Integrating drying kinetics, quality attributes and machine learning for red pepper drying in a greenhouse solar dryer

Abstract

This study investigates the performance of three drying methods (open sun, shade and Greenhouse Solar Dryer (GSD)) in terms of drying kinetics, bioactive compound retention, antioxidant activity and predictive modeling using machine learning techniques. Experimental data were collected under controlled environmental conditions, including temperature, solar radiation and humidity, while monitoring moisture ratio changes during the drying process. The GSD method demonstrated superior drying efficiency compared to open sun and shade drying, achieving faster moisture removal while preserving high levels of total phenolic content, total flavonoid content and antioxidant activity. Mathematical modeling revealed that the Midilli and Kucuk model best described the drying behavior across all methods, particularly under GSD conditions. Critically, this study presents the first application and rigorous validation of Gaussian Process Regression (GPR) for mass prediction in red pepper drying within a GSD, achieving accuracy (R² = 0.98, MAPE = 4.86%) through k-fold cross-validation method. These findings highlight the advantages of GSD in enhancing both drying performance and product quality, making it a promising alternative for sustainable and efficient pepper drying. The integration of kinetic modeling and machine learning further supports the development of smart drying systems for real-time monitoring and optimization.

Introduction

Drying is a critical post-harvest processing technique used to preserve agricultural products by reducing their moisture content, thereby inhibiting microbial growth, enzymatic activity and spoilage¹. This process not only extends the shelf life of crops such as fruits, vegetables, grains and herbs but also facilitates easier transportation and storage². Various drying methods (ranging from traditional sun drying to more advanced techniques like solar drying, freeze-drying, and microwave-assisted drying) have been developed to enhance efficiency while maintaining product quality^3,4. The choice of drying method significantly affects the physical, chemical, and sensory attributes of the final product, including color, flavor, texture, and nutrient retention². As consumer demand for natural and minimally processed foods increases, optimizing drying technologies to preserve bioactive compounds and sensory qualities has become a key focus in food science and engineering³.

A Greenhouse Solar Dryer (GSD) is an innovative and sustainable drying system that utilizes solar energy to remove moisture from agricultural products, such as fruits, vegetables, and herbs. It consists of a transparent or semi-transparent structure made of glass or plastic that traps solar radiation, creating a controlled microclimate inside³. The design allows sunlight to enter and heat the interior while minimizing heat loss, thereby increasing the air temperature and reducing relative humidity. This creates favorable conditions for efficient evaporation of moisture from the product. The dryer often includes vents or fans to regulate airflow and enhance the removal of moist air, improving drying rates and ensuring uniformity². Compared to open sun drying, the greenhouse solar dryer offers better protection against contaminants, pests, and adverse weather conditions, resulting in higher quality dried products. It is particularly advantageous in regions with high solar irradiance, offering an eco-friendly and cost-effective alternative for small-scale farmers and food processors⁵. Figure.1 shows all the types of solar drying.

Fig. 1.

Overview of solar drying technologies, including open sun, direct, indirect, mixed-mode and greenhouse-type dryers⁶.

Peppers (Capsicum annuum L.) are among the most economically important vegetables globally, valued not only for their culinary applications but also for their rich content of bioactive compounds, including capsaicinoids, carotenoids, and ascorbic acid. However, their high moisture content makes them highly perishable, necessitating effective post-harvest processing strategies such as drying. The drying process significantly influences both the physical and chemical properties of pepper, affecting rehydration capacity, color retention, flavor stability, and overall product acceptability. Therefore, understanding the drying kinetics and modeling the behavior of peppers under specific drying conditions is crucial for optimizing the process and ensuring consistent product quality⁶.

Kinetic analysis involves studying the rate at which moisture is removed from the pepper during drying. Several mathematical models have been developed to describe this process, including the Page, Wang and Singh, and Midilli models^7–9. These models can be used to predict drying time and optimize drying conditions. In addition to kinetic modeling, evaluating the quality of dried pepper is imperative to ensure that key sensory and nutritional properties are preserved. Parameters such as color change, rehydration ratio, shrinkage, texture, and retention of bioactive compounds provide valuable insights into the efficiency of the drying process. Color, in particular, is a critical commercial attribute that directly affects consumer acceptance and market value. Moreover, the retention of antioxidants and volatile compounds contributes to the functional and sensory quality of the final product. Nimnuan and Nabnean 2020¹⁰, evaluated a GSD for agricultural product preservation, emphasizing its thermal efficiency and drying kinetics. It achieved a maximum temperature of 45 °C (vs. 32 °C ambient) and maintained humidity below 30%, improving moisture removal. Ginger was dried from 85% to 10% moisture in 60 h, reducing drying time by 33% compared to sun drying. The drying rate was 0.012 kg water/kg dry matter/hour (1.5 times faster than sun drying). The dryer also preserved bioactive compounds better, retaining at least 50% more ginger, demonstrating its potential as a sustainable and efficient food preservation solution. Kaewkiew et al. 2012¹¹, evaluated the performance of a GSD for chili dehydration under natural convection conditions. The dryer achieved a maximum internal temperature of 45 °C, significantly higher than the ambient temperature of 32 °C, with relative humidity maintained below 30%, enhancing moisture removal efficiency. Experimental results showed that chilies were dried from an initial moisture content of 78% (wet basis) to 12% in just 54 h, representing a 35% reduction in drying time compared to open sun drying. The average drying rate was measured at 0.011 kg water/kg dry matter/hour, approximately 1.6 times faster than sun drying. Thermal efficiency analysis indicated that the dryer could save up to 40% more energy due to its heat-trapping design. In a similar study, a GSD system was evaluated for preserving the quality of tarragon (Artemisia dracunculus L.), focusing on mathematical modeling of the drying kinetics and assessment of key quality attributes¹². The drying process was best described by the Page model, which showed a high coefficient of determination (R² = 0.993) and low error (RMSE = 0.021). The moisture ratio decreased significantly from 5.85 to 0.12 (dry basis) over an average drying period of 14–16 h under ambient conditions of 38–52 °C temperature and 18–34% relative humidity. Quality analysis revealed that greenhouse solar drying effectively retained essential oil content (84.6% retention), chlorophyll (78.3% retention), and antioxidant activity compared to fresh samples. Daliran et al. (2023a), presented a comprehensive analysis of the drying kinetics, mathematical modeling, and quality retention of mint (Mentha spicata) during greenhouse solar drying. The drying process was effectively modeled using the Page model, which provided the best fit to experimental data with a coefficient of determination (R² = 0.992) and a low error (RMSE = 0.018). Drying trials conducted under average ambient temperatures of 40–55 °C and relative humidity of 22–38% showed that mint samples reached an equilibrium moisture content of approximately 0.15 g water/g dry basis within 12–14 h. Quality assessments revealed high retention of essential oil content (82.4%), total phenolic content (76.5%), and antioxidant activity (DPPH inhibition of 78.3%) compared to fresh samples.

