Simulation of Coke Quality Indicators Using Artificial Neural Network

The article shows the application of a neural network for modeling coke quality indicators Coke Reactivity Index (CRI) and Coke Strength after Reaction (CSR). Two optimization methods were used to train the neural network. The influence of the number of neurons on the simulation results was studied. The difference between experimental and calculated data on average does not exceed 2 %. The conclusion is made about the prospects of using a neural network to predict the values of CRI and CSR of coke.


Introduction
An important task of metallurgical coke production is to obtain coke of a given quality.
It is known (see, for example, [1]) that metallurgical coke can be characterized by two parameters: CRI and CSR. At present, there is no reliable model for calculating CRI and CSR based on the characteristics of charge materials and coking mode. In this regard, studies in the direction of establishing the dependence of coke quality on the characteristics of the charge are relevant.
In studies in this direction, regression and correlation analysis methods are often used (see, for example, [2]). In [2], a linear regression dependence between CRI and CSR was obtained with a correlation coefficient of 0.97; the determination coefficients between CRI and the volume fraction of internite, vitrinite reflection index, hygroscopic humidity are in the range 0.26 -0.27, which indicates a complex mutual influence of the factors considered.
It can be concluded that the problem of determining the characteristics of the quality of coke CRI and CSR can be attributed to an insufficiently formalized problem in which there are many influencing factors (for example, petrographic composition, degree of metamorphism, etc.), which are not always strictly possible to take into account.  The solution of insufficiently formalized problems is possible using artificial neural networks (see, for example, [3]). This approach was used in [2] to describe the quality of coke and in [4] to analyze the yield of chemical coking products.
To determine the weight matrices of a neural network, training examples are needed -the charge parameters and the values of CRI and CSR obtained for them. The data for the study and the results of the determination of CRI and CSR are provided by industrial enterprise and are shown in tables 1, 2.

Results and Discussions
A two-layer artificial neural network (TLANN) was used to simulate CRI and CSR, the structure of which is shown in Fig.1. The logistic function was used as a compressive function A two-layer artificial neural network (TLANN) was used to simulate CRI and CSR, the structure of which is shown in Fig. 1. The logistic function was used as a compressive function ( ) = 1 1+ − [5]. The number of neurons in the outer layer was chosen to be equal to two in the number of coke quality parameters CRI and CSR. The quantity in the inner (hidden) layer varied over a wide range to determine the effect of this factor on the simulation results.  To improve the quality of the simulation, the original data and results were preprocessed so that they were in a single range, usually from 0 to 1.
The method of error back propagation (see, for example, [5]) was used to train DEANS, in which the functional of the form was minimized Here The weight matrices were the minimization parameters w(1) and w(2) (see fig.1). The search for elements of the neural network weight matrices was carried out using two methods of unconditional optimization: the method of the steepest descent and the method of conjugate gradients (see, for example, [6]). In both approaches, it is necessary to determine partial derivatives of the functional E(w) on the elements of the weight matrices (1) and (2) . The following expressions for partial derivatives were obtained )) ⋅ ( (2) ) ⋅ (1) , = 1... , = 1... .
Corrections for weights, for example, in the method of the quickest descent at the step with the number are determined by the relations [6] ( -parameter of the method) (2) +1 = (2) + Δ (2) .
Calculations Δ are terminated if Δ become less than the specified accuracy of calculations.