## 1 Introduction
These non-stationary and nonlinear signals contain rich state information, such as vibrations, stresses, and strains, which can reflect the health status of mechanical systems and structures. Therefore, signal processing techniques in the field of structural health require the integration of time-domain, frequency-domain, and time-frequency-domain characteristics to provide a more comprehensive understanding of the nature of signals and improve the accuracy of diagnosis. In recent years, researchers have made unremitting efforts to achieve precise processing of signals in the field of structural health monitoring (SHM), particularly for non-stationary and nonlinear signals. The emergence of non-parametric time-frequency analysis techniques, such as short-time Fourier transform (STFT), wavelet transform (WT), and Wigner-Ville distribution (WVD), has found widespread application in SHM. These techniques can simultaneously provide information about signals in both the time and frequency domains, aiding in the development of a more comprehensive understanding of signal characteristics. However, these techniques have their limitations, such as the trade-off between time resolution and frequency resolution in STFT, the sensitivity of WT to the choice of basis functions, and the cross-term and noise sensitivity issues in WVD. To address these issues, adaptive signal processing techniques have emerged. Empirical mode decomposition (EMD) and its optimized models (e.g., ensemble EMD (EEMD) and multivariate EMD (MEEMD)) decompose signals into a series of intrinsic mode functions (IMFs) through an iterative process, with each IMF representing a natural oscillation mode in the signal. This method excels in processing nonlinear and non-stationary signals but also faces challenges in practical applications, such as endpoint effects and energy non-conservation. Furthermore, variational mode decomposition (VMD) and its variants (e.g., sparse VMD (SVMD) and adaptive VMD (AVMD)) achieve signal decomposition by minimizing a variational problem, offering higher flexibility and stability. The optimized model, empirical wavelet transform, combines the adaptive decomposition concept of EMD with the compact support framework of wavelet transform theory. By decomposing the signal into multiple frequency bands and constructing wavelet functions compatible with a wavelet filter bank for each band, it achieves adaptive decomposition of the signal. This approach can capture local features of the signal and is particularly suitable for processing nonlinear and non-stationary signals. The latest technology, deconvolution techniques such as minimum entropy deconvolution (MED) and maximum correlated kurtosis deconvolution (MCKD), enhance signal fault features through filtering processing, improving diagnostic accuracy. These techniques can be regarded as a method of adaptive signal processing. In the deconvolution process, it is often necessary to estimate the point spread function (PSF) or convolution kernel of the signal, a process that typically relies on adaptive algorithms like the expectation-maximization (EM) algorithm or blind deconvolution algorithms. These algorithms can automatically adjust parameters based on observed data and prior knowledge in order to optimize the deconvolution effect. The combination of deconvolution with the aforementioned adaptive and non-parametric time-frequency analyses elevates signal processing techniques to a new level. This paper aims to review key signal processing techniques in SHM, particularly non-parametric time-frequency analysis, adaptive decomposition, and deconvolution techniques, as shown in Figure 1. The first section introduces non-parametric time-frequency analysis. It begins by presenting the concept, applications, advantages, and disadvantages of STFT and discussing its widespread use in SHM. It then elaborates on the basic principles of WT, application examples, and its advantages and disadvantages compared to STFT.