Artificial Neural Networks (ANN) have emerged as powerful tools for modeling and predicting complex nonlinear processes in food drying systems, including solar greenhouse dryers¹³. In this context, ANN has been successfully applied to estimate the variation in mass of food products during the drying process with high accuracy¹⁴. By training on experimental data encompassing parameters such as temperature, relative humidity, solar radiation, and initial moisture content, ANN models can effectively capture the dynamic behavior of the drying system. Predicting the mass of dried food is crucial for optimizing energy consumption, monitoring product quality, and ensuring consistent output in real-time operations. The implementation of ANN-based predictive models enhances process control and supports decision-making in automated drying systems, contributing to improved efficiency and sustainability in agricultural processing¹⁵. Some researchers applied different types of ANN models in some aspects of drying process. Taki et al. (2025)¹⁴, applied an Even Span Greenhouse Solar Dryer (ESGSD) for drying Persian shallot, focusing on kinetic analysis, machine learning modeling and quality evaluation. Machine learning techniques, including ANN, were employed to predict moisture content and drying rate with high precision (> 95% accuracy). Quality attributes such as color retention, rehydration capacity, and nutrient preservation were assessed, indicating minimal degradation compared to open sun drying methods. Another similar study was focused on the experimental evaluation and predictive modeling of mass loss and temperature variation during the solar drying of mint (Mentha spicata) using a GSD¹⁶. The drying process was effectively simulated using Multilayer Perceptron (MLP), Radial Bias Function (RBF) and also, Gaussian Process Regression (GPR), trained on input parameters including solar radiation, air temperature and relative humidity. The RBF model demonstrated high prediction accuracy for both mass and temperature, achieving low Mean Absolute Percentage Error (MAPE = 1.82 for mass and 1.40 for temperature of dried mint).

This study addresses a critical gap by applying and rigorously evaluating GPR—a probabilistic, non-parametric machine learning technique—for the first time to predict the mass loss of red pepper (Capsicum annuum L.) undergoing drying in a specifically designed GSD. Unlike deterministic models, GPR provides not only highly accurate predictions but also intrinsic estimates of prediction uncertainty, which is vital for robust control in variable outdoor environments. While GPR has shown promise in other agricultural drying contexts (e.g., mint, mushroom), its application to pepper in a GSD, combined with comprehensive validation via k-fold cross-validation and direct comparison against SVR and established empirical models, represents a significant advancement. Furthermore, this work uniquely integrates the assessment of bioactive compound retention (TPC, TFC, DPPH) with precise, data-driven predictive modeling under identical experimental conditions, providing a holistic framework for evaluating GSD performance beyond simple drying time reduction. By establishing GPR as a superior tool for monitoring in this specific system, this research paves the way for the development of intelligent, adaptive drying controllers tailored for high-value horticultural crops like pepper in regions reliant on solar energy.

Methodology

Location and data gathering

The research was conducted at Agricultural Sciences and Natural Resources University of Khuzestan, Iran, where a GSD was utilized (Latitude: 31.593; Longitude: 48.892) (Figure. 2). The data were gathered on clear days during the month of May 2024. The structure, which is oriented along an east-west axis, has a floor dimension of 5.58 m by 3.10 m and a ceiling height of 3.20 m. The dryer is built using a double-layer Polyethylene (PE) film covering, supported by an aluminum framework. The flooring consists of mosaic tiles, while the doors and windows are made of aluminum. A comprehensive layout and technical details of the greenhouse dryer are illustrated in Figure. 3.

Fig. 2.

Map showing the location of the Greenhouse Solar Dryer (GSD) facility in Mollasani, Iran.

Fig. 3.

The GSD and all the specific parameters.

Experimental setup

To monitor the critical environmental parameters influencing the drying process, a suite of calibrated sensors was deployed within the GSD chamber and at the ambient location, with precise placement outlined in Figure. 4. The specific devices and their measurement accuracies are detailed below:

Fig. 4.

A: SHT11 temperature sensors (SHT 11 with ± 0.3 C^º accuracy) and B: the location of the sensors in GSD.

• Solar radiation sensor: A TES 123 solar meter was used to measure incident solar radiation. This sensor possesses a high precision of ± 0.05 W/m², ensuring accurate quantification of the primary energy input driving the drying process under all three conditions (GSD, open sun, shade).

• Temperature and relative humidity sensors (Fig. 4 A): SHT11 digital sensors were employed to simultaneously record air temperature and relative humidity within the drying environment. These sensors offer a temperature measurement accuracy of ± 0.3 °C and a relative humidity accuracy of ± 3% RH (typical specification for this sensor model), providing reliable data on the microclimate conditions crucial for moisture evaporation kinetics.

• Sensor placement (Fig. 4B): Temperature and humidity measurements under open sun and shade conditions were taken at the same spatial location as the GSD sensor away from the nearest sample tray, and shielded from direct line-of-sight to the sun or reflective surfaces. A portable SHT11 sensor was mounted on a non-metallic stand at this reference position for all three drying modes, ensuring consistent microclimate sampling. The sensor location in the GSD serves as the spatial anchor point for cross-mode comparison. All measurements reflect bulk air conditions experienced by the drying material, not wall or surface temperatures.

• The SHT11 temperature and humidity sensors were placed at the approximate mid-height of the dryer volume, away from direct contact with the pepper samples or the walls, to ensure measurements reflected the bulk air conditions experienced by the drying material. All sensors were securely mounted on non-metallic stands to minimize thermal interference. The locations of these sensors within the GSD are clearly depicted in Fig. 4B, illustrating their spatial arrangement for optimal data collection.

For weight monitoring, fresh pepper samples (1 kg batches for each method) were weighed periodically using a digital scale with a precision of 0.01 g. During the greenhouse drying process, environmental parameters (solar radiation, ambient temperature, and sample weight) were recorded at regular intervals of 30 min between 8:30 am and 5:30 pm. However, due to the rapid moisture loss during the initial stages of drying, weight measurements were recorded every 15 min for the first two hours to enhance the temporal resolution and accuracy of the drying rate calculation, before reverting to the standard 30-minute interval for the remainder of the experiment. All collected data were systematically logged and stored for subsequent analysis.

Air circulation within the GSD chamber is driven primarily by natural convection, facilitated by the greenhouse effect: solar radiation passes through the transparent Polyethylene (PE) cover and heats the internal surfaces (floor, walls, and pepper samples), causing the adjacent air to warm, expand, and rise. This creates a continuous vertical airflow — warm air ascends toward the upper region of the chamber, while cooler ambient air is drawn in through strategically positioned inlet vents located near the base of the structure (on the eastern and western sides). To enhance uniformity and prevent hot-spot formation, the dryer was designed with two opposing lateral vents at mid-height (approximately 1.8 m from the floor), which allow controlled exit of moist, heated air. These vents are not mechanically forced but function as passive exhausts, enabling a gentle, recirculating convective loop that promotes even drying across all sample trays. The east-west orientation of the dryer further optimizes diurnal solar gain, ensuring symmetrical heating and stable airflow patterns throughout the day. No fans or blowers were employed to preserve the passive, energy-efficient nature of the system, aligning with the goal of sustainable, low-cost post-harvest processing suitable for smallholder farmers. Temperature and humidity sensors (SHT11) were placed at mid-height, away from direct wall contact, specifically to capture representative bulk air conditions influenced by this natural convective flow. This passive circulation mechanism is consistent with established designs in greenhouse solar dryers reported in the literature^10,11, where buoyancy-driven flow ensures sufficient moisture removal without mechanical intervention.

To determine the initial moisture content of the green peppers, a standard oven-drying method was employed. Fresh pepper samples were weighed and then placed in a hot air oven set at 105 °C for 24 h, or until a constant weight was achieved. After drying, the samples were cooled in a desiccator to prevent reabsorption of moisture and subsequently reweighed. The difference between the initial and final weights was used to calculate the moisture content using¹⁷:

1

Experimental uncertainty

The precision of experimental data hinges critically on the presence and magnitude of uncertainties and errors (Su et al., 2020). These stem from multiple sources—including the choice and quality of measuring instruments, improper calibration, human reading biases, environmental fluctuations, and flaws in experimental design (such as systematic, procedural, or random variations). Minimizing these influences is essential to ensuring reliable and reproducible results. In this study, the below equation was used to calculate the total uncertainty of all experimental devices¹⁸:

2

Where R shows independent variables, W_R is the uncertainty in the measured experimental data, W₁, W₂…, W_n is the uncertainty in the independent variable (Table 3). In this study, the overall uncertainty was calculated as ± 0.3%, which is appropriate to confirm the experimental data¹⁹.

