Application of Artificial Neural Network for Predicting the Drying Kinetics and Chemical Attributes of Linden (Tilia platyphyllos Scop.) during the Infrared Drying Process

Abstract

This study analyzes the possibility of utilizing artificial neural networks (ANNs) to characterize the drying kinetics of linden leaf samples during infrared drying (IRD) at different temperatures (50, 60, and 70 °C) with sample thicknesses between 0.210 mm and 0.230 mm. The statistical parameters were constructed using several thin-layer models and ANN techniques. The coefficient of determination (R²) and root mean square error (RMSE) were utilized to evaluate the appropriateness of the models. The effective moisture diffusivity ranged from 4.13 × 10⁻¹² m²/s to 5.89 × 10⁻¹² m²/s, and the activation energy was 16.339 kJ/mol. The applied Page, Midilli et al., Henderson and Pabis, logarithmic, and Newton models could sufficiently describe the kinetics of linden leaf samples, with R² values of >0.9900 and RMSE values of <0.0025. The ANN model displayed R² and RMSE values of 0.9986 and 0.0210, respectively. In addition, the ANN model made significantly accurate predictions of the chemical properties of linden of total phenolic content (TPC), total flavonoid content (TFC), DPPH, and FRAP, with values of R² of 0.9975, 0.9891, 0.9980, and 0.9854, respectively. The validation of the findings showed a high degree of agreement between the anticipated values generated using the ANN model and the experimental moisture ratio data. The results of this study suggested that ANNs could potentially be applied to characterize the drying process of linden leaves and make predictions of their chemical contents.

1. Introduction

Linden (Tilia platyphyllos Scop.) is a medicinal plant, the tea prepared with which has a pleasant taste and which has several dozen different species and varieties [1]. It is rich in polyphenols and presents high antioxidant activity against DPPH radicals [2,3]. In addition, the nutritional content of linden, such as potassium and carbohydrates, has several applications with positive effects on one’s health, including the following: treatment of hypertension [4] and preparation of medicines that are sedative, stomachic, antispasmodic, and diuretic [5]. In addition, it is recommended that the leaves are not used as intensely as the flowers and that they are used as a diaphoretic, but the effect has not yet been experimentally evaluated [6]. Apart from all these, it has been reported that it is used to treat coughing related to common colds and as a sleep regulator [7]. Primarily in Turkey, three linden species, Tilia tomentosa Moench, Tilia platyphyllos Scop., and Tilia rubra, are found in the natural environment [8]. Many previous researchers have stated the agricultural value of linden, such as its relief of anxiety related to indigestion, irregular heartbeat, and vomiting [6,9,10,11,12].

The process of drying food is one of the postharvest preservation methods that are most frequently utilized. The processing of harvested agricultural crops helps to decrease the rate of spoiling, improve the storage time, and lower the amount of items’ total bulk weight before and after transportation. The enzymatic change brought about by the reactions linked to the drying of agricultural goods is deactivated as a consequence of heat and mass transfer, which ultimately leads to a reduction in the amount of moisture [13]. In addition, it facilitates the removal of beneficial components from various food products. Various techniques for drying, including hot-air drying (HAD), infrared drying (IRD), vacuum drying (VD), and microwave drying (MWD), have been used for drying crops [14,15,16]. IRD is the most efficient of these several drying processes, and it is a method that is utilized most frequently in industrial drying because of the inherently more uniformly dried product that it produces, which is innocuous and devoid of toxicity [17].

In the food processing industry, IRD radiation has been introduced, which reduces both energy usage and processing time [18]. The logic behind IRD is that a portion of the electromagnetic spectrum is mostly responsible for the heating impact that the Sun has [19]. It is only when infrared radiation is utilized to heat or dry wet items (since radiation travels through a substance) that it is effective. The qualities of the material and the wavelength of radiation both play a role in the depth to which it can penetrate. However, the drawback of IRD is that it is harder to dry heavier coatings, as it is a surface phenomenon. Furthermore, the surface of dry materials emits IRD radiation without heating the underlying substance. There is no requirement for a medium heating source to be placed between the IRD energy source and the substance that is dried [20]. IRD is often more convenient for thin material layers having a large surface subject to radiation. There are several research studies on mint documented in the scientific literature [21] that are relevant to the IRD process, as well as studies on pieces of pepper [22], onion [23], strawberry [24], and kiwifruit [25], all on separate plates. Therefore, knowing the optimal working standards and appropriate drying conditions and using appropriate drying techniques are of paramount importance to achieve quality together with reducing product costs and increasing the yield.

Earlier research investigated a variety of mathematical thin-layer drying models, including empirical, semi-conceptual, and conceptual ones, such as Page, Newton, and logarithmic models, to explain the drying kinetics of fruits and vegetables with the purpose of increasing the performance characteristics of the drying process as a whole [26,27]. The physical rules on which these models are based include aspects of mass, reaction kinetics, and thermodynamics, among others, which regulate the process. A model’s accuracy in predicting a thermal process is restricted by other elements, such as physical qualities, which are subject to change throughout the thermal process. In addition, these models are able to provide satisfactory regression findings from experimental data in a relatively short amount of time. However, mathematical thin-layer algorithms are experimental in nature, and they do not provide a physical interpretation of the drying procedure, with these differences depending on the product [18].

