## 2 The Effects of Temperature on UGW
The excitation frequency is set at 128 kHz, with a sine wave excitation modulated by a four-period Hanning window, and the guided wave signal is acquired using a pulse-echo technique. By incorporating the material properties of Q235 into COMSOL, UGW signals under different temperature distributions can be obtained. The simulation is conducted in two steps. First, the effect of uniform temperature changes across the entire pipeline on UGW signal is analyzed. Second, the impact of nonuniform temperature fields on UGW signal is examined. The results are presented in Figure 2.  
Figure 2: Cloud map of UGW simulation results. Figure 2 illustrates the cloud map of UGW propagating within the pipeline. The acoustic field in the pipeline is uniform and symmetrical, indicating that the T (0,1) mode is optimally excited. Figure 2 displays the UGW cloud map at propagation times of 0.1 ms, 0.5 ms, 0.9 ms, 1.3 ms, and 1.7 ms. To better analyze phase changes in the guided wave signal during propagation, four annular grooves are incorporated in the pipeline model. These grooves are placed at intervals of 60 cm and serve as signal reference points as shown in Figure 2. Each groove has a width of 4 mm and a depth of 2 mm. During the propagation process, an echo is generated each time the wave passes through an annular groove as depicted by the light-colored cloud image in Figure 2. The simulation is conducted twice, categorizing the temperature changes into a uniform region and a nonuniform region based on their variations. The received signal for the uniform temperature field (UTF) is shown in Figure 3, while the signal corresponding to the nonuniform temperature field (NTF) is presented in Figure 4.  
Figure 3 illustrates the UGW signals obtained at different temperatures. Due to the uniform nature of the temperature change, its effect on the phase shift is also consistent. As the wave propagates from the first to the fourth annular groove, and subsequently to the end echo, the signal phase shift gradually increases. The influence of the temperature change on the phase can be considered linear, aligning with the findings in the literature [22; 25], thereby validating the effectiveness of the simulation results. Figure 4: UGW signals at different temperatures during NTF. Figure 3: UGW signals at different temperatures during UTF. The UTF represents an ideal scenario, but in reality, it is often influenced by various complex environmental factors, making the NTF more common. Figure 4 shows the effect of different temperatures on UGW signals under the NTF. In this scenario, one end of the pipeline is at a high temperature, and the other is low. This NTF causes a nonuniform phase shift in signal. The first and second annular grooves are located in the normal temperature region as shown in Figure 2. They are therefore unaffected by temperature changes and show no phase shift. In contrast, the third and fourth annular grooves, along with the pipeline's end face, are situated in the temperature variation zone. Here, phase delays occur due to the impact of temperature changes. The higher the temperature and the longer the propagation path through the high-temperature region, the greater the phase shift. Figures 5 and 6 show the phase delay of the UGW signal. The phase delay of the signal in Figure 3 is displayed in Figure 5, with a superimposed fitted line. It can be observed that temperature has a clearly linear influence on the signal phase: the higher the temperature, the greater the phase delay. At the same temperature, the cumulative effect causes the signal phase to exhibit a pronounced linear change as the UGW propagation distance increases. Figure 6 illustrates the phase change of the signal in Figure 4. When the UGW propagates under a constant temperature, the phase remains nearly unchanged. However, upon entering a region with varying temperatures, it continues to exhibit a linear trend. In Figure 6, the signal in each temperature range is fitted with straight lines.