The experimental material for this study was the ‘Wen 185’ walnut selected from the walnut forest farm in Wensu County, Aksu Prefecture, Xinjiang. A total of 180 walnut samples were collected from 9 walnut orchards with varying management levels: 3 high-yield, 3 medium-yield, and 3 low-yield orchards. The walnut trees in these orchards are spaced 5 meters by 6 meters apart and are all 10 years old. Following harvest at ripeness, the walnuts underwent a process where the green skins were removed, and then they were dried in a well-ventilated environment until their moisture content reached approximately 6%. Subsequently, the walnuts were shelled, kernels extracted, crushed for 3 minutes using a FW-80 high-speed universal crusher, and thoroughly mixed. The crushed walnut kernels were then sealed in plastic bags and stored at 4 °C for subsequent spectral scanning and determination of tannin content.

NIR spectral data were collected using a Fourier-transform near-infrared spectrometer (Antaris II, Thermo Fisher Scientific, USA). The instrument was operated at a resolution of 8 cm^-1 with a gain setting of 2, using the built-in background as reference. Each spectrum was obtained as the average of 32 scans. Prior to spectral acquisition, walnut samples were equilibrated under controlled environmental conditions (25°C and 40% relative humidity) for 24 hours to ensure consistency with the instrument’s ambient environment, thereby minimizing spectral variability.

The instrument was preheated for 60 minutes before measurement. Spectra were recorded over the wavenumber range of 4000-10000 cm^-1. Ground walnut kernel powder was uniformly packed into quartz sample cups (30 mm diameter, 5 mm height, 1 mm wall thickness), with the sample surface leveled and aligned with the rim of the cup. Each sample was scanned three times, resulting in a total of 540 spectra for 180 samples. The final representative spectrum for each sample was obtained by averaging its three replicate scans. After each measurement, the sample cups were sequentially rinsed with tap water, distilled water, and then wiped clean with ethanol to ensure cleanliness and prevent cross-contamination.

Tannin content was determined according to the Chinese agricultural industry standard NY/T 1600-2008: Determination of tannin content in fruits, vegetables, and their products—Spectrophotometric method (Li et al., 1999). Precisely 1.00 g of ground walnut kernel sample was weighed and placed in a 100 mL volumetric flask. The sample was extracted using a boiling water bath for 30 minutes. After extraction, the mixture was cooled to room temperature and diluted to the mark with distilled water. The extract was centrifuged, and 2 mL of the supernatant was transferred into a 50 mL volumetric flask. Then, 1 mL of a sodium tungstate–sodium molybdate reagent and sodium carbonate solution was added, and the mixture was shaken thoroughly. After standing at room temperature for 2 hours, the absorbance of the solution was measured at 765 nm using a UV–Vis spectrophotometer.The tannin content was calculated using the following equation:

In the formula, X1 represents the tannin content in the sample (mg/g); C represents the gallic acid content obtained from the standard curve (mg); V1 represents the volume of the sample determination solution (ml); M represents the mass of the walnut sample taken (g); N represents the dilution factor; 1000 represents the conversion coefficient.

With the rapid development of machine learning algorithms, numerous advanced modeling techniques have been applied to the prediction of fruit quality traits, often outperforming traditional statistical methods (Tan et al., 2023). Random forest (RF) (Breiman, 2001), an ensemble learning algorithm composed of multiple decision trees, exhibits robustness to multicollinearity and performs well with imbalanced or incomplete datasets (Guo et al., 2025). In this study, the dataset was randomly split into a training set and a validation set at a 6:4 ratio. Model performance was evaluated using the coefficient of determination (R²), root mean square error (RMSE), and relative percent deviation (RPD). A model with R² approaching 1 and low RMSE indicates strong predictive capability. An RPD value between 1.4 and 2.0 suggests moderate reliability suitable for estimation, while RPD > 2.0 indicates a robust predictive model (Li et al., 2024).

Due to the “black-box” nature of many machine learning models, their internal decision-making processes are often opaque and difficult to interpret (Ye et al., 2024). The SHAP (Shapley additive explanations) algorithm addresses this issue by applying Shapley values—originating from cooperative game theory-to decompose the output of a model into contributions from each input feature (Li et al., 2025). This allows for a more transparent understanding of the model’s predictions and facilitates interpretability in complex systems.The experimental flowchart is shown in Figure 1.

