To address the issues of insufficient rigor in existing methods for quantifying apple watercore severity and the complexity and low accuracy of traditional classification models, this study proposes a method for watercore quantification and a classification model based on a deep convolutional neural network. Initially, visible/near-infrared transmission spectral data of apple samples were collected. The apples were then sliced into 4.5 mm thick sections using a specialized tool, and image data of each slice were captured. Using BiSeNet and RIFE algorithms, a three-dimensional model of the watercore regions was constructed from the apple slices to calculate the watercore severity, which was subsequently categorized into five distinct levels. Next, methods such as the Gramian Angular Summation Field (GASF), Gram Angular Difference Field (GADF), and Markov Transition Field (MTF) were applied to transform the one-dimensional spectral data into two-dimensional images. These images served as input for training and prediction using the ConvNeXt deep convolutional neural network. The results indicated that the GADF method yielded the best performance, achieving a test set accuracy of 98.73%. Furthermore, the study contrasted the classification and prediction of watercore apples using traditional methods with the existing quantification approaches for watercore levels. The comparative results demonstrated that the proposed GADF-ConvNeXt model is more straightforward and efficient, achieving superior performance in classifying watercore grades. Furthermore, the newly proposed quantification method for watercore levels proved to be more effective.

Deep learning methods have demonstrated impressive effectiveness in diagnosing bearing faults. Nevertheless, their performance tends to decline significantly in the presence of long-tailed distributions, where certain fault types are underrepresented, which is common in industrial environments where fault occurrences are rare. To address the challenges posed by long-tailed data in fault diagnosis, this paper proposes the Probabilistic Contrastive Quadratic Network (PCQNet), a novel framework designed to enhance the diagnostic capabilities of neural networks under class imbalance conditions. PCQNet consists of three core components: a quadratic convolutional residual network that strengthens feature representations through higher-order interactions; a Probabilistic Contrastive Loss (PCL) that models class features using the von Mises-Fisher (vMF) distribution, combining class expectations and prior probabilities to adaptively balance the contributions of each class, effectively mitigating long-tail bias; and a logit-adjusted cross-entropy loss that improves the discrimination ability for minority classes while enhancing classification fairness. The parabolic decay formula dynamically adjusts the dominance of these two loss functions during training, ensuring the model achieves both effective feature learning and accurate classification.The effectiveness of PCQNet is validated on one public dataset and two self-constructed datasets, demonstrating its superior performance in handling long-tailed data. Analysis of the attention mechanism derived from quadratic neurons further explains the excellent feature extraction capability of the quadratic network. Building on this analysis, ablation studies further verify the independent contributions and synergistic effects of each module, confirming their critical roles in improving diagnostic performance.

The content of the watercore in apples plays a decisive role in their taste and selling price, but there is a lack of methods to accurately assess it. Therefore, this paper proposes an OCRNet-based method for apple watercore content evaluation. A total of 720 watercores of apples from Mengzi, Lijiang, and Zhaotong City in Yunnan Province were used as experimental samples. An appropriate watercore extraction model was selected based on different evaluation indicators. The watercore feature images extracted using the optimal model were stacked, and the watercore content of apples in different regions was evaluated by calculating the fitted area of the stacked watercore region. The results show that the OCRNet model is optimal in all evaluation metrics when facing different datasets. The error of OCRNet is also minimized when extracting overexposed as well as underexposed images with 0.15% and 0.38%, respectively, and it can be used to extract the characteristics of the apple watercore. The evaluation result of the watercore content of apples in different regions is that Lijiang apples have the highest watercore content, followed by Mengzi apples, and Zhaotong apples have the least watercore content.