## 4 Temperature Influences on UGWs
Understanding these relationships is crucial for developing accurate and reliable SHM systems that account for temperature variations in composite structures. The comparisons with the surface-mounted results help to identify the influence of embedding on the temperature response of the UGW signals. In conclusion, the temperature had a significant impact on the peak amplitude and time-of-flight (ToF) of the first wave packet in UGW signals for panel thicknesses of 2 mm, 4 mm, and 9 mm. The peak amplitudes of the A\({}_{0}\) and S\({}_{0}\) modes generally increased with temperature, except for the S\({}_{0}\) mode of the 4 mm thick panel at 250 kHz. The ToF increased with temperature, except for the 2 mm thick panel at 50 kHz. Comparing the embedded temperature results to the surface-mounted temperature results in Figure 7c,d, some differences can be observed. For the peak amplitude of the A\({}_{0}\) mode (50 kHz), it decreased for the surface-mounted signals but increased for the embedded signals with increasing temperature for all panel thicknesses. Similarly, for the peak amplitude of the S\({}_{0}\) mode (250 kHz), the surface-mounted signals initially increased and then decreased with temperature, while the embedded signals consistently increased, but only for the 2 mm thick panel. Additionally, the ToF of the A\({}_{0}\) mode (50 kHz) increased for the surface-mounted signals but showed a decrease followed by an increase for the embedded signals in the 2 mm thick panel. These differences in temperature responses between embedded and surface-mounted signals highlight the influence of embedding on the behavior of UGWs. The bonding materials and coupling mechanisms in the embedding process can lead to variations in the temperature sensitivity of the UGW signals. Understanding these differences is crucial for developing accurate temperature compensation algorithms in SHM applications, especially when using embedded PZT transducers. Thermal expansions, for example, can have an impact on the relationship between peak amplitude, time-of-flight (ToF), and temperature. Changes in composite properties, such as density and thickness, as well as the dimensions of the PZT transducers and the propagation distances of UGWs, are influenced by thermal expansions. These changes, in turn, can affect the dispersion properties of composites, which are associated with the group velocity of UGWs and the thickness of the composite panel. Consequently, the difference in ToF at 50 kHz for the 2 mm thick panel compared to the other thicker panels may be due to the thickness-dependent dispersion properties of composites. Another factor to consider is the piezoelectric constants (\(d_{31}\) and \(g_{31}\)), which can affect the mechanical properties and piezo sensitivity between the embedded and surface-mounted PZT transducers. These properties have an impact on the amplitude properties of UGWs. Therefore, it is important to establish the relationship between phase and amplitude changes for composite panels, particularly in relation to their thickness, to develop reliable compensation algorithms for damage detection under different temperatures. Additionally, the PZT transducers and their bonding properties can be influenced by temperature-induced changes. The use of resin films for the embedded panels during the lay-up, as opposed to adhesive films for the panels with surface-mounted PZT transducers, can lead to differences in the temperature response. The selection of bonding materials, such as the resin film and adhesive film, is another factor that can affect the temperature results and should be carefully considered. Taking these factors into account ensures a comprehensive understanding of the temperature effects on UGWs and allows for the development of accurate compensation algorithms and reliable damage detection in composite structures under varying temperature conditions.