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This paper proposes a transformer fault diagnosis method based on ACGAN and CGWO-LSSVM to address the problem of misjudgment and low diagnostic accuracy caused by the small number and uneven distribution of some fault samples in transformer fault diagnosis. Firstly, generate adversarial networks through auxiliary classification conditions, The ACGAN method expands a small and imbalanced number of samples to obtain balanced and expanded data; Secondly, the non coding ratio method is used to construct the characteristics of dissolved gases in oil, and kernel principal component analysis is used, KPCA method for feature fusion; Finally, using the improved cubic gray wolf optimization algorithm, CGWO for least square support vector machines, optimize the parameters of the LSSVM model and construct a transformer fault diagnosis model. The results show that the proposed method has a low false alarm rate and a diagnostic accuracy of 97.66%, compared to IGOA-LSSVM the IChOA-LSSVM and PSO-LSSVM methods improved accuracy by 0.12, 1.76, and 2.58%, respectively. This method has been proven to solve the problems of misjudgment and low diagnostic accuracy caused by small sample sizes and uneven distribution. It is suitable for multi classification fault diagnosis of transformer imbalanced datasets and is superior to other methods.

The industrial load sample data categories are unbalanced, resulting in low classification performance for a few sample categories. An imbalanced industrial load identification method based on optimized CatBoost with entropy features is proposed. Firstly, multiple original samples of industrial load data and their corresponding switch states are selected from the dataset. The original samples are segmented in the time domain, dividing each sample into three time-domain intervals. The 27 time-domain features containing 8 types of entropy features are extracted from different time-domain intervals, resulting in the construction of an 81-dimensional original feature set. Next, the feature importance is calculated and sorted based on the Prediction Value Change method. The optimal subset of classification features for the corresponding device in the original sample is determined through forward feature selection, with the CatBoost classification accuracy being used as the decision variable. Secondly, the Borderline-SMOTE method is used to synthesize the sample data for balancing processing to obtain balanced switching sample data. Finally, the CatBoost classifier with Bayesian optimization and hyperBand hyperparameter optimization is constructed to identify industrial loads. The experimental results show that this method has the advantages of high feature extraction efficiency and high accuracy in identifying imbalanced small sample data.

To address the problems of low accuracy in fault diagnosis of oil-immersed transformers, poor state perception ability and real-time collaboration during diagnosis feedback, a fault diagnosis method for transformers based on the integration of digital twins is proposed. Firstly, fault sample balance is achieved through Iterative Nearest Neighbor Oversampling (INNOS), Secondly, nine-dimensional ratio features are extracted, and the correlation between dissolved gases in oil and fault types is established. Then, sparse principal component analysis (SPCA) is used for feature fusion and dimensionality reduction. Finally, the Aquila Optimizer (AO) is introduced to optimize the parameters of the Kernel Extreme Learning Machine (KELM), establishing the optimal AO-KELM diagnosis model. The final fault diagnosis accuracy reaches 98.1013%. Combining transformer digital twin models, real-time interaction mapping between physical entities and virtual space is achieved, enabling online diagnosis of transformer faults. Experimental results show that the method proposed in this paper has high diagnostic accuracy and strong stability, providing reference for the intelligent operation and maintenance of transformers.

Small and imbalanced fault samples have a profound impact on the diagnostic performance of a model in the process of locating and quantifying the rolling bearing damage of aeroengines in practice. Therefore, a Siamese Convolutional Neural Network-Bidirectional Long Short-Term Memory (CNN-BiLSTM) model was proposed in this paper. Random selection and cross combination methods were used to augment and balance sample sizes at first. Then, two weight-sharing CNN-BiLSTM models were used for adaptive extraction and distance measurement of weak fault features. Finally, the fault classification was performed based on feature distance. Model performance was verified using simulated fault test data of rolling bearings. The results showed that the Siamese CNN-BiLSTM model could achieve an accuracy of up to 96.0% for quantitative diagnosis and 98.0% for location diagnosis. This model was also capable of solving the imbalanced classification of samples and made it possible to transfer between different rotating speeds and working conditions.