Artificial neural networks (ANNs), as a part of computational intelligence, are thought to be difficult-to-understand tools for dynamic modeling and the analysis of complex systems [28]. The ANN method is inspired to the biological neural system as an advantageous statistical tool for nonparametric regression. The implementation of an ANN provides a wide variety of benefits in comparison with more traditional modeling methods, such as the capability of absorbing complex data interactions. Thus, ANNs have superior learning capacity, better flexibility, and an online, non-invasive nature [29]. Therefore, the ANN is a practical statistical model that is modeled after the biological brain system as an instrument for performing nonparametric regression [28].

The application of modeling techniques that make use of computational intelligence is one possible approach to mathematical thin-layer models because of their consistency and accuracy. The application of ANNs is met with great success in modeling and can enhance the drying procedure for several vegetables and fruits, for example, mushrooms [30], eggplant [31], and persimmon [32]. In light of this, the ANN method may be used to make accurate predictions of the drying kinetics of linden leaf samples subjected to IRD, and the literature provides only a limited amount of information on this topic. The use of these models in this application can decrease the necessary amount of time for the production process while optimize energy and quality of linden leaf samples and further minimizing costs. Therefore, this study aims to explore the drying properties of linden leaf samples at different temperatures (50, 60, and 70 °C) using IRD associated with ANN modeling as a method of non-destructive analysis for characterizing the drying behavior of linden leaves and predict the physiochemical properties of linden leaf samples.

2. Materials and Methods

2.1. Samples Preparation

Linden leaves, scientifically known as T. platyphyllos Scop., were gathered from the grounds of Ondokuz Mayıs university. In Turkey, Samsun city’s shoreline is home to an open-air university with location in the Black Sea area of the country. This herb leaf is widely regarded as one of the most popular goods available in the city. The linden tree has blooms that have five petals with a light greenish-yellow coloration. The bloom is full of pollen-bearing stamens and an ovary that is arranged in corymbose inflorescences, in which the peduncle is only partly linked to the inflorescence through a bract that is made of a membrane and is lanceolate in shape. It is around 8 cm long and has a rounded tip. Ahead of the process of drying, linden leaf samples were kept in a refrigerator at a temperature of 5 °C for further analyses. This being said, in this research study, only leaves that were free from defects and disease were selected and placed into the infrared drier as a control having a very thin coating (5 g). Fresh, dry, and powdered linden leaf samples are shown in Figure 1a–c.

2.2. Drying Experiments

The IRD method was employed with the assistance of a drying unit designed for use in the laboratory (Radwag balances and weighing scales; Warsaw, Poland). This gadget is capable of sending out electromagnetic radiation in the medium-frequency IR band of shortwave length. The linden leaf samples were dried at three different temperatures (50, 60, and 70 °C). In order to avoid contamination during the IRD procedure, the samples were spread out evenly throughout the whole pan, and the radiation in the infrared spectrum was reflected back from a region that was not covered by the samples. As the process of drying continued, at each drying temperature, periods of approximately 3 min were assigned for evaporating water in about 3 min intervals. The test was reproduced three times, and results showing an average decrease in weight were reported. Before any of the trials were performed, the IRD device was brought to the desired temperature for a period of 30 min to allow the temperature of the dryer to establish a state of equilibrium with the temperature of the air in the surrounding area.

2.3. Kinetics of the Drying Processes

The amount of fluctuation in moisture content that occurred throughout the IRD process was indicated in the moisture content ratio form (dimensionless) according to the equation presented in Equation (1).

$$\mathrm{MR}=\frac{\left({\mathrm{M}}_{\mathrm{t}}-{ \mathrm{M}}_{\mathrm{e}}\right)}{\left({\mathrm{M}}_{\mathrm{o}}-{ \mathrm{M}}_{\mathrm{e}}\right)}$$

(1)

where M_t represents the moisture content of the samples at time t, M_e is the equilibrium moisture content, and M_o represents the initial moisture content. The M_e values remained the same, as stated by Aghbashlo et al. [33], because of how low they were in comparison to the M_t and M_o levels, which resulted in almost no mistakes being made during the process. For the sake of simplification, the moisture ratio was represented in this study as given in Equation (2).

$$\mathrm{MR}=\frac{{\mathrm{M}}_{\mathrm{t}}}{{\mathrm{M}}_{\mathrm{o}}}$$

(2)

2.4. Effective Moisture Diffusivity and Activation Energy

In order to conduct an accurate analysis of the results obtained using the IRD technique on linden leaf samples, it was necessary to obtain an understanding of the process responsible for the transport of moisture within the samples as they dried. In the process of Fick’s diffusion, because of the ease with which it could represent the process of mass transfer, an equation in the form of a dimensional approach was used for the drying samples. Using this approach, the effective moisture diffusivity of the samples subjected to IRD was calculated. The solution proposed by Crank [34] to the diffusion problem posed by Fick is outlined in Equation (3).

