## 1 Introduction  
As the proportion of renewable energy integration and the large-scale application of power electronic devices increase, the fault arc issues in low-voltage distribution systems have become increasingly complex. Series fault arcs, due to their low current amplitude and strong coupling with load dynamic behavior, can easily lead to the failure of traditional overcurrent protection devices, becoming one of the primary causes of electrical fires [1]. Studies show that more than 30% of hidden electrical fires are directly related to undetected series arc faults [2]. Although existing detection technologies (such as high-frequency noise analysis [3], time-frequency domain threshold method [4]) have achieved some success, they still face bottlenecks such as redundant feature extraction and insufficient model generalization capability in modern distribution systems dominated by nonlinear loads [5]. Traditional optimization algorithms often fall into local optima, and deep learning models face issues such as high computational complexity and heavy reliance on massive annotated data [6], making it challenging to meet the dual requirements of real-time performance and lightweight design in low-voltage distribution systems. In recent years, the integration of machine learning and optimization algorithms has provided new approaches for arc fault detection. For example, a support vector machine (SVM) model optimized using genetic algorithms (GAs) improves detection efficiency through feature reduction [7], while the combination of deep learning and attention mechanisms enhances robustness under complex operating conditions [8]. Ref. [9] uses raw current signals as input to construct a one-dimensional convolutional neural network (ArcNet) and verifies the algorithm's real-time performance and accuracy on Raspberry Pi. Ref. [10] proposes an arc fault detection model based on a lightweight one-dimensional convolutional neural network, which is improved by using deep separable convolution. The GADF-CNN model proposed in Ref. [11] effectively extracts and classifies fault features. Ref. [12] introduces a domain adaptation framework based on multi-scale hybrid domain features (DA-MMDF) for cross-domain intelligent fault diagnosis under variable operating conditions. Ref. [13] employs a method of deep supervision without anchors and task alignment to encourage the model to make accurate and consistent predictions, significantly enhancing overall detection performance. Ref. [14] proposes a hybrid model framework of knowledge distillation convolutional neural networks-deep forest (KDCNNs-DF), which significantly improves classification accuracy. The patterns of arc changes are complex, and traditional diagnostic models, such as SVM, often suffer from issues like insufficient accuracy, overfitting, and high data requirements [15]. XGBoost, with its simplified calculations and high classification and computational efficiency, has gained widespread application. However, the determination of hyperparameters heavily relies on expert prior knowledge. To enhance the classification performance of XGBoost, some scholars have employed various optimization algorithms to refine the parameters of XGBoost. Nevertheless, common optimization algorithms still face challenges such as weak local search capabilities, average global search capabilities, and a tendency towards premature convergence [16; 17]. In response to the aforementioned challenges, this paper proposes a series arc fault detection method that integrates the artificial hummingbird algorithm (AHA) with XGBoost. By analyzing a large amount of arc fault data and selecting appropriate feature values based on the characteristics of the faults, the global search capability and dynamic adaptive mechanism of AHA are utilized to screen out key feature subsets sensitive to arcs from high-dimensional time-frequency domain features.