Predicting Supercritical Extraction of St. John’s Wort by Simple Quadratic Polynomial Model and Adaptive NeuroFuzzy Inference System Firefly Algorithm
Article Information
Ramin Tahmasebi Boldaji*^{1}, Hossein Rajabi Kuyakhi^{2}
^{1}Department of Chemical Engineering, College of Engineering, University of Isfahan, P.O. Box 8174673441, Isfahan, Iran
^{2}Department of Chemical Engineering, University of Guilan, Rasht 4199613769 Iran
^{*}Corresponding Author: Ramin Tahmasebi Boldaji. Department of Chemical Engineering, College of Engineering, University of Isfahan, P.O. Box 8174673441, Isfahan, Iran
Received: 17 May 2021; Accepted: 25 May 2021; Published: 28 May 2021
Citation: Ramin Tahmasebi Boldaji, Hossein Rajabi Kuyakhi. Predicting Supercritical Extraction of St. John’s Wort by Simple Quadratic Polynomial Model and adaptive neurofuzzy inference system firefly algorithm: A comparison study. Journal of Analytical Techniques and Research 3 (2021): 1427.
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In this study, the applicability of the adaptive neurofuzzy inference system (ANFIS) and response surface methodology (RSM) was evaluated to forecasting the supercritical extraction of St. John’s Wort. In this case, the ANFIS model was optimized by the firefly algorithm (FFA) to develop the performance of the model. The accuracy of the models was investigated by comparing the result of the models with experimental data. The precision of the RSM model has been investigated using statistical analysis (Pvalue<0.05, Fvalue=148.13, R2=0,99 R2 Adjusted=0.98, R2 Predicted =0.96). The data transfer power was proved by the BoxCox plot. Also, the polynomial model shows that it is much simpler and easier than other complex models. The results show, the ANFISFFA with R2=0.99, RMSE=1.79 and AARD%=2.79 have a high capability of predicting the St. John’s Wort extraction amount
Keywords
St. John’s Wort, RSM, ANFIS, Supercritical fluid, Statistical analysis
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Article Details
1. Introduction
Hypericum perforatum L. (St. John’s wort) is a plant that grows in Asia, Europe, and the north of Africa [1,2]. Attention on this plant has risen because of the antidepressant and anticancer properties of its extraction [35]. Recently, Supercritical solvents morally use [6]. Different parameters such as temperature and solvent/plant ratio are effective on extraction efficiency [7]. Catchpole et al Extracted St. John’s wort using supercritical carbon dioxide at pressures of 250 and 300 bar and 313 K and at 300 K; and 323 K with ethanol as cosolvent [8]. Manila et al studied the effect of fluid density, time, and temperature of supercritical extraction for the separation of hyperforin and adhyperforin [9]. The results showed that the extraction is strongly dependent on the supercritical carbon dioxide density. Glisic et al investigated the extraction of hyperforin and adhyperforin from St. John's Wort (Hypericum perforatum L.) by supercritical carbon dioxide Supercritical extraction in a semibatch autoclave [10]. Extractions were investigated at three different pressures at temperatures of 313 and 323 K. The results showed that increasing the pressure increases the extraction.
In contrast to conventional methods, the interaction between variables can be determined by statistical techniques [1115]. In recent years, machine learning approaches is attracted researchers’ interest in the modeling of different processes [1622]. Kunjiappan et al [23] used Response surface methodology and adaptive neurofuzzy inference system to the analysis of ultrasoundassisted extraction of bioactive polyphenols from Garcinia indicia. Esfe and Kamyab [24] applied the ANN and RSMbased method to study the relative thermal conductivity (RTC) and relative viscosity (RV) of alumina nanoparticles (Al2O3 NPs) in water as nanofluid (NF). Geyikçi, et al [25] established response surface methodology (RSM) and artificial neural network (ANN) to predict the lead removal from industrial sludge.
