J. Cent. South Univ. Technol. (2011) 18: 1976-1984

DOI: 10.1007/s11771-011-0931-z

Artificial neural network modeling of gold dissolution in cyanide media

S. Khoshjavan¹, M. Mazloumi², B. Rezai¹

1. Department of Mining and Metallurgy Engineering, Amirkabir University of Technology,Hafez Avenue, Tehran, Iran;

2. Department of Mining Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran

? Central South University Press and Springer-Verlag Berlin Heidelberg 2011

Abstract: The effects of cyanidation conditions on gold dissolution were studied by artificial neural network (ANN) modeling. Eighty-five datasets were used to estimate the gold dissolution. Six input parameters, time, solid percentage, P₈₀ of particle, NaCN content in cyanide media, temperature of solution and pH value were used. For selecting the best model, the outputs of models were compared with measured data. A fourth-layer ANN is found to be optimum with architecture of twenty, fifteen, ten and five neurons in the first, second, third and fourth hidden layers, respectively, and one neuron in output layer. The results of artificial neural network show that the square correlation coefficients (R²) of training, testing and validating data achieve 0.999 1, 0.996 4 and 0.998 1, respectively. Sensitivity analysis shows that the highest and lowest effects on the gold dissolution rise from time and pH, respectively. It is verified that the predicted values of ANN coincide well with the experimental results.

Key words: artificial neural network; gold; cyanidation; modeling; sensitivity analysis

1 Introduction

Gold cyanidation has been used as the princinal gold extraction technique since the late 19th century. Cyanide is universally used because of its relatively low cost and great effectiveness for gold dissolution.

The dissolution of gold in cyanide media is a heterogeneous process. The main problem in examining the dissolution of gold in the given medium including gold ores is determining the dependence of the dissolution of the process on the main process parameters (time, temperature, pH, oxygen dissolved, solid percentage and concentration of the cyanide). This information is necessary to determine the optimum conditions for modeling of gold leaching in cyanide media. Many researchers studied on dissolution and modeling of gold ores cyanidation [1-8].

Artificial neural network (ANN) technique is a relatively new branch of the ‘artificial intelligence’ (AI) and has been developed since 1980s. At present, ANN technique is considered to be one of the most intelligent tools for modeling complex problems. This technique has the ability of generalizing a solution from the pattern presented during training. Once the network is trained with a sufficient number of sample datasets, for a new input of relatively similar pattern, predictions can be done on the basis of previous learning [9].

In this work, the aim is to study the effect of leaching parameters on gold cyanidation and their limitations. The main purpose is to find the important factors which impact on the amount of gold extraction and optimize the process by 85 groups of data obtained from gold cyanidation data sets in batch experiments. The ANN modeling is used for simulation and extraction estimation of gold cyanidation.

2 Artificial neural network modeling

2.1 Theoretical background

Artificial neural network models have been studied for two decades, with an objective of achieving human like performance in many fields of knowledge engineering. Neural networks are powerful tools that have the ability to identify underlying highly complex relationships from input–output data only [10].

The study of neural network is an attempt to understand the functionality of a brain. Essentially, ANN is an approach to artificial intelligence, in which a network of processing elements is designed. Further, mathematics carries out information processing for problems whose solutions require knowledge that is difficult to describe [11-12].

Compared with the traditional pattern recognition, ANN can provide an exact description for multi dimension and non-linear problem [13].

The fundamental unit of ANN is the neurons which are arranged in layers, and are categorized as the input (I), hidden (H) and output (O) neurons depending on in which layer they are located. Neurons in each layer are linked to each of those in the layers immediately next to it through the connections known as synapses. Each of synapses is characterized by a weight factor, which can be adjusted to target the desired output signal. As a non-linear modeling technique, the ANN modeling involves in linking up the input and output data through a particular set of non-linear basic functions [14-16].

Various algorithms are available for training of neural networks, but the back-propagation algorithm is the most versatile and powerful technique, which provides the most efficient learning procedure for multilayer perception (MLP) neural networks. Also, the fact that the feed forward back-propagation neural network (BPNN) algorithm is especially capable of solving predictive problems makes it so popular [17].

For this research, a five-layer ANN is found to be optimum with architecture of twenty, fifteen, ten and five neurons in first, second, third and fourth hidden layers, respectively, and one neuron in output layer. To differentiate between various processing units, bias values are introduced in transfer functions. In the BPNN, with the exception of input layer neurons, all other neurons are associated with a bias vector and a transfer function [18]. Figure 1 illustrates the flowchart of a typical two-hidden-layer BPNN model [19].

