Predicting the Conversion Ratio for the Leaching of Celestite in

Article pubs.acs.org/IECR

Predicting the Conversion Ratio for the Leaching of Celestite in Sodium Carbonate Solution Using an Adaptive Neuro-Fuzzy Inference System Melih Iṅ al* Technical Education Faculty, Electronics and Computer Education, Kocaeli University, Umuttepe Campus 41380, Kocaeli, Turkey S Supporting Information *

ABSTRACT: In this study, an adaptive neuro-fuzzy inference system (ANFIS) was used to predict conversion kinetics as the percent ratio of SrSO4 to SrCO3 in sodium carbonate solution. The results of the ANFIS were compared to a previous study of multilayer perceptron (MLP) artificial neural networks (ANNs) that used the same data set. The ANFIS model showed proper fitting to the experimental data according to the mean absolute error (MAE) and determination coefficient (R2 value). The ANFIS model can easily determine the conversion ratio of SrSO4 to SrCO3. Hence, it is possible to predict the ratio without measuring parameters under different experiments. The Matlab program was used for all coding. Moreover, a user interface program was developed in Simulink to simulate the ANFIS model for entering combinations of input parameters. The ANFIS output showed a satisfactory result in terms of overall performance.

1. INTRODUCTION Artificial intelligence (AI) techniques such as artificial neural networks (ANNs), fuzzy logic, and especially their combination, adaptive neuro-fuzzy inference system (ANFIS), are commonly used in different disciplines for modeling experimental data. Razzak stated that the modeling of poorly defined and uncertain systems that are not well-suited for conventional mathematical approaches can be solved using fuzzy inference systems.1 Sometimes, the system might not be uncertain, but the collected data can be caused to be uncertain. Prosser determined the effects of more than 30 variables in his review article on uncertainty in the collection and interpretation of leaching data. Equations from different models fit well for different values of the same parameter.2 This means that it would be better to use artificial intelligence to match the effects of the different models’ equations according to the values of the same parameter. ANFIS models have been applied to different disciplines. Some examples of these models that have most recently been published are as follows: ANFIS, unlike FIS, automatically produces adequate rules with respect to input and output data and takes advantage of the learning capability of neural networks. Moreover, the main point of the fuzzy inference system (FIS) approach is to determine fuzzy if−then rules from experts’ opinions.3 Saghaei and Didehkhani used the concept of neural networks and especially ANFIS, which are efficient models for function approximation, clustering, and pattern recognition.4 Bingöl et al. applied comparison of a multiple linear regression (MLR) and ANFIS for modeling the batch sorption process of Cu(II) onto date palm seeds. The experimental and model outputs displayed acceptable results for MLR and ANFIS. It was determined that ANFIS can be effectively used to predict the sorption of Cu(II) onto date palm seeds.5 Razzak et al. applied the both ANN and ANFIS modeling techniques to study the radial and axial solids holdup distributions in a liquid−solid circulating fluidized bed © 2014 American Chemical Society

(LSCFB) system. They analyzed the effects of different operating parameters such as auxiliary and primary liquid velocities and superficial solids velocity on the radial phase distribution at different axial positions of the riser in the developed models. The models gave good agreement with the experimental data.6 ANN and ANFIS were compared to model environmental indices of strawberry production on the basis of input materials. The results revealed that ANFIS models, because they employ fuzzy rules, are able to predict 10 environmental indices with minimum error and the highest accuracy.7 Some studies of the leaching of celestite are presented as follows: Castillejos et al. investigated the effects of the variables stirring speed, particle size, Na2CO3 and Na2SO4 concentrations, temperature, solution pH, and solid/liquid ratio on the leaching of celestite (SrSO4) particulate samples with Na2CO3 solutions. The model takes into account the fact that, under the conditions investigated, the Na2CO3 concentration changes substantially during the course of the reaction.8 Erdemoğlu and Canbazoğlu studied the effects of variables for leaching temperature, retention time, and solid-to-liquid ratio and the effects of variables for precipitation−carbonation time, temperature, amount of carbonating agent, and addition of oxygen to carbon dioxide in the leaching of strontium sulfide (SrS) with water. They also compared Na2CO3 with CO2 as a carbonating agent for the precipitation of SrCO3 from leach solution. In their study, each experiment was repeated at least three times, and the arithmetic averages of the results were used to evaluate the experiments. It was concluded that sodium carbonate provides a higher precipitation rate and more strontium recovery than its carbon dioxide counterpart.9 Owusu and Received: Revised: Accepted: Published: 4975

