Mineral flotation using microorganisms and/or their derived products is called “bioflotation.” This is a promising process due to its low environmental impact; however, it is also a very complicated process, due to its multidisciplinary character, involving mineralogy, chemistry, and biology. So, the optimization of this process is an important challenge. This study assessed the implementation of a quadratic model and an artificial neural network (ANN) for the optimization of hematite and quartz floatability and recovery. The flotation process was carried out using a biosurfactant extracted from the Rhodococcus erythropolis bacteria. Quadratic model was adjusted by genetic algorithms techniques and validated using analysis of variance (ANOVA). Multilayered feed-forward networks were trained using a backpropagation algorithm, implemented using MATLAB R2017a. The topologies of the neural networks included 2 neurons in the input layer and 1 neuron in the output layer in both models, while the hidden layer varied according to the performance of the model. The results showed that the ANN model can predict the experimental results with good accuracy, when compared to quadratic model. Sensitivity analysis showed that the studied variables (pH and biosurfactant concentration) have an effect on the mineral recovery.

The mining industry has recently been facing different challenges that affect mineral processing, such as the depletion of high-grade ore and environmental regulations [1,2]. The first compels the mineral industry to process low grade ores, fine mineral particles, and flotation tailings to produce material suitable for a global market. Thus, it has become very important to develop appropriate and environmentally friendly technologies which complement the conventional techniques used for mineral concentration. In this context, biobeneficiation has been developed, which refers to the selective removal of undesirable mineral constituents from an ore through interaction with microorganisms and/or their metabolic products, thus enriching it with respect to the desired valuable minerals [3,4]. Bioflotation exploits differences in the surface characteristics of solids suspended in an aqueous medium, adjusting and controlling their surface energies and interfacial tensions [5,6] using microorganisms with hydrophobic properties [3,5,7,8]. In bioflotation, microbial cells and their by-products are used as collectors, depressors, and also as frothers. Their use is justified by environmental and technological factors, as mentioned by several authors [1,3,4,9–11]. According to these authors, the use of these bioreagents can improve mineral recovery. However, the adhesion of microbial cells onto mineral surfaces is strongly related to attractive and repulsive forces between the bacterial wall and the mineral surface and the biomolecules that are responsible for the adhesion and selective floatability of the minerals are surface active substances which are excreted or bound to the microorganism surface [12]; they are therefore known as biosurfactants. The application of these biosurfactants in mineral flotation is a recent development and some relevant studies can be found, as for example, the study of a biosurfactant extracted from Lactobacillus pentosus used as a frother [13], the use of rhamnolipid as frother for the flotation of coal [14] and copper ore [15], the use of the biosurfactant produced by Pseudomonas aeruginosa on hematite [16], and the separation of copper from pyritic copper using a biosurfactant-producing mixotrophic bacterium [17].

In order to investigate such processes, several mathematical modelling can be applied. Response surface methodology (RSM) is a set of mathematical techniques that describe the relation between several independent variables (individually and through their cumulative interactions) and responses [18–20]. The RSM method is based on the fit of mathematical model (linear, square polynomial functions, etc.) to the experimental results generated from the designed experiment and the verification of the model obtained by means of statistical techniques [18,21].

Artificial intelligence modelling has been considered for prediction, control and optimization of various processes. Genetic algorithm (GA) is an artificial intelligence technique used in computing to find the optimum values of process parameters on feasible solution space. They are inspired in evolutionary techniques such as mutation, selection, and crossover to solve complex computational problems [22].

Other technique is artificial neural network (ANN). ANN-based software models allow for variable predictions based on input data. An ANN consists of a large number of simple elements called neurons. These neurons are generally arranged into three layers: input, hidden, and output (three-layer network) (see Fig. 1). Each neuron of the input layer receives information from the input (independent) variables. The hidden layer is fully connected to every neuron in the input and output layers, estimates the strengths of the relationships between variables, and contains activation functions that calculate the weights to be assigned to each variable in order to explore their effects. The output layer produces the predicted values.