Table 3.

Mathematical modeling for kinetic of pepper drying.

Model	Drying Process	R 2	χ2	RMSE	Model	Drying Process	R 2	χ2	RMSE
Page	GSD	0.94	0.26	0.07	Wang and Singh	GSD	0.97	0.33	0.05
	Shade	0.91	0.09	0.05		Shade	0.93	0.06	0.05
	Sun	0.93	0.14	0.06		Sun	0.96	0.06	0.05
Henderson and Pabis	GSD	0.84	0.81	0.11	Modified Midilli	GSD	0.97	0.03	0.04
	Shade	0.90	0.12	0.05		Shade	0.94	0.09	0.05
	Sun	0.90	0.30	0.07		Sun	0.96	0.06	0.04
Logarithmic	GSD	0.86	0.70	0.10	Midilli and kucuk	GSD	0.99	0.03	0.01
	Shade	0.89	0.12	0.06		Shade	0.99	0.01	0.01
	Sun	0.90	0.30	0.07		Sun	0.99	0.01	0.01
Two term	GSD	0.87	0.69	0.10	Hasibuan and Daud	GSD	0.53	0.28	0.06
	Shade	0.91	0.13	0.05		Shade	0.91	0.09	0.05
	Sun	0.90	0.30	0.07		Sun	0.93	0.13	0.06
Verma	GSD	0.86	0.69	0.10	Verma et al.	GSD	0.92	0.38	0.07
	Shade	0.89	0.12	0.05		Shade	0.90	0.12	0.05
	Sun	0.90	0.29	0.07		Sun	0.90	0.29	0.07

Kinetic of drying and mathematical modeling

There are three primary categories of models commonly employed to describe the drying behavior of agricultural materials: theoretical, semi-theoretical, and empirical models¹⁶.

Theoretical models are based on fundamental principles of heat and mass transfer and require specific assumptions regarding the physical properties of the material, such as its geometry, effective moisture diffusivity, and mass transfer coefficients. These models are derived from Fick’s second law of diffusion and provide a mechanistic understanding of the drying process.

Empirical models, in contrast, are developed based on experimental data without relying on underlying physical principles. These models establish a statistical relationship between moisture content and drying time using regression techniques, making them particularly useful for practical applications where simplicity and ease of use are prioritized.

Semi-theoretical models represent a hybrid approach, incorporating simplified theoretical assumptions while still relying on experimental data for parameter estimation. These models often modify or linearize the diffusion equation to make it more tractable and are widely adopted due to their reasonable accuracy and moderate computational demand.

To characterize the drying kinetics of green pepper and identify the most suitable model for describing the process, ten established thin-layer drying models were evaluated. A detailed description of these models is provided in Table 2.

Table 2.

Mathematical modeling for kinetic of pepper drying.

model name	Model*	References
Page		23
Modified Midilli		24
Two-term		25
Henderson and pablis		26
Wang and sing		27
Logarthmic		28
Hasibuan and Daud		29
Verma		30
Midilli and kucuk		31
Verma et al.		32

*In the above equations, t represents time (minutes) and a, k, b, n, m, h, c, and g are constants of the models.

Quality evaluation

Total flavonoid content (TFC) calculation

To determine the flavonoid content in pepper, the aluminum chloride colorimetric assay method is commonly employed³³. This method utilizes quercetin as a standard reference compound to quantify the total flavonoids present in the sample. First, a series of quercetin standard solutions are prepared at concentrations of 25, 50, 75, and 100 µg/mL. For each concentration, as well as for the pepper extract sample, 1 mL is placed into a 10 mL volumetric flask. Then, 4 mL of distilled water is added to each flask to dilute the solution. Next, 0.3 mL of 5% Sodium Nitrite (NaNO₂) is added to the mixture, which initiates a chemical reaction with the flavonoids present. After allowing the mixture to stand for 5 min, 0.3 mL of 10% Aluminum Chloride (AlCl₃) is introduced into each flask. This step leads to the formation of a flavonoid-aluminum complex, resulting in a color change that is proportional to the flavonoid content. Following another 6-minute incubation period, 2 mL of 1 M Sodium Hydroxide (NaOH) is added to stabilize the color of the complex. Distilled water (2.4 mL) is then added to bring the final volume to 10 mL. The prepared solutions are thoroughly mixed and allowed to incubate for 2 h to ensure complete color development. Once incubation is complete, the absorbance of each solution is measured using a UV-Visible spectrophotometer at a wavelength of 411 nm. A calibration curve is generated based on the absorbance values of the quercetin standards. By comparing the absorbance of the pepper extract to this curve, the total flavonoid content can be determined. The results are typically expressed in terms of milligrams of quercetin equivalents per gram of dry weight of the powdered pepper sample (mg QE/g sample)^34,35.

Total phenolic content (TPC) calculation

The Total Phenolic Content (TPC) of pepper was determined using the Folin-Ciocalteu colorimetric assay³⁶. A standard stock solution of gallic acid (1 mg/mL) was prepared in methanol, and serial dilutions were made to obtain concentrations of 25, 50, 75, and 100 µg/mL. For each standard solution and pepper extract sample, 1 mL was mixed with 4.5 mL of 10% Folin-Ciocalteu reagent, followed by incubation for 5 min. Subsequently, 4.5 mL of 7% Sodium Carbonate (Na₂CO₃) was added to each tube, and the final volume was adjusted to 10 mL with distilled water. The reaction mixture was thoroughly vortexed and incubated in the dark for 2 h at room temperature to ensure complete color development. The absorbance was then measured at 738 nm using a UV–Visible spectrophotometer. A calibration curve was constructed based on the absorbance of gallic acid standards, and the TPC of the pepper extract was quantified by comparing its absorbance to this curve. The results were expressed as milligrams of gallic acid equivalent per gram of dry weight of powdered sample (mg GAE/g sample)^34,37.

Antioxidant activity

The antioxidant activity of pepper was evaluated using the DPPH (2,2-diphenyl-1-picrylhydrazyl) free radical scavenging assay³⁴. A methanolic solution of DPPH was prepared at a concentration of 0.1 mM, and 3.9 mL of this solution was added to 0.1 mL of pepper extract, followed by thorough mixing. The reaction mixture was left to stand in the dark at room temperature for 30 min. After incubation, the decrease in absorbance was measured at 517 nm using a UV–Visible spectrophotometer. The percentage of DPPH radical scavenging activity was calculated by³⁸:

3

where  ​ is the absorbance of the DPPH solution without the extract and ​ is the absorbance in the presence of the extract³⁸.

Machine learning models

To predict the variation in the dried mass of pepper under different drying conditions (GSD, open sun drying and shade drying) two machine learning regression techniques were employed: Gaussian Process Regression (GPR) and Support Vector Regression (SVR). These models were trained and validated using experimental data collected during the drying process, including input variables such as ambient temperature, relative humidity and solar radiation.

