# Study on Denoising Method of Weld Defect Signal Based on SSA-VMD-WPD
## 1 Introduction  
In response to the increasing demand in the non-destructive testing field, phased array ultrasonic technology has garnered more attention. Ultrasound phased array systems are increasingly being used with the goal of higher contrast, speed, and reliability, as well as higher spatial resolution, to achieve more effective data collection and imaging, thereby enabling more accurate and reliable defect localization [1; 2]. As early as the 1950s, a patent application for a probe with ultrasound beamforming capabilities was considered the precursor to phased array ultrasonic systems [3]. In the 1980s, the first phased array ultrasonic testing instrument was successfully developed. However, at that time, phased array ultrasonic systems were bulky and complex, primarily used in critical manufacturing sectors such as power generation equipment, the nuclear industry, and large forgings [4; 5; 6]. Currently, a series of products from companies such as Olympus in Japan, M2M in France, Sonotest in the UK, AOS in the US, and Sonotron in Israel are widely used. Additionally, the Institute of Acoustics at the Chinese Academy of Sciences has developed a phased array ultrasonic dynamic focusing system, and Tianjin University, in collaboration with multiple research units, has developed the phased array ultrasonic testing device PWA-01, which can achieve fully automatic detection of pipeline welds, reaching the level ofsimilar technologies abroad. Several research units have conducted research on the system development and equipment production of phased array ultrasonics, advancing three-dimensional imaging, full-focusing imaging, and digitization in phased array ultrasonic testing [7; 8; 9]. The A-scan data collected by the ultrasonic phased array testing instrument inevitably contain mixed noise data [10], the sources of noise are diverse [11], and the quality of information obtained from ultrasonic defect signals in experimental research is constrained by noise interference, thus limiting the accurate assessment of defect information and consequently affecting the accuracy of detection [12; 13]. Therefore, specific signal processing is typically required for the acquired ultrasonic non-destructive testing signals, involving operations such as denoising, filtering, and feature extraction through signal processing techniques [14]. Currently, commonly used signal denoising methods include the fast Fourier transform, wavelet transform, singular value decomposition, empirical mode decomposition and its variations, and variational mode decomposition methods [15; 16; 17; 18; 19]. Researchers have achieved good results by optimizing denoising methods through the introduction of optimization algorithms and by combining multiple methods to construct joint denoising models. [PERSON] et al. [12] proposed a denoising method combining wavelet denoising and empirical mode decomposition (EMD), indicating a significant improvement in denoising effectiveness compared to traditional methods; [PERSON] et al. [20] applied wavelet analysis and modal empirical decomposition to the original signal for denoising and signal reconstruction, achieving the elimination of spurious signals. Similarly, [PERSON] et al. [21] utilized Discrete Wavelet Transform (DWT) and the proposed EWT-EMD method for denoising Electromyography (EMG) signals. The proof was that the EWT-EMD was practical and advantageous for improving noise removal while preserving important signal properties. And the method applied in this paper was wavelet packet analysis and variational modal decomposition method; wavelet packet analysis was the continuation of wavelet transform theory; compared with wavelet transform, only decomposing the low-frequency components, wavelet packet analysis could decompose the low-frequency part and high-frequency part at the same time, so for non-smooth signals, wavelet packet analysis had a stronger denoising ability.