January 16, 2014 February 19, 2014 February 27, 2014 February 27, 2014 dx.doi.org/10.1021/ie500225a | Ind. Eng. Chem. Res. 2014, 53, 4975−4980

Industrial & Engineering Chemistry Research

Article

Litz explained the significance of strontium carbonate (SrCO3) as an industrial reagent and its commercial applications. In the process of water leaching of SrS, they achieved a 92% leaching efficiency for strontium.10 Aydoğan et al. examined the leaching of celestite (SrSO4) for producing SrCl2, which is the main source for SrCO3, in hydrochloric acid with BaCl2 solution. They stated that the reaction of celestite conforms to the shrinking-core model.11 Torres et al. studied the behavior of SrSO4, SrCO3, and Al2O3 mixtures at high temperatures. They found that the samples of mixtures of SrCO3 and SrSO4 that were sintered at 1300 °C had a dense microstructure free of porosity.12 In this article, recently published works on ANFIS and leaching of celestite are summarized. The rest of the article is organized as follows: Section 2 provides a brief description of materials and methods, and section 3 describes the results of the ANFIS model and compares them with ANN13 results. Finally, section 4 discusses the conclusions and outcomes of the study.

2. MATERIALS AND METHODS ANFIS has a feed-forward neural network structure in which each layer is a neuro-fuzzy system component, as developed by

Figure 3. Regression results of the training stage. n

2

R =1−

Figure 2. Sample of a Gaussian membership function.

Jang et al.14−16 In this study, the performances were statistically measured in terms of the mean absolute error (MAE) and determination coefficient (R2) as follows 1 n

n

∑ abs(CONVpred − CONVexp) i=1

n

∑i = 1 (CONVpred − AvCONVexp)2

(2)

where n is the number of samples; CONVpred and CONVexp are the values of predicted and experimental conversion ratios, respectively; and AvCONVexp is the average value of the experimental conversion ratio. The experimental data used in the training and testing stages of ANFIS model are presented in the Supporting Information (Table S1). The experimental data were first used in a different fashion for the experimental work of Bingol et al.13 The experimental data were prepared by Bingol et al.13 as follows: Leaching experiments were conducted in a 1-L Pyrex beaker with a rubber cover in a thermostatically controlled water bath equipped with a thermometer. Moreover, a Heidolph Mark RZR 2021 model mechanical stirrer with a propeller was used for stirring. In this study, training and testing data were separated to represent all different sections of experimental data. Then, the first four columns of data, which are inputs of the ANFIS model, were normalized by dividing by 10000, 10000, 10000, and 1000, respectively. Because the last column is target values of the ANFIS model as measured experimental data, they were used in their original values. The data listed in the Supporting Information (Table S1) were first used as different input− output combinations in another study for developing an ANN model.13 The results of these two models are compared in the following section. The inputs of the ANN model,13 which has the structure of a feed-forward multilayer perceptron (MLP), are experimental conversion (%), stirring speed (rpm), mole ratio (Na2CO3/ SrSO4), particle size (μm), and temperature (°C); output is the measured conversion ratio of SrSO4 to SrCO3. Because there are five inputs, five neurons are used in the input layer. Also, two hidden layers with eight neurons each and one neuron for the output layer are used in the ANN model. In the ANN structure, the input layer has a linear transfer function, and the hidden and output layers have a tangent hyperbolic function.

