Detecting sub-healthy pear with core browning using variable mode decomposition and reconstruction for vibro-acoustic signals

Core browning is one of the most common physiological disorders in pears, particularly threatening the quality and market value of the fruit. Once the lesion is confined within the carpel wall and does not break through the core line, the fruit is defined as "sub-healthy" pears. Timely and accurate detection of such pears is often required to implement the targeted storage and sales strategies for their commercial value. In this study, an effective approach was developed to detect the sub-healthy pears with core browning using vibro-acoustic signals, advanced signal processing, and deep learning. The high accuracy of detection facilitated early intervention. A vibro-acoustic non-destructive detection was also employed to acquire the response signals of pears. The variable step size variational mode decomposition (VSS-VMD) was proposed to decompose the response signals. Subsequently, characteristic components were selected to highly correlate with the original signals, according to the grey correlation degree and mutual information for signal reconstruction. A ResNet50-1D-SVM hybrid model was constructed to extract deep features from the reconstructed signals for classification. The SHAP (Shapley additive explanations) was used to determine the feature attributions and their contributions to the classification performance and generalization. The results showed that the VSS-VMD achieved optimal decomposition of the pear vibro-acoustic signals when the modal number K was set to 7 and the penalty factor α was set to 10 152. This method suppresses modal aliasing and minimizes information loss between decomposed components and the original signal. Characteristic components after signal reconstruction significantly reduced the mutual information between signals of various categories. The distinguishability of category-specific signals was improved effectively. The overall classification accuracy, F1-score, Kappa coefficient, and Matthews correlation coefficient of the model with reconstructed signals as input (ResNet50-1D-RecF-SVM) reached 91.44%, 91.49%, 88.02%, and 87.21%, respectively, which were 9-14 percentage points higher than those with original signals as input (ResNet50-1D-SVM), and misclassification occurred only between adjacent categories. SHAP analysis revealed that the 35 features were determined as influential features, including 20 positive features and 15 negative features, while the remaining 221 features were redundant features. Then, two interpretable models, ResNet50-1D-InfF-SVM (using 35 influential features) and ResNet50-1D-PosF-SVM (using 20 positive features) were constructed to evaluate the contribution of deep features. These 35 influential features made great contributions to the classification and generalization. Among them, the 20 positive features improved the classification accuracy, with the first two features accounting for 85.72% of the total accuracy increase. Although the 15 negative features suppressed classification, they played a vital role in generalization. Once these negative features were excluded, all classification performance metrics of the model on the external validation set (98 independent samples) decreased, and the decreases were more than 2 percentage points larger than those when the negative features were retained, indicating that feature selection during model construction should be approached with caution. The detection accuracy of sub-healthy pears was effectively improved to provide for the non-destructive detection of early internal diseases in pears, apples, and potentially other fruits. Also, there was a great contribution of features to the classification and generalization of the model. The findings can highlight the potential of advanced signal processing and machine learning in the field of non-destructive testing. The proposed method can effectively improve the detection accuracy of sub-healthy pears and provide a reference for the non-destructive detection of early internal diseases in pome fruits.