## 1 Introduction
Furthermore, [PERSON] et al. [22] successfully segmented target leaves from similar backgrounds using an automatic segmentation method based on KR. Additionally, [PERSON] et al. [23] achieved promising results in tool wear monitoring using KR. In addition to the prediction characteristic utilized by the above methods, the potential of the KR decomposition characteristic [24] is investigated in this paper. Considering that the vibration acceleration signal collected from a multiple degree-of-freedom (DOF) TV system can be described by numerous modal component signals carrying parameter information, a Nadaraya-Watson (NW) kernel estimator [25; 26] based on KR is constructed, and the multi-level kernel regression residual decomposition (KRRD) method is presented. By applying multi-level KRRD to the collected vibration signal, a multi-level decomposition frame is formed, encompassing a set of modal component signals represented by the kernel regression signals that reflect the dynamic characteristics of the physical parameters. Meanwhile, a noise interference component signal represented by a residual signal can be separated from the vibration signal. In this step, the multiple DOF parameter identification problem is transformed into a single DOF parameter identification problem. This transformation improves the signal-to-noise ratio (SNR) and provides convenience for subsequent analysis. Time-frequency (TF) methods are powerful tools for analyzing non-stationary signals, which can track TV characteristics on both time and frequency scales [27]. Wavelet transform (WT), the most used method for TF analysis, embodies the concept of localization and overcomes the limitation of fixed window size across different frequencies. The TF windows for fitting TV characteristics are essentially fitting a curve with multiple horizontal lines. [PERSON] et al. [28] presented a WT-based method to identify the load parameter, and the performance was validated through numerical simulations. [PERSON] et al. [29] successfully identified the parameters using a modal identification algorithm based on WT. Nevertheless, the TF resolution of WT is restricted by HUP, which has a significant impact on the accuracy of TV system parameter identification [30]. Polynomial chirplet transform (PCT) [31] is a recently developed TF method, which is more precise in TF characterization by introducing a frequency demodulated operator. The frequency demodulated operator can make the horizontal line fitting the TF characteristic rotate an angle adaptively, i.e., the parameter variation satisfies the short-term linear variation assumption. Therefore, the TF resolution is significantly improved, and more TV information [32] can be reflected. Compared with other TF methods based on the short-term time-invariant assumption, PCT based on the short-term linear variation assumption is more suitable for analyzing non-stationary signals. [PERSON] et al. [33] investigated PCT and demonstrated that it can produce a good TF distribution for a wide range of signals with continuous instantaneous frequency (IF). [PERSON] et al. [34] optimized PCT and constructed a synthetic simulation signal to verify its effectiveness. Meanwhile, the optimized method was applied to field seismic data, and the tight sandstone gas reservoirs can be effectively identified. [PERSON] et al. [35] compared PCT with two parameter identification methods based on the Hilbert transform and verified the parameter identification performance of PCT by experiments. However, PCT is not suitable for multi-modal compound signals. Therefore, the combination of PCT with multi-level KRRD can better track the TF variation. The ambiguity function (AF) is widely used in the field of radar and sonar, which can reflect the resolution characteristics of two targets with different distances and speeds, i.e., the signal correlation in the time domain. [PERSON] et al. [36] proposed a generalized formulation based on AF, solving the problem of multiple-input multiple-output radar beampattern design successfully.