softsensor model of economic and technique indexes, the optimized setpoint model utilizing casebased reasoning technology, and the selftuning PID decoupling controller based on the ISFLA. Firstly, the milling granularity and the discharge ratio predicted by the softsensor model are named as the input parameters of the setpoint model. Then, through the casebased reasoning, the milling ore feed ratio and the water feed velocity of the pump pool are optimized. Finally, the selftuning PID decoupling controller is adopted to achieve the optimized control on the milling discharge ratio and milling granularity ultimately.
The structure of the proposed wavelet neural network softsensor model optimized by the improved SFLA is shown in Figure
Softsensor model structure of grinding process.
Considering a multiinput singleoutput (MISO) system, the training sample set can be expressed as
The input vector
Wavelet neural network (WNN) is similar to BP neural network with the same topology, which adopts the wavelet base function as the transfer function of hidden layer nodes [
Structure of wavelet neural network.
In Figure
The parameters of output layers of the wavelet neural network are calculated as
Standard wavelet neural network uses the gradient descent method to train the structural parameters. But the inherent characteristics of gradient descent method make the WNN training process convergence slow, easy to fall into local minimum, and easily lead to oscillation effect [
Shuffled frog leap algorithm [
SFLA is an evolutionary computation algorithm combining deterministic method and stochastic method. Deterministic algorithm can make effective use of strategic information to guide the search response and the random element to ensure the flexibility and robustness of the algorithm searching patterns. The SFLA is described in detail as follows. First, an initial population of
In each memeplex, the frogs with the best fitness and worst fitness are identified as
Frog leaping rules.
During the natural memetic evolution of the frogs, the worse frog is affected by the better frog to leap for the better one in order to get more food. According to the above description of the initial frog leaping rule (shown in the Figure
This frog leaping rule increases the algorithm search scope in a certain degree. Combined with the characteristics of SFLA, the paper puts forward a new frog leaping rule (shown in the Figure
Two wavelet neural network softsensor models optimized by the improved SFLA are set up in the paper for predicting the grinding granularity and grinding discharge ratio. The algorithm procedure of ISFLAbased WNN softsensor model is shown in Figure
Algorithm procedure of optimization of WNN softsensor model based on ISFLA.
Combined with the proposed new frog leaping rule, the algorithmic procedure of the ISFLAbased wavelet neural network training is described as follows.
Initialize the frog population size
Randomly initial the population of
The
The frog in the memeplex
If the frog doesn’t achieve the meme evolution,
The frog in the meme group
The frogs in the iterated memeplex
The model migration method [
Basic principles block diagram of PMBPS.
Due to the fluctuations in ore grade and other working conditions of the grinding process, the current softsensor results are no longer accurate so that the softsensor model must be adaptive corrected. At the moment, a small amount of datum may be adopted to set up a new softsensor model based on the model migration (linear correction and planning) from the original softsensor model to be adapted to the new working conditions. In this paper, the migration modeling method based on the inputoutput correction programming method is adopted, whose basic principle is shown in Figure
IOSBC migration modeling principles chart.
Assume the original softsensor model:
Through the output space migration and plan a new model is obtained as follows
Then, the input space is shifted and revised. The input
Therefore, the new model is obtained by the inputoutput offset correction of the original model, which is described as follows:
New sample datum can be used to train the correct parameters:
Aiming at the grinding and classification process, the grinding granularity and grinding discharge ratio softsensor model is set up based on the wavelet neural network. Firstly, the inputoutput data set is shown in Table
Input data set of forecasted grinding granularity.
Number  Water of ore feed (m^{3}/h)  New ore feed (T/h)  Divide overflow concentration (%)  Grinding current (A)  Grader current (A)  Grinding granularity (%) 

1  20.45  95.13  80.83  55.3  5.1  80.24 
2  23.23  110.14  82.08  56.9  5.3  82.97 
3  24.27  104.67  83.98  54.3  5.8  86.69 
4  25.34  102.87  87.32  55.9  5.2  84.36 







300  23.87  103.09  86.23  55.4  5.6  81.56 
Predictive output of grinding granularity.
Predictive Output
Predictive error
Predictive output of mill discharge rate.
Predictive Output
Predictive error
Usually the average relative variance (ARV) [
Predictive AVR.
SFLAWNN  WNN  