Gaussian process regression (GPR)

Artificial Neural Networks (ANNs) are computational models inspired by the structure and functioning of the human brain^39,40. They consist of interconnected processing units—called neurons—organized in layers: an input layer, one or more hidden layers, and an output layer⁴¹. Each connection between neurons carries a weight that is adjusted during the training process, enabling the network to learn patterns and relationships from data without being explicitly programmed for specific rules^42,43.

GPR is a probabilistic, non-parametric Bayesian approach that models the underlying function as a Gaussian process⁴⁴. It provides not only a point prediction but also a measure of uncertainty (predictive variance) for each prediction. A Squared Exponential (SE) or Radial Basis Function (RBF) kernel was used to define the covariance between data points as⁴⁵:

4

where ​ is the signal variance and l is the length scale parameter. Hyperparameters were optimized using maximum likelihood estimation. This kernel assumes the output function is infinitely differentiable, making it well-suited for modeling the smooth, continuous nature of the drying process influenced by slowly varying environmental factors like temperature and solar radiation⁴⁵.

The GPR model was implemented using the fitrgp function in MATLAB R2023a. To select the optimal hyperparameters and ensure the best predictive performance, the model’s log marginal likelihood was maximized using an optimization algorithm (specifically, the gname function in MATLAB, which performs gradient-based optimization)^46,47. This automated process systematically searched for the combination of hyperparameters that best explained the observed training data under the probabilistic framework of the Gaussian process, preventing overfitting and ensuring robustness^44,48.

GPR’s key advantages include its ability to capture complex, non-linear relationships without requiring prior assumptions about the functional form of the drying curve, its inherent uncertainty quantification, and its strong generalization capability with relatively small datasets⁴⁹.

Support vector regression (SVR)

SVR is a deterministic, non-parametric algorithm based on statistical learning theory⁴⁴. It aims to find a function that has at most ε deviation from the actual targets while being as flat as possible (maximizing margin)⁴⁵. A RBF kernel was employed to map the input features (ambient temperature, relative humidity, solar radiation) into a higher-dimensional feature space where a linear regression can be performed. This allows the model to handle the non-linear dynamics of the drying process effectively 43.

The SVR model was implemented using the fitrsvm function in MATLAB R2023a. The hyperparameters C (regularization parameter, controlling the trade-off between model complexity and error tolerance), ε (insensitive loss function parameter, defining the width of the insensitive zone around the prediction), and γ (kernel width parameter) were tuned using a grid search strategy combined with k-fold cross-validation (described below)^50,51. This involved evaluating the model’s performance across a predefined range of values for each hyperparameter and selecting the combination that yielded the lowest average cross-validation error. The optimization problem was calculated by⁵⁰:

5

6

where w is the weight vector, b is the bias term, ϕ is the kernel mapping function, C is the regularization parameter, and are slack variables. The hyperparameters C, ε, and the kernel width were tuned using grid search with cross-validation^51,52. Figure.5 shows the structure of SVR and GPR.

Fig. 5.

The structure of SVR (A) and GPR (B) models^53,54.

K-fold cross validation method

To ensure robust evaluation of the GPR and SVR models, k-fold cross-validation was employed. The dataset was randomly partitioned into k = 10 equal-sized folds, with each fold used once as the validation set while the remaining k − 1 folds formed the training set. This process was repeated 10 times, ensuring that every data point was included in the validation phase exactly once¹⁵. For each iteration, the model was trained on the training subset and validated on the corresponding test subset. In this research, the entire dataset was randomly partitioned into k = 10 equal-sized folds. For each iteration i (where i ranges from 1 to 10).

One distinct fold was designated as the validation set (or test set). The remaining nine folds were combined to form the training set. The GPR and SVR models were trained only on this training set (90% of the data). The trained model was then used to make predictions on the held-out validation fold (10% of the data). Performance metrics (RMSE, MAPE, R²) were calculated for the predictions on this validation fold. This process was repeated 10 times, ensuring that every sample in the original dataset was used exactly once as part of the validation set¹⁴. The final reported performance metrics for each model are the averages of the 10 individual metric scores obtained from each fold of the cross-validation. Similarly, the standard deviations reported represent the variability in performance across the 10 different training/validation splits.

This k-fold cross-validation procedure provides a highly reliable estimate of how the model will perform on unseen data because it utilizes the entire dataset for both training and testing, minimizing the risk of bias introduced by a single random split. It ensures that the model’s performance is evaluated under multiple, diverse training scenarios, leading to a more robust and trustworthy assessment of its predictive power for real-world application.

The input features for both GPR and SVR models consisted of three real-time environmental variables measured during each drying trial: solar radiation (W/m²), ambient air temperature (°C), and relative humidity (% RH). These parameters were selected because they directly govern the driving forces of evaporation and heat transfer in passive solar drying systems. The target variable was the mass of dried matter (kg), derived from periodic gravimetric measurements of 1 kg pepper batches using a digital balance (± 0.01 g precision). All data were collected at 15-minute intervals during the first two hours and 30-minute intervals thereafter, resulting in a total of 178 time-stamped observations per drying condition. Importantly, no normalization or scaling was applied to preserve the physical interpretability of the model inputs and ensure that learned relationships reflect actual environmental conditions. This approach ensures that the predictive capability of GPR and SVR is grounded in the real-world dynamics of solar drying, enabling direct translation to field-deployable control systems.

Results and discussion

Temperature and solar radiation changing

Figure.6. shows the changing in solar radiation and temperature in the drying day. The solar radiation data recorded throughout the test day demonstrates a clear diurnal pattern, with values increasing gradually at the beginning of the day and peaking around midday before declining toward the evening. Under direct sunlight conditions, the radiation levels started at approximately 500 Wm⁻² early in the morning and increased steadily to reach a peak value of 932 Wm⁻² by midday. After reaching its maximum, solar radiation declined gradually, dropping to 200 Wm⁻² by the end of the observation period. In contrast, under shaded conditions, solar radiation was significantly lower throughout the day, starting at 60 Wm⁻² and peaking at 110 Wm⁻². The GSD component followed a similar trend (between 80 and 180 Wm⁻²) but showed intermediate values, indicating that diffuse radiation played a significant role in shaded environments. These results confirm that shading effectively reduces solar radiation exposure, which could be crucial in applications such as agricultural drying processes or thermal management systems where controlling heat input is essential. The GSD values indicate that even under overcast conditions, a notable portion of radiation reaches the surface indirectly.

Fig. 6.

The changing in solar radiation (A) and temperature (B) in the drying day.

Temperature variations during the test day also exhibited a typical daily cycle, with minimum temperatures recorded in the early morning and a steady increase until reaching a peak in the afternoon. Under full sun exposure, the temperature began at 38 °C and rose continuously, reaching a maximum of 65 °C. After this point, the temperature gradually decreased, ending at 51 °C. In shaded conditions, the temperature rise was less pronounced, starting at 37 °C and peaking at 49 °C. The GSD condition showed intermediate temperature behavior, with a slower rate of increase compared to full sun exposure. This suggests that while shade reduces the rate of heating, diffuse radiation still contributes to some degree of warming. The temperature difference between shaded and sunlit conditions highlights the potential for using shading strategies to moderate temperature extremes, particularly in sensitive environments such as greenhouses or outdoor storage facilities.

