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In this paper, prediction of copper and molybdenum grades and their recoveries of an industrial flotation plant are investigated using the Artificial Neural Networks (ANN) model. Process modeling has done based on 92 datasets collected at different operational conditions and feed characteristics. The prominent parameters investigated in this network were pH, collector, frother and F-Oil concentration, size percentage of feed passing 75 microns, moisture content in feed, solid percentage, and grade of copper, molybdenum, and iron in feed. A multilayer perceptron neural network, with 10:10:10:4 structure (two hidden layers), was used to estimate metallurgical performance. To obtain the optimal hidden layers and nodes in a layer, a trial and error procedure was done. In training and testing phases, it achieved quite correlations of 0.98 and 0.93 for Copper grade, of 0.99 and 0.92 for Copper recovery, of 0.99 and 0.92 for Molybdenum grade and of 0.99 and 0.94 for Molybdenum recovery prediction, respectively. The proposed neural network model can be applied to determine the most beneficial operational conditions for the expected Copper and Molybdenum grades and their recovery in final concentration of the industrial copper flotation process.

Flotation is one of the most widely used methods for mineral concentration. The separation process is a surface- chemistry based process for the separation of fine particles that is based on difference in wettability at the solid particle surfaces. Flotation is mainly used in mineral concentration, treatment of industrial wastewater and the water purification [

Artificial Neural Networks are successfully applied for the modeling and control of complex systems such as copper flotation [

ANNs are based on neurons, the duties of which are to estimate complex nonlinear associates existing between ANN input and output variables [

The use of neural networks to predict the efficiency of deinking from paper by flotation was reported by Labidi et al. [

Moolan et al. used an image analysis and a feed forward neural network to predict flotation recovery and grade from the froth surfaces and structures. They also predicted the effects of some froth characteristics such as froth stability, bubble size and froth structure on froth solid concentration by a neural network [

Massinaei and Doostmohammadi [

Jorjani et al. [

In this paper, a multilayer feed forward neural network was applied to estimate the copper and molybdenum grades and their recoveries of flotation concentrate based on operational parameters of the industrial flotation process. In this work, operational parameters were pH, collector, frother and F-Oil concentration, size percentage of feed passing 75 microns, moisture content in the feed, solid percentage, and grade of copper, molybdenum and iron in the feed. Modeling was performed by means of a neural network, MATLAB software package.

This paper is arranged as follows. Section 2 presents the industrial flotation process. The ANN prediction model is presented in Section 3. Results and discussion are given in Section 4. Conclusions are put forth in Section 5.

The Sarcheshmeh copper ore body Located in southeast Iran that contains 1 billion tonnes averaging 0.80% copper and 0.03% molybdenum. It has been processing 40,000 t/d (old plant since 1982) and 22,000 t/d (new plant since 2002) of ore.

A simplified flow sheet of Sarcheshmeh flotation circuit is shown in ^{3}, the cleaner, scavenger banks each have three and five cells of 50 m^{3}, respectively. The coarse portion of the combined rougher and

scavenging concentrates (i.e. underflow of secondary cyclone) is ground by using regrind mill that is a 3.962-m by 5.791-m ball mill. The tailings of the rougher flotation are discarded to the final tails, and the concentrate is reground. The concentrate of copper was produced by the stages of flotation cleaning and re-cleaning. In this flotation circuit, reagents of sodium isopropyl xanthate and Nascol 1451 (dithiophosphate and mercaptobenzothiazol) are used as collector and reagents of methyl isobutyl carbonyl and Dow 250 (polypropylene glycol methyl ether) are used as frother.

After flotation stages, a concentrate was produced with an average grade of 28% - 30% copper and 0.7% - 0.8% molybdenum. From the previous experience, some factors that have an important role in the flotation of copper ore were selected as the input variables [

ANNs are developed on the basis of the human brain and its neural system that composed of billions of neurons which are interconnected by synapses. Similarly, an artificial neural network is made up of many processing elements that are also called neurons.

The output of each neuron is calculated with applying the weight and bias parameters and then, as the input is fed to the next layer’s neurons. The output of each neuron is passed by an activation function (transfer function) [

In the ANN, each neuron computes the net weighted input by the following equations:

where x_{1}, x_{2}, … , x_{n} are the input variables; wk_{1}, wk_{2}, … , wk_{n} are the synaptic weights of neuron k; u_{k} is the sums of the linear combination of each neuron; b_{k} is the bias; _{k} is the output of each neuron. The most important issue in the ANN arrangement is to determine the number of hidden layers and nodes. Usually, the optimum number of hidden layers and neurons in each layer are found by a trial and error method [

In this research, the best structure and geometry of the ANN model 10-10-10-4 (

A back propagation feed forward neural network with two hidden layers was constructed for modeling of the industrial flotation process.

In this study, for the modeling problem, pH, collector, frother and F-Oil concentration, size percentage of feed passing 75 microns, moisture content in feed, solid percentage, grade of copper, molybdenum and iron in feed were considered as inputs to the network. Variables of copper, molybdenum grade and recovery in the final concentrate were used as the network output.