Internally, weight and bias are adjusted by the training algorithm (backpropagation algorithm). During the training process, the backpropagation algorithm learns associations between a specified set of inputs and outputs [23]. The training process works as follows: first, the input values are propagated forward to the hidden layer, and then, sensitivities are propagated backward in order to minimize the error; at the end of the process, the weights are updated [24].

Neural models have previously been used in mineral processing, as reported by Zhang et al. [25] and Bhunia et al. [26]. Thus, this study aims not only to model hematite and quartz recovery (%) by the use of a neural model based on input variables (pH and concentrations), but also to determine the optimal conditions through response surface analysis.

These models (artificial-inspired) are powerful data modelling and optimization tools, which are capable to represent complex nonlinear relationships between independent variables and responses of a system.

Thus, this study is focused on the use of a biosurfactant extracted from the Rhodococcus erythropolis bacteria in the flotation of hematite and quartz. Two techniques using artificial intelligence (GA and ANN) were considered, in order to analyze and interpret the effects on bioflotation process. Comparison between the models was performed clarifying optimal conditions.

2Materials and methods2.1Sample preparationA pure quartz sample and a hematite sample (92% Fe2O3) were provided by a local supplier (Belo Horizonte, Minas Gerais State) to be used in this study. The samples were crushed and screened to −3mm. Then, the samples were dry-ground in a porcelain mortar and wet-screened. The desired size fraction (+75–106μm) was used for flotation studies. Next, the quartz sample was washed with a KOH (0.1mol/L) solution to remove any impurities present on the surface and then the sample was washed several times with double-distilled water until the pH suspension maintained its initial pH. Finally, the quartz and hematite samples were dried and stored in a desiccator.

2.2Microorganisms, media, growth and biosurfactant extractionThe R. erythropolis strain was supplied by the Chemical, Biological and Agricultural Pluridisciplinary Research Center (CPQBA) and was developed in a tryptic soy broth (TSB)-containing solid medium. Stocks of the bacteria were prepared frequently using this medium in Petri plates and stored in a freezer at 12°C. Afterwards, the bacterial cells were separated from the culture by centrifugation at 4500rpm for 8min and then re-suspended twice with deionized water. The bacterial concentration was estimated based on the optical density.

Crude biosurfactant extraction was performed following the procedure of Moreau et al. [27]. The centrifuged cells were re-suspended in ethanol (500mL for 1L of broth) and autoclaved at 1atm and 121°C for 20min. The insoluble part was removed by centrifugation (4500rpm), and then the soluble part was dried at 40°C for 24h. After this time, this material was dissolved in water and the insoluble part was separated from the soluble part by centrifugation (4500rpm) and filtration (25μm). The final solution is the crude biosurfactant solution and the biosurfactant concentration was determined by dry-weight measurement.

2.3Microflotation experimentsThe floatability of the minerals was evaluated in a modified Hallimond tube. One gram of the mineral was added to a 0.16L solution of known biosurfactant concentration. The mineral was conditioned with the biosurfactant at a desired pH inside the Hallimond tube under constant stirring for 5min. Finally, the microflotation tests were carried out using an air flow of 25mL/min for 2min. The settled and floated fractions were carefully separated, washed, dried, and weighed. The floatability was then calculated as the ratio of floated and non-floated mineral amounts to the total sample weight.

2.4Process modelling2.4.1Response surface methodology (RSM) and genetic algorithm (GA)Response surface methodology (RSM) is an empirical statistical and mathematical techniques employed for multiple regressive analysis using predictions from quadratic model. The statistical significant (≤p≤0.05) of model was developed using analysis of variance (ANOVA). ANOVA compares the variation due to the deviations from the measurements of generated responses. From this comparison, it is possible to assess the regression used to predict responses, including the sources of experimental variance.