$$\frac{\partial {\mathrm{M}}_{\mathrm{t}}}{\partial \mathrm{t}}=\nabla · \left({\mathrm{D}}_{\mathrm{eff}} \nabla { \mathrm{M}}_{\mathrm{t}}\right)$$

(3)

Supposing that the rate of diffusion remains constant and that the initial moisture distribution is uniform, Crank’s solution is cylindrical in shape. Equation (4) depicts the sample shape that was taken.

$$\mathrm{MR}=\frac{8}{{\mathsf{\pi }}^2}{\displaystyle \sum }_{\mathrm{n}=1}^{\infty }\frac{1}{{\left(2\mathrm{n}+1\right)}^2} \exp \left(-\frac{{\left(2\mathrm{n}+1\right)}^2{\mathrm{D}}_{\mathrm{eff}} \mathrm{t}}{{\mathrm{r}}^2}\right)$$

(4)

where D_eff is the effective moisture diffusivity measured in squared meters per second, r is the radius of the sample measured in meters, and n is the positive integer, while the drying time is denoted by t (s). Equation (4) was constrained to only be applied in order to simplify the mathematical representation; the first term ultimately leads to Equation (5).

$$\mathrm{MR}=\frac{8}{{\mathsf{\pi }}^2} \exp \left(-\frac{{\mathsf{\pi }}^2{\mathrm{D}}_{\mathrm{eff} }\mathrm{t}}{{\mathrm{r}}^2}\right)$$

(5)

The activation energy is the lowest possible value of energy that must be present for drying to take place. The energy required for activation calculations for the IRD technique was derived from the correlation between the Arrhenius equation and the effective moisture diffusivity equation used to calculate the samples’ average temperature, and the results are presented in Equation (6).

$${\mathrm{D}}_{\mathrm{eff}}={ \mathrm{D}}_{\mathrm{o}}\exp \left(-\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}\left(\mathrm{T}+273.15\right)}\right)$$

(6)

where D_o represents the pre-exponential factor, E_a represents the activation energy (kJ/mol), R stands for the universal gas constant (8.3143 × 10⁻³ kJ/mol), and T represents the sample’s average temperature as a whole (K). The values of E_a for each of the IR experiments were applied to various degrees of linden leaf thickness, and the measurements were taken from the values of the resulting slope via the process of drawing the fitting curve between the logarithm of the distance and 1/(T + 273.15) (Equation (7)).

$$\mathrm{Slope}=-\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{R}}$$

(7)

2.5. Mathematical Thin-Layer Modeling

The drying data from the experiments were obtained and then fitted to five different mathematical models. The particular mathematical models that were used were Page, Midilli et al., Henderson and Pabis, and logarithmic models, and models based on logarithms and Newton’s laws, as shown in

Table 1. Mathematical thin-layer drying models.

Model No.	Model Name	Model Expression	Reference
1	Page model	MR = exp (−ktn)	[26]
2	Midilli et al. model	MR = a exp (−kt) + bt	[35]
3	Henderson and Pabis model	MR = a exp (−kt)	[36]
4	Logarithmic model	MR = a exp (−kt) + c	[37]
5	Newton model	MR = exp (−kt)	[31]

. The mathematical models that were used were derived from the analysis of non-linear least squares by means of the Sigma plot program (version 10.0; Systat Software Inc., San Jose, CA, USA). The utilization of such models results in more accurate forecasts while requiring fewer assumptions [32].

2.6. Artificial Neural Network

A neural network is organized in layers that are interconnected with one another. According to Haykin [38], an ANN may be broken down into three distinct categories of constructions based on the nature of their connections: (1) the single-layer feed-forward network, (2) a network with many layers of feed-forward connections, and (3) a recurrent network. A multi-storey building is one of these constructions. In the modeling of food and agricultural systems, layered feed-forward networks are utilized on a regular basis. A forward neural network consists of one or more hidden layers (h), in addition to an initial layer (n) and a production layer (m). The number of independent variables is proportional to the number of neurons present in the initial and last layers and is representative of the number of inputs (independent variables) and outputs (dependent variables, respectively). In the course of this investigation, a multi-layer feed-forward network was utilized. This construction was employed with three input parameters (drying time, temperature, and thickness) and 1–3 hidden layers, in addition to the five output parameters of moisture ratio, total phenolic content, total flavonoid content (TFC), DPPH, and total flavonoid assay (FRAP), as is seen in Figure 2. During the model training process, a back-propagation method was utilized, and in each and every one of these examples, the sigmoid function was utilized, as shown in Equation (8).

$$\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{1+{ \mathrm{e}}^{-\mathrm{x}}}$$

(8)

The datasets were prepared by randomly dividing the data into training and test datasets, 70% and 30%, respectively. The structure of the selected hidden layer was a single-layer ([3], [6], [9]), two-layer ([3, 3], [6, 6], [9, 9]), or three-layer ([3, 3, 3], [6, 6, 6] [9, 9, 9]) matrix, where for example, [9], [9, 9], and [9, 9, 9], represented one, two, and three hidden layers with 9, 18, and 27 neurons, respectively, as illustrated in Figure 2. The software that was utilized was Weka 3.6, which was developed in Hamilton, New Zealand, for the analysis of the ANN model. In general, ANNs are capable of performing neural fitting and prediction, as well as other related tasks. In this particular instance, it could be possible to make predictions about the future without employing neural network technologies tailored to the subject matter.

