## 1 Introduction
When noise is inevitably introduced during the data collection step, the higher-order mode become increasingly sensitive to noise and may seem unreliable. Therefore, an appropriate denoising method is crucial for the extraction of the accurate bridge modes, especially for those in the higher frequency range. The commonly adopted signal denoising processing technologies include feature extraction [23], empirical mode decomposition (EMD) and its variants [24; 25; 26; 27], the wavelet threshold [28], and a moving average filter [29]. However, these methods could not guarantee signal integrity. For instance, EMD may suffer from mode aliasing [24]. [PERSON] et al. [25] proposed a denoising method based on ensemble empirical mode decomposition (EEMD) with multi-scale principal component analysis, which improved signal decomposition but still struggled with wavelet-based limitations. [PERSON] et al. [26] improved EEMD to enhance the stability and reliability of EMD, although reconstruction errors remained significant. [PERSON] [27] proposed complete ensemble empirical mode decomposition (CEEMDAN), which mitigates mode aliasing by applying EMD to white-noise-augmented signals and averaging the results. [PERSON] [29] introduced a moving average method that was effective in suppressing periodic interference, making it particularly suitable for high-frequency oscillations. [PERSON] et al. [28] numerically compared the denoising performances of different wavelet thresholds. [PERSON] et al. [30] combined CEEMDAN with threshold screening singular value decomposition (SVD) to improve the signal-to-noise ratio and preserve fault features in vibration signals. [PERSON] et al. [31] integrated CEEMDAN and principal component analysis (PCA) to reduce high-frequency noise while retaining low-frequency information and minimizing mode aliasing. However, this technology relied on single-noise involved assumptions and involved lossy PCA-based compression, which may lead to information loss due to repeated decomposition. To balance noise suppression and signal detail retention in the denoising process, a novel method named CEEMDAN-NSPCA is presented in this work. Unlike conventional methods that standardize input signals, it may potentially amplify noise, and this method avoids standardizing the signal and instead focuses on preserving low-frequency components while denoising high-frequency content. The process begins by decomposing the noisy signal using CEEMDAN to obtain intrinsic mode functions (IMFs). High-frequency IMFs are then selectively identified and subjected to dimensionality reduction using PCA, without normalization. Finally, the denoised high-frequency components are combined with the unaltered low-frequency IMFs to reconstruct a denoised signal. In addition, the wavelet threshold is another option to improve CEEMDAN [32]. The IMF components obtained from CEEMDAN are selected by the correlation coefficient criterion and then filtered by the wavelet threshold algorithm. However, the direct removal of certain IMF components risks discarding valuable signal information alongside noise. To address these limitations, this study proposes an enhanced denoising method called CEEMDAN-IWT, which integrates CEEMDAN with an improved wavelet threshold (IWT) technique [33]. Initially, the CEEMDAN method decomposes the signal into multiple IMFs. The high-frequency IMFs are then subjected to wavelet decomposition, then filtered by the wavelet coefficients using an improved wavelet threshold. The filtered IMFs are subsequently reconstructed via wavelet inverse transform. Finally, the denoised signal is obtained by combining the reconstructed high-frequency IMFs with the original low-frequency IMFs, achieving effective noise reduction while preserving critical signal features. Excluding the introduction, there are three sections including methodology, simulation examples, and conclusions in this work.