## 1 Introduction  
Pipelines play an important role in urban construction and modern industry, serving as a necessary means for the long-distance transportation of resources. However, due to the complex working environment of pipelines, their structural layers are vulnerable to corrosion, fatigue damage, and other forms of damage, which can cause material leakage, pollute the environment, and pose a threat to human life and property safety. Ultrasonic guided waves can not only detect damage in long-distance pipelines, but also provide a new method for damage detection in pipelines in complex environments, thus contributing to the monitoring of pipeline structural health. Up until now, scholars have conducted a series of studies on damage detection in single-layer pipeline structures, but the research focus has mainly been on the identification and localization of individual defects. [PERSON]. [1] verified through a simulation that the elliptical localization method had a higher accuracy when locating damage in circular pipes but, at the same time, it was found that the circumferential localization error was greater than the axial localization error. [PERSON] et al. [2] proposed a method for the damage detection and localization of pipeline structures based on the sparse estimation of the measurement signal, using a reference signal. Damage detection was achieved by calculating the second estimation error of the signal, while localization was achieved through the recursive sparse estimation of the sliding window of the damage signal. [PERSON] [3] conducted research on the localization and imaging of circumferential defects in pipelines, and achieved the axial localization of damage using the Hilbert transform, providing a high recognition accuracy. However, the complexity of the working environment in pipelines renders them susceptible to multiple defects, leading researchers to investigate the detection of multiple defects in single-layer pipeline structures. [PERSON] et al. [4] studied dual defects in pipelines, and found that the reflection coefficient is more sensitive to the relative axial distance than the relative circumferential position, with periodic variations. [PERSON] [5] proposed a weak ultrasonic-guided wave detection method based on the Lyapunov exponent of the Lorenz system, and the simulation and experimental results verified that this method could accurately determine the amount and location of damage in pipelines for health-monitoring purposes. [PERSON] [6] proposed a frequency-domain synthetic aperture focusing technique, based on phase shift, which overcame the limitations of traditional ultrasonic imaging methods in directly reflecting the imaging results of pipeline defects. The method could accurately determine multiple defects in pipelines for health-monitoring purposes. [PERSON] et al. [7] proposed a three-point axial localization method and circular trajectory imaging method for single and dual defect localization and imaging in pipeline segments, using an elliptical localization imaging method, based on a plate structure. The accuracy of the method was verified through simulation and experiments. [PERSON]. [8] conducted impact tests on pipelines under different working conditions before and after damage, and the results showed that using the damage index as a damage discrimination index could not only identify the location of a single defect in pipelines, but also recognize multiple damages in pipelines under different service conditions. [PERSON]. [9] conducted a defect localization study on dual defects in single-layer pipeline structures under different working conditions, and the results showed that the circumferential distribution map drawn based on the defect echo peak value could identify the circumferential position of dual defects. In actual engineering applications, pipelines are mostly layered structures, but scholars have mainly focused on single defects [10; 11; 12], and conducted less research on double defects [13].