AVR of grinding granularity  0.1183  0.5700 
AVR of grinding discharge ratio  0.0212  0.0790 
As seen from Figures
The general procedure of the casebased reasoning process includes retrievereusereviseretain. In the CBR process, the case retrieval is the core of CBR technology, which directly determines the speed and accuracy of decision making. The basic procedure of the casebased reasoning technology [
Basic flowchart of casebased reasoning.
The casebased reasoning process is mainly divided into four basic steps [
Grinding process is a complex nonlinear industrial controlled object. Combining the real problems that exist in grinding process control with the theory of casebased reasoning, the basic procedure of the set point optimization strategy is shown in Figure
Diagram of the grinding intelligent setpoint control based on casebased reasoning.
The basic procedure is described as follows. Firstly, the working conditions, the process indicators, and the process datum are dealt with for the case reasoning. Then, the case retrieval and case matching are carried out for obtaining the matched case. If the matched case is not obtained, the new case will appear and be studied and stored into the database. Thirdly, the matched case will be reused and corrected. Finally, maintain the case database, output the results, and store the datum.
The most commonly used knowledge representation methods have production rules, semantic networks, frames, decision trees, predicate logic and fuzzy relations, and so forth. In theory, the form that knowledge is represented by in the case is not a new knowledge representation method, but it is an abstract knowledge representation based on the past ones, which means that the case is a logical concept. The case must be based on the existing variety knowledge representation methods. That is to say that almost all the existing knowledge representation methods can be used as the implementation of the case representation. A typical case generating process is essentially refinement process of case databases. It represents a large number of similar cases and experiences in common and can reduce not only the retrieval process in the selected set of objects but also other parts of the analog process the workload.
The case model in the CBR process is described as
Case matching and case retrieval are important steps in the casebased reasoning process and the key of the information extraction from the case databases. In general, the case matching strategy includes the serial and parallel search methods. In the serial search process, the cases are organized with the hierarchical manner. The topdown refinement layer by layer retrieval approach is adopted, which means the more down the layer, the higher the similarity. The parallel searching strategy weakens the level features among the cases. The retrieve method is to return to the most similar case by retrieving many cases. The commonly used search strategies have nearest neighbor strategy, inductive reasoning strategy, and knowledge guidance strategy.
If the current working condition is
The similarity function between
So the static similarity threshold adopted in the paper is described as follows:
In the actual production process, because the case library does not have a case fully matching with the current work under normal circumstances, the retrieved solution parameters matching the working conditions are not directly selected as the control parameters of the current conditions. Therefore, the similar case solution retrieved must be reused. That is to say that the CBR system will adjust the retrieved case solution according to the specific circumstances of the new case to get the solution of the input new case. The adjustment strategy uses the existing process knowledge to obtain the current working parameters based on the differences between the input case working conditions and the retrieval case working conditions. The SSTDbased case reuse strategy is described as follows:
In order to prove the effectiveness of case reuse, the case must be amended in the new implementation process in order to form the effective feedback. Usually the case model obtained by the casebased reasoning can be directly applied to the current working conditions. However, due to some differences between the current working conditions and the retrieved cases in some characteristics, the retrieved cases cannot be directly used in the current conditions. The retrieved case must be amended to adapt to the current issue.
The main contents of the case correction mainly include the amendments of the case features and structures. If
Case storage strategy is to store the new cases and their solutions into case database according to a certain strategy. The case storage is the base of the case library. By doing so, the case database keeps growing and expanding to increase the searching scope of the case database. At the same time, the maintenance of case database has become an essential work. In the case of storage, the new case
The paper mainly studies the relationship between the input variables (grinding ore feed ratio and pump water feed velocity) and output variables (grinding granularity and grinding discharge ratio). Through experiments, the dynamic process model of the grinding circuit includes the ball milling mechanistic model, based on material balance, the empirical model of hydrocyclones, the pump pool hybrid model based on the mechanistic model and empirical model. Through the step response of the grinding process, the system transfer function model [
The mathematical model of the grinding process described in formula (
Selftuning PID Decoupling controller.
Diagonal matrix decoupling procedure is described as follows [
Additionally,
For meeting
So
So obtain two SISO systems:
PID control is a regulator based on the linear combination of the proportion, differential, and integral of the bias, whose transfer function is described as follows [
Firstly, the ZN method is adopted to determine the initial parameters of PID controller. So the two groups of PID controller parameters (
Four performance indicators IAE, ITAE, ISE, and ITSE are described in (
The original twoinputtwooutput (TITO) system is decoupled into two independent singleinputsingleoutput (SISO) channels by adopting diagonal matrix decoupling methods. The parameters of the PID controller are optimized by the proposed ISFLA.
The simulation parameters are selected as follows: frog population size
Output response curves of M1.
Output response curves of M2.
For model M1 and M2, the parameters of the PID controller tuned by a variety of methods are shown in Tables
PID controller parameters of M1.
PID parameters  ZN  ISE  IAE  ITAE  ISTE 


6  13.5  7.8  12.6  12.44 

35  26.3  9.29  14.52  28.84 

0.1  0.2  0.38  0.38  0.38 
PID controller parameters of M2.
PID parameters  ZN  ISE  IAE  ITAE  ISTE 


4  6.89  6.85  8.64  4.95 

23.2  14.15  12.22  4.64  10.37 

1  0.67  0.74  1.05  0.73 
Output response performance index of M1.
Performance Index  ZN  ISE  IAE  ITAE  ISTE 

Overshoot  48.1  25.1  27.8  25.1  23.2 
Rising time  0.78  0.69  0.71  0.73  0.72 
Regulated time  4.2  2.5  2.7  2.4  2.5 
Output response performance index of M2.
Performance index  ZN  ISE  IAE  ITAE  ISTE 

Overshoot  48.9  25.3  26.2  20.1  25.1 
Rising time  0.79  0.74  0.75  0.72  0.73 
Regulated time  4.5  2.5  2.6  2.3  2.6 
Under the premise that the other process variables remain unchanged, the grinding ore feed ratio and pump water feed velocity before and after optimization have a different influence on the performance indexes of the grinding process. Because the ultimate impact factors on the economic efficiency of grinding process are the concentrate grade and tailings grade. So the industrial application experiments are carried out under the proposed datadriven integrated modeling and intelligent control method in the grinding process. The technique indexes controlled scopes are described as follows. Concentrate grade
Concentrate grade before intelligent optimization.
Concentrate grade after intelligent optimization.
Tailings grade before intelligent optimization.
Tailings of grade after intelligent optimization.
As seen from Figures
For the grinding process, a complex industrial controlled object, an integrated automation, and control system are researched in detail, which includes the economic and technical indicators of softsensor model, the setpoint optimized model based on the casebased reasoning methods, and the selftuning PID decoupling controller. Simulation and industrial experimental results show that the proposed datadriven integrated modeling and intelligent control methods have a better feasibility and effectiveness to meet the realtime control requirements of the grinding production process.
This work is partially supported by the Program for China Postdoctoral Science Foundation (Grant no. 20110491510), the Program for Liaoning Excellent Talents in University (Grant no. LJQ2011027), and the Program for Research Special Foundation of University of Science and Technology of Liaoning (Grant no. 2011zx10).