The first step in a BPNN is the feed forward operation (Fig.1). During this operation each input neuron Y_i receives an input signal and broadcasts this signal to the connected neurons Z₁, …, Z_n in the first hidden layer. The total input parameters to the Z_j neuron from the input layer is [19]

                                             (1)

In the first hidden layer, w_ij and θ_j are new and old weights, respectively. Each of these neurons then computes activation and sends its result to the connected neurons K₁, …, K_p in the second hidden layer. The total input to the K_k neuron from the first hidden layer is [19]

                                          (2)

In the second hidden layer, w_jk and θ_k are new and old weights, respectively. Each neuron in the second hidden layer computes its activation and sends its result to the output neuron. The total input to the output neuron o from the second hidden layer is [19]

                                          (3)

where w_ko and θ_o are the new and old weights, respectively, in the output layer. Finally, the output neuron yields the network output according to the activation function (o=f[o(in)_o]). The activation function is the same for all neurons in any particular layer of a neural network.

The second step of learning process is backward pass, which is concerned with error computation and connection weight updates. For this purpose, the network is presented with a pair of patterns, an input pattern and a corresponding desired output pattern. The network computes its own output pattern using its (mostly incorrect) weights and thresholds. Then, the actual output is compared with the desired output to determine the error. An objective function is defined as E=0.5(t-o)², and connection weights are updated using generalized delta rules [9, 19].

Fig.1 Flowchart of typical two-hidden-layer BPNN

For example, the update of the weights connecting the second hidden layer with the output is given by [19]

                                                             (4)

Training of the network is basically a process of arriving at an optimum weight space of the network. The incremental weight is given by

                                                             (5)

where μ is the learning rate parameter and E is the error function. Similar weight updates can be obtained for weights connecting the second and the first hidden layer, and the first hidden layer and the input layer [9, 19].

This procedure is repeated with each pattern pair of training exemplar assigned for training the network. Each pass through all the training patterns is called a cycle or epoch. The process is then repeated, as many epochs as needed, until the error within the user specified goal is reached successfully. This quantity is the measure of how the network has learned [9].

In the procedure of ANN modelings, the following contents are usually used:

1) Choosing the parameters of ANN,

2) Collecting of data,

3) Pre-processing of database,

4) Training of ANN,

5) Simulation and prediction by using the trained ANN.

In this work, these stages were used in the development of the model.

2.2 Data sets

One of the most important stages in the ANN technique is data collection. The data are divided into training, testing and validating datasets using sorting method to maintain statistical consistency.

Datasets for testing are extracted at regular intervals from the sorted database and the remaining datasets are used for training. The same datasets are used for all networks to make a comparable analysis of different architecture. In this work, 85 datasets were collected, among which 30% were chosen for testing and validating datasets.

The data were obtained from our laboratory experiments as explained below:

The gold extraction was carried out in a bench scale experiments by the composition of: pH (10.2-11), NaCN mass fraction (10^-4-6×10^-4), temperature (20-30 °C), dissolved oxygen ((8-16)×10^-6), solid percentage (36%- 42%) and P₈₀ particle size (57-75 μm). Considering the main factors, time, temperature, NaCN content, pH, solid percentage, P₈₀ of particle size, experiment scheme is designed, as listed in Table 1.

Table 1 Ranges of variables in gold extraction (as determined)

2.3 Input parameters

In the present work, input parameters include pH, NaCN content, temperature, dissolved oxygen, solid percentage and P₈₀ particle size to predict the gold extraction.

In the present work, all inputs (before feeding to the network of Matlab software) and output data in training phase, preprocesses the network training set by normalizing the inputs and targets so that they have means of zero and standard deviations of 1 according to Eq.(6):

N_p=(A_p-A_p,mean)/A_p,std                                                     (6)

where A_p is the actual parameter, A_p,mean is the mean of actual parameters, A_p,std is the standard deviation of actual parameter and N_p is the normalized parameter (input). N_p of each data has been used in network, then targets of each parameter are converted to actual parameter, and after these processes figures have been drawn.

2.4 Training and testing of model

As mentioned above, the input layer has six neurons X_i (i=1, 2, …, 6). The number of neurons in the hidden layer is supposed to be Y, the output of which is categorized as P_j (j=1, 2, …, Y). The output layer has one neuron which denotes the amount of gold extraction. It is assumed that the connection weight between input and hidden layers is W_ij, the connection weight between hidden and output layers is W_hj, and K denotes the learning sample numbers. A schematic presentation of the whole process is shown in Fig.2.

Nonlinear (LOGSIG, TANSIG) and linear (PURELIN) functions can be used as transfer functions (Fig.3). The logarithmic sigmoid function (LOGSIG) is defined as [18]

                                                               (7)

Whereas, the tangent sigmoid function (TANSIG) is defined as [18]

                                                              (8)

where e_x is the weighted sum of the inputs for a processing unit.