Performance of the process was assessed by analysing the predicted data which depend on the input variables and their relationship [21]. A quadratic model was used to describe hematite and quartz recovery, as seen in Eq. (1).

where xi and xj are variables (i and j range from 1 to k); β0,βj,βjj,βij are the model intercept, linear, quadratic and interaction coefficients, respectively [21,28].The genetic algorithms (GAs) were used in order to estimate the coefficients from quadratic model. GA is an adaptive heuristic search algorithm inspired by the evolutionary ideas of natural selection and genetic. This strategy adjusts the parameters based on dependent and independent variables and has gained popularity over traditional optimization techniques last years. Firstly, an initial population of chromosomes is generated randomly as initial conditions and the chromosomes evolved in next iterations (generations) had a better fitness value when compared to their predecessors. To reproduce new generations, it was implemented different genetic operators. The objective function was minimizing sum squared error (errors between experimental and predicted data). The development of this strategy was performed using MATLAB R2017a.

The significance of regression coefficients was evaluated by F-test and the model adequacies were checked in terms of the values of R2.

2.5Development of neural network modelArtificial neural networks perform a nonlinear mapping between inputs and outputs. The fact that ANNs require minimal prior knowledge of the system makes them an alternative method for the generation of process models. The ANN employed here is a feed forward multilayer perceptron with three independent layers (input, hidden and output). Input neurons receive the input variable (pH and biosurfactant concentrations in mg/L) values and store the scaled input values. Meanwhile, hematite and quartz recovery (%) were the output layer variables. The quantity of neurons in the hidden layer was defined by the smallest error criterion and a constant number of effective parameters. The activation functions in the hidden layer were logistic (logsig) and hyperbolic tangent sigmoid transfer functions (tansig) and the output layer used a linear transfer function (purelin).

The training was implemented in MATLAB R2017a using some algorithms to optimize parameters (weights and bias) using a gradient descent approach, based on the negative of the error gradient. The training algorithm makes use of two more parameters, the learning rate and momentum coefficient. Both of these parameters were optimized along with the number of hidden layer neurons available. So, several algorithms were tested: adjusting only the momentum coefficient (traingdm), adjusting only the adaptive learning rate (traingda), and adjusting both (traingdx).

Approaches based on the quasi-Newton method of adjusting the parameters were tested, such as the Levenberg–Marquardt algorithm (trainlm), and used in conjunction with Bayesian regularization (trainbr). The stop criterion was based on the minimum test error, even though the training set error may continue to decrease with further training. Table 1 presents a summary of all the algorithms used in this work. Finally, the quality of the training process was assessed using the total sum squared error (SSE) as a criterion, comparing the observed and predicted values of the network (Eq. (2)).

Different training algorithms used in this work.

Training function | Description |
---|---|

Trainbr | Updates the weight and bias values according to Levenberg–Marquardt optimization. It minimizes a combination of squared errors and weights and then determines the correct combination so as to produce a network that generalizes well. The process is called Bayesian regularization. |

Traingdx | Updates weight and bias values according to gradient descent momentum and an adaptive learning rate. |

Traindga | Updates weight and bias values according to gradient descent with adaptive learning rate. |

Traindgm | Updates weight and bias values according to gradient descent with momentum. |

Trainlm | Updates weight and bias values according to Levenberg–Marquardt optimization. |

Trainoss | Updates weight and bias values according to the one step secant method. |

The coefficient of determination (R2) is one measure of how well a model can predict the data, as expressed in Eq. (3).

3Results and discussionIn order to understand the fundamentals of the bioflotation process, it is important to characterize the biosurfactant. The bacterial cell-wall is composed of several macromolecules such as peptidoglycans, lipopolysaccharides, lipoproteins, and teichoic, mycolic, and teichuronic acids [29]. There are several methods for estimating the cell-wall composition of a microorganism, including X-ray methods, Fourier transform infrared spectroscopy (FTIR), and biochemical analysis. Table 2 presents the results of the biosurfactant biochemical characterization in terms of protein, carbohydrate, and lipid content by the biuret, antrona, and Bligh and Dyer methods, respectively. We observe that protein is present in a high proportion, which explains the hydrophobic character of the material. According to several authors, the hydrophobic character of a microorganism/metabolic product is determined by its protein content, while the hydrophilic character is related to its polysaccharide content [11,30–32].

