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Essay: Artificial Neural Network, Flotation, Separation Efficiency

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  • Artificial Neural Network, Flotation, Separation Efficiency
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An artificial neural network and regression procedures were used to predict the separation efficiency of Cu and selectivity indices of Mo and Fe of the copper flotation concentrate on different operational conditions. Flotation parameters, such as chemical reagent dosages (Collector, frother, Fuel-oil), Feed rate, solid percentage and the Feed grade of Cu, Fe and Mo, were used as inputs for both methods. A three-layered back propagation neural network (BPNN) with a structure of 9-10-10-3 is selected to estimate the separation efficiency of Cu and Gaudin selectivity indices of Cu-Mo and Cu-Fe. In the ANN model, standard Bayesian regularization was used as a training function in which, it is unnecessary that the validation data set be apart from the training data set. The advantage of this algorithm is the minimization of weights and linear combinations of squared errors of producing the appropriate network. In training and test stages, the quite satisfactory correlation coefficient of 1 for train outputs and 0.93, 0.9 and 0.88 for test outputs was achieved, respectively. The results show that the proposed approach models can be used to determine the most advantageous industrial conditions for the expected separation efficiency and Gaudin selectivity indices in the froth flotation process.

Keywords: Artificial Neural Network, Flotation, separation efficiency, Selectivity index, estimation

1- Introduction

The froth flotation is a separation method that is used for selective separation of hydrophobic minerals from hydrophilic ones. It is one of the most important methods for beneficiation of sulfide ores. The progress of froth flotation amended the recovery of desired minerals such as copper and lead bearing minerals [1].

The sulfide copper ore commonly contains molybdenum as a by-product, which can be selectively separated by using the flotation process. The main valuable content of porphyry copper ores included Chalcocite and Chalcopyrite as sulfide minerals and Malachite and Azurite as oxide minerals. The most important associated gangue minerals that could be present were iron-bearing minerals such as pyrite, quartz, muscovite, carbonate, and albite [2]. The Sarcheshmeh copper ore is the one of the largest in the world, containing 1 billion tons averaging 0.9% copper and 0.035% molybdenum. This plant has been processing about 41000 tons of ore per day since 1982. The mine produces 140000 t of copper and 3500 t of molybdenite concentrate per year [3]. In the last decades, many scholars have reported the application of the ANN method as the attractive method in mineral processing plants to control and model the process such as grinding stage control, flotation process, image analysis, hydrometallurgical processing, coal washery process and so on [4-6]. The previous researches that have been carried out in mineral processing can be mentioned: Kalyani et al. simulated the froth flotation process for the beneficiation of coal fines. In this work, the network weights have been estimated and used to compute the parameters of the coal flotation process [7]. Jorjani et al. predicted the combustible value and combustible recovery of coal flotation concentrate by the regression and ANN methods based on proximate and group macerals analysis [8]. Al-Thyabat used the feed-forward artificial neural network (FFNN) to study the effect of feed mean size, collector dosage and impeller speed on flotation recovery and grade. The results showed that grade was more sensitive to changes in flotation parameters than recovery [9]. Kamran Haghighi et al. applied the neural network tool for modeling the transition of heavy metals from Ni–Cd zinc plant residue. The inputs of this network are pH, flow rate of acidic influent, particle size and time. In a different work, they investigated the synergistic effect of LIX 984N and D2EHPA on the separation of iron from zinc solution. The results showed that there is an excellent agreement between the experimental data and the predicted values [10,11]. Singh and Rao studied the image processing and RBFNN techniques for ore sorting and ore classification [12]. Nowadays, high-grade resources are becoming scarcer and acquiring the pure product with the least amount of impurity would be difficult. It is important to have a view on what happens if the grade of feed from the point of view Cu content and gangue minerals is changed. Thus, the aim of this work is to investigate the possibility of the ANN model based on estimation of separation efficiency and selectivity index for the copper flotation process. This paper is managed as follows: The next section briefly describes the industrial plant. The ANN modeling is introduced in Sect. 3. The method of separation efficiency and selectivity index prediction in an industrial flotation process using ANN is discussed in Sect. 4. Finally, Sect. 5 presents the conclusion.

1-1-Flotation process Description

The flow sheet of Sarcheshmeh copper flotation circuit is shown in Fig. 1. In this process, the copper ore (-75 µm) is used as the feed of a rougher bank. There, copper flotation is carried out at a pH of (11.5-12.5) by using the chemical reagents such as Z11 as a collector and MIBC and Dowfroth 250 as a Frother. The flotation section included the rougher, cleaner, and scavenger cells with a regrind mill. A re-grind mill is used to grind the coarse particles (i.e. Underflow of the secondary cyclone) of the combined rougher and scavenging concentrates.

