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.

Moldy core in apples is one of the most common internal diseases that is caused by fungi. The apples with mold are confined to the core by the endocarp wall, also called sub-healthy fruit. It is also the risk of storage deterioration. However, the identification of the sub-healthy apples is still challenging, due to the minor differences between healthy and slightly diseased apples. In this study, a non-contact vibration device was developed to acquire the vibration signals. The apple was impacted by the air jet under the optimal operating parameters, which were determined as follows: air pressure of 600 kPa, excitation distance of 55 mm, and excitation time of 2 ms. The laser Doppler vibrometer was employed for the sense signal. Furthermore, the signals of the vibration response were converted into the time-domain Gramian angular summation fields (GASF) images, frequency-domain GASF images, and S transform time-frequency images. These multi-domain images were combined and then input into the vision transformer (ViT) network, in order to extract the depth features. Subsequently, a cluster analysis was conducted on these features using the uniform manifold approximation and projection (UMAP). The clustering performance of the deep features was quantitatively evaluated using the silhouette coefficient, Calinski-Harabasz score, and Davies-Bouldin index. The depth features with the best clustering performance were fed into the k-nearest neighbor (kNN), support vector machine (SVM), logistic regression (LR), random forest (RF), and decision tree (DT) classifiers. A comparison was made of the performance of the classification. The better classification was combined with the Shapley additive explanations (SHAP) analysis to determine the attributes of the deep features, and then explain the contributions of the various features to classification and generalization. In the classification task of the sub-healthy apples, the high clustering performance was observed in the depth features of the class token from the eighth encoder block layer to the twelfth encoder block of the ViT network. The deep features from the eighth encoder block were selected for the subsequent analysis. As such, the highly discriminative deep features were extracted using fewer computational resources. The ViT-kNN model achieved relatively better classification with the overall accuracy, F1-score, Kappa coefficient, and Matthew’s correlation coefficient values of 83.10 %, 82.18 %, 74.14 % and 74.08 %, respectively, using the layer of the depth features. The 768 deep features were used by the ViT-kNN model. Among them, 60 features were determined as the influential features, including 35 positive features and 25 negative features. Then, two interpretable models, ViT-InfF-kNN (using 60 influential features) and ViT-PosF-kNN (using 35 positive features) were constructed to determine the contribution rate of the deep features. The 60 influential features greatly contributed to the classification and generalization of the improved model. The remaining features (the 768 features, removing 60 influential features) contributed little to the overall classification, and also interfered with the identification of the diseased fruits. Yet they still contained a small amount of useful information to distinguish the healthy fruit. In these 60 influential features, 35 positive features contained more information to identify the healthy fruits. Although the 25 negative features inhibited the classification, there was an important impact on the generalization of the model. The feature selection during model construction should be approached with caution. This study can provide a strong reference for the early internal disease detection of the pome (pears and apples) fruit. Also, there was a great contribution of the features to the classification and generalization of the model. Therefore, the vibration technology was integrated with the visible-near infrared spectroscopy in future work, in order to detect the sub-healthy apples with the moldy core.

In this study, a nondestructive vibro-acoustic setup was employed to acquire the vibro-acoustic signals of pear fruit. The signals were decomposed using the empirical mode decomposition (EMD). Different methods were used to suppress the end effect and mode mixing to achieve the optimal signal decomposition components. Then, the decomposition components of the vibro-acoustic signals were used as the input to construct a discriminant model based on convolution neural networks with spatial pyramid pool (CNN-SPP). The results showed that the improved slope-based method was better able to suppress the EMD end effect for the vibro-acoustic signals. The complementary complete ensemble empirical mode decomposition with adaptive noise (CCEEMDAN) method could exhibit better performance for suppressing mode mixing after end effect suppression. Thus, the obtained components were used as the input to construct a CCEEMDAN-CNN-SPP-based discriminant model. The overall classification accuracy of the model was 93.66% for pears with core browning, the discrimination accuracy was 94.44% for sub-healthy pears, and the misjudgment rate was 6.35% for diseased fruit. This improved the accuracy of vibro-acoustic identification of pears with early-stage mild disease. This study lays a foundation for the development of an online detection system for sub-healthy fruits in the future.

Korla pear is a characteristic fruit in Xinjiang. Among them, the crisp texture is one of its excellent quality parameters. However, the crispness differences of Korla pears can vary gradually in recent years, due to the origin, variety, and maturity. The current sensory evaluation by experts or trained panelists can be the most accurate to detect the crispness. However, the evaluation process has been limited to the time-consuming and labor-intensity. The accuracy of evaluation can gradually decrease over time. Alternatively, instrument detection can share fast and stable advantages over sensory evaluation. In this study, the instrument detection was performed on the Korla pear flesh crispness using mechanical-acoustic information fusion. 50 pears were selected to test the crispness every 7 days during the 35-day storage periods, resulting in a total of six crispness gradient samples: crisp, relatively crisp, slightly crisp, slightly mealy, relatively mealy, and mealy. Then, the mechanical-acoustic signals during the rupture of pear flesh were synchronously collected at 51 200 Hz sampling rate using a universal material testing machine combined with a microphone. Subsequently, the information on jaggedness analysis interval in mechanical-acoustic signals was fused at the data level. The correlation between mechanical-acoustic signals was utilized to align with the processing mode of the human brain's comprehensive perception of crispness. Later, mechanical-acoustic fusion signals were converted into the different images of the Gramian angular summation field (GASF), Gramian angular difference field (GADF), symmetric dot pattern (SDP), Markov transition field (MTF), and recurrence plot (RP). The deep features of different images were extracted by the ResNet50 network. 8, 8, 9, 10, and 10 principal components were obtained after PCA dimensionality reduction. Furthermore, Pearson’s correlation analysis was made to obtain the absolute mean correlation coefficients between principal components of different image features and sensory crispness scores. The results showed that the MTF image was the most suitable to quantitatively characterize the crispness scores of pear flesh with the highest absolute mean correlation coefficient. Finally, the principal components of MTF images were input into the KNN, ELM, RF, and SVR optimized by PSO. The ResNet50-SVR model achieved the best prediction accuracy and stability. The R_P², RMSEP, and RPD values were 0.96, 0.24, and 4.88, respectively. Consequently, this finding can provide a strong foundation for instrument detection of the crispness of fruits and vegetables.