Using data sourced from 15 periglacial debris flow gullies in the Parlung Zangbo Basin of southeast Tibet, the importance of 26 potential indicators to the development of debris flows was analyzed quantitatively. Three machine learning approaches combined with the borderline resampling technique were introduced for predicting debris flow occurrences, and several scenarios were tested and compared. The results indicated that temperature and precipitation, as well as vegetation coverage, were closely related to the development of periglacial debris flow in the study area. Based on seven selected indicators, the Random Forest-based model, with its weighted recall rate and Area Under the ROC Curve (AUC) greater than 0.76 and 0.77, respectively, performed the best in predicting debris flow events. Scenario tests indicated that the resampling was necessary to the improvement of model performance in the context of data scarcity. The new understandings obtained may enrich existing knowledge of the effects of main factors on periglacial debris flow development, and the modeling method could be promoted as a prediction scheme of regional precipitation-related debris flow for further research.

Accurate and timely information on forest disturbance drivers is important for sustainable forest management, global carbon cycle accounting, and climate change response. However, forest disturbance classification is difficult due to two major challenges: limited labeled samples and highly imbalanced disturbance class distribution. In this article, a new framework for multi-type forest disturbance classification based on collaborative semi-supervised learning and sample generation was proposed. First, forest disturbance is detected using long-term remote sensing time series data and disturbance detection algorithms. Spatiotemporal, spectral and terrain features of different disturbance types are extracted. On this basis, to address the problem of imbalanced and small-sample conditions, a collaborative classification strategy is developed. Based on a small number of labeled samples, Support Vector Machine (SVM) and Random Forest (RF) are used to build dual base classifiers. A confident learning (CL) framework is applied to select high-confidence pseudo-labeled samples from unlabeled data. Then, a latent diffusion model (LDM) is introduced to generate high-fidelity pseudo-samples. This increases the sample size and balances the class distribution. Based on the augmented dataset, the dual classifiers are iteratively optimized using a co-training strategy, which improves model generalization under complex conditions. The results show that the proposed framework could generate high-quality pseudo-samples and effectively reduce class imbalance. The overall accuracy (OA) of the proposed framework reaches 93.2%, which is 5.7% and 4.4% higher than single classifier baselines, respectively. After introducing the LDM-based balancing mechanism, performance is further improved by 1.8% compared with the pure semi-supervised framework. This study provides an efficient and reliable solution for large-scale forest ecosystem monitoring.

Multilevel modeling (MLM) is commonly used in psychological research to model clustered data. However, data in applied research usually violate one of the essential assumptions of MLM—homogeneity of variance. While the fixed-effect estimates produced by the maximum likelihood method remain unbiased, the standard errors for the fixed effects are misestimated, resulting in inaccurate inferences and inflated or deflated type I error rates. To correct the bias in fixed effects standard errors and provide valid inferences, small-sample corrections such as the Kenward-Roger (KR) adjustment and the adjusted cluster-robust standard errors (CR-SEs) with the Satterthwaite approximation for t tests have been used. The current study compares KR with random slope (RS) models and the adjusted CR-SEs with ordinary least squares (OLS), random intercept (RI) and RS models to analyze small, heteroscedastic, clustered data using a Monte Carlo simulation. Results show the KR procedure with RS models has large biases and inflated type I error rates for between-cluster effects in the presence of level 2 heteroscedasticity. In contrast, the adjusted CR-SEs generally yield results with acceptable biases and maintain type I error rates close to the nominal level for all examined models. Thus, when the interest is only in within-cluster effect, any model with the adjusted CR-SEs could be used. However, when the interest is to make accurate inferences of the between-cluster effect, researchers should use the adjusted CR-SEs with RS to have higher power and guard against unmodeled heterogeneity. We reanalyzed an example in Snijders & Bosker (2012) to demonstrate the use of the adjusted CR-SEs with different models.

