## 1 Introduction  
A spillway radial gate (SRG), as a critical drainage structure, is widely used as a dam discharge gate due to its advantages, such as the absence of gate slots and favorable downstream flow conditions. During power generation and flood discharge operations, the SRG must be opened and closed in a timely manner to control flow, making its safe operation crucial to both dam efficiency and the safety of downstream lives and property [1, 2]. The SRG primarily bears loads on its panel, which are then distributed by horizontal and vertical beams, and finally transferred to the pier through supporting arms. However, accident investigations have revealed that SRGs often fail due to instability in the supporting arms. In addition to intrinsic factors like water flow excitation and the structure's natural frequencies, fatigue and corrosion are also significant causes of arm instability [3, 4]. As such, real-time or periodic safety monitoring of the gate is essential. Installing sensors on the gate for prototype observation is one of the most direct and commonly used methods to assess gate conditions or analyze the causes of vibration [5]. Gate vibrations involve several complex nonlinear issues, including material nonlinearity and contact nonlinearity, which exhibit chaotic characteristics in the vibration signals. Moreover, the harsh and complex operational environment of the gate results in sensor-measured signals often containing noise, which introduces disturbances during further processing. For instance, noise can lead to false modal identification during a modal parameter analysis and reduce efficiency in condition monitoring [6]. Traditional noise reduction methods, such as mean and median filtering, rely on statistical principles, using local signal characteristics to remove noise. However, these methods are often limited when dealing with non-stationary signals or when noise characteristics vary significantly. Additionally, they require sufficient sample data for an effective analysis. Recently, with the development of non-stationary signal processing techniques, methods like Empirical Mode Decomposition (EMD) [7], Variational Mode Decomposition (VMD) [8], and Wavelet Threshold Denoising (WTD) offer a multiscale analysis to effectively remove noise across various frequency ranges [9]. EMD is suitable for processing nonlinear and non-stationary time series but faces challenges like mode mixing, sensitivity to parameter settings, and end effects, making the separation of characteristic frequencies and noise in signals less accurate. In comparison, VMD provides better robustness in sampling and noise suppression, effectively reducing mode mixing and achieving more precise decomposition results. However, VMD is sensitive to the number of decomposition modes (K) and the penalty factor (\(\alpha\)), which can lead to over-decomposition or under-decomposition [10]. Too few modes may miss important signal features, while too many modes may introduce unnecessary noise or patterns. A larger penalty factor (\(\alpha\)) results in smoother solutions, potentially losing signal details, whereas a smaller penalty factor may lead to non-smooth solutions or even oscillations. With advances in mathematical optimization, optimizing VMD parameters can enhance accuracy, reduce subjectivity in parameter selection, and improve computational efficiency. This enables a more effective handling and analysis of complex signals, laying a solid foundation for further signal processing and feature extraction. Numerous researchers [11; 12; 13; 14; 15] have studied the selection and application of VMD parameters (K and \(\alpha\)). [PERSON] [14] proposed an improved cuckoo search algorithm to optimize VMD, demonstrating its accuracy through experiments and simulations. [PERSON] [15] used the whale optimization algorithm to adaptively determine VMD parameters, improving the efficiency of a bearing fault diagnosis.