All data preprocessing, spectral feature selection, and model development were performed using MATLAB^® (Version R2023a; MathWorks, 2023) and Python. Chemical and spectral mean values were calculated using Microsoft Excel^® (Version 2016; Microsoft Corporation, 2016). All visualizations and figures were generated using Origin^® (Version 2021; OriginLab Corporation, 2021). For model interpretation, the SHAP Python package (Lundberg and Lee, 2017) was employed, which is based on the Shapley additive explanations framework.

The tannin content in walnut kernels can be determined using a specific formula (Equation 3). The results indicate significant variability in tannin content among samples, demonstrating notable distinctions and representativeness. a comparison of orchard sample data under various management models is presented in Figure 2a, revealing distinct differences. The average tannin content differs among orchards managed under different models, facilitating model development. Figure 2b illustrates the near-infrared spectral range of 4000–10000 cm^-1. The spectral curves under different management modes exhibit similar overall shapes, running roughly parallel to each other, with spectral reflectance increasing as wavelength increases.The absorption features observed in the spectra, particularly in the regions around 4000–5000 cm^-1 and 7000–9000 cm^-1, are likely associated with the characteristic vibrational modes of tannin molecules. Tannins, as polyphenolic compounds, contain abundant hydroxyl (-OH) groups, whose overtone and combination bands typically appear in the NIR region. Specifically, the first overtone of O-H stretching vibrations often occurs around 7000 cm^-1, while combination bands involving O-H bending and stretching vibrations may contribute to the absorption features in the 4000–5000 cm^-1 range.

Outliers in the dataset were identified and removed using the Monte Carlo simulation method. A total of 2000 iterations were performed. In each iteration, 60% of the samples were randomly selected as the training set, and the remaining 40% were used for validation. The training data were preprocessed using mean centering (“center”), and a partial least squares (PLS) regression model was constructed using 20 latent variables. The resulting regression coefficients were applied to the validation samples to obtain predicted values, and prediction errors were calculated accordingly.As shown in Figure 3, samples that fell outside the dashed boundary lines were identified as outliers. These samples exhibited either a mean prediction error greater than the overall mean or a standard deviation exceeding the global standard deviation. The criteria for outlier elimination were set as: standard deviation > 2 and mean > 10. Based on these thresholds, nine samples—No. 30, 42, 57, 69, 101, 128, 131, 133, and 161—were identified as outliers and removed from the dataset.After eliminating these nine samples, the remaining 171 samples were retained for subsequent modeling. This outlier removal step led to a significant improvement in model performance, enhancing the reliability and stability of the predictive results.

After applying 11 mathematical transformations to the raw reflectance spectra (R), including reciprocal (1/R), logarithmic (log R), reciprocal-logarithmic (log(1/R)), as well as first- and second-order derivatives, significant differences in spectral reflectance patterns were observed (Figure 4). As shown in Figure 4a, the original spectra are relatively smooth, lacking prominent peaks or absorption valleys, making it difficult to extract subtle features associated with walnut kernel tannin content. Figures 4b-d display the results of the 1/R, log R, and log(1/R) transformations. Although the spectral shapes remain smooth, there are still no clearly distinguishable peaks or valleys. These transformations are designed to compress high reflectance values or balance the distribution of reflectance intensities, thereby enhancing blended spectral features. However, they do not effectively amplify small differences between adjacent wavelengths, limiting their ability to highlight features relevant to tannin concentration.In contrast, Figures 4e-h demonstrate the effect of the first derivative transformation, which significantly improves spectral sensitivity to tannins. This is achieved by computing the rate of change between adjacent wavelengths, resulting in sharper spectral variation and an increased number of peaks and valleys. The first derivative effectively emphasizes local variations, inflection points, and abrupt changes, while suppressing low-frequency noise and reducing the impact of spectral overlap. However, this method is also more susceptible to high-frequency noise, which may reduce model robustness (Li et al., 2024; Liu et al., 2024).Figures 4i-l illustrate the spectral changes after applying the second derivative transformation. Compared to the first derivative, the number of spectral peaks and valleys is further increased. This occurs because the second derivative reflects the curvature rate of change in the spectral profile, which smooths flatter regions and removes weaker spectral information, thereby retaining only the most prominent features. While this transformation enhances key features, it also amplifies noise and may cause loss of useful bands, leading to reduced model stability (Wang et al., 2023; Zhong et al., 2023). Overall, although both derivative methods improve feature extraction, excessive noise sensitivity in the second derivative makes the first derivative more suitable for further modeling.