2.7. Determination of Chemical Characteristics

The maceration method was used to extract the powdered material with methanol and distilled water (80:20, volume/volume) for 12 h at room temperature; then, the mixture was centrifuged for 20 min. A sinbo SCM 2934 spice grinder with a capacity of 55 g and a stainless-steel blade was used to grind the linden samples. The supernatant was utilized for the purposes of estimating antioxidants and the activity of antioxidants. The total phenolic content (TPC) was determined using a technique known as the Folin–Ciocalteu method [39]; therefore, we thoroughly combined a volume of 0.5 mL of the extract and 2.5 mL of Folin–Ciocalteu reagent. After waiting for 5 min, 2 mL of Na₂CO₃ solution at a concentration of 20% was added to the mixture, and it was then allowed to stand in the dark for a period of 2 h. At a wavelength of 760 nm, the absorbance was measured. For the calibration curve, gallic acid was used as the standard, and the result was stated as milligrams of gallic acid. The overall flavonoid content was determined according to Gao et al. [40]. A colorimetric assay with AlCl₃ was used to assess total fluorescent content (TFC). In a test tube that already had 0.75 mL of distilled water, 0.25 mL of the extract was added to the tube. A volume of 0.15 mL of a 5% solution was added after adding sodium nitrite solution to the mixture; this was allowed to react for 5 min. The next step was to add 0.3 mL of 10% aluminum chloride. After waiting for 5 min, 1 mL of a sodium hydroxide solution at a concentration of 1 M was added. The amount of absorption was 510 nm when it was measured. In order to calibrate the catechin concentration, a standard curve was constructed. TFC was given in milligrams of catechin equivalents (CEs) per gram of sampled material.

The scavenging activity of free radicals was determined by employing the stable DPPH free radical as the measuring tool, as described by Brand-Williams et al. [41]. Methanolic extract in the amount of 0.5 mL was added to the mixture; then, we added a 2 mL solution of methanol containing 200 mmol/L of DPPH, and the reaction mixture was vigorously shaken. After being allowed to incubate at room temperature for 120 min, the absorbance of DPPH in the positive control (Trolox) and the samples was evaluated at a wavelength of 517 nm. A comparison was made between the scavenging activities of the DPPH free radical and that of Trolox, which is an analog of vitamin E that is water soluble. The findings were reported in millimoles of Trolox equivalents (TEs) per gram of powder. In this experiment, the ferric reducing antioxidant power (FRAP) test was performed according to Benzie and Strain [42]. Extract in the amount of 0.50 mL was combined with FRAP reagent (3 mL) and allowed to sit for 5 min. FRAP reagent was composed of 300 mM acetate buffer, pH 3.6, and 10 mM TPTZ dissolved in HCl (40 mM), in addition to FeCl 3.6H₂O (20 mM). At a wavelength of 593 nm, an absorbance reading was taken with a spectrophotometer. The samples were evaluated, and the calculations were performed with the use of the ferrous sulfate calibration curve (0.0–1.0 mM) for quantification. The findings were reported in terms of millimoles Fe (II) per gram of the samples’ dry weight.

2.8. Model Evaluation

Model evaluation was carried out by utilizing software that is part of Statistical Analysis System (SAS; version 9.3; Institute, Inc., Cary, NC, USA). The comparison of the mean significant differences between different drying time intervals while employing the IRD technique was carried out using an ANOVA (5% level of significance and 95% confidence intervals) and the Duncan test. The findings of replicate measurements were reported as mean ± standard error values. The accuracy of the fitting of the computational intelligence (ANN) and mathematical thin-layer models to the experimental data was determined using statistical indicators. These model evaluators were the coefficient of determination (R²) and the root mean square error (RMSE). They were mathematically calculated in accordance with what is emphasized in Equations (9) and (10).

$$R^2=1-\frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}{\left({\mathrm{V}}_{\mathrm{pred}}-{\mathrm{V}}_{\exp }\right)}^2}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}{\left({\mathrm{V}}_{\mathrm{pred}}-{\mathrm{V}}_{\mathrm{m}}\right)}^2}$$

(9)

$$\mathrm{RMSE}=\sqrt{\frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}{\left({\mathrm{V}}_{\mathrm{pred}}-{\mathrm{V}}_{\exp }\right)}^2}{\mathrm{N}}}$$

(10)

where V_pred represents the projected value, V_exp represents the actual observation derived from the experimental data, and V_m represents the mean value. The average of the actual observations was obtained, with N standing for the total number of observations. The values of R² and RMSE were as follows: The quality of the fitting was considered to be superior when both the value of R² and the value of RMSE were reduced.