Fig. 2 presents an FTIR spectrum of the biosurfactant, showing its main functional groups. There is a broad band centred around 3417cm−1 that may be attributed to hydrogen bonded (O–OH) hydroxyl groups and N–H amine groups. The absorption bands in the range of 1630cm−1 may be assigned to alkene (C=C), carbonyl (C=O), and C=N groups belonging to bacterial cell proteins. The bands between 1300 and 1400cm−1 are characteristic of the CH3 and CH2 stretching modes of hydrocarbon chains. The band at 1080cm−1 represents the asymmetric stretching of phosphate groups in teichoic acids and complex vibration modes of polysaccharides, C–O esters, or carboxylate acid vibrations [33,34].

The floatability of hematite as a function of pH and biosurfactant concentration is shown in Fig. 3. In flotation processes, the pH is the most relevant factor because it affects the activation of the functional groups of the biosurfactant and of the mineral surface. The highest floatability value was attained in an acidic media, achieving 98% floatability at pH 3 using 150mg/L of biosurfactant. In neutral and basic media, the floatability of hematite was too small to be considered.

Moreover, the higher the biosurfactant concentration, the higher the hematite floatability; this effect was clearly observed at low concentrations (25 and 50mg/L). At higher concentrations, however, the floatability seemed to be constant, e.g. at pH 3, the hematite floatability achieved values of 98% at 75, 100, 125, and 150mg/L.

3.2Flotation of quartz using the biosurfactantFig. 4 shows the quartz floatability using the crude biosurfactant extracted from the R. erythropolis by hot ethanol. As in the previous experiments, the floatability of quartz was also affected by the pH and biosurfactant concentration, presenting similar behaviour with high floatability values in an acidic medium and the higher the biosurfactant concentration, the higher the floatability. The most striking difference is that the highest quartz floatability reached at pH 3 and 150mg/L was around 33%.

The previous experiments demonstrated that the biosurfactant has a higher selectivity for hematite. This means that the molecules of the biosurfactant prefer to adsorb onto hematite particles more than quartz particles.

In order to demonstrate the selectivity of the biosurfactant, some flotation tests dealing with hematite-quartz systems were developed (Table 3). The experiments were carried out at the optimum conditions, which were determined previously; the mineral system was composed of hematite and quartz in a 1:1 ratio.

According to these results, we can conclude that the biosurfactant has a great selectivity for hematite and thus it is possible to use this kind of biomolecule in the processing of iron ore.

3.3Response surface MethodologyThe experiments were performed, in order to find the optimum combination of parameters for maximum recovery of hematite and quartz (Table 4). The process parameters (independent variables) selected for optimization were pH and biosurfactant concentration (mg/L).

Combination of two variables (pH and biosurfactant concentration) and their responses (experimental and predicted) for hematite and quartz recovery.

Run | pH | BS (mg/L) | Hematite recovery (%) | Quartz recovery (%) | ||||
---|---|---|---|---|---|---|---|---|