In this work, the ANFIS, ANFISFFA and RSM were applied for the prediction of supercritical carbon dioxide extraction. The result obtained were compared with the experimental data. The models showed good agreement with the actual data. Statistical analysis confirmed the adequacy of the ANFIS FFA model.
2. Methods
2.1 Experimental data
In this investigation, St. John’s wort extractions yield were collected in a previous article [10,5] to develop an ANFIS model in analogy with the RSM model. The dried St. John’s Wort was obtained from southern Serbia. The particle size was about 400 µm and the moisture content was 7.55wt %. Supercritical extraction was performed in a semibatch Autoclave Engineers Screening System at 313 and 323 K and 10, 15 and 20 Mpa. To evaluate the ANFIS model performance the collected data divided into 70% and 30% for train and test, respectively.
3. MODELS
3.1 ANFIS
ANFIS was proposed by Jang and Sun [26]. This learning technique is more flexible because of combining the learning law with Fuzzy rules [27,28]. Because of this advance, it became a powerful technique for function approximation application. There are five layers in the ANFIS structure, which is shown in Figure 1. ANFIS includes a fuzzification layer, normalized layer, defuzzification layer, and an output layer. adaptive nodes create a fuzzy set of input quantities in the first layer. In the second layer, the weight of the rules (w_{i}) resulted by multiplying the input values of nodes by each other. The normalization of the weight of rules happens in the third layer. Defuzzification is fulfilled in the fourth layer, and finally, the output is extracted [22]. In this study, the ANFIS model was proposed through the Takagi and Sugeno type of fuzzy rules.to this aim, a Gaussian membership function has been used. As, mentioned to develop the model dataset was divided into 30% for a test and 70% for a train. The detail of the developed ANFIS structure reported in Table 1. To this aim, temperature (K), pressure (MPa), and m CO2/m plant (g/g) were used to predict extraction values. The ANFIS model shows the high capability to estimate the extraction values with R^{2}=0.979 and R^{2}= 0.98 for test and train respectively.
Parameters 
Description 
Fuzzy type 
Sugeno 
Mf function 
Gaussian 
Initial FIS 
Genfis 3 
No. MF 
4 
No . Input 
3 
No. Output 
1 
Optimal method 
Hybrid 
Max epoch 
2000 
Initial step size 
0.001 
Step size decrease rate 
0.059 
Step size increase rate 
0.95 
Table 2: Detail of ANFIS model structure.
3.2 ANFISFFA model
The FFA as an intelligent algorithm was first reported by Yang [29]. This algorithm is being extremely applied to resolve diverse complex optimization problems. More details about the FFA and its adjustment can be found in the literature [30]. In the modeling of the ANFISFFA, the
selection of appropriate quantities of the γ, β0, α,
the number of iteration and population size have the most effect on the performance of ANFISFFA [31]. T train the ANFISFFA, trial and error method was selected and based on the results, the values of 1, 2, 0.98, 1500, and 45 were selected for the γ, β0, α, a number of iteration and population size, respectively.
Figure 1: Layer structure of ANFIS model.
3.3 Experimental design
DesignExpert Software provides powerful tools to layout an ideal experiment on process, mixture or combination of factors and components. This software presents comparative experiments, screening, characterization, optimization and combined designs [32] and provides test matrices for screening up to 50 factors. Statistical significance of these factors is established with an analysis of variance (ANOVA). ANOVA is provided to establish statistical significance. Graphical tools help identify the impact of each factor on the eligible results [33]. In this study, central composite design (CCD) with three levels and three parameters) temperature K, pressure MPa and m CO2/m plant g/g) was used to predict the extraction amount. In this modeling, a simple quadratic equation is obtained for this purpose. Analysis of variance (ANOVA) was used to evaluate the regression coefficients (Table1).
Model 
Sum of squares 
Df 
Mean square 
Fvalue 
Pvalue 
2547.5 
6 
424.58 
148.13 
<0.0001 significant 

