## 1 Introduction
[PERSON] initially proposed a classification method based on Kalman filters to reduce noise, which improves classification accuracy while preserving defect feature information [10]. However, wavelet filters are superior to Kalman filters in field noise reduction [11]. Wavelet denoising is a time-frequency analysis method that is suitable for non-stationary signal analysis. However, when wavelets are used to analyze pipeline defects, prior knowledge of the signal, appropriate basis function, and decomposition level is required. Moreover, high-frequency noise cannot be completely decomposed, so the reconstructed signal will be distorted. The empirical mode decomposition (EMD) denoising method is a time-frequency analysis method which can decompose complex signals into multiple inherent modal functions based on the signal's the local characteristic time scale. This method has good adaptive decomposition ability and can handle the denoising of non-stationary and non-linear signals. However, it is prone to modal aliasing during noise reduction [12]. Ensemble empirical mode decomposition (EEMD) obtains the intrinsic mode function (IMF) component by adding white noise, which can alleviate the problem of mode aliasing; however, the process is complex and time-consuming. Therefore, the complete EEMD (CEEMD) method was proposed. In this method, which is based on EMD, different positive and negative noise signals are added to obtain the final IMF component. This method not only compensates for the mode-aliasing problem of EMD, but is also faster than the EEMD method. Moreover, it obtains a more thorough decomposition and reduces noise better. In recent years, scholars have increasingly used EMD to reduce signal noise in different fields such as mechanical vibration, earthquake, and pipeline fault detection [13; 14; 15]. For example, [14] used the HHT method, which is based on EMD, to study the characteristics of the seismic and explosion waves of natural minerals in coal mines to provide specific guidance for engineering practice. The derivative extremum field mean mode decomposition (DEMMD) method has been employed to study the denoising of pipeline detection signals [16]. However, mode-aliasing and end effects in EMD affect the effectiveness of modal analysis. In addition,EMD is unstable in terms of computation time, and the decomposition performance of multi-frequency signals that consist of similar frequencies is not ideal. Many theoretical studies have been conducted to address the disadvantages of EMD, mainly focusing on the mode-aliasing problem and construction of the mean curve. For example, [17] proposed using EEMD to add white noise to the original signal to reduce the mode-aliasing problem to a certain extent; however, the amount of calculation was impractical. Moreover, if the original signal has a low signal-to-noise ratio (SNR), residual noise remains in the reconstructed signal. The CEEMD method not only reduces the among of calculation and reconstruction error, but also reduces mode aliasing; however, some problems remain [18]. Using CEEMD, ref. [19] proposed a new fully integrated EMD called CEEMD with adaptive noise (CEEMDAN). The adaptive addition of Gaussian white noise at each stage of the decomposition process enables the method to handle non-stationary and non-linear signals well, yielding an extremely low complete decomposition reconstruction error. Reference [20] proposed the improved CEEMDAN (ICEEMDAN) method, which obtains good denoising accuracy and completeness and can fully compensate for the shortcomings of the above methods. Although the ICEEMDAN method has many advantages in terms of noise reduction, it only has a significant effect on high-frequency noise signals, and the algorithm performs poorly in the steady state. With regard to signal noise reduction, least mean squares (LMS) not only more comprehensively decomposes the IMF component, but also improves the steady state of the algorithm.