Mathematical and intelligent modeling of stevia (Stevia Rebaudiana) leaves drying in an infrared‐assisted continuous hybrid solar dryer

Abstract Drying characteristics of stevia leaves were investigated in an infrared (IR)‐assisted continuous‐flow hybrid solar dryer. Drying experiments were conducted at the inlet air temperatures of 30, 40, and 50°C, air inlet velocities of 7, 8, and 9 m/s, and IR lamp input powers of 0, 150, and 300 W. The results indicated that inlet air temperature and IR lamp input power had significant effect on drying time (p < .05). A comparative study was performed among mathematical, Artificial Neural Networks (ANNs), and Adaptive Neuro‐Fuzzy System (ANFIS) models for predicting the experimental moisture ratio (MR) of stevia leaves during the drying process. The ANN model was the most accurate MR predictor with coefficient of determination (R2), root mean squared error (RMSE), and chi‐squared error (χ2) values of 0.9995, 0.0005, and 0.0056, respectively, on test dataset. These values of the ANFIS model on test dataset were 0.9936, 0.0243, and 0.0202, respectively. Among the mathematical models, the Midilli model was the best‐fitted model to experimental MR values in most of the drying conditions. It was concluded that artificial intelligence modeling is an effective approach for accurate prediction of the drying kinetics of stevia leaves in the continuous‐flow IR‐assisted hybrid solar dryer.

useful properties. Although low temperatures of between 30°C and 50°C are recommended by researchers for drying of medicinal plants, however, drying at such temperatures significantly prolongs the drying time and consequently decreases the capacity of drying instruments (Aboltins & Kic, 2016;Müller & Heindl, 2006;Sava Sand, 2015;Şekeroğlu et al., 2007). Several studies on the drying of plants were conducted by researchers (Aboltins & Kic, 2016;Arslan & Özcan, 2012;Bahammou et al., 2019;Bhardwaj et al., 2019;Moussaoui et al., 2020;Nadi & Abdanan, 2017;Venkatachalam et al., 2020). Téllez et al. (2018)  Infrared (IR) drying is a combination of radioactive (at the surface of drying object) and conductive (inside of the object) heating technique in which the energy of IR waves is absorbed by the drying product, causing molecular vibration and in turn, simultaneously warming the surface and inner layers of the product (Doymaz, 2012;Nozad et al., 2016). IR spectra in the wavelength range of 2.5 to 200 μm are usually applied for drying purposes (Zare et al., 2015). IR treatment has been reported to have many potential advantages over conventional drying methods such as higher drying rate, more energy efficiency, uniform or even product temperature, minimized losses and better quality of dried product, and less dust generation because of less airflow across the product (Lee, 2020;Sakare et al., 2020;Yadav et al., 2020). Furthermore, IR resource is less expensive in comparison with other new methods such as dielectric or microwave .
Mathematical modeling of the drying kinetics of agricultural and food materials is a very important cognitive aspect that helps to have a better understanding and description about the drying behavior of the drying matter. Formulating the drying characteristics of foodstuffs is a very useful tool in the improvement of the design and the control of the drying process in the food industry (Tzempelikos et al., 2015). Mathematical modeling of thin layer drying of mint leaves in hot water recirculating solar dryer was carried out by Moradi et al. (2020) who reported that an approximation of diffusion model has the highest correlation with the experimental moisture ratio (MR) with coefficient of determination (R 2 ) of 0.98, root mean squared error (RMSE) of 0.041, and chi-squared error (χ 2 ) of = 0.0017. Mathematical modeling has been performed on the MR behavior of stevia leaves under a convective tray dryer. Experimental drying curves were modeled using eleven mathematical models, and the Midilli-Kucuk model was found to give the best fit quality with a R 2 of more than 0.99 (Lemus-Mondaca et al., 2015).
Although mathematical modeling is a useful method to study the drying process of materials, but finding the best comprehensive mathematical model is difficult and time consuming, especially when there are several parameters affecting the drying process.
Intelligent modeling approaches such as Artificial Neural Networks (ANN) and Adaptive Network-based Fuzzy Inference System (ANFIS) are being used increasingly in the agricultural and food studies. ANN is a well-known technique that has been widely applied for simulation of drying kinetics of agro-food products in several studies (Bai et al., 2018;Chasiotis et al., 2020;Tiwari, 2020).
ANFIS is newer intelligent soft-computing approach that employs the capabilities of neural networks and fuzzy inference systems.