YEXP | YRSM | YANN | YEXP | YRSM | YANN | |||

1 | 3 | 0 | 4 | 36.18 | 6.27 | 0.90 | 7.34 | 1.96 |

2 | 3 | 25 | 83.25 | 60.71 | 78.49 | 10.80 | 12.91 | 8.73 |

3 | 3 | 50 | 93.19 | 80.35 | 94.73 | 15.10 | 17.68 | 16.22 |

4 | 3 | 75 | 97.99 | 95.13 | 97.74 | 22.81 | 21.66 | 23.20 |

5 | 3 | 100 | 97.88 | 105.02 | 98.33 | 27.68 | 24.85 | 28.35 |

6 | 3 | 125 | 97.79 | 110.05 | 98.5 | 33.63 | 27.25 | 31.01 |

7 | 3 | 150 | 98.19 | 110.19 | 98.6 | 30.30 | 28.85 | 31.53 |

8 | 5 | 0 | 4.25 | 12.87 | −1.16 | 1.35 | 0.26 | 0.98 |

9 | 5 | 25 | 31.25 | 34.18 | 42.08 | 5.96 | 4.84 | 6.37 |

10 | 5 | 50 | 73.24 | 50.62 | 63.86 | 9.95 | 8.63 | 10.11 |

11 | 5 | 75 | 73.92 | 62.18 | 78.00 | 12.92 | 11.62 | 11.78 |

12 | 5 | 100 | 84.93 | 68.87 | 83.91 | 11.65 | 13.83 | 11.99 |

13 | 5 | 125 | 85.74 | 70.68 | 85.77 | 10.49 | 15.24 | 11.70 |

14 | 5 | 150 | 86.38 | 67.62 | 86.35 | 11.78 | 15.86 | 11.53 |

15 | 7 | 0 | 3.60 | −1.52 | 5.65 | 1.20 | −2.87 | 1.41 |

16 | 7 | 25 | 19.6 | 16.59 | 21.25 | 2.81 | 0.73 | 3.10 |

17 | 7 | 50 | 23.63 | 29.82 | 24.23 | 3.06 | 3.53 | 3.93 |

18 | 7 | 75 | 29.68 | 38.17 | 24.92 | 4.28 | 5.54 | 4.39 |

19 | 7 | 100 | 27.79 | 41.65 | 25.31 | 5.47 | 6.76 | 4.70 |

20 | 7 | 125 | 26.67 | 40.25 | 25.95 | 4.57 | 7.19 | 4.95 |

21 | 7 | 150 | 23.18 | 33.98 | 27.76 | 4.96 | 6.82 | 5.16 |

22 | 9 | 0 | 4.45 | −6.98 | 5.37 | 1.00 | −2.04 | 0.12 |

23 | 9 | 25 | 10.88 | 7.91 | 12.2 | 2.16 | 0.57 | 1.64 |

24 | 9 | 50 | 12.33 | 17.93 | 13.69 | 2.95 | 2.39 | 2.65 |

25 | 9 | 75 | 16.29 | 23.07 | 14.26 | 3.99 | 3.42 | 3.29 |

26 | 9 | 100 | 16.98 | 23.34 | 14.68 | 4.30 | 3.65 | 3.66 |

27 | 9 | 125 | 16.67 | 18.73 | 15.08 | 3.89 | 3.09 | 3.85 |

28 | 9 | 150 | 13.96 | 9.25 | 15.50 | 3.99 | 1.74 | 3.93 |

29 | 11 | 0 | 3.05 | −3.52 | 4.36 | 1.15 | 2.75 | 1.63 |

30 | 11 | 25 | 7.30 | 8.17 | 7.60 | 2.01 | 4.37 | 2.63 |

31 | 11 | 50 | 8.23 | 14.97 | 8.64 | 3.08 | 5.21 | 3.20 |

32 | 11 | 75 | 12.21 | 16.91 | 9.32 | 2.45 | 5.25 | 3.50 |

33 | 11 | 100 | 10.59 | 13.96 | 9.94 | 5.01 | 4.50 | 3.62 |

34 | 11 | 125 | 11.47 | 6.15 | 10.58 | 3.00 | 2.95 | 3.65 |

35 | 11 | 150 | 8.485 | −6.55 | 11.24 | 3.55 | 0.62 | 3.62 |

The quadratic models relating the hematite (RHem) and quartz (RQtz) recovery with the independent parameters namely pH and biosurfactant concentration are shown in Eqs. (4) and (5), respectively. These models were used as the fitness function. For hematite recovery (RHem), the parameters of GA were population size of 5000, generations of 7000, mutation of 0.2 and crossover of 0.8. For quartz recovery (RQtz), the parameters of GA were population size of 5000, generations of 9000, mutation of 0.4 and crossover of 0.7. The following constraints were applied:

This technique always searches by solutions in global optimal, avoiding inappropriate responses.

