## 1 Introduction  
The rapid progression of industrial automation and informatization has significantly elevated the importance of fault-diagnosis technologies in maintaining the reliability and safety of industrial systems [1]. In complex settings such as the chemical, manufacturing and energy sectors, the capacity for precise and timely fault detection is crucial for optimizing production efficiency and averting potential accidents [2; 3; 4]. Recent advancements in big data and the Internet of Things (IoT) have led to widespread sensor integration across these systems, generating substantial data volumes that enhance the monitoring and diagnostic processes [5; 6]. This influx of operational data, while beneficial, often overshadows the sparse fault data, creating a significant imbalance that challenges traditional data-intensive machine learning and deep learning methodologies [7; 8]. This disparity underscores the need for robust few-shot learning techniques that can effectively function in environments with limited fault data, marking a critical area of research in industrial intelligence [9; 10]. Despite the significant achievements of Few-Shot Learning (FSL) in fields such as natural language processing and image classification [8; 11; 12; 13], its application in the complex domain of fault diagnosis, particularly when handling intricate industrial data, continues to face numerous challenges. Research has shown that existing FSL approaches can be broadly categorized into generative and discriminative model methods, each with its strengths and limitations. For instance, generative models, as described by [PERSON] et al. [11], often enhance model performance in data-scarce environments by generating new samples, whereas discriminative models focus on learning distinguishing features from limited data. [PERSON] et al. [8] have classified fault-diagnosis methods for small and imbalanced datasets into data augmentation, feature extraction and classifier design. Despite their excellence, these methods commonly exhibit weaknesses such as poor generalization capabilities, sensitivity to adversarial examples and high algorithmic complexity, which can lead to suboptimal performance in industrial applications that demand rapid and accurate diagnostics. Recent studies have shifted focus to addressing FSL fault-diagnosis challenges through meta-learning [14; 15; 16], with a significant proportion of recent research in time-series signal fault diagnosis concentrating on this approach [17]. However, the practical utility of meta-learning is limited by its high dependency on data quality and distribution, which can adversely affect performance in industrial settings due to data noise and outliers [18]. Meta-learning algorithms like MAML, although quick to adapt to new tasks, require multiple gradient updates, which increases the computational load and can lead to overfitting on sparse data, thus diminishing generalization capabilities [19]. Task sequencing meta-learning introduces a novel method for optimizing the selection and order of learning tasks, but significant differences between tasks can lead to unstable knowledge transfer, affecting the learning outcomes [20]. In recent years, GAN-based data-augmentation algorithms have garnered considerable attention for addressing small-sample problems in fault diagnosis. These algorithms typically follow a sequence of steps: initially collecting data under various fault conditions, then training a GAN model using real signals and finally training classifiers with both real and synthetic signals [21]. This approach enables GAN-based data augmentation to generate a diverse set of samples from limited fault data, thereby enhancing the performance of diagnostic models. For instance, [PERSON] et al. developed a novel multi-module gradient penalty GAN specifically for generating samples for mechanical fault diagnosis [22]. Furthermore, research by [PERSON] et al. utilized a WGAN-GP-based auxiliary classifier to generate high-quality spectra to overcome small-sample challenges [23].