Several applications of ANFIS in food processing and technology
were reported in a reviewed study conducted by Al-Mahasneh et al. (2016). ANFIS is also successfully used to model the drying of foodstuffs (Ojediran et al., 2020;Prakash & Kumar, 2014).
A comparison between ANFIS, ANN, and mathematical modeling was applied by Kaveh et al. (2018) for predicting the drying characteristics of almond kernels in a convective dryer. It was reported that ANFIS had better prediction ability. It was also reported by Abbaspour-Gilandeh et al. (2020) that the ability of ANFIS model was higher than ANN to predict the drying kinetics of quince slices in a hot-air dryer.
A review of the literature showed that a comparative study has not been done to analyze the drying process of medicinal plants.
Also, there are limited reports on the evaluation of medicinal plants drying in IR-assisted continuous solar dryers. Therefore, the aim of F I G U R E 1 (a) Experimental setup of the drying system: (1) photovolaic solar panels; (2) solar water heater; (3) gas water heater; (4) gas-liquid heat exchanger; (5) drying chamber, (b) Interior view of drying chamber: (6) belt conveyor; (7) temperature and humidity sensor; (8) infrared lamp (a) (b) 1 2 3 5 6 7 8 4 this study was to investigate the drying behavior of stevia plant in a continuous dryer using the combination of direct and indirect solar systems along with solar-powered IR radiation as auxiliary heating source.

| Drying apparatus
In order to dry the product, an IR-assisted continuous belt conveyor dryer was developed as the drying system ( Figure 1a). The four-floor continuous-flow dryer was equipped with a hybrid of solar and gas water heaters, as main heating source of the system. A water pump was used to deliver water from water heater tank to a gas-liquid heat exchanger. The heat exchanger was of tube-fin type with the liquid on the tube side. The ambient air from a centrifugal blower was passed through the heat exchanger and got the heat from the hot water current inside the pipes of the heat exchanger. The velocity of the inlet air to the drying chamber was adjusted using an inverter The input power of IR lamps was adjusted using a rotational potentiometer and a digital multimeter (TES Model 232, Taiwan).

| Sample preparation
During the experiments, the stevia leaf samples were collected daily from cultivated stevia plants in the research fields of the University of Guilan, Rasht, Iran. The Fresh leaves were carefully separated from the stems and poured into polyethylene bags until the drying process. The initial mass of the samples was 30 g which was measured using a digital balance with an accuracy of 0.001 g (A&D Model GX-1000, Japan).

| Drying conditions
Experiments were conducted between August and September of 2019, in the renewable energy site of the University of Guilan, Rasht, Iran. The IR-convective drying experiments of stevia leaf samples were carried out in the continuous-flow dryer at three levels of inlet air temperatures (30, 40, and 50°C), three levels of inlet air velocities (7, 8, and 9 m/s), and three levels of IR lamp input powers (0, 150, and 300 W). The experiments were carried out in three replications.
In order to prevent leaf samples from physical damages and avoid losses during drying, the samples were carefully placed inside mesh bags and then the bags were positioned on the belt conveyor beds to be dried.

| MR measurement and calculations
In order to determine the moisture content (

| Mathematical models
In order to find the most appropriate models for predicting the kinetics of drying stevia leaves, the experimental data of MR versus drying time were fitted with ten of the most common mathematical models (Babu et al., 2018;Ertekin & Heybeli, 2014;Kaveh et al., 2018;Onwude et al., 2016), (Table 1). The constants of the tested models were determined using the curve fitting toolbox of MATLAB programming software (MATLAB R2018b; The Mathworks Inc., Natick, MA, USA).  of ANFIS structure is shown in Figure 2b.

| Statistical criteria
The predicted MR values of the developed models (mathematical, ANN and ANFIS) were compared to the experimental MR data based on three statistical criteria, namely R 2 , RMSE and χ 2 which were calculated using the Equations (13-15) (Qadri et al., 2020): where MR exp,i and MR pred,i are, respectively, the ith experimental and predicted MR data from N total MR values, and MR exp is the average of experimental MR values. The models with the highest R 2 and the least RMSE and χ 2 were selected as the most precise MR predictors. (13) Mathematical models used to describe the MR curves of stevia leaves, a, b, c, k, k1, and k2 are constants

Model name Model Equation Equation
No.

Wang and Singh
Henderson and Pabis ae −kx (4) Logarithmic Approximation of diffusion Page Two-term Simplified Fick's diffusion Midilli and Kucuk ae −kx n + bx (12) F I G U R E 2 Schematic images of ANN structure with two hidden layers and eight neurons in each hidden layer (a) and ANFIS structure with two input MFs (b)

| Drying kinetics and overall drying time
The average initial moisture content of stevia leaves was 77.63 ± 0.1% thin-layer infrared drying of mint leaves (Ertekin & Heybeli, 2014).
The same results were obtained for some other products (Selvi, 2020;Younis et al., 2018;Zare et al., 2015). Figure 6 shows a graphical comparison of the overall drying time at different drying conditions, where the small letters above the bars indicate Duncan's multiple range test (p < .05). It can be seen in Figure 6 that for a given inlet air temperature of 30°C, and the input air velocity of 7 m/s, the overall drying time reduced significantly from 600 min to about half when the IR lamp power increased from zero to 300 W. Such a significant effect of IR lamp application was also observed for inlet air temperatures of 40 and 50°C. The increase of inlet air temperature also significantly decreased the overall drying time samples. In this study, it was observed that although the overall drying time was decreased by increasing the inlet air velocity, but its effect was not significant on the drying time. The overall drying time decreased from 600 min to 105 min when the drying condition was changed from inlet air temperature of 30°C, inlet air velocity of 7 m/s, and no IR radiation to an inlet air temperature of 50°C, inlet air velocity of 9 m/s, and IR power of 300 W.