A final product with an average grade of 28–30 % Cu (chalcopyrite and chalcocite), 0.7–0.8 % Mo and 27-28 % Fe is obtained after flotation stages. The total recovery is fluctuating between 83% to 87%, depending on the operating parameters and ore types. From the previous experience, some factors that can be more effective and have had an important role in the flotation of copper ore were selected as the ANN input variables. Then the separation efficiency of Cu [13] and Gaudin’s selectivity indices of Cu-Mo and Cu-Fe [14] are calculated and are given by the following equations:


(1 [13]


(2 [14]


Where Rm % is recovery of the valuable mineral (Cu), Rg % is recovery of the gangue (Mo-Fe) into the concentrate; Ra is the recovery of Cu in the flotation concentrate and Jb is the recovery of gangues (Mo-Fe) in the tailing fraction.

1-2- Artificial Neural Network modeling

The ANN is the computational model that contains the numeral units with interpolations called neurons. These neurons indicate some features of the ANN biological construction [11]. In comparison with the conventional method, a conventional algorithm will employ complex sets of equations, and will apply to only a given problem and exactly to it.

The ANN will be (a) computationally and algorithmically very simple and (b) it will have a self-organizing feature to allow it to hold for a wide range of problems. ANNs are based on the terms called neurons and their duties are the estimation of complex nonlinear associates existing between ANN input and output variables to an arbitrary degree of accuracy [15, 16]. Meanwhile, the ANN is an important tool for interpolation between experimental data. Thus, the aim of this work is to evaluate the FFNN model described in the literature to predict the copper flotation variables considering with separation efficiency and selectivity index of copper as the valuable mineral versus iron and molybdenum as the gangue minerals. The ANN has been used for complex systems that cannot be modeled by using mathematical methods. In this approach, the best solution for any given problem is attained by trial and error. The neurons in ANN have two important parts, summing and weight parameters [17]. In this study, the MLP structure has been used for ANN modeling. In order to obtain the appropriate structure for ANN, the following stages were carried out:

a) Selecting and preprocessing of data.

b) Dividing the samples to two sets: training and testing sets.

c) A selection of model geometry.

In this approach, the industrial data from the Sarcheshmeh flotation plant is used as a series of input and output matrixes to learn the network, and during the run of each training epoch, the network calculated the error to compare the experimental outputs and predicted values [18]. Based on these stages and with respect to the aforementioned, the developed code in MATLAB software was used for training and testing the neural network model. Training the network was carried out with the standard Bayesian regularization back propagation algorithm. On the other hand, in this training method, optimizing the weights and biases was performed by Levenberg–Marquardt. The Bayesian training algorithm is one of the best approaches to improving generalization performance of the network for function approximation problems [19]. This is due to it being unnecessary that the validation data be set apart from the training data set. This is noticeable for the small size of the data set. The advantage of this algorithm is the minimization of weights and linear combinations of squared errors of producing the appropriate network and well generalization [19, 20].

1-3- Data Preprocessing

In this study, the pre-processing stage was used, which can result in the neural network training more efficiently. Pre-processing of the network training set was done by normalizing the inputs and targets using the following equation:




Where, Xn and Xi are normalized and actual values, respectively. and Std is the mean value and standard deviation of each subset (inputs-outputs). The normalized data have the mean and Variation of 0 and 1, respectively.

Thus, nine inputs and three outputs, network models were developed in which, pH value, chemical reagents (collector, frother and Fuel oil dosage gr/ton), Feed rate (thousand tons), solid percent % and the Feed grade of Cu, Fe and Mo were considered as the input variables. On the other hand, to evaluate the process, Cu separation efficiency (SE) and Gaudin’s selectivity index of Cu-Mo and Cu-Fe are selected as an output variable in the flotation concentrate. The maximum, minimum, mean and standard deviation of input variables in different operating conditions are given in Table 1. These data are divided into the input and target matrix. (74) (80% of the whole data) and (18) (20% of the whole data) data is reserved as the training and test subsets, respectively.

2- Result and discussion

2-1- Structure of appropriate ANN network

Selection of an appropriate structure for a network is obtained by changing the number of neurons, hidden layer and the kind of transfer and training functions. While, the number of layer and neurons in each layer is selected in good mode, the effect of transfer and training function would be negligible and avoidable [21-24]. A three-layered back propagation neural network (BPNN) is formed as the structure of this study. As can be seen, Fig. 1 shows the aforementioned structure. 92 industrial data sets, collected during one year, were applied to develop the ANN structure.


As mentioned above, the network based on three layers is selected to estimate the separation efficiency of Cu and Gaudin selectivity indices of Cu-Mo and Cu-Fe. Linear (purelin) and Tangent sigmoid (tansig) functions were applied to the output layer and transfer inputs at the hidden layer, respectively. The optimum number of neurons selected via a trial and error procedure is suggested by Anderson and McNeill [25]. At the beginning, the network was performed with two neurons in each layer and increased the number of neurons every other layer up to ten in which, the least mean square value (MSE) and root mean squared error (SSE) were attained. On the other hand, in each run, if the results compared between targets (inputs to networks) and outputs (answers of network) were wrong, the ANN emendates the network interpolations (weights and biases) [19, 26]. Finally, the best structure and geometry of the network were attained as 9-10-10-3 arrangements, capable of simultaneously predicting the SE(Cu), SI(Cu-Mo) and SI(Cu-Fe) in the flotation process.