Fig.2 ANN process flowchart

Fig.3 Sigmoid and liner transfer functions [18]

3 Results and discussion

Network architecture mode was designed to reach an appropriate architecture, and MLP networks with one and two hidden layers were examined. As errors of the one-hidden-layer networks were high, three-hidden layer network was selected for simulation (Table 2). To determine the optimum network, the sum of square error (SSE) was calculated for various models by the following formula:

                                                          (9)

where T_i, O_i and N represent the measured output, the predicted output and the number of input–output data pairs, respectively [20-21].

Table 2 Results of comparison between some of models

The network with architecture 6-20-15-5-1, which has the minimum SSE, is considered as the optimum model. This network is shown in Fig.4.

For evaluation of a model, a comparison between predicted and measured values of gold extraction can be fulfilled. For this purpose, mean square error, MAE (E_a) and mean relative error (E_r) can be used. E_a and E_r are computed as [20-21]

                                                               (10)

                                                           (11)

where T_i and O_i represent the measured and predicted output.

For the optimum model, E_a and E_r are equal to 3.65 and 0.043, respectively. Comparison between measured and predicted gold dissolution in cyanide media for training, testing and validating data are shown in Figs.5(a), 5(b) and 5(c), respectively. Correlations achieved from these figures, between measured and predicted gold dissolution from training, testing and validating data indicate that the network has a high ability for predicting gold extraction (Fig.6).

Fig.4 Suggested ANN for case study

Fig.5 Comparison of measured and predicted gold extraction for different samples for training data (a), testing data (b) and validating data (c)

Fig.6 Correlation between measured and predicted gold extraction for training data (a), testing data (b) and validating data (c)

3.1 Sensitivity analysis

A useful concept has been proposed to identify the significance of each input factor on the output factors using a trained network. This enables us to hierarchically recognize the most sensitive factor affecting the output (gold extraction). This is performed by incorporating values of ‘relative strength of effect’ (RSEs) [20, 22]. After a BPNN has been trained successfully, the neural network is no longer allowed to adapt. The output for a one-hidden-layer network can be written as

                                                            (12)

where

                          (13)

                                                         (14)

where w is a connected weight, θ is a threshold and o_i is the value of input unit. Thus, we have

O_k=

 (15)

Since the activation function is sigmoid Eq.(10), it is differentiable. The variance of O_k with the change of O_j for a network with n hidden layers can be calculated by the differentiation of the following equation:

                          (16)

where   denote the hidden units in the n, n-1, n-2, …, 1 hidden layers, respectively [20, 22]. Obviously, it is no matter what the neural network approximates, all items on the right hand side of Eq.(14) always exist. According to Eq.(16), a new parameter  can be defined as the RSE for input unit i on output unit k [20, 22].

Definition of RSE: For a given sample set S={s₁, s₂, s₃, …, s_j, …, s_r} where S_j={X, Y}, X={x₁, x₂, x₃, …, x_p}, Y={y₁, y₂, y₃, …, y_p}, if there is a neural network trained by back-propagation algorithm with this set of samples,  exists as

                              (17)

where C is a normalized constant which controls the maximum absolute value of  as unit and the function G denotes the differentiation of the activation function. G, w and e are all the same as those in Eq.(16).

It should be noted that the control of RSE is done with respect to the corresponding output unit, which means that all RSE values for every input unit on corresponding output unit are scaled with the same scale coefficient. Hence, it is clear that RSE ranges from 0 to 1 [20, 22].

Compared to Eq.(16), RSE is similar to the derivative equation except for its scaling value. But, it is a different concept from the differentiation of the original mapping function. RSE is a kind of parameter which can be used to measure the relative importance of input factors to output units, and it shows only relative dominance rather than differentiation of one to one input and output. The larger the absolute value of RSE, the greater the effect the corresponding input unit on the output unit. RSE is a dynamic parameter which changes with variance of input factors. Here, the RSE will be used for a sensitivity analysis of the influence of factors on the back break phenomenon predicted by a trained neural network.

Figure 7 shows the average RSE values of the factors calculated for all of 85 field data used in the previous sections. It is concluded that input parameters, including time, temperature, NaCN content and P₈₀ of particle size are the most effective factors on the gold cyanidation. It can be seen in Fig.7 that time and pH are usually the maximum and minimum sensitive parameters, respectively.

Fig.7 Sensitivity analysis between gold extraction and gold cyanidation parameters

3.2 Performance of ANN

To verify the veracity of the ANN model, 85 experiment data were chosen. The verified results reveal that the predicted values coincide well with the experimental results, as shown in Fig.6. It is indicated that model of ANN exactly reflects the correlation between the input and output layers. The function of gold cyanide leaching parameters influencing on gold extraction is found. In Figs.8-13, measured and experimental values of gold extraction are compared.

