Neural simulation of ball mill grinding process

This study is aimed at getting simplified model of mill filling technological process of fine crushing in a closed-circuit grinding with screen separation. Optimal and simple model structure are supposed to be used in adaptive predictive control loop. The minor factors that directly affect the mill load indicator are not taken into account, since some of them cannot be directly measured, and other ones affect the process only in the long term. In this paper the athors considered mill filling process identification in the center-discharge ball mill by the method of neural networks (NN). The method includes the identification of the nonlinear process using nonlinear autoregressive with external input (NARX) neural network. The most accurate model was found by varying the structural parameters of the network. The best models were tested in the course of the actual grinding process. The best estimation of the NN model to the real object is obtained with 72.1% match.


Introduction
Optimal control remains a complex problem in the mining industry for many years due to various uncertainties in the models of control objects, nonlinearities, changes in parameters and their interdependences [1]. Figure 1 shows the parameters that directly affect to the apatite-nepheline fine crushing process in a closed-circuit grinding with a ball mill and vibrating screens separation. points of the grinding cycle in order not to clog the chutes and changing the density of the output pulp product to the flotation process. The flowrate of reagents does not affect the processes occurring in the mill. The reagents are fed in the mill to obtain the necessary properties of the output pulp product for flotation. The topsize product returning to the mill from screen separation cannot be measured either qualitatively or quantitatively. The topsize product flow is a dependent parameter on the main input material flows for a stationary process, because the constancy of the technical characteristics of vibrating screens. Other inputs are short-duration perturbations such as ore moisture, ambient vibration and long-term perturbations such as volume of balls in the mill and working volume of the mill [2,3]. Thus, the number of input parameters indicates the complexity of the object.
The main output parameter of the control object is a load, i.e. material mill filling [4]. Practice shows that the stabilization of the load at the optimum level gives maximum quality indicators of the grinding and a possibility to avoiding the mill overload. The mill overload is achieved if the mill overflows with a material. The overload indicator is the vibration which is measured on the main bearing housing at the discharge chute. This parameter is also called as «noise». The overload adversely affects to the service life of the equipment and the implementation of the grinding plan. In addition, load stabilization is important for the energy efficiency of the entire production process due to the high energy consumption of the process [4].
Modern control systems for grinding include a load stabilization algorithm based on various control approaches [1,6,7]. Domestic algorithms are developed on a cascade PID controller, and still often operate in manual mode or to a limited extent due to the fear of overloading of the mill. PID is stable and efficient, but only around the set of nominal operating points. The permissible overshoot value, determined by the experience of operating the apatite-nepheline fine crushing process control system, is 3% for the control channel. PID approach does not allow achieving this quality of regulation in the mode of the maximum productivity of the mill. Also, advanced control algorithms are actively used and very promising. Model Predictive Control (MPC) is the most popular and successful strategy in non-stationary process control with parameter changes. A special feature of the approach is the using of the process model to calculate the predicted response of the process at future times. The optimal model is the most important part of the MPC strategy. Such a model should cover the key dynamic characteristics of the process and allow calculating predictions [8]. To apply MPC strategy for a particular industrial process, it is necessary to build a custom simulation mathematical model of the object. Thus, to simulate the process of filling the mill with the material, we choose key measuring channel characterizing mill load dynamic: flowrate of ore in the mill / «noise».

Description of the method of modelling
The task is to synthesize the optimal structure of the neural model of the control object, to determine the initial parameters of the neural network of the neural model at the current operating point of the control object. The method included the identification of the object with using Neural Network Toolbox 8.4 with the Time Series Tool for the synthesis of custom neural networks with delay lines for input and output signals. The presence of delay lines provides the dynamics of the model, i.e., current output ( 1) yt is predicted as a weighted sum of past output values and current and past input:  One important aspect of identification of nonlinear systems is choosing the right time delays for each of the input variables and choosing the number of regressors, i.e., the number of previous samples of each variable that will be considered in the system model at a given moment [9]. The choice of fixed and variable factors is based on the analysis of literary sources [10,11]. Therefore, the following key factors have changed to build a autoregressive neural network model of the of the The data are measured from apatite-nepheline grinding process for training networks. The measurements were provided every second for about 10 hours of mill operation. There were 33555 training input/output samples with 1 second sample time. The input data is the flowrate of ore (t/h) and the output data is the «noise» (%). Trained NNs were checked on training data, on test data and on online data during the grinding process. For online test the laptop is connected to the local computer network of the grinding section automation system. Modbus OPC server is used to establish a connection to the Simulink model and PLC-system. Access to the data "inside" the SCADA-server is carried out according to the standard Modbus rules. We focused on finding the best fitting neural network and in the end compared the best fitting neural network with others Matlab System Identification Toolbox techniques for nonlinear identification: tree partition method, wavelet method, Hammerstein-Wiener model.

Results and discussion
It is established that the increase in the number of delays of the output signal by 1 decrease the fit on training data by 2-3 times. That's why further networks were built with one delay of the output signal. In general, 42 neural networks were synthesized varying dx from 1 to 7 and number of neurons from 7 to 12.   The results in the table 1 are sorted in descending order of fit on the real process data. Three models of other NARX techniques are shown in the end of table 2: 'A' -Hammerstein-Wiener model with 1 output and 1 input (linear transfer function nb = 2, nf = 3, nk = 1, input nonlinearity: pwlinear with 10 units, output nonlinearity: pwlinear with 10 units); 'B' -nonlinearity: wavenet with 25 units, standard regressors: na = 1, nb = 5, nk = 1; 'C' -tree partition method.
An increase in the number of neurons in the hidden layer in the general trend showed an increase in modelling accuracy. The number of input feedbacks of the neural network greater than 3 had an advantage over the others. Comparing with other methods of nonlinear identification, the result of repeating the object on the training sample (33555 samples) and on the test sample (30000 samples) in nonlinear models was higher than the neural models. But on a real process data, these models showed poor results relative to NNs. As in [12], neural networks showed the best results.