3. Results and Discussion

3.1. Behavior of the Drying Process

The changes in the moisture ratio over time following the application of the IRD technique at different temperatures (50, 60, and 70 °C) are illustrated in Figure 3. The moisture ratios of the linden leaf samples used for the analysis may be determined from the plot. The effectiveness of the IRD approach was reduced as the drying time increased. The rates of drying were achieved using the IRD technique during the time when the rate was decreasing. Figure 3 makes it abundantly evident that the drying time, as a result, decreased as the drying progressed. The moisture ratio values of 0.20 and 0.42 were obtained after a drying time of 10 min and at temperatures of 60 and 70 °C. After 37 min of drying, a moisture ratio of 0.20 was discovered to be present in the substance at 50 °C. The amount of moisture in the material fell to 0.10 g [H₂O] kg⁻¹ [DM], depending on the temperature at which it was dried, within around 20 to 50 min (Figure 3). In addition, the findings demonstrated that the increase in the drying temperature led to a steeper slope, and the amount of time it took to dry the samples was cut down by around 250%. Based on these findings, it could be deduced that the moisture of samples obtained from linden leaves transferred from the inner layer to the surface as the air became dryer. The temperature increased to a point at which water vapor escaped from the surface of the dry material to the surrounding air atmosphere, resulting in an increase in the pace of drying that occurred as a result of a higher temperature. The results were in accordance with the findings of other studies on the drying patterns of different types of materials [17,32,43]. In addition, the drying rate curves became steeper as the drying temperature increased. This discovery may be found in accordance with the findings of a number of different investigations using the IRD method [23,24].

3.2. Effective Moisture Diffusivity and Activation Energy

Table 2. Values of effective moisture diffusivity and activation energy in linden leaf samples subjected to IRD.

Drying Temperature (°C)	Deff (m2/s)	D0 (m2/s)	Ea (kJ/mol)
50	4.13 × 10−12
60	4.47 × 10−12	1.746 × 10−9	16.339
70	5.89 × 10−12

displays the many values that could be assigned to the effective moisture diffusivity (D_eff). The D_eff values ranged anywhere from 4.13 × 10⁻¹² m²/s to 5.89 × 10⁻¹² m²/s on average. According to what is presented in Table 2, D_eff noticeably rose with the increase in the drying temperature from 50 °C to 70 °C. This outcome could have been due to the increase in the activity of water molecules at higher temperatures, which led to a rise in moisture diffusivity. The values of D_eff that were found in this research study fell within the typical range of 10⁻⁶ to 10^–12 m²/s when applied to the drying of food materials. The values of D_eff were consistent with those found in other investigations on the drying of strawberries (2.40–12.1 × 10⁻⁹ m²/s), the drying of apples (2.27–4.97 × 10⁻¹⁰ m²/s), the drying of persimmon slices (1.330–9.221 × 10⁻⁹ m²/s), and the drying of pumpkins (1.19–4.27 × 10⁻⁹ m²/s) [32,44,45,46].

On the other hand, the Arrhenius diffusivity constant, sometimes referred to as the “pre-exponential factor” equation (D₀), for linden leaves was estimated to be 1.746 × 10⁻⁹ m²/s by the researchers. The amounts of energy required for activation in IRD were obtained by plotting ln(D_eff) versus 1/(T + 273.15). Unlike the activation energy, however, this was proportional to the gradient multiplied by the universal gas constant (R), as seen in Figure 4. The energy required for activation was calculated using the IRD value, which may be found in Table 2. The value of E_a in IRD was 16.339 kJ/mol. This result was within the range of 15–40 kJ/mol found for several foods [47]. When activation energies of vegetables and fruits were assessed, more than 90% of the activation energy values that were found in previous studies ranged between 14.42 and 43.26 kJ/mol, for example, 28.60 kJ/mol for bamboo [48]. The activation energy found in the present study for linden leaves was relatively low. The E_a value shows the sensitivity of diffusivity to temperature. This means that the lower the E_a value is, the lower the sensitivity of diffusivity to the temperature is; so, a lower value indicates high moisture diffusivity. Hence, in the present study, about 16.339 kJ/mol of energy was required for moisture diffusion and subsequent evaporation from the surface of the leaves.

3.3. Comparison of Different Mathematical Models of Thin Layers

During IRD, mathematical thin-layer algorithms were utilized to characterize the drying kinetics of linden leaf samples.

Table 3. Mathematical drying model evaluation for linden leaves samples subject to IRD.