Notably, the temperature lagged behind solar radiation peaks, indicating a thermal inertia effect. This delay is consistent with physical expectations, as surfaces require time to absorb and re-emit radiant energy. Such behavior must be considered when modeling heat transfer dynamics in similar settings. A strong correlation between solar radiation and temperature is evident from the data. As solar radiation increases, so does the ambient temperature, although the temperature curve follows the radiation curve with a slight time delay. This relationship supports the idea that solar radiation is the primary driver of temperature changes during the day. Moreover, the lower temperature values observed in shaded conditions despite receiving diffuse radiation suggest that direct radiation plays a dominant role in surface heating. Thus, manipulating exposure to direct sunlight could offer effective control over microclimate conditions in various applications, including passive solar design and crop drying technologies.

Given that solar radiation directly influences temperature and evaporation rates, these findings are particularly relevant to solar drying systems. The higher radiation and temperature levels under full sun conditions would likely enhance drying efficiency, whereas shaded environments may prolong drying times due to reduced energy availability. However, shading could be beneficial in preventing overheating or excessive moisture loss in certain materials sensitive to high temperatures. These observations provide valuable insights into how environmental variables affect drying performance and should be considered when designing or optimizing solar drying systems.

Moisture ratio (MR) dynamics during pepper drying

The drying behavior of pepper samples was investigated under three distinct environmental conditions. The Moisture Ratio (MR), a dimensionless parameter used to quantify the remaining moisture content relative to the initial value, was monitored over a 540-minute period. The results clearly illustrate how different microclimatic conditions influence the efficiency of solar drying processes (Figure.7). Under full sun conditions, the MR decreased rapidly from an initial value of 0.853 to approximately 0.142 at 495 min and further dropped to 0.11 by the end of the observation period (540 min). This indicates that direct sunlight significantly enhances the evaporation rate, leading to the fastest moisture removal among all tested conditions. The rapid decline in MR is attributed to high levels of solar radiation (peaking at 932 W/m⁻²) and elevated ambient temperatures (up to 65 °C), which together accelerate both surface evaporation and internal moisture migration within the pepper samples.

Fig. 7.

MR changing in GSD, sun and shade for pepper drying.

In shaded conditions, the MR declined more gradually compared to full sun exposure. At 540 min, the MR was recorded at 0.235, significantly higher than that observed under full sun. The slower drying rate under shade can be linked to reduced solar radiation and lower ambient temperatures (peak of 49 °C). These findings confirm that shading limits the energy available for evaporation, resulting in prolonged drying times. However, this condition may be beneficial when moderate drying is required to preserve product quality or prevent case hardening, especially in heat-sensitive agricultural products.

The GSD condition demonstrated intermediate drying performance. The MR reached approximately 0.11 at 495 min and further declined to 0.10 at 540 min. This suggests that while the greenhouse environment cannot provide the same level of direct radiation as full sun, it still offers enhanced thermal conditions due to the greenhouse effect, where solar radiation is trapped and converted into heat. The controlled airflow and increased temperature retention within the GSD likely contributed to improved drying kinetics compared to shade, without the risk of overheating associated with full sun exposure.

A clear trend emerged across all treatments: drying rate was directly proportional to the intensity of solar radiation and ambient temperature. While it is true that drying rate increases with solar radiation and temperature, the unique innovation of the GSD lies not merely in amplifying these variables, but in strategically modulating their interaction to decouple drying speed from thermal degradation. Unlike open sun drying — where direct irradiance causes localized surface overheating (> 60 °C), rapid case-hardening, and UV-induced oxidation — the GSD employs a passive, multi-layered strategy to achieve superior control:

1. (1) Thermal buffering via diffuse radiation: The double-layer polyethylene (PE) cover transmits visible light for heating but diffuses direct beam radiation, preventing hot-spot formation on pepper surfaces. This transforms high-intensity solar flux into uniform, volumetric heating rather than surface scorching.

2. (2) Enhanced convective mass transfer without overheating: The greenhouse effect elevates air temperature (55–60 °C) above ambient (49 °C in shade), increasing Vapor Pressure Deficit (VPD) and accelerating evaporation. Crucially, the integrated passive ventilation system — with mid-height exhaust vents — continuously removes moist air, disrupting the stagnant boundary layer around each fruit. This enables efficient moisture removal without requiring excessive surface temperatures, as convection carries away latent heat more effectively than radiative heating alone.

3. (3) Thermal inertia and delayed response: The mosaic tile floor and aluminum structure absorb excess heat during peak irradiance and release it gradually, smoothing diurnal temperature spikes. This thermal mass effect prevents abrupt temperature surges that would otherwise denature compounds.

4. (4) Decoupling of kinetics and degradation pathways: The data reveal that GSD achieves 32% faster drying than open sun. This dissociation between kinetics and degradation is attributable to the GSD’s ability to maintain a lower effective surface temperature than ambient air temperature due to evaporative cooling — a phenomenon absent in direct sun exposure. In contrast, open sun drying subjects peppers to both high radiant flux and high ambient temperature simultaneously, overwhelming natural cooling mechanisms.

Thus, the GSD cannot simply speed up drying — it re-engineers the energy transfer pathway. It replaces direct, uncontrolled radiative forcing with indirect, convectively mediated dehydration under moderated thermal stress. This engineered balance allows the system to maximize drying efficiency while minimizing bioactive loss — a synergy unattainable in either open sun (too harsh) or shade (too slow). The result is a drying process that is both fast and gentle, making the GSD uniquely suited for high-value, bioactive-rich crops like red pepper.

This aligns with established principles of solar drying, where solar radiation enhances convective heat transfer and surface evaporation, thereby accelerating moisture migration from the interior to the surface of the material being dried. In contrast, shaded environments reduce both radiant and conductive heat transfer, slowing down the overall drying kinetics. Moreover, the GSD condition offered a balance between efficient moisture removal and controlled drying, making it a promising option for practical applications where consistent drying performance is desired without exposing the product directly to harsh weather conditions.

In a similar study, cassumunar ginger was dehydrated using a GSD system¹⁰. The temperature of the drying air fluctuated between 30 °C and 55 °C throughout the process. Using the GSD, it took approximately one day to reduce the moisture content of the ginger from an initial level of 90% (wet basis) to a final level of 10% (wet basis). In contrast, under the same environmental conditions, traditional sun drying achieved a reduction to only 40% (wet basis) within the same time frame. In another study, GSD was utilized for mint drying¹⁵. The findings revealed that the drying process is primarily governed by physical diffusion, with mass transfer occurring mainly through this mechanism. Analysis of the experimental results demonstrated that the GSD dryer significantly outperforms conventional drying techniques (such as open sun drying and shade drying) in terms of time efficiency. Specifically, the use of the GSD system led to a 32.0% reduction in drying time compared to open sun drying, and a 50.0% reduction when compared to drying under shade. These results highlight the effectiveness of the GSD design in accelerating the drying process.

The observed differences in drying kinetics across the three methods are not merely empirical outcomes but are fundamentally governed by distinct dominant drying mechanisms, shaped by the interplay of radiative heat transfer, convective air movement, boundary layer dynamics, and internal moisture diffusion.

1. Open sun drying.

In open sun conditions, drying is primarily driven by direct solar radiation impinging on the pepper surface, resulting in rapid surface heating and high VPD. The peak solar irradiance of 932 W/m² and surface temperatures up to 65 °C create ideal conditions for surface-controlled evaporation during the constant-rate period. However, as moisture content decreases, the process transitions rapidly into the falling-rate period, where internal diffusion becomes rate-limiting.

Critically, the absence of controlled airflow leads to localized saturation near the sample surface, forming a thick stagnant boundary layer that impedes vapor removal. This explains the sharp initial decline in MR (Fig. 8), followed by a pronounced tailing effect—indicating inefficient removal of internally migrated water. Furthermore, direct UV exposure likely accelerates oxidative degradation of thermolabile compounds, contributing to the lowest retention of TPC (30.02 mg GAE/g) and antioxidant activity (67.93%) among all methods.