Figure 1. Schematic diagram of the ANFIS model.

MAE =

∑i = 1 (CONVpred − CONVexp)2

(1) 4976

dx.doi.org/10.1021/ie500225a | Ind. Eng. Chem. Res. 2014, 53, 4975−4980


Article

Figure 4. Three-dimensional plots of inputs in the trained ANFIS model.

algorithm, the Gaussian function was used. A set of random values distributed uniformly between −0.1 and +0.1 was used to initialize the weights of the networks, whereas tuples were scaled between −1.0 and +1.0 for inputs and between −0.8 and +0.8 for outputs before training. Random and sequential training strategies were followed.13 A schematic diagram of the Sugeno type ANFIS model is shown in Figure 1. Because the structure of the ANFIS model has four inputs and each input has three Gaussian membership functions (gaussmfs), the ANFIS model has a total of 81 fuzzy rules (3gaussmfs4inputs = 81). These three gaussmfs can be defined as “SMALL”, “MEDIUM”, and “LARGE” by analogy with an earlier study.17 The 81 fuzzy rules produced by the ANFIS model for predicting the conversion ratio (CONVpred) in terms of input parameters are represented as follows: (1) IF (Leaching time is SMALL) AND (Stirring speed is SMALL) AND (Particle size is SMALL) AND (Temperature is SMALL) THEN (CONVpred = p1 × Leaching time + q1 × Stirring speed + r1 × Particle size + s1 × Temperature + t1) (2) IF (Leaching time is SMALL) AND (Stirring speed is SMALL) AND (Particle size is SMALL) AND (Temperature is MEDIUM) THEN (CONVpred = p2 × Leaching time + q2 × Stirring speed + r2 × Particle size + s2 × Temperature + t2)

Figure 5. Regression results of the testing stage.

The ANN model13 was trained with the use of extended delta-bar-delta (EDBD) learning algorithm. In the EDBD 4977



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Figure 6. Simulink model of the ANFIS conversion ratio.

training stage, three-dimensional surface views of the inputs are shown according to leaching time and conversion ratio. It can be said that the ANFIS model would be fit to the kinetic analysis of the conversion procedure. These procedures have been well studied in the mechanochemical processing of celestite.13 Moreover, the nonlinear transition of the conversion kinetics of SrSO4 to SrCO3 in sodium carbonate solution can be modeled by ANFIS, as can be clearly seen in Figure 4. In Figure 4, normalized values of the inputs are shown. Therefore, when these values are examined, they must be multiplied by their normalization factors, such as 10000 for the first three inputs and 1000 for the fourth input, as shown in the Supporting Information (Table S1). After the training stage, the test data were applied to the ANFIS model to determine the generalization ability of the model. In the testing stage of the ANFIS model, MAE and R2 were calculated as 3.0317 and 0.98895, respectively. The regression results are shown in Figure 5 for the test data. The Sugeno-type ANFIS model was also defined as a Simulink model to examine different input and output combinations. In Figure 6, a Simulink model of the ANFIS conversion ratio for evaluating any input combination of the system is illustrated. Hence, different circumstances that are not represented in the database can be examined by this Simulink model of the ANFIS conversion ratio. The experimental conversion ratio, which is the last parameter of the database, was tested for determination by the Simulink model of the ANFIS.

