## 1 Introduction
To address the few-shot fault diagnosis problem with insufficient on-site data, the current main solutions are divided into two aspects: the first it to extend the data, which is not only expensive but also mostly relevant to only normal data, making it difficult to obtain effective fault samples. The second is to rely on few-shot learning methods to achieve a solution [14]. Accurate diagnosis of HVCB faults becomes a challenge with a small sample size. In response to the above challenges, [PERSON] and [PERSON] [15] proposed a multi-grained cascade forest (gcForest) integration method based on decision trees. The model has the advantages of easy training, low computational overhead, and high parallel computing potential. [PERSON] et al. conducted a comparative study of various tree-based fault diagnosis models to demonstrate the accuracy of gcForest in creating a diagnosis with small samples [16]. It has been applied to hyperspectral image classification and in bearing fault diagnosis and other fields [17; 18], achieving good results. [PERSON] et al. utilized a hybrid learning model of CNN and gcforest to diagnose bearing faults [19]. [PERSON] et al. improved the gcForest algorithm by introducing kernel principal component analysis in cascade forests, which outperforms traditional methods when analyzing the experimental vibration data of flip chips [20]. Although the gcForest model performs well in many applications, the results largely depend on the adjustment of model hyperparameters. Optimization of hyperparameters is rarely studied in the regression and classification tasks of machine learning. In a gcForest model, the selection of hyperparameters such as the maximum number of cascaded layers (\(m\)), the quantity of decision trees (\(c\)) in each random forest, and the quantity of classifiers (\(n\)) in each layer of the cascaded structure significantly affects the performance of the model. Therefore, its parameters can be adjusted through the optimization algorithm, and the optimal parameters of the model can be iteratively searched to improve the model's diagnostic accuracy [21]. [PERSON] [22] proposed a random forest (RF) algorithm based on an improved harmony search to make RF predictions better. [PERSON] et al. [23] have suggested utilizing the particle swarm optimization (PSO) algorithm for optimization of model parameters and have achieved desirable outcomes. Although the PSO algorithm is widely used and straightforward to implement, it is prone to local optima and may lead to deviations in the results. For this reason, we propose a model that uses the grey wolf optimization (GWO) algorithm to optimize gcForest parameters for fault diagnosis of HVCBs (henceforth referred to as GWO-gcForest) in the case of insufficient data samples. To the best of the author's knowledge, this is the first time that the GWO-gcForest model has been applied to the field of HVCB mechanical fault diagnosis. In this research, the vibration signal of the HVCB is subjected to feature extraction to determine characteristic parameters. Subsequently, the parameters \(m\), \(c\), and \(n\) of the gcForest model are iteratively optimized using the GWO algorithm, leading to the identification of optimal model parameters. Consequently, a GWO-gcForest fault diagnosis model is established. Using this model, an example analysis is conducted to accurately classify the type of fault in the circuit breaker, thereby validating the efficiency of the proposed approach. Furthermore, the diagnostic capability of the model is assessed in scenarios involving different sample sizes and unbalanced samples, further confirming the method's efficacy. The main contributions of this study are as follows:  
1. The vibration signals of different types of faults are subjected to wavelet packet decomposition. The third layer of wavelet packet decomposition coefficients are reconstructed, and the energy entropy of each frequency band is calculated and used as a feature vector. 2.