On the variability of technological indicators in the extraction of precious metals

: in the conditions of significant variability of processed polymetallic ores of the Akbastau Deposit, it is essential to minimize the variability of technological indicators of enrichment. Due to the multifactorial nature and non-linearity of the flotation process, the use of classical regression models does not provide the necessary level of reliability, therefore, there is a significant variability in the extraction of precious metals. To solve this problem, the paper substantiates the use of the neural network modeling methodology, which allows to estimate the variability of gold and silver extraction depending on the variation of the content of metals in the ore.


Introduction
Traditionally, the problem of variability is solved by calculating the regression dependence between the parameters of the source ore and the extraction of metal, but this approach does not always lead to positive results [1][2][3]. Due to the multifactorial nature and non-linearity of the flotation process, the use of classical regression models does not provide the necessary level of reliability, which is why there is a significant variability in the extraction of precious metals [4,5].

Main part 2.1 Multiple regression equation
To solve this problem, technological indicators for silver and gold in the processed ores from the Akbastau Deposit for the period from 22.01.2018 to 22.07.2018 were analyzed. The statistical array included 315 observations. Statistical estimates of the studied parameters are presented in Table 1 [6][7][8]. In the analysis of the source data, there is considerable variability in the extraction of precious metals: gold is in the range of 23-95% (the content of metal in the ore is 0.4-2.1 g/t), silver in the range of 20-88% (the content of metal in the ore is 4.3-55.3 g/t) [9] The correlation matrix for the studied array is presented in Table 2.  The correlation matrix shows a negative correlation between the content of precious metals in the ore and their extraction into the copper concentrate [10,11]. At the same time, there is a strong positive correlation between the metal content in the ore and in the copper concentrate, which is also quite evident in the trends shown in Figures 1 and 2.  The dispersion of values in the graph in Figure 3 show the difficulty in identifying the causes of significant variability in the extraction of precious metals. An attempt was made to classically calculate the multiple regression equation, the results of which are presented in Table 3. The term "BETA" refers to the equation's regression coefficients on a standardized scale, i.e., according to Equation 1.
(1) Based on the values of standardized coefficients, we can make a conclusion. The silver content in the ore, compared to the content of other elements in the ore, significantly affects the extraction of silver. The influence of other elements on the output function is not significant, according to Kolmogorov's criterion [12]. Moreover, the negative correlation between the content of silver in the ore and the extraction of metal is technologically difficult to explain.
The Thus, we can conclude that it is rather unpromising to use classical regression models for flotation.
The output function is extraction of silver. Input variables are marked in the table of sensitivity of output functions to variations of initial features (Table 5). Statistical estimates of the model are presented in Table 6.  The results of the analysis of the sensitivity of the output function to variations in the initial characteristics show that the greatest influence on the variability of silver extraction is the variation in the content of zinc in the ore. The adequacy of the obtained model is estimated by the correlation coefficient R=0.82. The neural network model allows to obtain generalized response functions, i.e., an evaluation of the variability of silver extraction based on the variation in the content of metals in the ore (Fig. 4-6). The curves shown in the figures are described by the equations shown in the figure captions.  The decrease in silver extraction with an increase in the copper content in the ore is higher (Fig. 4) is probably due to the increased sulfide content and the development of electrochemical corrosion processes in the ore body [14].
The function of the silver extraction reaction to the variation of the zinc content in the ore (Fig. 5) clearly reflects the presence of observations of copper and copper-zinc ores in the initial statistical array.
The function of the silver extraction reaction to the variation of the silver content in the ore (Fig. 6) shows that copper ores are characterized by a decrease in the extraction of silver into the copper concentrate with an increase of the silver content in the ore. This observation requires additional research. For copper-zinc ores, the classical dependence εAg = f(αAg) was observed.
The results of the calculation of the multiple regression equation for gold recovery are presented in Table 7.
Thus, the regression equation on a standardized scale shows no influence of the initial ore parameters on gold extraction (according to Kolmogorov's criterion) [15]. Due to that, an MLP 4:4-10-5-1:1 (10) neural network model (multi-layer perceptron) was calculated for the studied array, the architecture of which is shown in Table 8.
The output function is extraction of gold. Input variables are marked in the table of sensitivity of output functions to variations of initial features (Table 5). Statistical estimates of the model are presented in Table 10. The results of the analysis of the sensitivity of the output function to variations in the initial characteristics show that a variation in the content of copper in the ore has the greatest influence on the variability of gold recovery. The adequacy of the obtained model is evaluated by the correlation coefficient R=0.82. The neural network model allows to obtain generalized response functions, i.e., an evaluation of the variability of gold extraction based on the variation in the content of metals in the ore (Fig. 7-9). The curves shown in the figures are described by the equations shown in the figure captions.  The function of the reaction of gold extraction to the variation in the zinc content in the ore (Fig. 8) clearly reflects the presence of observations of copper and copper-zinc ores in the initial statistical array.
The function of reaction of gold extraction to the variation of gold content in the ore (Fig. 9) shows that a decrease in gold extraction in the copper concentrate with increased gold content in the ore is typical for copper ores, like as it was with silver. This observation requires additional research and may be a consequence of the genetic features of the deposit. For copper-zinc ores, the classical dependence εAu = f(αAu) was observed.

Laboratory tests
Based on the results of this study, a series of experiments in controlled conditions were conducted. The experiments consider the operation regime of a plant that processes ore from Akbastau in order to assess the variability of technological indicators based on the variation of the content of useful elements in the ore. For this task, 5 ore samples with different metal content were taken from this deposit. The chemical composition of the samples is shown in Table 11. Technological indicators of enrichment for a series of experiments are presented in Table 12.