(3) IF (Leaching time is SMALL) AND (Stirring speed is SMALL) AND (Particle size is SMALL) AND (Temperature is LARGE) THEN (CONVpred = p3 × Leaching time + q3 × Stirring speed + r3 × Particle size + s3 × Temperature + t3) ... (79) IF (Leaching time is LARGE) AND (Stirring speed is LARGE) AND (Particle size is LARGE) AND (Temperature is SMALL) THEN (CONVpred = p79 × Leaching time + q79 × Stirring speed + r79 × Particle size + s79 × Temperature + t79) (80) IF (Leaching time is LARGE) AND (Stirring speed is LARGE) AND (Particle size is LARGE) AND (Temperature is MEDIUM) THEN (CONVpred = p80 × Leaching time + q80 × Stirring speed + r80 × Particle size + s80 × Temperature + t80) (81) IF (Leaching time is LARGE) AND (Stirring speed is LARGE) AND (Particle size is LARGE) AND (Temperature is LARGE) THEN (CONVpred = p81 × Leaching time + q81 × Stirring speed + r81 × Particle size + s81 × Temperature + t81) where pi, qi, ri, si, and ti are adaptive parameters of the ANFIS model with i = [1, 2, ..., 81]. An illustration of the Gaussian membership function (gaussmf) of the temperature input is given in Figure 2. Because the lowest MAE was given with the gaussmf between other membership functions, it was used in the ANFIS model. Initially, an FIS was defined for training of the ANFIS model. In the training stage of the ANFIS model, MAE and R2 were calculated as 1.1878 and 0.99845, respectively. The regression result, which was evaluated by the “postreg” Matlab function, is shown in Figure 3. At the beginning of the training stage, the output of the ANFIS model was initially zero for all input combinations. Then, it converged for each state of the inputs as seen in Figure 4. In Figure 4, the first subplot is shown as an example of the initial circumstance of any parameters. After the

3. RESULTS AND DISCUSSION The results of the ANFIS model were compared to a study of multilayer perceptron (MLP) artificial neural network (ANN) in which the same data sets were used.13 The relationship between the data sets of both training and testing values was examined for the ANN13 and ANFIS models. The assessments of the target values of the experimental conversion ratio and the 4978



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4. CONCLUSIONS In this study, an ANFIS model was used to predict the experimental conversion ratio of SrSO4 to SrCO3 in sodium carbonate solution. The results of the ANFIS model were compared to a previous study of an ANN that used the same data set. According to the lower correlation coefficient, the ANFIS model shows better fitting to the experimental conversion ratio data than the earlier model. The nonlinear transition of the conversion kinetics of SrSO4 to SrCO3 in sodium carbonate solution is properly modeled by ANFIS. It can be concluded that the ANFIS model is a robust alternative for predicting the experimental conversion ratio of SrSO4 to SrCO3 in sodium carbonate solution. Moreover, the nonlinear activities of the conversion ratio of the system are accurately predicted by the proposed ANFIS model.

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ASSOCIATED CONTENT

S Supporting Information *

Training and testing data of the ANFIS model (Table S1) and predicted values of the ANN13 and ANFIS models (Table S2). This material is available free of charge via the Internet at http://pubs.acs.org.

Figure 7. Target and predicted conversion ratios.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +902623032241. Fax: +902623032203. E-mail: melih. [email protected], [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author is grateful to Dr. Deniz Bingöl for her valuable discussion made in an earlier phase of the manuscript. REFERENCES