Drying Temperature (°C)	Model No.	Model Parameters	R2	RMSE
50	1	k = 0.0472, n = 1.0381	0.9992	0.0090
	2	k = 0.0413, n = 1.0933, a = 0.9998, b = 0.0003	0.9999	0.0025
	3	a = 1.0128, k = 0.0538	0.9990	0.0098
	4	a = 1.0096, k = 0.0547, c = 0.0053	0.9991	0.0099
	5	k = 0.0532	0.9988	0.0104
60	1	k = 0.0955, n = 0.9915	0.9935	0.0257
	2	k = 0.0716, n = 1.1305, a = 0.9984, b = 0.0009	0.9992	0.0102
	3	a = 1.0032, k = 0.0937	0.9935	0.0256
	4	a = 0.9844, k = 0.1028, c = 0.0286	0.9969	0.0188
	5	k = 0.0934	0.9935	0.0245
70	1	k = 0.2584, n = 0.7815	0.9931	0.0269
	2	k = 0.1300, n = 1.1340, a = 0.9914, b = 0.0013	0.9984	0.0152
	3	a = 0.9935, k = 0.1625	0.9896	0.0330
	4	a = 0.9611, k = 0.1866, c = 0.0405	0.9998	0.0055
	5	k = 0.1635	0.9896	0.0312

presents different mathematical models, such as Page, Midilli et al., Henderson and Pabis, logarithmic, and Newton, that suited the data, considering the experimental moisture content data of the sample. Despite the fact that each of the five models was suitably chosen for the experimental data, the Page model satisfactorily characterized the drying kinetics of linden leaf when it was fitted to the experimental data. Samples had R² values of more than 0.9900 and RMSE values of less than 0.0200 under all IRD conditions. Temperatures were taken from Table 3, and as shown here, results that were comparable to those observed using the other four models were achieved. Similar results were obtained using the other four models; we found the top model to fit the experimental data with the highest R² of >0.9990 and the lowest RMSE of <0.0150 at all three temperatures (50, 60 and 70 °C), except for the Henderson and Pabis model and the Newton model, which illustrated R² values of 0.9896 and 0.9896 at 70 °C, respectively. Khaled et al. [32] similarly stated the suitability of the Page, Midilli et al., Henderson and Pabis, logarithmic, and Newton models for predicting the drying kinetics of persimmon slices samples. Younis et al. [48] found similar results, indicating the evaluation of the suitability of the Page, Midilli et al., Henderson and Pabis, logarithmic, and Newton models, as well as any other relevant models, in a discussion on the drying characteristics of garlic slices.

3.4. Results of Artificial Neural Network

When employing the ANN model in the IRD approach, time, temperature, and various degrees of linden leaf thickness were employed to make predictions regarding the moisture ratio. The statistical findings of training and validation are shown in

Table 4. Statistical results of drying kinetics of linden leaf samples for the ANN model using IRD.

No. of Hidden Layers	No. of Neurons	Training		Test
		R2	RMSE	R2	RMSE
1	3	0.9620	0.0654	0.9978	0.0152
1	6	0.9602	0.0666	0.9943	0.0194
1	9	0.9717	0.0566	0.9866	0.0302
2	3, 3	0.9549	0.0706	0.9974	0.0132
2	6, 6	0.9769	0.0546	0.9986	0.0210
2	9, 9	0.9743	0.0568	0.9974	0.0327
3	3, 3, 3	0.9424	0.0795	0.9962	0.0215
3	6, 6, 6	0.9672	0.0616	0.9971	0.0163
3	9, 9, 9	0.9704	0.0587	0.9961	0.0412

. The training datasets were utilized in order to determine the optimal combination of neuronal and hidden layer counts for multi-layer modeling using neural networks to find out which method had the most accurate predicting ability. The findings of IRD found that the design with two hidden layers consisting of 12 and 18 neurons (6 and 6 neurons; 9 and 9 neurons) produced the greatest results when compared with the findings of the training set (0.9769 and 0.9743) and the test set (0.9986 and 0.9974). While at one hidden layer consisting of 3, 6, and 9 neurons; two hidden layers consisting of 6 neurons; and three hidden layers consisting of 9, 18, and 27 neurons, respectively (Table 4). Additionally, it was discovered that the networks were vulnerable to the number of neurons in the deepest layers of their bodies. Therefore, fewer neurons led to underfitting, whereas an excessive number of neurons led to overfitting, causing an excessive amount of fitting. Khaled et al. [32] provided evidence indicating that an ANN consisting of two hidden layers and 12 neurons accurately anticipated the changes in persimmon moisture content during the various stages of vacuum drying (VD) and hot-air drying (HAD) at varied drying temperatures of 50 °C, 60 °C, and 70 °C for sample thicknesses of 5 mm and 8 mm. ANN models consisting of two covert layers were also shown to accurately forecast the drying behavior of other fruits and vegetables, such as pepper, apple slices, and mushroom, in the case of microwave–vacuum drying [49,50].

3.5. Comparison between Mathematical Thin-Layer Models and Artificial Neuron Networks

The greatest findings produced using the computational intelligence (ANN) model, as well as the top two mathematical thin-layer models (Page and Midilli et al), for the prediction of the moisture ratios are summarized in

Table 5. Statistical results of drying kinetics of linden leaf samples for computational intelligence and mathematical models using IRD.

