## 1 Introduction  
A large number of engineering structures in aerospace, civil engineering, and other fields are subjected to environmental random excitation and exhibit time-varying (TV) characteristics. However, the corresponding random excitation force is difficult to measure, which causes significant errors in parameter identification using traditional methods. Furthermore, even if the environmental random excitation force is stationary, the collected vibration signal of the TV structure is non-stationary, thus limiting the performance of parameter identification methods based on the short-term time-invariant assumption. In addition, the collected TV vibration signal lacks an exact mathematical analytical expression. These problems must be urgently addressed as they are crucial for structural design, vibration testing, and health monitoring. Therefore, there is a need to effectively carry out physical parameter identification for TV systems under random excitation [1, 2, 3]. Vibration analysis-based methods have been extensively studied and applied in the field of parameter identification [4, 5], and have been proved as the most effective way. These methods can be classified into two types. The first type is based on the short-term time-invariant assumption [6, 7, 8], in which TV systems are analyzed. These methods utilize various signal processing tools to identify parameters within a short-term interval, achieving the purpose of identification through overall fitting. The second type is based on the modal concept [9; 10], and the TV systems can be analyzed. Through decomposition methods, the collected vibration acceleration signal from the TV system can be decomposed into a series of modal component signals, and the resulting single-component signal is then used for parameter identification [11; 12; 13; 14]. However, some flaws (excessive calculation, theoretical deficiencies, endpoint effect) still exist in the widely used decomposition methods, short-time Fourier transform (STFT) [15] and empirical mode decomposition (EMD) [16]. STFT is limited by the Heisenberg uncertainty principle (HUP), which leads to some limitations in the analysis of TV signals. At the same time, the selection of the window function depends on manual experience, and the length of the analyzed signal can result in inaccurate analysis results or excessive calculation. EMD, as a data-driven adaptive method, can separate several intrinsic mode functions (IMFs) from the vibrations signal based on signal scale information. However, the method lacks a clear and widely accepted theoretical background. Furthermore, the endpoint effect is a significant flaw of EMD, i.e., no signal sampling points are considered at the application boundary of EMD, resulting in obvious swings at the ends of the signal caused by interpolation technology. These swings propagate throughout the entire signal and lead to abnormal amplitudes and peaks near the boundaries of the decomposed IMFs. The endpoint effect can cause problems such as envelope shape change, modal mixing, unstable signal boundary calculation, and an inaccurate IMF decomposition result. As a non-parametric technology, kernel regression (KR) [17; 18] essentially utilizes a kernel function as the weight function of signal sampling points to establish a prediction model and find the non-linear relationship between signal data to adapt to the characteristics of data autocorrelation decaying with time. In recent years, KR technology has become increasingly popular in the field of price predication, fault detection, and image processing. [PERSON] et al. [19] developed a KR-based price prediction model in view of the large fluctuation of electricity prices in the electricity market, accurately forecasting price trends according to historical data. Similarly, [PERSON] et al. [20] explored a multi-task KR method, demonstrating its advantageous prediction capabilities. [PERSON] et al. [21] proposed a novel kernel function algorithm with validated prediction ability and improved model generalization potential.