# Fault Diagnosis of Universal Circuit Breakers Based on Variational Mode Decomposition and WOA-DBN
## 1 Introduction  
The universal circuit breaker is a critical control and protection device in power systems [1, 2]. Its operational state directly influences the security of the power grid and the reliability of the power supply [3]. However, universal circuit breakers are susceptible to malfunctions that might seriously jeopardize the electrical system's ability to operate safely [4]. Therefore, diagnosing the operational state of universal circuit breakers and detecting faults is paramount [5]. The feature extraction technique of vibration signals and the fault diagnosis models are the primary fields of interest in studying the fault diagnosis of universal circuit breakers. Universal circuit breakers generate vibration signals during operation that contain substantial characteristic information [6, 7]. However, these vibration signals are complex and high-dimensional and require signal processing with feature extraction. Insufficient extraction may lead to under-representation, while too many feature dimensions can lead to redundant representations, affecting diagnostic results' accuracy [8]. Researchers have conducted extensive investigations into universal circuit breaker feature extraction methods. Fourier transform is adequate in identifying frequency information and processing periodic signals. However, it struggles with nonlinear and non-stationary signals and cannot capture instantaneous changes in the time and frequency domains of the signal [9]. Wavelet transform efficiently highlights localized information in the time-frequency domainand helps analyze nonlinear and unstable vibration signals. [10]. However, it is susceptible to the influence of adjacent harmonics. Empirical Mode Decomposition (EMD) applies to processing nonlinear and non-stationary signals. It can address the issue of near harmonics by decomposing signals into multiple Intrinsic Mode Functions (IMFs) [11]. However, EMD suffers from mode aliasing and end effects [12]. Compared to EMD [13], Ensemble Empirical Modal Decomposition (EEMD) resolves the modal aliasing and end-point effects problems. However, it requires manual selection of the amplitude parameter, lacks a solid theoretical basis, and can lead to inaccurate signal decomposition. VMD is a method that can effectively handle nonlinear and non-stationary signals [14]. It exhibits superior fault feature extraction capabilities. VMD can resolve harmonic issues through IMF decomposition [15] and avoid mode aliasing and end effects. Moreover, VMD is grounded in a solid theoretical foundation [16], allowing for the scientific selection of hyperparameters, and its results have been extensively verified. Applying the VMD method to the feature extraction process of universal circuit breaker vibration signals [17] is expected to yield promising results. For universal circuit breakers, support vector machines (SVM), random forests, and neural networks often utilize fault diagnostic models [18; 19; 20; 21]. SVM can handle high-dimensional vibration signal data and maintain good diagnostic accuracy in small sample spaces. However, adjusting its kernel function and hyperparameters can be challenging. Additionally, SVM is a binary classifier, which increases model complexity when dealing with multiclassification problems [22]. Random forests are effective in handling multiclassification problems and have easier parameter tuning. However, they have limitations regarding model expressiveness and high-dimensional feature mapping [23]. Neural network models are widely employed because they capture highly complex data relationships in large sample spaces and effectively handle multiclassification problems. However, the working characteristics of universal circuit breakers make it difficult to obtain many fault samples, which limits the potential application of neural network models [24; 25; 26]. The emergence of DBNs [27] has provided new approaches to address these challenges.