## 1 Introduction  
In the power system, transformers are critical devices that convert electrical energy from one voltage level to another, playing an indispensable role in the transmission and distribution of electrical energy. The normal operation of transformers is crucial for ensuring the stable operation of the power grid and the quality of power supply [1, 2, 3]. However, due to the long-term operation of transformers in harsh environments, such as high temperature and high voltage, as well as the influence of load changes, electrical faults, and other factors, transformers may have various potential fault hazards. Unpredictable accidents can cause serious social impacts. Therefore, strengthening transformer condition monitoring and fault diagnosis is of great significance. The common faults of transformers mainly include mechanical faults, insulation faults, and overheating faults. Among them, electrical faults caused by mechanical faults occur most frequently, with iron-core faults accounting for a large proportion of these [4]. According to statistical research, iron-core faults are mostly caused by mechanical structural problems in the initial stage, and as the degree of the fault deepens, they pose a threat of damage to the clamping force and insulation of the iron core, and even lead to serious electrical faults, such as the multi-point grounding of the iron core [5]. How to detect the operating status of transformer iron cores and diagnose faults, as well as detect internal faults and potential safety hazards in transformers early to avoid accidents, has gradually become a focus of research for scholars at home and abroad. The main methods for detecting the state of transformer iron cores include offline detection and online detection [6]. Offline detection involves performing maintenance after the transformer has stopped, such as testing insulation resistance. However, power outage maintenance can cause significant economic losses and result in high costs. Online detection involves detecting the operating status of the transformer through real-time monitoring, without the need to shut down the transformer. At present, the monitoring methods for transformer core faults mainly include gas chromatography analysis and measuring the presence or absence of a current in the grounding wire. These methods focus more on judging the core faults of large oil-immersed transformers, but the overall structure of dry-type transformers is significantly different from that of oil-immersed transformers, and many judgment methods are not fully applicable. Compared with many traditional methods, transformer state monitoring based on vibration signals has no electrical connection to the electrical system as a whole and will not have any impact on the normal operation of the power system. It also has strong anti-interference ability and high sensitivity, and can quickly, safely, and reliably monitor the operating status of transformers, diagnose faults, and better ensure the safe and reliable operation of transformers [7; 8]. At present, vibration-signal diagnosis often uses machine learning methods such as support vector machines and K-means clustering for fault identification and classification. For example, [PERSON] et al. [9] used wavelet packet transform to analyze the vibration signals of transformer windings in different states. The energy spectrum entropy of the vibration signal was used as the feature input vector, and an improved multi-class support vector machine was used to train and test the feature vectors, achieving the classification diagnosis of transformer windings in different states. Reference [10] proposed two effective feature extraction techniques and used corresponding feature vectors to train SVM classifiers, demonstrating the effectiveness of this method through experiments. [PERSON] et al.