Abstract:
Soluble solids content (SSC) is a crucial indicator for evaluating the internal quality of apples, as its level directly reflects the fruit's sweetness, maturity, and overall eating quality. Therefore, establishing a non-destructive prediction model for SSC based on near-infrared spectroscopy is of great significance for fruit grading. However, factors such as instrument noise, environmental interference, and individual fruit variability during data collection introduce epistemic uncertainty, thereby affecting data quality. Traditional regression models struggle to effectively handle such uncertain data, thereby limiting their predictive accuracy and generalization capability. To address this issue, this paper proposed a multivariate linear evidence regression tree model based on the E
2M algorithm (E
2M-MLERT). Firstly, spectral data were collected from 439 Red Fuji apple samples using the Thermo Scientific™ Antaris™ II FT-NIR Analyzer to obtain near-infrared spectra, while SSC values were determined via physicochemical methods. Secondly, data preprocessing was carried out. To eliminate physical interference and improve the quality of the spectral signal, four different preprocessing methods were applied to the collected near-infrared spectra, namely Savitzky-Golay smoothing, standard normal variate (SNV), multiplicative scatter correction (MSC), and first-order derivative. Among the four spectral preprocessing methods, SNV preprocessing achieved the best performance in the prediction task, yielding an optimal classification accuracy of 91.67%, so SNV is used as the optimal preprocessing strategy. Based on evidence theory, the measurement results of soluble solids content are expressed as interval mass functions to create an uncertainty dataset. This study screens stable spectral features using variance thresholds, selects the splitting features and thresholds for the root node based on maximizing error reduction to divide the data space; finally, it builds multiple linear evidential regression model at each leaf node to predict apple grading for uncertain data after nonlinear feature space division, thereby constructing a E
2M-MLERT model. Multiple linear regression (MLR) was employed as the baseline model. Four comparative experiments were designed, each adopting a stratified random sampling strategy to partition the dataset of 439 samples into training and test sets at a ratio of 7:3, with 307 samples used for training and 132 for testing. In the comparison of conventional regression models, the linear regression tree (LRT) model attained the highest accuracy of 93.18%, representing an improvement of 0.76 percentage points over the baseline MLR model. After uncertainty-aware data processing, the E
2M-MLERT achieved a maximum classification accuracy of 94.70% in the comparison of evidential regression models, outperforming the multiple linear evidential regression (MLER) model by 2.28 percentage points. In the tree-model comparison, the E
2M-MLERT improved upon the LRT by 1.52 percentage points. In terms of computational efficiency, a variance threshold was designed to reduce the number of candidate split features from
1557 to approximately 30. Compared with the LRT, the computational complexity of the E
2M-MLERT was reduced to O(N). Across the four experimental datasets, the average classification accuracies of the MLR model, the MLER model, the LRT model, and the proposed E
2M-MLERT model were 89.58%, 91.48%, 91.29%, and 92.80%, respectively. This method not only effectively handles the uncertainty inherent in spectral data, but also fully exploits local sample characteristics and potential nonlinear relationships, thereby yielding more accurate and intuitive grading results. The proposed method provides a reliable approach for non-destructive assessment of apple internal quality under uncertain measurement conditions.