(1) Razzak, S. A. Hydrodynamics modeling of an LSCFB riser using ANFIS methodology: Effects of particle shape and size. Chem. Eng. J. 2012, 195−196, 49. (2) Prosser, A. P. Review of uncertainty in the collection and interpretation of leaching data. Hydrometallurgy 1996, 41, 119. (3) Güneri, A. F.; Ertay, T.; Yücel, A. An approach based on ANFIS input selection and modeling for supplier selection problem. Expert Syst. Appl. 2011, 38, 14907. (4) Saghaei, A.; Didehkhani, H. Developing an integrated model for the evaluation and selection of six sigma projects based on ANFIS and fuzzy goal programming. Expert Syst. Appl. 2011, 38, 721. (5) Bingö l, D.; Iṅ al, M.; Ç etintaş, S. Evaluation of Copper Biosorption onto Date Palm (Phoenix dactylifera L.) Seeds with MLR and ANFIS Models. Ind. Eng. Chem. Res. 2013, 52 (12), 4429. (6) Razzak, S. A.; Rahman, S. M.; Hossain, M. M.; Zhu, J. Artificial Neural Network and Neuro-Fuzzy Methodology for Phase Distribution Modeling of a Liquid−Solid Circulating Fluidized Bed Riser. Ind. Eng. Chem. Res. 2012, 51 (38), 12497. (7) Khoshnevisan, B.; Rafiee, S.; Mousazadeh, H. Environmental impact assessment of open field and greenhouse strawberry production. Eur. J. Agron. 2013, 50, 29. (8) Castillejos, A. H. E.; de la Cruz del, F. P. B.; Uribe, A. S. The direct conversion of celestite to strontium carbonate in sodium carbonate aqueous media. Hydrometallurgy 1996, 40, 207. (9) Erdemoğlu, M.; Canbazoğlu, M. The leaching of SrS with water and the precipitation of SrCO3 from leach solution by different carbonating agents. Hydrometallurgy 1998, 49, 135. (10) Owusu, G.; Litz, J. E. Water leaching of SrS and precipitation of SrCO3 using carbon dioxide as the precipitating agent. Hydrometallurgy 2000, 57, 23.

Figure 8. Absolute errors of both the ANFIS and ANN models.

predictions of the ANFIS and ANN13 models are shown in Figure 7. It can be said that the ANFIS model gives good agreement with the experimental data except for the ninth data index. Because the ninth data index shows a large difference for the ANFIS model, it would be suitable to show the absolute errors of both the ANFIS and ANN models according to the target values of the experimental conversion ratio, as in Figure 8. Moreover, the absolute errors of both the ANFIS and ANN models are reported in the Supporting Information (Table S2). Furthermore, the predicted values of the experimental conversion ratio for both the ANFIS and ANN13 models are given in the Supporting Information (Table S2), along with the MAE and R2 values. The values of MAE and R2 of the data for the ANFIS model were calculated as 1.88 and 0.9954, respectively, whereas they were 2.05 and 0.9949, respectively, for the ANN model.13 According to the lower R2 value, the ANFIS model shows better fitting to the experimental conversion ratio data than does the ANN model.13 Additionally, the MAE values of the ANFIS model were smaller than that of the ANN model.13 Therefore, the ANFIS model was able to predict the experimental conversion ratio with minor MAE. 4979



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(11) Aydoğan, S.; Erdemoğlu, M.; Aras, A.; Uçar, G.; Ö zkan, A. Dissolution kinetics of celestite (SrSO4) in HCl solution with BaCl2. Hydrometallurgy 2006, 84, 239. (12) Torres, J. T.; Almanza, J. R.; Flores, A. V.; de J. Castro, M. R.; Herrera, M. T. Thermal behavior of SrSO4−SrCO3 and SrSO4− SrCO3−Al2O3 mixtures. Mater. Charact. 2007, 58, 859. (13) Bingol, D.; Aydogan, S.; Gultekin, S. S. Neural model for the leaching of celestite in sodium carbonate solution. Chem. Eng. J. 2010, 165, 617. (14) Jang, J. S. R.; Sun, C. T.; Mizutani, E. Neuro-Fuzzy and Soft Computing, Prentice Hall: Upper Saddle River, NJ, 1997. (15) Jang, J. S. R. ANFIS: Adaptive network-based fuzzy inference systems. IEE Trans. Syst. Man. Cybern. 1993, 3, 665. (16) Jang, J. S. R. Self-learning fuzzy controllers based on temporal backpropagation. IEE Trans. Neural Networks 1992, 3, 714. (17) Iṅ al, M. Determination of dielectric properties of insulator materials by means of ANFIS: A comparative study. J. Mater. Process. Technol. 2008, 195, 34.

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Predicting the Conversion Ratio for the Leaching of Celestite in

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