## 4 Experimental Setup for Pipeline Heating with NTF  
To simulate the potential nonuniform temperature variations that may occur in real-world scenarios and to validate the algorithm, local heating of the pipeline is conducted. The experimental setup is illustrated in Figure 8.  
The experimental pipeline measures 6 m in length, 219 mm in diameter, and 6 mm in thickness. A magnetostrictive patch transducers is positioned 60 cm from one end, with an excitation frequency set to 128 kHz and a sine wave modulated by a four-period Hanning window. UGW monitoring is conducted once per minute during the experiment. At the opposite end, a water bag is used for heating, creating NTF: one end at normal temperature and the other at high temperature. The water bag is 1.8 m in length. Once filled with water, its outer wall comes into full contact with the inner wall of the pipeline, ensuring efficient heat transfer. This setup divides the pipeline into heating and nonheating areas. After heating, the stable NTF can be categorized into three zones: a low-temperature zone (LTZ) near the unheated end, with temperatures ranging from 24 \({}^{\circ}\)C to 30 \({}^{\circ}\)C; a high-temperature zone (HTZ) at the heated end, with the temperatures ranging from 78 \({}^{\circ}\)C to 83 \({}^{\circ}\)C; and a temperature transition zone (TTZ) between them, with temperatures ranging from 30 \({}^{\circ}\)C to 78 \({}^{\circ}\)C as shown in Figure 9.  
As shown in Figure 9, the heating process lasts for 100 min. By the 90 th min, the pipeline reached thermal equilibrium, with minimal temperature change over the final 10 min. Therefore, it takes 90 min for the pipeline to be heated from 24 \({}^{\circ}\)C to 80 \({}^{\circ}\)C at one end, establishing a stable temperature field. In HTZ and LTZ, the surface temperature remains stable and uniform. TTZ experiences sharp temperature changes due to the influences of both adjacent zones, resulting in significant NTF. Specific operations for the nonuniform heating of the pipeline are as follows: Place the water bag inside the pipeline and fill it with water to ensure full contact with the inner wall. Heat the water from 26 \({}^{\circ}\)C to 90 \({}^{\circ}\)C; it can maintain the temperature at the end of  
Figure 8: Experimental setup for pipeline heating with NTF. the pipeline at a maximum of 80 \({}^{\circ}\)C, thus creating an NTF. A temperature measuring gun (shown in Figure 8) can be used to record the temperature change curve of the pipeline at various times and positions, shown in Figure 9.  
The temperature change curve of the pipeline over time, shown in Figure 9, indicates that the initial temperature is 24 \({}^{\circ}\)C. As heating continued, one end of the pipeline begins to warm up, with UTF occurring in the areas covered by the water bags, while other areas quickly return to normal temperature. After 90 min of heating, the water temperature reaches 90 \({}^{\circ}\)C, and the surface temperature of the pipeline stabilizes at 80 \({}^{\circ}\)C due to continuous heat dissipation. To evaluate the phase change in the UGW in pipes with NTF, five metal hoops are installed as reference points for signal phase analysis, shown in Figure 8. Hoop No.1 and No.2 are in LTZ, No.3 is in TTZ, and No.4 and No.5 are in HTZ. The metal hoops are tightly attached to the pipeline surface, generating clear echo signals as shown in Figure 10.  
Figure 10 shows the echo signal curve under UTF at room temperature (24 \({}^{\circ}\)C). Positions 1 to 5 correspond to the echo signals from five metal hoops, while position 6 indicates the amplitude of the end face. Six echoes are clearly visible. The reflected signal amplitudes from the metal hoops fluctuate and decrease with increasing distance, due to incomplete pre-stressing and guided wave attenuation. In this analysis, the pipeline is considered an ideal elastic body. However, in practice, there is always some energy dissipation.