Data pre-processing can be effective in the process of training the neural network [_{N}) for each raw input/output dataset was calculated using the following equation:

where X_{N} is the normalized value of each input or output variable, X is an original value of a variable, and X_{max} and X_{min} are maximum and minimum original values of the variables, respectively.

In this research, several networks were created, trained, and tested. The optimum number of hidden layers and nodes in each layer were determined by the trial and error procedure. A total of 92 data sets were used in the predictions by ANN; 69 and 23 data sets were applied for training and testing the network, respectively for estimation of copper and molybdenum grades and their recovery. In the present work, a feed forward back propagation with parameters shown in

Variable | Min | Max | Mean | Standard deviation |
---|---|---|---|---|

pH | 12.09 | 12.39 | 12.3034 | 0.0559 |

Collector dosage (g/ton) | 10.5 | 25.0673 | 18.5813 | 2.9573 |

Frother dosage (g/ton) | 12 | 22.5 | 16.3130 | 2.0084 |

F-Oil dosage (g/ton) | 1 | 5.9486 | 3.3258 | 0.7240 |

Solid percentage (%) | 25.1106 | 29.0876 | 27.4425 | 0.8253 |

Moisture percent (%) | 4.4367 | 5.4665 | 4.8356 | 0.2116 |

Size percent of feed passing 75 micron | 61.1934 | 66.7105 | 63.0652 | 0.9499 |

Copper grade in feed (%) | 0.5528 | 0.8221 | 0.6674 | 0.0540 |

Molybdenum grade in feed (%) | 0.0194 | 0.0403 | 0.0270 | 0.0036 |

Iron grade in feed (%) | 3.7106 | 6.5878 | 4.8260 | 0.6401 |

Variable | Min | Max | Mean | Standard deviation |
---|---|---|---|---|

Copper grade in final concentrate (%) | 18.6122 | 28.8488 | 24.5525 | 1.7797 |

Copper recovery in final concentrate (%) | 82.6762 | 90.1167 | 86.3908 | 1.8602 |

Molybdenum grade in final concentrate (%) | 0.4811 | 1.1309 | 0.7321 | 0.1535 |

Molybdenum recovery in final concentrate (%) | 47.2212 | 79.4940 | 64.3083 | 7.4264 |

Parameter | ANN |
---|---|

Number of layers | 4 |

Number of neurons in input layer | 10 |

Number of neurons in first hidden layer | 10 |

Number of neurons in second hidden layer | 10 |

Number of neurons in output layer | 4 |

Transfer function of the first hidden layer | Tan sigmoid |

Transfer function of the second hidden layer | Tan sigmoid |

Transfer function of the output layer | Linear |

Number of epochs | 292 |

Learning rate | 0.1 |

Momentum | 0.9 |

process by which derivatives of the network error, with respect to network weights and biases, can be computed (

reduction with an increase of epochs is shown in

where Y is predicted values,

The ANN model has been developed by considering two hidden layers in the MLP configuration and training using the back propagation algorithm. During each iteration, the error signal travels backwards through the network, starting at the output neurons and ending at the input synapses. The neural network learns the relations contained in between the input and the output variables and correlates the variables by the optimal weights that minimize the differences between the estimated and observed output values. For each iteration, an error between the predicted and the observed values is propagated backward from the output layer towards the input layer through the hidden layers. This work continued until the predicted and the target values are in a good agreement (the convergence criteria is met) [

When the training stage was completed, the network testing stage was begun for its generalization capability. The testing phase for its generalization ability was done by investigating its capability to estimate NN output sets that were unfamiliar data sets to the neural network. For this purpose, 29 new data sets were selected that were not included in the training stage. The testing stage shows that the model can predict copper and molybdenum grades and their recoveries quite satisfactorily. The correlation coefficient (R) values in the testing stage for copper, molybdenum grades and copper, molybdenum recoveries were 0.93, 0.92 and 0.92, 0.94 respectively (

1) This paper has demonstrated that the artificial neural network can be applied to determine the relationships between inputs (i.e. pH, collector, frother and F-Oil concentration, size percentage of feed passing 75 microns, moisture content, solid percentage, grade of Copper, Molybdenum, and Iron in feed) and outputs (i.e. Copper, and Molybdenum grades and their recoveries).

2) Feed forward ANN with 10-10-10-4 structure is capable of predicting copper and molybdenum grades and their recoveries, simultaneously. The optimum structure is determined by the trial and error procedure.

3) In the testing stage, the used model could estimate copper and molybdenum grades and their recoveries, satisfactorily. The correlation coefficient (R) values for testing sets were 0.93, 0.92 and 0.92, 0.94 in copper, molybdenum grades and their recoveries predictions, respectively, the results of which were quite satisfactory.

4) The proposed method can be applied as an expert system in copper flotation to evaluate the operational conditions for the expected grade and recovery without spending extra time and cost.

The authors would like to thank the Sarcheshmeh Copper Concentration Plant for supporting this research.

Ebrahim Allahkarami,Omid Salmani Nuri,Aliakbar Abdollahzadeh,Bahram Rezai,Mostafa Chegini, (2016) Estimation of Copper and Molybdenum Grades and Recoveries in the Industrial Flotation Plant Using the Artificial Neural Network. International Journal of Nonferrous Metallurgy,05,23-32. doi: 10.4236/ijnm.2016.53004