The adequacy of the models was tested by ANOVA (Table 5) and the results indicated that the equation adequately represented the relationship between the independent variables and responses.

Analysis of variance (ANOVA) for the hematite (RHem) and quartz (RQzt) recovery (%).

Source of variation | d.f. | SS | MS | F-value | ||||
---|---|---|---|---|---|---|---|---|

RHem | RQzt | RHem | RQzt | RHem | RQzt | RHem | RQzt | |

Regression | 6 | 6 | 78,844.30 | 3177.90 | 13,140.72 | 529.60 | 74.64 | 62.60 |

Residual | 28 | 28 | 4929.50 | 237.04 | 176.05 | 8.460 | ||

Total | 34 | 34 | 83,773.80 | 3414.91 |

RHem: F6;28;0.05=2.45; correlation coefficient: R2=94.12.

RQzt: F6;28;0.05=2.45; correlation coefficient: R2=93.06.

The ANOVA results for RHem and RQzt show F-value of 74.64 and 62.60, which suggests that the variability in hematite and quartz recovery can be adequately predicted by the RSM model. The values of R2 were calculated to be 0.9412 and 0.9306 (respectively), describing a compatibility with experimental data. The data predictions are showed in Table 5.

Fig. 5a shows the regression plot of hematite recovery (%) experimental and predicted. Fig. 5b shows the regression plot of quartz recovery (%) experimental and predicted. The data points on these plots lie, reasonably, near to a straight line, lending support to the conclusion that experimental variables have the significant effects and that the underlying assumptions of the analysis are satisfied.

By supplying the models with conditions of variables, it was possible to visualize the interactions between independent variables over dependent variable using response surface plots, as seen in Fig. 6.

Response surface plots show the pH and biosurfactant concentration effects by varying from 3 to 11 and from 0 to 150mg/L. The optimum conditions for recovery of hematite consist of a pH between 3 and 5 and a biosurfactant concentration between 50 and 150mg/L. While for quartz model the maximum value is not reached. This is a good result, because application in hematite-quartz bioflotation system with a good selectivity is promoted (results showed in Table 3).

3.4Neural network modelNeural network-based modelling of the bioflotation process using experimental data was used to demonstrate that the hematite and quartz recovery are functions of pH and biosurfactant concentration. The experimental data were collected during the study in duplicate and the average between the two measurements was used. The dataset was randomly split into sets of training data (65%) and testing data (35%) and normalized in the range [–1,1]. Since there was no theoretical principle used to determine the proper network topology, the number of hidden neurons was chosen using a cross validation technique to obtain the best result.

The number of neurons in the hidden layer was varied from 4 to 11 (Table 6) and the network was trained and tested after each addition of a neuron. All the simulation scenarios were proposed using two input neurons corresponding to pH and biosurfactant concentration (mg/L). The output layer was hematite and quartz recovery (%), activated by a purelin function.

Results of the neural models with varying number of neurons in the hidden layer, different activation functions, and training algorithms.

Neurons in hidden layer | Activation function | Training algorithm | SSE | R2 | A | B |
---|---|---|---|---|---|---|