Fig.8 Predicted and experimental effect of time on gold extraction (solid percentage 40%, NaCN content 2×10^-4, pH 10.5, 20 °C and P₈₀ of particle 55 μm)

Fig.9 Predicted and experimental effect of NaCN on gold extraction (20 °C, pH 10.5, solid percentage 42%, P₈₀ of particle 57 μm and leaching time 2 h)

Fig.10 Predicted and experimental effect of solid percentage on gold extraction (pH 10.5, NaCN content 2×10^-4, P₈₀ of particle 65 μm, leaching time 24 h and temperature 30 °C)

3.3 Effect of every factor on gold extraction

Figure 6 shows that the ANN model has a good result as a whole, and can reflect the general effect of all factors on gold extraction. However, it is not known if the model can explain the specific effect of every factor on gold extraction.

Fig.11 Predicted and experimental effect of P₈₀ of particle on gold extraction (solid percentage 40%, NaCN content 2×10^-4, pH 10.5, 20 °C and leaching time 1 h)

Fig.12 Predicted and experimental effect of temperature on gold extraction (P₈₀ of particle 55 μm, dissolved oxygen 8×10^-6, solid percentage 42%, NaCN content 5×10^-4, pH 10.6 and leaching time 3.5 h)

Fig.13 Predicted and experimental effect of pH on gold extraction (20 °C, NaCN content 2×10^-4, P₈₀ of particle 57 μm, solid percentage 42% and leaching time 5.5 h)

Data of six group have been chosen for every factor in order to verify the model further. The results are shown in Figs.8-13.

As seen in Fig.8, the predicted effect of time on gold extraction by using ANN model is the same as the experimental results. It is well known that the time of leaching in the cyanidation has great influence on gold extraction. Figure 8 shows the influence of time on gold extraction. Increasing the time in cyanidation results in an increase in gold extraction significantly.

The effect of NaCN content on gold extraction is shown in Fig.9. It is verified that the predicted values of ANN coincide well with the experimental results. Gold extraction increases obviously with increasing the NaCN content in cyanide media.

It is known that solid percentage can decrease the amount of gold extraction. Figure 10 shows the same effect as the reference, namely, the higher the solid percentage, the slower the gold extraction. It is the reason that high solid percentage decreases the probability of effective contact between cyanide and gold bearing particle.

The effect of particle size on gold extraction, as seen in Fig.11, shows that gold extraction decreases sharply by increasing the particle size. This can be explained by the fact that with an increase in particle  size, surface area of particle will be decreased. It is noticed that the predicted and experimental effective tendency is well consistent.

The temperature has a great influence on gold extraction. Figure 12 shows the amount of gold extraction increases significantly by increasing the temperature. The predicted value gives the same results. Increasing the temperature provides the energy for the gold cyanidation reaction.

It is well known that the pH of the reaction has the lowest influence on gold extraction. By increasing the pH, the amount of gold extracting is increased. It is evident that after pH reaches 10.6 increasing the pH has reverse effect on gold extraction. Figure 13 shows the effect of this factor on gold cyanidation.

From such an analysis, it is concluded the ANN model not only exactly predicts gold extraction, but predicts the effect of every factor on amount of gold extraction in the cyanidation of gold ore process.

4 Application of model

From the simulation and predictions (see Figs.6-13) made using the ANN model, it is evident that the model could be a useful tool in assessing the correlations of gold extraction in the cyanide leaching of gold ore process parameters.

Thus, the best combination of parameters for high amount of gold extraction in the cyanide leaching of gold ore can be obtained by using this model. Simultaneously, the experiment performance and fuzzy testing can be omitted.

5 Conclusions

1) The optimum ANN architecture is found to be six neurons in the input layer, three hidden layers with 20, 15 and 5 neurons, respectively, and one neuron in the output layer.

2) In the ANNs method, results of the artificial neural network show that square correlation coefficients of the training, testing and validating data (R²) achieve 0.999 1, 0.996 4 and 0.998 1, respectively.

3) By applying the ANN method, it is concluded that the most important factors on the gold extraction are the time, the temperature, the particle size and the cyanide content in pulp.

4) Network RSEs show that time (0.44), temperature (0.163), particle size (0.14), NaCN content (0.1), solid percentage (0.091) and pH (0.08) are effective parameters on the gold extraction, respectively.

5) RSE of time is 0.44 and it has the highest effect on gold extraction.

6) The results of predicted data from neural network and measured data show that the time, NaCN content and temperature have positive effects on the gold extraction. With increasing these parameters, the gold extraction by cyanide media will be increased. The negative effects of input parameters are related to the particle size and slid percentage. These parameters have reverse effects on the gold cyanidation.

7) The optimum pH for gold extraction in cyanide media is 10.6.

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(Edited by YANG Bing)

Received date: 2011-03-09; Accepted date: 2011-07-11

Corresponding author: S. Khoshjavan; Tel: +98-914-363-9099; E-mail: saber.khoshjavan@gmail.com