The large number of wavelength variables in the original spectral data may introduce redundancy, which can impair modeling efficiency and increase computational load during subsequent analysis. Therefore, effective selection of characteristic wavelengths is essential for building efficient and accurate predictive models.Pearson correlation analysis was performed using MATLAB R2023a to assess the relationships between the measured tannin content and spectral reflectance values from both the raw spectra (R) and its 11 mathematically transformed forms. Spectral variables that passed a significance threshold of P < 0.01 and had correlation coefficients exceeding the critical value (|r| > 0.123) were retained as characteristic wavelengths.As shown in Figure 5, the correlation coefficient (r) reflects the strength and direction of the relationship between individual wavelengths and measured tannin content. The color gradient in the figure indicates the magnitude of correlation: darker tones represent stronger positive or negative associations, while lighter tones indicate weaker correlations.

Table 1 summarizes the number of characteristic wavelengths identified under the original spectrum and various mathematically transformed spectra, along with the maximum, minimum, and mean values of their positive and negative Pearson correlation coefficients. Compared to the original reflectance spectrum (R), transformations such as 1/R, log R (lgR), and log(1/R) increased the number of selected wavelengths but did not yield significant improvements in correlation strength.In contrast, derivative-based preprocessing significantly enhanced the correlation between spectral variables and tannin content in walnut kernels. Specifically, under first derivative transformations, spectra such as R′, (1/R)′, lg′R, and lg′(1/R) produced a moderate number of characteristic wavelengths but showed substantially improved correlations, with maximum absolute r values of 0.399, 0.392, 0.424, and 0.386, respectively.Second derivative transformations also improved correlation levels, particularly for lg″(1/R) and lg″R, which reached correlation values as high as ±0.400. Taking both the number of selected wavelengths and the correlation strength into consideration, the mean absolute correlation coefficient (|r|) was used as the evaluation criterion. As a result, R′, lg′R, and lg′(1/R) were selected as the most effective mathematical preprocessing methods for subsequent model development.

Research indicates that the wavelet transform offers significant advantages over traditional mathematical transformations in spectral processing. To investigate these advantages, continuous wavelet transform (CWT) analyses were conducted on R, R’, lg’R, and lg’(1/R) (Equations 1 and 2), denoted as R_CWT, R’_CWT, lg’R_CWT, and lg’(1/R)_CWT, respectively. R was utilized to represent the correlation between the wavelet coefficients and tannin levels in walnut kernels. As illustrated in Figure 6, CWT processing resulted in an overall increase in the correlation between the spectral data and walnut tannin. The correlation exhibited a trend of initially increasing and then decreasing from scale 2¹ to 2¹⁰. Notably, at scale 2⁴, R_CWT and lg’R_CWT reached their maximum correlation values of 0.446 and 0.430, respectively. The maximum value for R’_CWT at scale 2⁵ was 0.448, while the maximum R for lg’(1/R)_CWT at scale 2⁷ was 0.388. As the decomposition scale increased, the number of characteristic bands across the four CWT treatments generally exhibited an upward trend (Figure 6).

As shown in Figure 7, the mean absolute Pearson correlation coefficient (|r|) for R_CWT and R′_CWT reached their respective maximum values at scale 2⁹, with values of 0.178 and 0.208. For lg′R_CWT and lg′(1/R)_CWT, the highest mean |r| values (both 0.240) were observed at scale 2⁸.Considering both the number of characteristic wavelengths and the strength of their correlations, scale 2⁹ was selected as the optimal decomposition scale for R_CWT and R′_CWT, while scale 2⁸ was determined to be optimal for lg′R_CWT and lg′(1/R)_CWT.In subsequent tannin prediction modeling, wavelet coefficients extracted from these four spectral forms at their respective optimal scales will be used as independent variables for model construction.