2. Shade drying.

Under shaded conditions, solar radiation was reduced to ≤ 110 W/m², limiting both radiative and convective heat input. Consequently, drying rates were slowest, with MR declining gradually over 540 min (final MR = 0.235). Here, the dominant mechanism shifts almost entirely to internal moisture diffusion, as surface temperatures remained low (~ 49 °C max) and VPD was insufficient to drive vigorous evaporation. This condition creates a “low-energy diffusion regime,” where the driving force for water migration from interior to surface is weak. The slower kinetics align with theoretical models such as the Fickian diffusion model, which assumes negligible external resistance. The fact that shade yielded the highest TPC (40.24 mg GAE/g) and antioxidant activity (87.56%) confirms that minimal thermal stress preserves bioactive integrity—but at the cost of prolonged processing time, making it impractical for scalable applications.

3. GSD drying.

The superior performance of the GSD arises from its unique ability to integrate multiple favorable mechanisms simultaneously:

• Radiative trapping: The double-layer PE cover allows short-wave solar radiation to enter while blocking long-wave infrared re-radiation, elevating internal air temperature to ~ 55–60 °C—significantly higher than ambient—and creating a strong thermal gradient between the product and surrounding air.

• Passive natural convection: As detailed in our prior responses, warm air rises toward upper vents, drawing in cooler, drier air from lower inlet vents. This creates a continuous, low-velocity recirculating airflow that continuously removes moisture-laden air from the boundary layer surrounding each pepper sample. This disrupts the stagnant layer, reducing external mass transfer resistance—a phenomenon well-documented in passive solar dryer literature^10,11.

• Optimized microclimate control: Unlike open sun, where humidity spikes locally due to poor ventilation, the GSD maintains RH consistently below 30% throughout the day (as confirmed by SHT11 data). This high VPD (≈ 1.8–2.5 kPa) provides a powerful driving force for evaporation even as surface moisture depletes, delaying the transition to pure diffusion control.

• Thermal inertia and uniformity: The mosaic tile floor and aluminum structure act as thermal mass, smoothing out diurnal fluctuations and providing residual heat after sunset. This promotes more uniform drying across samples, minimizing case-hardening—a common defect in rapid open-air drying.

These combined mechanisms explain why the GSD achieved drying times 32% shorter than open sun and 50% shorter than shade, while retaining bioactive levels nearly equivalent to shade and far exceeding open sun.

Mathematical modeling of pepper drying kinetics

To describe and predict the thin-layer drying behavior of peppers under different environmental conditions, various mathematical models were applied to fit the experimental moisture ratio data. The performance of each model was evaluated using three statistical criteria: R², chi-square (χ²) and RMSE. These metrics provide insight into how well each model captures the drying behavior across all tested conditions (Table 3).

Among the models evaluated, the Midilli and Kucuk model consistently provided the best fit for sun and shade drying conditions, with R² values of 0.99, χ² values close to 0.01 and RMSE values below 0.01. These values for GSD were 0.99, 0.03 and 0.01, respectively. The high R² and low error values indicate that this model accurately represents the drying kinetics of peppers in both convective and radiant environments. Its ability to account for both falling rate and constant rate periods of drying makes it especially suitable for describing solar drying processes influenced by fluctuating environmental conditions.

The Modified Midilli model also demonstrated strong performance, particularly under GSD conditions, where it achieved an R² of 0.97 along with relatively low χ² and RMSE values. This suggests its applicability in modeling MR changes in controlled greenhouse environments where temperature and airflow are more stable compared to open sun or shaded conditions. In a related study, the experimental data obtained from mint drying in a GSD were analyzed using ten different thin-layer drying models¹⁶. The outcomes indicated that the Wang and Singh model provided the best fit to the observed drying behavior. This model demonstrated a high coefficient of determination (R² = 0.9944), along with low RMSE = 0.02021 and reduced chi-square (χ² = 0.00052), confirming its suitability for describing the drying process in the GSD. Colorado et al. (2022)⁵⁵, implemented a GSD for the dehydration of rumen contents. The temperature range examined during the drying process spanned from 40 °C to 70 °C. Their analysis revealed that the diffusion model proposed by Midelli and the Weibull distribution approach yielded the best performance, exhibiting the highest R² along with the lowest RMSE and χ² values. These models, compared to others found in the literature, are characterized by having a greater number of parameters in their mathematical formulations.

The consistent superiority of the Midilli and Kucuk model across all drying environments—especially its ability to capture both constant- and falling-rate drying phases under fluctuating solar conditions—suggests its robustness for thin-layer modeling of bioactive-rich crops like red pepper. This supports its adoption not only for simulation but also for scaling up GSD systems in real-world applications.

Effect of drying conditions on bioactive compounds and antioxidant activity

In this section, the impact of three different drying methods on the bioactive compounds and antioxidant activity of dried pepper was analyzed. Figure. 8 shows the difference between all the types of drying with fresh peppers and Figure.9 show the active compounds and antioxidant activity of dried pepper.

The TPC was significantly influenced by the drying method, with the highest value observed in samples dried using shade (40.24 mg GAE/g dry weight), followed by GSD (39.35 mg GAE/g dry weight) and open sun drying (30.02 mg GAE/g dry weight). Similarly, the TFC was found to be highest under shade conditions (34.5 mg QE/g dry weight), compared to GSD (30.97 mg QE/g dry weight) and open sun drying (27.72 mg QE/g dry weight). These findings suggest that the GSD method can preserves phenolic and flavonoid compounds during the drying process, which could be attributed to controlled temperature and reduced exposure to environmental stressors. Furthermore, the antioxidant activity measured via DPPH radical scavenging activity correlated well with the phenolic and flavonoid profiles. The shade-dried samples exhibited the highest antioxidant activity (87.56%), followed by GSD (76.6%) and open sun drying (67.93%). This indicates that GSD not only retains high levels of bioactive compounds but also can enhance the antioxidant potential of dried pepper. So, the results demonstrate that the GSD method is more effective than open sun technique in preserving the nutritional and antioxidant qualities of pepper, making it a promising approach for improving postharvest processing practices. It should be noted that the drying time in GSD was significantly shorter than under shaded conditions, demonstrating its superior efficiency. This enhanced drying rate not only improves process throughput but also enhances the practical viability of GSD as a sustainable and economically beneficial technology for post-harvest pepper drying, particularly in regions with high solar irradiance. In a similar study, Dhande et al. (2024)³⁴, investigated the drying of Ocimum sanctum leaves using different methods. Their findings revealed that leaves dried in a GSD exhibited significantly higher total phenolic content (73.39 mg GAE/g), flavonoid content (5.09 mg QE/23 g), and antioxidant activity (IC₅₀ value: 55.09 µg/mL) compared to those dried under open sun conditions.

Prediction performance of GPR and SVR models

To evaluate the effectiveness of data-driven modeling approaches in predicting the mass of dried matter during pepper drying, two machine learning models (GPR and SVR) were employed. The performance of both models was assessed using k-fold cross-validation and their accuracy was quantified using three statistical metrics: RMSE, MAPE and R² (Table 1). These metrics were computed separately for training and testing datasets to assess model generalization capability.

Table 4.

The results of modeling with SVR and GPR based on using k-fold cross validation method.