Hematite recovery model | ||||||

5 | logsig | traingdx | 1.100 | 0.986 | 0.97 | 1.10 |

5 | logsig | trainbr | 0.315 | 0.997 | 0.99 | 0.24 |

5 | tansig | trainbr | 0.261 | 0.998 | 1.00 | 0.16 |

5 | logsig | trainlm | 0.233 | 0.998 | 1.00 | 0.12 |

6 | tansig | traingdx | 1.240 | 0.984 | 0.97 | 1.20 |

6 | tansig | trainoss | 0.369 | 0.996 | 0.99 | 0.32 |

10 | tansig | trainbr | 0.196 | 0.998 | 1.00 | 0.09 |

10 | tansig | trainlm | 0.114 | 0.999 | 1.00 | −10E−3 |

10 | logsig | trainlm | 0.114 | 1.000 | 1.00 | −2×10E−3 |

10 | logsig | trainoss | 0.252 | 0.998 | 1.00 | 0.04 |

10 | logsig | traingda | 3.660 | 0.951 | 0.90 | 4.40 |

10 | tansig | traingda | 1.310 | 0.983 | 0.97 | 1.60 |

9 | tansig | traingdm | 3.800 | 0.948 | 0.90 | 3.90 |

9 | logsig | traingdm | 1.360 | 0.982 | 0.96 | 1.40 |

9 | logsig | trainbr | 0.015 | 0.997 | 0.99 | 0.21 |

111111Quartz recovery model | ||||||

4 | logsig | traingdx | 0.856 | 0.981 | 0.96 | 0.26 |

4 | logsig | traingda | 3.900 | 0.872 | 0.76 | 1.60 |

4 | tansig | trainbr | 0.047 | 0.994 | 0.99 | 0.09 |

4 | logsig | traingdm | 1.690 | 0.952 | 0.90 | 0.76 |

4 | logsig | trainlm | 0.420 | 0.996 | 0.99 | 0.04 |

4 | tansig | trainlm | 0.378 | 0.998 | 1.00 | 0.02 |

9 | logsig | traingdx | 0.641 | 0.989 | 0.98 | 0.19 |

9 | logsig | traingda | 1.210 | 0.970 | 0.91 | 0.82 |

9 | logsig | trainlm | 0.331 | 0.999 | 1.00 | 0.02 |

9 | logsig | trainbr | 0.465 | 0.995 | 0.99 | 0.09 |

9 | tansig | trainbr | 0.482 | 0.994 | 0.99 | 0.04 |

11 | tansig | trainbr | 0.482 | 0.994 | 0.99 | 0.09 |

11 | tansig | trainlm | 0.325 | 0.999 | 1.00 | −8×10E−4 |

11 | logsig | traingdx | 0.566 | 0.991 | 0.98 | 0.12 |

11 | logsig | traingda | 0.935 | 0.979 | 0.96 | 0.18 |

Each ANN model generated a prediction regarding the analysis that was performed. Model 1 was adjusted to predict the hematite recovery and model 2 to predict the quartz recovery, both by bioflotation. Model 1 had five neurons in the hidden layer, tansig as activation function, trainbr as training algorithm (shown in Fig. 7a), and the value of the SSE was 0.261. The best configuration for model 2 had four neurons in the hidden layer, tansig as the activation function, trainbr as the training algorithm (shown in Fig. 7b), and an SSE value of 0.378. Despite several topologies showing satisfactory performance, the number of effective parameters of the chosen models were 18.1 and 12.5 for the hematite and quartz recovery models, respectively; the lowest values among the possible models were discarded due to overfitting. This happened because the Bayesian method (in the trainbr algorithm) develops a model with the smallest number of effective parameters by removing unnecessary parameters.

The models’ predictions are plotted as percentage of hematite and quartz recovery (%) in Fig. 8a and b, respectively. As shown in this figure, the predicted data from the models are in agreement with the observed data, showing R2 values of 0.998 and 0.994, respectively. The models are capable of accurately predicting the highest and lowest hematite and quartz recovery values. These results show that the bioflotation of two minerals may be assessed based on the functional relationship between pH and biosurfactant concentration produced by R. erythropolis.

Several studies previously performed by other researchers have also shown that ANN-based models can be used for optimization. Secato et al. [35] developed a neural model to predict biosurfactant production (mg/L) and dry weight (g/L) from sources of waste by Bacillus subtilis. The topology consisted of 2 neurons in the input layer corresponding to media components (glycerol and waste candy), 4 neurons in the hidden layer, and 1 output neuron, achieving R2 values of 0.998 and 0.982 for predictions of biosurfactant production and dry weight, respectively, showing the wide applicability of ANN models.