Prior to model construction, the full dataset was randomly divided into training and validation sets at a ratio of 6:4. A total of 102 samples were randomly assigned to the training set for model development, while the remaining 69 samples were used as the validation set for performance evaluation. As shown in Figure 8, presents violin plots of tannin content for the three datasets.the tannin content across all samples ranged from 4.73 to 20.17 mg/g. The distribution patterns of tannin content were generally consistent among the full dataset, training set, and validation set. The outer contours reflect kernel density estimates, with wider sections indicating larger sample concentrations.and illustrates the distribution of standard deviation, median, and coefficient of variation (CV) across the datasets.The mean tannin content of the full dataset was 13.17 mg/g, while the training and validation sets had mean values of 13.06 mg/g and 13.33 mg/g, respectively. The mean, median, and standard deviation of tannin content were comparable across the three sets. Moreover, the full dataset exhibited CV and mean values intermediate between those of the training and validation sets, indicating that the partitioning was statistically balanced and representative. These results support the suitability of the sample division for constructing a robust and generalizable prediction model for walnut kernel tannin content.

In this study, random forest (RF) models were developed to predict tannin content in walnut kernels using both full-spectrum data and selected characteristic wavelengths derived from various spectral preprocessing techniques. The spectral variables served as independent variables, while measured tannin content was used as the dependent variable.To optimize RF model performance, key hyperparameters were systematically tuned. Specifically, the number of decision trees was set to 200, the minimum leaf size was fixed at 10, Bayesian optimization was performed with 50 iterations, and five-fold cross-validation was used to ensure predictive accuracy and model generalizability. The modeling results are presented in Figure 9.The results showed notable differences in model performance between full-spectrum and characteristic wavelength inputs under different spectral preprocessing strategies. Overall, models based on selected characteristic wavelengths outperformed those using full-spectrum data, particularly in terms of the coefficient of determination (R²). Most models based on characteristic wavelengths achieved R² values above 0.70, whereas nearly half of the full-spectrum models showed signs of overfitting.This indicates that selecting informative wavelengths can effectively eliminate irrelevant spectral information, thereby enhancing model performance. Moreover, under the same preprocessing method, the difference in R² values between the training and validation sets was smaller when using characteristic wavelengths, further demonstrating improved model stability.Although full-spectrum models exhibited slightly better RMSE and RPD values in the training set, their RPD values differed substantially between training and validation sets—with a maximum difference of 0.928—suggesting weaker generalization capability. In contrast, the RPD values of characteristic wavelength models in the validation set were typically above 2.2, indicating higher predictive accuracy and better robustness across different preprocessing methods. Nearly half of the full-spectrum models had RPD values below 1.4, further underscoring their limited stability.In summary, feature wavelength selection reduced spectral redundancy and improved model robustness. While full-spectrum models performed slightly better in certain metrics, models based on characteristic wavelengths offered superior comprehensive performance in terms of accuracy, stability, and computational efficiency, making them more suitable for tannin estimation.Notably, models constructed using first derivative spectra combined with continuous wavelet transform (CWT) achieved the highest prediction accuracy and stability. This highlights that integrating first derivative preprocessing with CWT significantly enhances the model’s ability to predict tannin content and offers a reliable strategy for improving spectral model performance.

Due to the inherent “black-box” nature of machine learning algorithms, assessing the influence of input features plays a crucial role in model interpretation and optimization (Ye et al., 2024). To identify the most influential spectral variables and explain their contributions to the model’s predictions, the SHAP algorithm was employed. Visualization of model interpretability was performed using the SHAP library in Python.Specifically, SHAP values were used to evaluate the contribution of each selected wavelength in the best-performing RF prediction model. As shown in Figure 10A, the top 10 most important features are visualized in a SHAP beeswarm plot. The features are ranked in ascending order based on their cumulative contribution to the model. It is evident that the most influential spectral regions are located within the 4000-4999 cm^-1 and 7000-8999 cm^-1 ranges. The horizontal axis represents SHAP values, while the vertical axis displays the features ranked by their overall impact. Figure 10B presents a bar plot of the mean absolute SHAP values for all features, indicating the average contribution of each variable across all predictions. Features with higher SHAP values contributed more significantly to the model’s output. Figure 10C shows waterfall plots for two randomly selected samples, illustrating the contribution of individual features to the prediction result. Positive SHAP values indicate an increase in the predicted tannin content, whereas negative values suggest a decrease. The vertical axis ranks the features by cumulative SHAP impact. Blue bars represent features that reduced the prediction, while red bars represent features that increased the prediction.