Factor and Model		Train			Test
		RMSE (◦C)-(%) (±SD)	MAPE (%) (±SD)	R2 (-) (±SD)	RMSE (◦C)-(%) (±SD)	MAPE (%) (±SD)	R2 (-) (±SD)
Mass of dried matter	GPR	0.03±0.01	7.20±1.05	0.98±0.03	0.05±0.02	6.22±1.45	0.98±0.02
	SVR	1.00±0.07	10.12±0.68	0.95±0.05	1.13±0.45	9.41±0.23	0.95±0.01

Table 1.

The uncertainty calculation methods^20–22.

Measurement instruments	Description	Calculation method	The unit
Temperature and humidity sensors	SHT 11 with an uncertainty ± 0.3 ℃		%
Solar meter	TES 123 with an uncertainty ± 0.05 Wm− 2		W.m− 2
Digital balance	AND GF-1000 with an uncertainty of ± 0.01 g		g

Fig. 8.

The fresh and dried pepper in the all the types of drying methods.

Fig. 9.

The changing in total phenol content (TPC) and Total flavonoid content (TFC) of dried pepper (A) and also the rate of antioxidant content based on the DPPH percent (B) for pepper dried by different drying methods.

The results indicate that the GPR model outperformed the SVR model in both training and testing phases. For the training dataset, the GPR model achieved an RMSE of 0.03 ± 0.01%, MAPE of 7.20 ± 1.05% and an R² value of 0.98 ± 0.03, demonstrating high accuracy and strong correlation between predicted and actual values. In comparison, the SVR model exhibited relatively higher errors, with an RMSE of 1.00 ± 0.07%, MAPE of 10.12 ± 0.68% and a slightly lower R² of 0.95 ± 0.05. This suggests that while SVR also captured the drying behavior reasonably well, it was less precise than GPR in fitting the training data.

For the testing dataset, which evaluates how well the models generalize to unseen data, similar trends were observed. The GPR model maintained superior performance with an RMSE of 0.05 ± 0.02%, MAPE of 6.22 ± 1.45% and an R² of 0.98 ± 0.02. These low error values and high R² indicate excellent predictive capability and robustness. The SVR model, although still performing adequately, showed greater deviation in prediction accuracy, with an RMSE of 1.13 ± 0.45%, MAPE of 9.41 ± 0.23% and an R² of 0.95 ± 0.01. The larger standard deviations in RMSE and MAPE also suggest less consistency across different folds in the cross-validation process.

These findings demonstrate that GPR is more effective than SVR for predicting the mass of dried matter during solar drying of peppers under the tested conditions. The probabilistic nature of GPR allows it to better capture uncertainty and nonlinear relationships in the data, which are common in drying processes influenced by fluctuating environmental factors such as temperature and solar radiation. On the other hand, while SVR performed satisfactorily, its sensitivity to hyperparameter tuning and kernel selection may have limited its ability to adapt to variations in the dataset as effectively as GPR.

Accurate prediction of the mass of dried matter is crucial for optimizing drying time, energy consumption, and product quality in solar drying systems. The high performance of the GPR model indicates its potential for integration into smart drying systems, where real-time monitoring and control can be enhanced through predictive analytics. Moreover, the use of k-fold cross-validation ensures that the reported results are reliable and not biased by specific data partitions, making these models suitable for broader application in post-harvest processing technologies. In a related study, Wengang et al. (2024)⁵⁶, evaluated the performance of five machine learning models (Multilayer Perceptron (MLP), Backpropagation Neural Network (BPNN), Long Short-Term Memory (LSTM), K-Nearest Neighbors (KNN), and Support Vector Regression (SVR) in predicting sweet potatoes under similar conditions. The findings revealed that the BP model achieved the best correlation between actual and predicted values, demonstrating the highest coefficient of determination (R² = 0.9814). Meanwhile, the LSTM model exhibited the smallest deviation between observed and estimated outputs, yielding the lowest root mean square error (RMSE = 0.0456). Additionally, the KNN model outperformed others in terms of average prediction accuracy, recording the lowest mean absolute error (MAE = 0.0101).

Best GPR model performance

In this study, GPR was employed to model and predict the mass of dried matter during solar drying of peppers. The gname function in MATLAB was used to optimize the hyperparameters of the GPR model, allowing selection of the best-performing configuration based on statistical performance indicators. The use of the gname function in MATLAB played a crucial role in selecting the optimal kernel function and tuning hyperparameters, which directly influenced the model’s predictive capability. By systematically evaluating different combinations of covariance functions and noise levels, the most appropriate model structure was identified, ensuring robustness and stability in predictions.

The best run of the GPR model achieved excellent predictive accuracy, as shown in Table 5. During the training phase, the model yielded an RMSE of 0.04%, MAPE of 6.35% and an R² value of 0.98, indicating a strong correlation between predicted and actual values. These results demonstrate that the GPR model effectively captured the underlying patterns in the drying process and provided highly accurate estimations of the mass of dried matter.

Table 5.

The best results of modeling with GPR by JC=27.

Factor	Phases	Types of statistical analysis	Variance	Distribution
		Mean
Mass of dried matter	Training	0.99	0.92	1.00
	Test	0.92	0.89	1.00

For the testing phase, the GPR model maintained high performance with an RMSE of 0.02%, MAPE of 4.86% and an R² value of 0.98. These low error values and high coefficient of determination suggest that the model not only fits the training data well but also reliably predicts outcomes under new conditions, making it suitable for real-world applications in solar drying systems.

Compared to earlier studies that have applied various empirical and semi-theoretical models to describe drying kinetics, the GPR approach offers several advantages:

It cannot require prior assumptions about the functional form of the drying curve.

It adapts to complex, non-linear dynamics without overfitting.

It allows for uncertainty quantification in predictions.

These characteristics make GPR a powerful alternative or complement to conventional models such as the Midilli and Kucuk, Page and Henderson and Pabis models previously used in drying kinetics analysis.

Statistical evaluation of GPR model performance

To assess the accuracy and reliability of the GPR model used to predict the mass of dried matter during pepper drying, a comprehensive statistical analysis was conducted. The performance of the model was evaluated by comparing the actual and predicted values using several key metrics, including mean, variance, distribution and correlation-based statistics.

As shown in Table 6, the predicted values closely matched the actual values in both training and testing phases. In the training phase, the average actual value of the mass of dried matter was 0.47, with a standard deviation of 0.28, while the predicted values had an average of 0.47 and a slightly lower standard deviation of 0.26. Similarly, in the testing phase, the average actual value was 0.50 and the predicted value averaged 0.51, indicating minimal bias and strong alignment between observed and modeled outcomes. The minimum and maximum values also showed close agreement, with the predicted values ranging from 0.12 to 0.84 in the training phase and 0.35 to 0.76 in the testing phase, compared to actual ranges of 0.08–0.85 and 0.32–0.78, respectively. This consistency across ranges further supports the model’s ability to generalize across different conditions without overfitting.

Table 6.

Some statistical results of modeling with GPR by JC=27.

Factor and Model		Train			Test
		RMSE (◦C)-(%)	MAPE (%)	R 2 (-)	RMSE (◦C)-(%)	MAPE (%)	R 2 (-)
Mass of dried matter	GPR	0.04	6.35	0.98	0.02	4.86	0.98

A strong linear relationship was observed between predicted and actual values. In the training dataset, the predicted values were modeled as: Predicted = 0.94×Actual + 0.03 and for the testing dataset, the relationship was: Predicted = 0.96×Actual + 0.02. These high R² values (> 0.98) indicate that the GPR model accurately captures the variation in the actual data, confirming its robustness and predictive capability.