| Mathematical modeling
Different mathematical models according to Table 1 were evaluated for predicting MR variations of stevia leaf samples during the drying process. The statistical criteria and the constants of the best-fitted models in each drying condition are presented in Table 2. It can be Air v (m/s) was also reported applicable to describe the drying process of some other plant leaves such as savory (Arslan & Özcan, 2012), Vernonia amygdalina (Alara et al., 2018), peppermint (Torki-Harchegani et al., 2016), Asparagus officinalis (Okur & Baltacıoğlu, 2018), and

| ANN modeling
Different architectures of ANN were constructed with one and two hidden layers, and different transfer functions and training algorithms were assessed for predicting the MR of stevia leaves. The optimum numbers of neurons in the hidden layers of these architectures were determined based on statistical criteria, and the most accurate topologies are listed in Table 3. In general, the ANNs with two hidden layers had better results than those with one hidden layer. Also, the ANNs with LM training algorithm were more accurate than those with SCG training algorithm. According to Table 3 ANN methodology has been also reported by Sarimeseli et al. (2014) for predicting the infrared drying behavior of thyme leaves, and other researchers who have used the ANN technique for modeling the drying kinetics of different crops (Bai et al., 2018;Khaled et al., 2020).
The performance criteria of the selected ANN model were also better than those achieved by mathematical models. Higher MR prediction accuracy of ANNs compared to mathematical models was also reported by Karakaplan et al. (2019) for estimating the MR of spearmint during drying process, and by Omid et al. (2009) for modeling the drying kinetics of pistachio nuts. It should also be noted that the ANN enables us to easily provide a predictive model of the drying process for medicinal plants. Such ANN model can include all designated drying condition in a single structure.

| ANFIS modeling
The top six most efficient ANFIS models for MR prediction are presented in Table 4. According to the performance parameters, the  ANFIS model was successfully used to predict the drying kinetics of quince slices during IR drying (Ziaforoughi et al., 2016). ANFIS was also reported to have the reliable ability to be applied in modeling and controlling of drying systems (Al-Mahasneh et al., 2016).
As can be observed from  Figure 7 shows that the experimental versus ANN predicted data ( Figure 7a) are less scattered around the diagonal line than the experimental versus ANFIS predicted data ( Figure 7b). This proves that the neural network-based model is a more accurate MR predictor than ANFIS model. The R 2 , χ 2 , and RMSE values of the ANN model on the test dataset were 0.9995, 0.0005, 0.0056, respectively, which were superior than those obtained by ANFIS model (R 2 = 0.9936, χ 2 = 0.020, and RMSE = 0.0243) on test dataset. Similarly, Lertworasirikul (2008) reported that the multilayer feed-forward neural networks were slightly better than ANFIS and mathematical models for the prediction of MR of semi-finished cassava crackers. Rad et al. (2018) reported that the ANN model

| CON CLUS ION
In this study, drying behavior of stevia leaves in an IR-assisted continuous-flow hybrid solar dryer was investigated. Investigation of drying kinetics of stevia leaves showed that the falling rate of MR was increased by increasing input power of IR lamps and increasing the inlet air temperature. The overall drying time was significantly decreased by increasing the drying parameters of inlet air temperature and IR lamp power. Employing solar-powered IR lamps in the continuous-flow hybrid solar dryer significantly reduced the overall drying time which leads to improved dryer capacity with no excessive consumption of fossil energy. It can be concluded that the developed dryer system configuration in this study for stevia leaves drying has the advantages of high drying capacity and low usage of fossil energy.
Variations of MR values of stevia leaves were modeled using mathematical, ANN, and ANFIS models. It was observed that although all of these methods can effectively predict the drying kinetics of stevia leaves, but the ANN model was the most accurate with the best performance statistics. Besides their excellent predictive capabilities, ANN and ANFIS models, can be easily and simply trained to cover all drying conditions in one comprehensive model. These artificial neural learning techniques can be used for developing intelligent drying control systems with high reliability. The results of this study showed that the ANN model is the most suitable method for monitoring the IR-assisted hot-air drying process of stevia plant. The applied dryer system and the proposed predictive model in this study, provide useful information toward the development of a clean, sustainable and intelligent technology for drying the medicinal plants.

ACK N OWLED G M ENT
The authors would like to thank the University of Guilan for providing the laboratory facilities for conducting this project. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.