## 6 Conclusions  
This paper proposes a signal phase local matching method for temperature compensation and UGW monitoring in pipelines experiencing NTF, which often occur in real-world scenarios. The influence of temperature on material properties is analyzed using simulation software, followed by the establishment of a three-dimensional simulation to further examine how temperature affects UGW signals. Three heating experiments with NTF are conducted to validate the method's effectiveness in temperature compensation and defect detection, comparing its performance with the BSS method. The main conclusions are as follows:  
The impact of temperature changes on the material parameters is nearly linear. The Young's modulus and density decrease with increasing temperature, while the Poisson's ratio increases. These variations in the material properties lead to phase shifts in the UGW signals, resulting in nonuniform phase shifts under an NTF.  
In an NTF, the BSS method employs a global stretching factor, which can cause over-compensation in the nonvariable temperature regions while undercompensating in variable temperature regions, making practical application challenging. Conversely, the proposed LPM method effectively calculates the cosine similarity of local signal segments, allowing for precise phase matching and overcoming the uneven phase changes caused by temperature fluctuations. A method for calculating a damage index is also proposed to assess defect.  
By utilizing local phase matching and an efficient damage index, LPM achieves strong temperature stability and high detection accuracy.  
The three heating experiments demonstrate that LPM provides excellent resolution for detecting defects in both high and low-temperature areas within an NTF ranging from 24 \({}^{\circ}\)C to 80 \({}^{\circ}\)C, being almost unaffected by temperature changes. Consequently, it exhibits good temperature stability and a broader range of practical applications.  
In future work, we will test LPM on other materials and in real-world conditions to further validate its ability.  
Conceptualization, Y.H. and F.L.; methodology, S.X.; software, P.Z.; validation, S.X., P.Z. and Z.T.; formal analysis, Q.W.; investigation, S.X.; writing--original draft preparation, S.X.; writing--review and editing, Y.H.; visualization, Q.W.; supervision, Q.W.; project administration, P.Z.; funding acquisition, Y.H., F.L. and Z.T. All authors have read and agreed to the published version of the manuscript. This research was funded by National Key R&D Program of China under Grant (2023 YFF0716600), and Research on the Deep Application of Large Storage Tank Integrity Management (AQWH202208). The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors.  
Conflicts of Interest: Authors [PERSON] and [PERSON] were employed by the company Pipe China (Xuzhou) Pipeline Inspection Corporation Limited. Author [PERSON] was employed by the company Hangzhou Zheda Jingyi Electromechanical Technology Corporation Limited. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.