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基于多元线性证据回归树的苹果近红外光谱分级方法

Apple near-infrared spectral grading method based on multiple linear evidential regression tree

  • 摘要: 仪器误差、环境噪声、样本异质性导致苹果可溶性固形物含量测量时数据存在波动,针对这类数据的认知不确定性,该研究提出一种基于多元线性证据回归树的苹果分级方法。首先,以烟台红富士苹果为对象,采用无损检测系统采集苹果近红外光谱数据,并基于证据理论将可溶性固形物含量的测量结果表征为区间质量函数;其次,通过方差阈值筛选稳定光谱特征,基于最大化误差衰减选择根节点的分裂特征和分裂阈值来划分数据空间;最后,在每个叶节点构建多元线性证据回归模型,实现非线性特征空间划分后对不确定数据的苹果分级预测,从而构建完整的多元线性证据回归树模型。为验证所提方法的有效性,设计4组对照试验,将传统多元线性回归模型、线性回归树模型与该研究提出的多元线性证据回归模型、多元线性证据回归树模型进行系统比较。结果表明,各模型的平均分级准确率分别为89.58%、91.29%、91.48%和92.80%,对比试验结果显示,线性回归树模型、多元线性证据回归模型和多元线性证据回归树模型的分级准确率均高于传统多元线性回归模型,且多元线性证据回归树模型表现最佳。综上,该研究提出的多元线性证据回归树模型通过度量并利用不确定性,提升了苹果分级预测的性能,为苹果的在线无损检测分级提供一种可靠的解决方案。

     

    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 E2M algorithm (E2M-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 E2M-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 E2M-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 E2M-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 E2M-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 E2M-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.

     

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