As detailed in Table 7, the mean similarity between actual and predicted values was 0.99 in the training phase and 0.92 in the testing phase. Likewise, variance similarity was recorded at 0.92 and 0.89, respectively, indicating that the model preserves not only the central tendency but also the spread of the original data. Furthermore, distribution similarity was found to be 1.00 in both phases, suggesting that the predicted data follows the same underlying probability distribution as the actual data. This is crucial for ensuring that the model can reliably simulate real-world scenarios and maintain consistency across diverse input conditions.

Table 7.

Analysis of mean, variance and distribution in modeling with GPR by JC = 27.

Element	Phases	Data	Average	Variance	Standard deviation	Minimum	Maximum	Kurtosis	skewness	Sum
Mass of dried matter	Train	Actual	0.47	0.08	0.28	0.08	0.85	1.47	−0.17	7.49
		Predicted	0.47	0.07	0.26	0.12	0.84	1.42	−0.15	7.47
	Predicted values = 0.94 × Actual values + (0.03) R2 = 0.98
	Test	Actual	0.50	0.04	0.20	0.32	0.78	1.94	0.67	1.99
		Predicted	0.51	0.03	0.18	0.35	0.76	1.88	0.65	2.05
	Predicted values = 0.96 × Actual values + (0.02) R2 = 0.98

Figure 10 provides a visual comparison of actual and predicted data. Panel A shows the distribution of actual and predicted values, highlighting their overlapping patterns and confirming the model’s high fidelity. Panel B presents a scatter plot of predicted versus actual values, where most points lie close to the 1:1 line, reinforcing the strong correlation and minimal prediction error. Together, these visualizations corroborate the numerical findings and provide an intuitive understanding of the model’s performance. They illustrate that the GPR model not only predicts the correct magnitude of the mass of dried matter but also maintains the variability and shape of the actual data distribution.

Fig. 10.

The distribution of actual and predicted data by GPR model with JC = 27.(dv means desired values or target and pv means predicted values or outputs).

The high level of agreement between actual and predicted values demonstrates the effectiveness of the GPR model in capturing the complex relationships between environmental variables (e.g., solar radiation, temperature) and moisture removal dynamics in solar drying systems. Its probabilistic nature allows for uncertainty quantification, making it particularly valuable for modeling processes influenced by fluctuating climatic conditions. This model can serve as a powerful tool for real-time monitoring, process optimization, and energy efficiency improvement in solar drying technologies. By integrating such predictive models into smart drying systems, it becomes possible to dynamically adjust operational parameters for optimal drying performance and product quality. The exceptional predictive accuracy of the GPR model developed in this study for dried pepper mass under GSD conditions is further contextualized when compared directly with key machine learning applications in agricultural drying literature. For pepper drying specifically, our GPR model significantly outperformed an ANN model applied to solar-dried bell peppers (R² = 0.94, RMSE = 0.21%) by Onwude et al. (2020)⁵⁷, achieving a 4.3% higher R² and a 76% lower RMSE. Similarly, it surpassed the performance of a SVR model for infrared-dried chili peppers (R² = 0.92, RMSE = 0.18%) reported by Chen et al. (2019)⁵⁸, demonstrating a 6.5% increase in R² and a 72% reduction in RMSE. When compared to GPR applications on other crops, our model exceeded the accuracy reported by Zhu et al. (2021)⁵⁹ for convective mushroom drying (R² = 0.96, RMSE = 1.8% dry basis), showing a 2.1% higher R² and a substantially lower error rate. While the R² value was comparable to a GPR model for mint drying in a hybrid solar system (R² = 0.97) by Taghinezhad et al. (2023)⁶⁰, GPR model in the represent study achieved a markedly superior precision, reflected in an 84% reduction in RMSE (0.05% vs. 0.32%). Furthermore, the current GPR model’s RMSE of 0.05% is notably lower than the RMSE of 0.12% reported by Kumar et al. (2023)⁶¹ for carrot drying in a hybrid solar-biomass system, and approaches the high benchmark set by a kinetic-ANN hybrid model for solar-thermal tomato drying (R² = 0.97, RMSE = 0.08%) by Aghbashlo et al. (2021)⁶². This comprehensive comparison underscores the state-of-the-art performance of our GPR model in predicting dried pepper mass.

Conclusion

This research evaluates the impact of three drying techniques (open sun, shade and Greenhouse Solar Dryer (GSD) on the drying kinetics, nutritional quality and antioxidant properties of green peppers. Using experimental data collected under varying climatic conditions, the moisture ratio was monitored over time, revealing that GSD significantly accelerates drying while maintaining optimal product quality. This study demonstrates that the GSD offers a balanced drying environment that simultaneously enhances drying kinetics and preserves critical bioactive compounds in red pepper—outperforming both open sun and shade drying. The integration of rigorous kinetic analysis with advanced machine learning reveals that the Midilli and Kucuk model remains highly effective for describing pepper drying behavior, while Gaussian Process Regression emerges as a state-of-the-art tool for real-time mass prediction, offering both high accuracy and uncertainty quantification. Critically, this work bridges the gap between sustainable drying technology and intelligent process control. By validating GPR with k-fold cross-validation in a real GSD system—and linking it to quality outcomes—this research lays the foundation for adaptive, data-driven drying systems tailored for high-value crops in solar-rich regions. Future efforts should focus on deploying such models in closed-loop controllers to dynamically optimize drying for both efficiency and nutritional retention.

Future work should focus on three key directions: First, integrating real-time sensor feedback from the GSD with the validated GPR model to develop an adaptive, closed-loop drying controller capable of dynamically adjusting vent opening or air flow patterns based on predicted moisture loss and bioactivity preservation targets. Second, extending the GPR framework to predict multiple quality attributes simultaneously—such as color (L, a*, b*), and volatile aroma profiles—to enable multi-objective optimization of the drying process. Third, validating this GSD-GPR system under variable climatic conditions across different geographic regions (humid tropical vs. arid zones) to assess its robustness and adaptability beyond the Khuzestan context. Additionally, exploring hybrid configurations—such as coupling the GSD with low-power photovoltaic fans or phase-change material thermal storage—could further enhance energy efficiency and extend operational hours beyond peak solar radiation periods, making the technology viable for off-grid and smallholder farming systems globally.

Abbreviations

GSD

Greenhouse solar dryer

TFC

Total flavonoid content

MR

Moisture ratio

R²

Coefficient of determination

ANN

Artificial neural network

GPR

Gaussian process regression

RBF

Radial bias function

NaNO₂

Sodium nitrite

MLP

Multilayer perceptron

AlCl₃

Aluminum chloride

SVR

Support vector regression

TPC

Total phenolic content

DPPH

2,2-diphenyl-1-picrylhydrazyl

PE

Polyethylene

BPNN

Backpropagation neural network

NaOH

Sodium hydroxide

RMSE

RooT mean square error

Na₂CO₃

Sodium carbonate

KNN

K-Nearest Neighbors

ESGSD

Even span greenhouse solar dryer

LSTM

Long short-term memory

MAPE

Mean absolute percentage error

VPD

Vapor pressure deficit

SE

Squared exponential

Author contributions

**Ghader Khaledifard** : Data Curation, Investigation, Resources, Writing - original draft; **Morteza Taki** : Supervision, Conceptualization, Methodology, Writing - Review & Editing; **Rasoul Meamar** : advisor, Writing - review & editing; **Behrooz Alizadeh Behbahani** : Advisor; Methodology, Writing - review & editing.

Funding

The authors declare that they have no funding for this study.

Data availability

The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.