Model		R2	RMSE
Computational intelligence	ANN	0.9986	0.0210
Mathematical model	Logarithmic	0.9998	0.0055
	Page	0.9992	0.0090
	Midilli et al.	0.9999	0.0025

. The best results found by applying the ANN to IRD were R² of 0.9986 and RMSE of 0.0210 considering two hidden layers with 12 neurons. On the other hand, the mathematical thin-layer models found the range of R² to be from 0.9992 to 0.9999 and that of RMSE to be between 0.0090 and 0.0025 for IRD at the temperatures of 50 °C and 70 °C. It could be seen that the prediction of the moisture ratios with the model developed using the ANN gave the highest R² result and the lowest RMSE compared with the mathematical thin-layer models (Page, Midilli et al., and logarithmic models) with values of >0.9900 and <0.0100, respectively (Table 5). According to the findings, the ANN produced the greatest outcomes, which was consistent with the findings of previous research [32,47] that backed the usage of an ANN as a data prediction approach to help to enhance the outcomes. In conclusion, the findings of this study showed that the computational model could be applied to real-world problems using ANN in the processes of drying linden leaf samples under a variety of conditions. Therefore, using the ANN approach in drying resulted in an improvement in drying performance in general; managing the drying process and the input factors could maximize energy efficiency, product quality, and profit.

3.6. Total Phenolic Content (TPC) and Total Flavonoid Content (TFC)

To avoid mistakes caused by differences in dry matter contents, the results were calculated using dry matter values. The TPC in fresh leaves was substantially higher than that in dried leaves (p ≤ 0.05). Similarly, a new research study indicated that dried plant materials contained more polyphenolic antioxidants than fresh plant materials [51].

Table 6. Total phenolic and flavonoid contents in fresh and dried linden leaves.

Temperature (°C)	TPC (mg/g, DW)	TFC (mg/g, DW)
Fresh	127.73 ± 0.76 b	0.567 ± 0.015 b
50	95.184 ± 0.47 a	2.790 ± 0.150 a
60	99.756 ± 0.63 a	2.631 ± 0.084 a
70	99.756 ± 0.63 a	2.583 ± 0.145 a
Significance	<0.001	<0.001

Total phenolic content (TPC) and total flavonoid content (TFC). a, b: different letters within the same column show statistical differences (p < 0.01).

displays the TPC and TFC concentrations in linden leaves processed at various temperatures.

Due to heteroscedasticity, a nonparametric permutation test was performed to examine the data. To prevent mistakes resulting from variances in dry matter contents, TPC and TFC values were adjusted and evaluated based on dry matter values. The TPC in linden leaves varied significantly between fresh and dried samples, with values ranging from 95.184 ± 0.63 mg/g to 127.73 ± 0.76 mg/g (Table 6). The TPC in dried leaves (at 50, 60, and 70 °C) was considerably (p-value < 0.001) lower than that in fresh leaves. The decrease in TPC following IR drying may have been due to enzymatic reactions. In addition, the TPC significantly decreased between fresh and dried samples, most likely due to the production of several antioxidant molecules with differing degrees of antioxidant activity. Rababah et al. [52] observed the same outcomes in sage, lemon balm, and thyme, and López et al. [53] did so in blueberry. When evaluating the number of phenolic compounds after drying, greater TPC values were discovered in fresh leaves than in dried samples. It was also reported by Felipe et al. [54] that the drying process could reduce the overall phenol level by roughly 30%.

In contrast, as shown in Table 6, the Duncan test suggested that there were no significant differences among the temperatures (50, 60, and 70 °C). This suggested that linden leaves were thermostable within the temperature range investigated. This may indicate that the phenolic compounds present in linden leaves are thermostable. Złotek et al. [55] made similar observations about the drying process. In addition, some researchers hypothesized that not only the number of antioxidants but also the synergy between them and the other leaves could impact the differences in the antioxidant capacity of material extracts [56].

Similarly, when the TFC was analyzed, a propensity for the phenol content to be directly proportionate was noted. Table 6 displays the TFC content of linden leaves, which varied significantly between fresh and dried samples, ranging from 0.567 ± 0.015 mg/g to 2.790 ± 0.150 mg/g. This may have been due to the decrease in solution viscosity caused by an increase in the temperature as the lime leaves changed from a wet to dry state and the corresponding increase in solubility [57]. Roshanak et al. [58] observed that dried green tea contained a higher concentration of TFC than fresh samples. In a separate investigation, Azad et al. [59] studied the effects of the IR drying process on Angelica Gigas Nakai Powder and discovered that the temperature rise decreased the total flavonoid concentration in comparison with the fresh sample. Even though the highest TFC value among temperature applications was obtained at 50 °C, there were no statistically significant changes (0.001) in the data due to the temperature rise. As with the total phenol content measurements, the TFC values were unaffected by the rise in the temperature. Sugar moieties and methoxyl groups protect flavonoids from various drying processes, such as IR, microwave, and ultrasonic-induced degradation, while hydroxyl groups and the presence of non-phenolic chemicals increases their stability [60]. In this investigation, regardless of the kind of flavonoids and the amount of substituents, the flavonoid content did not vary. In addition, the present study’s TFC results correlated with those of Olsson et al. [61]. According to their findings, heating did not affect the total flavonol content in sweet cultivars and red onion cultivars.