A m (CO2)/m (plant) 
2178.18 
1 
2178.18 
759.93 
<0.0001 
B pressure 
67.3 
1 
67.3 
23.48 
0.0013 
C temperature 
128.27 
1 
128.27 
44.75 
0.0002 
AC 
38.73 
1 
38.73 
13.51 
0.0063 
A^{2} 
318.65 
1 
318.65 
111.17 
<0.0001 
B^{2} 
36.39 
1 
36.39 
12.7 
0.0074 
Residual 
22.99 
8 
2.87 


R^{2}_{Adjusted}=0.98 





R^{2}_{Predicted}=0.95 





C.V.%=5.38 





Table 1: Analysis of variance quadratic polynomial model.
3.3.1 Quadratic Response Surface: In this study, a quadratic model is needed to obtain the proper performance. A quadratic polynomial model can express the results. The regression model performed is as follows [34]:
In the secondorder polynomial model, Y is the response value, and X_{i} and X_{j} is independent variables. Regression coefficients, β_{i} is a linear coefficient, β_{ij} is a quadratic coefficient, β_{ii} is an interaction coefficient, and β_{0} is a constant. Also, i, j and e are the error terms. Equation 7 is a polynomial model of actual coefficients which shows the amount of extraction by supercritical fluid.
M (extract)/m (plant) = +0.85867 + [10.27119 × (m (CO2)/m (plant)] + [5.06266 × pressure]  [0.120363 × temperature]  [0.034742 × [(m (CO2)/m (plant)]^{2 }]  [0.024742 × (m (CO2)/m (plant) × temperature ]  [0.151149 × pressure^{2}] (12).
The overall prediction ability and statistical significance of the model are evaluated by the R^{2} coefficient and Fisher test(Fvalue) [35]. But the value of R^{2} alone cannot indicate the adequacy of the model. For this reason, the adjusted R^{2} coefficient is also used. BoxCox Chart (Figure 2) shows the data transfer power [6]. The lowest point on this chart represents the best transition. The value of P is less than 0.05. The values of R^{2} are also close to 1. These values indicate the adequacy of the model obtained [6,34,36].
Figure 2: BoxCox plot for power transforms.
4. Model evaluating
The performance of the established models was evaluated by R^{2}, MSE, AARD%, and RMSE in Table 4. From Table 4, the ANFISFFA model shows high capability with the lowest error values against ANFIS, and RSM. Also From Figure 3, the regression plot shows the high performance of ANFISFFA. Figure 4 illustrates error histograms for trained models. As can be seen, the ANFISFFA model has lower error distribution and it prove the accuracy of the ANFISFFA model. The deviations quantities obtained by models are shown in Figure 5. It is obviously seen that the lowest deviation is noted for ANFISFFA. The average relative deviation percentage values for RSM, ANFIS and ANFISFFA are 5,9, 3.9 and 0.025.
Figure 3: regression plot for ANFIS ANFISFFA and RSM
Figure 4: error histogram for ANFIS and RSM
Figure5: deviation plot for a) ANFIS, b) ANFISFFA, and c) RSM.
A comparison of the equation obtained by response surface methodology and ANFISFFA Output with the experimental data is demonstrated in Figure 6. The graph obtained by the quadratic model and the output of ANFISFFA is in good agreement with actual values. Also, the ANFISFFA model has the best performance to estimate the extraction amounts based on a statistical parameter is shown in Table 4.
Figure 6: Comparison of quadratic polynomial models with laboratory data
Statistical parameters 
ANFISFFA 
ANFIS 
RSM 
R^{2} 
0.991 
0.98 
0.95 
MSE 
3.21 
6.01 
16.12 
RMSE 
1.79 
2.45 
4.01 
AARD% 
2.72 
3.76 
6.44 
Table 4: Comparison of ANFIS and RSM based on statistical parameters.
Various factors and parameters affect the extraction of plants. Extraction from the plant by supercritical carbon dioxide changes with a change in pressure and solventtosolid ratio. As can be seen from the experimental data, the extraction rate increases with increasing pressure [5]. The extraction rate also increases with increasing fluid to plant ratio. Extraction temperature also increases the extraction efficiency, but excessive temperature destroys the bioactive compounds.
3.5. Sensitivity analysis
Sensitivity analysis was carried to appraise the effect of the input variable on the ANFIS model's performance. The relevancy factor of each parameter was calculated from equation 15.
Where x_{il} denotes quantities of lth input, x_{i} is the mean values of the input, t_{l }refers to lth output, and t is attributed to mean values of output [37]. Based on Figure 7, the m CO2/m has the most effect on the performance of the ANFISFFA model with the highest importance factor for modeling.
Figure7: Sensitivity analysis using relevancy factor.
5.Conclusion
In this study, RSM and ANFIS methods were used to forecasting the amount of supercritical carbon dioxide extraction from the St. John’s Wort. the ANFIS was optimized with FFA algorithm. The ANFISFFA and RSM results were compared with experimental data. The resolute obtained shows the high capability of two models for the prediction of extraction amounts. Statistical analyzes were performed including F values, Pvalue, R^{2}, r^{2}_{adj}, r^{2}_{pre}, and BoxCox diagram. R^{2} values close to 1, low Pvalues, and Fvalue indicate the accuracy of the model. Data transfer power was evaluated by the BoxCox plot. Based on the statistical parameter and graphical method ANFISFFA indicated a high capability to predict the amount of supercritical carbon dioxide extraction from the St. John’s Wort. (R^{2}=0.99, MSE=3.21, AARD%=2.72 and RMSE=1.79).
Acknowledgements
The authors are thankful to Masoud Alikhani and Reza Deylam Salehi for their consistent support and whose comments helped in improving the quality and presentation of this article.
Conflicts of Interest:
The authors declare no conflict of interest.
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