2-2- Evaluation of ANN Prediction

There are several ways of measuring error in this paper. The ANN model was evaluated by MSE, which is depicted in Eq (4):




Where m is the number of observations, Yi is the predicted value of the ith pattern by ANN; and T is the actual value.

In the best condition, the outputs were in good agreement with targets in which, the mean square error performance function (MSE) of the training data sets was attained at 1.4289e-11 and 187 Epochs. The MSE value is shown in figure 3. To evaluate the ANN model error and simulated data, the R square value was used. The error was calculated via MSE or RMSE, which are a risk function, corresponding to the expected value of the squared error loss or quadratic loss.

2-3- Network accuracy of SE prediction

In order to evaluate the ability of model estimation of training and testing data for the metallurgical performance (i.e. separation efficiency and selectivity indices of copper flotation process in companying Fe and Mo minerals), the following layout including i) fitting, ii) regression, iii) error and iiii) histogram diagrams were attained from the model. These plots show that the predicted values are in good agreement with targets and the prediction error value is shown in Fig.4 (a-d). As can be seen in Fig.4 (a), the separation efficiency values, calculated from equation (1) are exactly fitted on the predicted ones from the network. Fig.4 (b) shows that the R-square value for the testing sets was highest as possible (R2=1), indicating that the performance of the selected network (9-10-10-3) is the best. Fig.4 (c) shows that the error range is between +1.5e-5 and -1.5e-5 that demonstrates the ANN model accuracy. The MSE and RMSE values for this output are obtained at 2.0679e-11 and 4.5474e-06, respectively. Fig.4 (d) indicates the error histogram of outputs that can investigate the inconsistent errors. The large center peak indicates very small errors or outputs that are very close to the target values. The smaller endpoint spikes denote clearly incorrect results [27]. As seen from Fig.4 (d), the high frequencies of error histogram are concentrated on the zero error, meanwhile it can be concluded the predicted values are in good agreement with target values.

In addition, to investigate the accuracy of the present model, the test data were applied to the ANN model. The result of test data from Fig.5 (a-b) indicated the satisfactory fitting of predicted values with measured values. The correlation coefficient value of test data was obtained at 93%.

2-4- Network accuracy of SI(Cu-Mo) and SI(Cu-Mo) Predict

In the same work, the model estimation of Gaudin’s selectivity index for copper concentrate is appraised by equation (2), in which Cu is the valuable mineral and Mo is the gangue mineral. These results are indicated in Fig.6 and Fig.7 (a-d). As can be seen from Fig.6 and Fig.7 (a), the predicted values from the two models are entirely fitted on the real values. Fig.5 and Fig.6. b) indicate the correlation between the model response and targets in which R-square value is 1 illustrating the good agreement between the predicted and target values. Fig.6 and Fig.7 c) illustrate the error variation interval and error histogram for SI(Cu-Fe) and SI (Cu-Mo) prediction, and the error range is between +1e-5 and -1e-5 for SI(Cu-Fe) and +6e-5 and -6e-5 for SI (Cu-Mo), which is the negligible interval and indicates that the model of ANN has a very accurate representation of the industrial results. The MSE and RMSE values for SI(Cu-Fe) and SI (Cu-Mo) are obtained as (1.6233e-11 and 4.029e-06) and (5.954e-12 and 2.4401e-06), respectively. Fig.6 and Fig.7 d) indicate the error histogram of outputs that can investigate the inconsistent errors, indicating that there is a good fit between the outputs of the model and results of experiments. As previously mentioned, the result of test data for both outputs (i.e SI (Cu-Fe) and SI (Cu-Mo)) is depicted in Fig. 8 (a-b) and Fig. 9 (a-b). As can be seen from these figures, fitting of SI (Cu-Fe) in comparison with SI (Cu-Mo) was better. Also, the obtained R value from test data of the ANN model for SI (Cu-Fe) and SI (Cu-Mo) was 90% and 88%, respectively.

3- Conclusion

A four-layer back propagation neural network was developed and optimized to predict the separation efficiency of Cu and Gaudin’s selectivity indices of Cu-Mo and Cu-Fe in the flotation concentrate as a function of pH, chemical reagents (collector, frother and Fuel oil dosage gr/ton), Feed rate (thousand tons) and Feed grade of Cu, Fe and Mo. The geometry of a network, giving the minimized mean square error (MSE) and sum squared error (SSE) was a four-layer network having 10 neurons with tangent sigmoid transfer function (tansig) at each hidden layer and linear transfer function (purelin) at the output layer based on the Bayesian training algorithm. With respect to lot results (the fitting, regression, error and histogram plots), ANN outputs are very close to the industrial results with the best correlation coefficient (R2=1) for each output and MSE 2.0679×10-11, 1.6233×10-11 and 5.954×10-12 for SE of Cu, SI(Cu-Fe) and SI(Cu-Mo), respectively. Also, the results of test data were satisfactory, and the correlation coefficient of SE of Cu, SI(Cu-Fe) and SI(Cu-Mo) were attained as 0.93, 0.9 and 0.88, respectively. Therefore, this approach could be effectively used to study the obdurate effects of the selected inputs on the separation efficiency and Gaudin’s selectivity indices of the copper flotation circuit with Mo and Fe as the gangue minerals.


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