As evidenced by these findings, drying processes have diverse effects on TPC and TFC. This conclusion implies that in addition to the Midilli drying model, the simpler Page model may be preferable for drying linden leaves using an infrared thin-layer drying approach. In addition, 50 °C could be sufficient in terms of phenol concentration and flavonoid content in an IR process for drying thin layers of lime leaves. Higher temperatures, such as 60 °C or 70 °C, can be avoided to conserve energy. Still under investigation are the functional aspects of food drying that are influenced by complex chemical interactions.

3.7. Results of Artificial Neuron Networks to Predict Chemical Properties of Linden Leaf Samples

Temperatures and linden leaf thickness levels were used to predict total phenolics (mg/g, DW), total flavonoids (mg/g, DW), DPPH (mmol/g, DW), and FRAP (mmol/g, DW) using the ANN model.

Table 7. Statistical results of chemical characteristics of linden leaf samples for ANN approach using IRD.

No. of Hidden Layers	No. of Neurons	Total Phenolics (mg/g, DW)		Total Flavonoids (mg/g, DW)		DPPH, mmol/g, DW		FRAP, mmol/g, DW
		R2	RMSE	R2	RMSE	R2	RMSE	R2	RMSE
1	3	0.9969	2.8914	0.9884	0.1393	0.9977	3.1420	0.9816	1.0760
1	6	0.9965	3.1026	0.9882	0.1404	0.9977	3.1396	0.9824	1.0485
1	9	0.9965	3.0855	0.9877	0.1439	0.9975	3.3549	0.9839	1.0017
2	3, 3	0.9975	2.6100	0.9891	0.1346	0.9978	3.0660	0.9845	0.9808
2	6, 6	0.9974	2.6835	0.9890	0.1356	0.9978	3.0664	0.9840	0.9986
2	9, 9	0.9972	2.7533	0.9888	0.1370	0.9978	3.0894	0.9833	1.0197
3	3, 3, 3	0.9970	2.8433	0.9881	0.1401	0.9979	3.0421	0.9826	1.0402
3	6, 6, 6	0.9968	2.9741	0.9876	0.1439	0.9980	2.9317	0.9818	1.0690
3	9, 9, 9	0.9965	3.0873	0.9873	0.1460	0.9979	3.0024	0.9812	1.0906

illustrates the statistical results of the four chemical properties obtained by applying the multi-layer feed-forward network structure on the drying experimental data of the samples. The ANN dataset was used to assess the optimum number of neurons and hidden layers for multi-layer neural network modeling for determining the best predictive power. In the case of total phenolics, total flavonoids, and FRAP, we found that the architecture with two hidden layers with 6 (3 and 3) neurons obtained the best results of R² (0.9975, 0.9891, and 0.9845) and the lowest RMSE (2.6100, 0.1346, and 0.9808) as compared with those with one hidden layer (3, 6, and 9 neurons), two hidden layers (12 and 18 neurons), and three hidden layers (9, 18, and 27 neurons), respectively (Table 6). On the other hand, for DPPH, the highest results were found with the architecture with three hidden layers with 18 (6, 6, and 6) neurons, which obtained the best result of R² (0.9980) and the lowest RMSR (2.9317) as compared with those with one hidden layer (3, 6, and 9 neurons), two hidden layers (6, 12, and 18 neurons), and three hidden layers (9 and 27 neurons), respectively (Table 7). In addition to this, it was discovered that the networks were vulnerable to the number of neurons hiding in their layers under the surface. Because of this, lower neuronal populations led to underfitting.

4. Conclusions

In this research study, the possibility of employing an ANN as a modeling tool to predict the drying process and the chemical features of linden leaf samples was investigated. The effectiveness of the IRD strategy was tested in practice by drying samples of linden leaves. According to the findings, IRD had a major impact on the rate at which moisture evaporated, the diffusivity of water, and the activation energy in linden leaf samples. A rise in the drying temperature and sample thickness had an effect on the drying kinetics and moisture diffusivity of samples. The effective moisture diffusivity ranged from 4.13 × 10⁻¹² m²/s to 5.89 × 10⁻¹² m²/s, and the average value was 5.89 × 10⁻¹² m²/s. The activation energy was 16,339 kilojoules per molecule. The drying kinetics of linden were satisfactorily described using logarithmic models and those developed by Midilli et al. (R² > 0.9900). The ANN model had the greatest R² value, which was 0.9986. By comparing mathematical thin-layer models and the ANN, the ANN outputs were shown to be more accurate. In addition, the ANN model made significantly accurate predictions of the linden chemical attributes of TPC, TFC, DPPH, and FRAP, with R² values of 0.9975, 0.9891, 0.9980, and 0.9845, respectively, and RMSE values of 2.6100, 0.1346, 2.9317, and 0.9808, respectively. Because of this, the ANN model was capable of describing a greater variety of experimental data than the theoretical models, which were restricted to certain experimental circumstances. Thus, the ANN may be regarded as a viable alternative modeling approach for the purpose of understanding the drying behavior of linden leaf samples. In addition, ANNs could be successfully applied to industrial drying processes, online monitoring, and management operations. Nevertheless, further research is necessary to determine the capacity of ANNs to accurately forecast the changes that occur in the nutritional profile of fruits and vegetables as a result of drying.