## 4 Temperature Influences on UGWs  
Temperature changes can have a significant impact on the amplitude and phase of ultrasonic guided waves (UGWs), which can compromise the reliability of diagnosis if not properly compensated for. While several studies have investigated the influence of temperature on UGW signals in thick composite laminates [21; 33; 38], none of the research has reported whether the thickness of the composite laminate affects temperature compensation algorithms when using embedded PZT transducers. Therefore, in this section, the temperature influences on the peak amplitude and time-of-flight of the first wave packet of embedded signals were evaluated for panel thicknesses of 2 mm, 4 mm, and 9 mm. To assess the temperature effects, the composite panels were placed inside an environmental chamber, and the temperature range was set from \(-40\)\({}^{\circ}\)C to 80 \({}^{\circ}\)C with a temperature step of \(10\)\({}^{\circ}\)C. A transducer pair path 1-2, as shown in Figure 1a, was used for measurement. Five-cycle Hanning-windowed toneburst signals were employed at frequencies of 50 kHz and 250 kHz. Each composite panel was allowed to dwell at each temperature step for 20-30 min to ensure it reached the target temperature and maintained a stable state. Figure 6 presents an example of the embedded signals at 50 kHz and 250 kHz for a 2 mm thick panel under different temperatures. The peak amplitude of each first wave packet of the embedded signals was automatically computed to measure amplitude reduction and phase shift. The analysis of the peak amplitude and time-of-flight of the embedded signals under varying temperatures provides insights into the temperature effects on UGW propagation and helps determine appropriate compensation algorithms. By quantifying the amplitude reduction and phase shift, the researchers can develop temperature compensation techniques that ensure accurate and reliable diagnosis in the presence of temperature variations. Figures 7 and 8 present the relationships between temperature and the peak amplitude, as well as the time-of-flight (ToF) of the first wave packet of the embedded signals at 50 kHz (A\({}_{0}\) mode) and 250 kHz (S\({}_{0}\) mode) for the 2 mm, 4 mm, and 9 mm thick panels. These figures also include the surface-mounted results for comparison. In Figure 7a, the peak amplitude of the A\({}_{0}\) mode exhibits an increasing trend with temperature for all panel thicknesses at 50 kHz. However, the slopes of the amplitude increase vary for different thicknesses. Similarly, in Figure 7b, the peak amplitude of the S\({}_{0}\) mode shows temperature dependence at 250 kHz. For the 2 mm and 9 mm thick panels, the amplitude increases with temperature, while for the 4 mm thick panel, the amplitude decreases as temperature increases. Figure 6: Examples of embedded UGWs under different temperatures at (a) 50 kHz and (b) 250 kHz. Figure 7: Cont. Figure 8: Relationships of the temperature with the time-of-flight at **(a)** 50 kHz and **(b)** 250 kHz and at **(c)** 50 kHz and **(d)** 250 kHz for surface-mounted UGW. Figure 7: Relationships of the temperature with the peak amplitude at **(a)** 50 kHz and **(b)** 250 kHz for embedded UGW and at **(c)** 50 kHz and **(d)** 250 kHz for surface-mounted UGW. Figure 8a illustrates the ToF of the A\({}_{0}\) mode for the 2 mm thick panel. It initially decreases from \(-40\)\({}^{\circ}\)C to 20 \({}^{\circ}\)C and then increases from 20 \({}^{\circ}\)C to 80 \({}^{\circ}\)C at 50 kHz. However, for the 4 mm and 9 mm thick panels, the ToF increases with temperature. In Figure 8b, the ToF of the S\({}_{0}\) mode increases with temperature for all panel thicknesses at 250 kHz. These findings highlight the temperature effects on the peak amplitude and ToF of the embedded signals for different thicknesses. The amplitude and ToF variations with temperature provide insights into the behavior of UGWs and the need for temperature compensation algorithms.