At present, there have been no reported applications of neural models to the bioflotation of hematite and quartz from biosurfactant produced by R. erythropolis nothing was reported, proving the importance of this study.

Table 7 presents the optimized parameter values (weights and bias) obtained from the training step with the trainbr algorithm. Thus, these models can be used to predict hematite and quartz recovery under different experimental conditions using the pH and biosurfactant concentration values.

Optimized parameters (weight and bias) of the ANN used to predict hematite and quartz recovery.

Parameters connecting the input and hidden neurons | Parameters connecting the input and hidden neurons | ||||
---|---|---|---|---|---|

wj1(i=1) | wj2(i=2) | θj | wj1(i=1) | bk | |

Hematite recovery model | |||||

j=1 | 2.6887 | 3.2980 | 6.1719 | 2.2197 | −2.5090 |

j=2 | 4.8102 | 4.6587 | 4.9593 | 0.2706 | |

j=3 | 4.1106 | −0.9099 | 1.9254 | −0.8386 | |

j=4 | 1.0129 | −1.3113 | 0.5067 | 1.2393 | |

j=5 | 1.0665 | −1.0131 | 0.1526 | −1.3443 | |

Quartz recovery model | |||||

j=1 | 1.8825 | 0.9750 | 0.9635 | −0.7121 | −0.4226 |

j=2 | 0.9659 | 0.8321 | 1.2158 | 1.4986 | |

j=3 | −1.6863 | 0.1914 | −1.8916 | 1.1197 | |

j=4 | 0.1546 | 0.1125 | 0.0178 | −0.1905 |

It is possible to plot surface curves from the trained parameters of the ANN and assess the nonlinear correlations. Sensitivity analyses of the effects of each independent variable on the system are shown in Fig. 9.

The response surfaces of the hematite and quartz recovery (%) were predicted by the neural model based on variations in pH and biosurfactant concentration (mg/L). It can be seen that the curves have a similar pattern for each proposed model.

As shown in Fig. 9, analysis from the neural model suggests the optimum conditions for recovery of hematite consist of a pH between 3 and 5 and a biosurfactant concentration between 50 and 150mg/L, also seen in quadratic model.

3.5Comparison of quadratic and ANN modelsBoth quadratic and ANN models were compared with their predictive capability, as can be seen in Table 4. Despite the models are different, the range indicating optimal recovery values is almost the same. The results showed that ANN models have higher modelling ability rather than quadratic models for hematite and quartz recovery, according to the observed results of regression plots and R2.

It is important to highlight that for application in hematite-quartz bioflotation system, the optimum values imply a higher selectivity for hematite, as mentioned above. Even at the beginning of the optimum region, the neural model is considered more suitable for optimizing the experimental conditions than quadratic model. This is because the ANN model can reach recovery values near to 100% (maximum possible experimental value), while quadratic model exceed that value.

4ConclusionsIn the current work, the biosurfactant extracted from Rhodococcus erythropolis bacteria was used as a collector of hematite and quartz. The biosurfactant presents a higher selectivity for hematite than for quartz, achieving flotation values near to 100%, while that of quartz was around 33%. This selectivity was corroborated by mineral system tests. In order to better understand the effects of the experimental conditions, two modelling approaches were assessed, quadratic (determined by GA) and ANN models in process optimization. This work found that ANN models were superior to the quadratic models, in terms of the coefficient of determination (R2) and error indices. The use of a neural model is an important tool for interpolation between experimental data. With this strategy, we were able to assess the model quality based on R2 and error index values of 0.99 and 0.280, respectively. To the best of our knowledge, this is the first report on the comparison between these strategies for hematite and quartz bioflotation. The use both of them models as an optimization tool would have a huge impact on industrial scale mineral processing.

Conflicts of interestThe authors declare no conflicts of interest.

The authors acknowledge CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), ITV-VALE, CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) and FAPERJ (Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro) for their financial funding.

*et al*.