Many practical applications suffer from imbalanced data classification, in which case the minority class has degraded recognition rate. The primary causes are the sample scarcity of the minority class and the intrinsic complex distribution characteristics of imbalanced datasets. The imbalanced classification problem is more serious on small sample datasets. To solve the problems of small sample and class imbalance, a hybrid resampling method is proposed. The proposed method combines an oversampling approach (synthetic minority oversampling technique, SMOTE) and a novel data cleaning approach (weighted edited nearest neighbor rule, WENN). First, SMOTE generates synthetic minority class examples using linear interpolation. Then, WENN detects and deletes unsafe majority and minority class examples using weighted distance function and k-nearest neighbor (kNN) rule. The weighted distance function scales up a commonly used distance by considering local imbalance and spacial sparsity. Extensive experiments over synthetic and real datasets validate the superiority of the proposed SMOTE-WENN compared with three state-of-the-art resampling methods.

The paper presents a novel probability-informed approach to improving the accuracy of small object semantic segmentation in high-resolution imagery datasets with imbalanced classes and a limited volume of samples. Small objects imply having a small pixel footprint on the input image, for example, ships in the ocean. Informing in this context means using mathematical models to represent data in the layers of deep neural networks. Thus, the ensemble Quadtree-informed Graph Self-Attention Networks (QiGSANs) are proposed. New architectural blocks, informed by types of Markov random fields such as quadtrees, have been introduced to capture the interconnections between features in images at different spatial resolutions during the graph convolution of superpixel subregions. It has been analytically proven that quadtree-informed graph convolutional neural networks, a part of QiGSAN, tend to achieve faster loss reduction compared to convolutional architectures. This justifies the effectiveness of probability-informed modifications based on quadtrees. To empirically demonstrate the processing of real small data with imbalanced object classes using QiGSAN, two open datasets of synthetic aperture radar (SAR) imagery (up to 0.5 m per pixel) are used: the High Resolution SAR Images Dataset (HRSID) and the SAR Ship Detection Dataset (SSDD). The results of QiGSAN are compared to those of the transformers SegFormer and LWGANet, which constitute a new state-of-the-art model for UAV (Unmanned Aerial Vehicles) and SAR image processing. They are also compared to convolutional neural networks and several ensemble implementations using other graph neural networks. QiGSAN significantly increases the F1-score values by up to 63.93%, 48.57%, and 9.84% compared to transformers, convolutional neural networks, and other ensemble architectures, respectively. QiGSAN outperformed the base segmentors with the mIOU (mean intersection-over-union) metric too: the highest increase was 35.79%. Therefore, our approach to knowledge extraction using mathematical models allows us to significantly improve modern computer vision techniques for imbalanced data.

Deep learning-related technologies have achieved remarkable success in the field of intelligent fault diagnosis. Nevertheless, the traditional intelligent diagnosis methods are often based on the premise of sufficient annotation signals and balanced distribution of classes, and the model structure is so complex that it requires huge computational resources. To this end, a lightweight class imbalanced diagnosis framework based on a depthwise separable Laplace-wavelet convolution network with variable-asymmetric focal loss (DSLWCN-VAFL) is established. Firstly, a branch with few parameters for time-frequency feature extraction is designed by integrating wavelet and depthwise separable convolution. It is combined with the branch of regular convolution that fully learns time-domain features to jointly capture abundant discriminative features from limited samples. Subsequently, a new asymmetric soft-threshold loss, VAFL, is designed, which reasonably rebalances the contributions of distinct samples during the model training. Finally, experiments are conducted on the data of bearing and gearbox, which demonstrate the superiority of the DSLWCN-VAFL algorithm and its lightweight diagnostic framework in handling class imbalanced data.