## 3 Temperature Effect  
Temperature change has significant effects on ultrasonic wave velocities in metals, rock, and concrete [14, 17, 33, 34]. Temperature effects are commonly considered as an undesired noise in ultrasonic measurements. [PERSON] et al. [19] proposed using a reference sample identical to the test sample to compensate for the temperature change effect. However, a reference sample is not always available in engineering practice, and the temperature  
Figure 6: Relative wave velocity changes and Poisson’s ratio development calculated from different time windows. The reference signal was obtained at 30 h.  
effects on the reference are not always the same as in the test structure. Recently, [PERSON] and [PERSON] [15] used the relationship between wave velocity and temperature to determine the acoustic nonlinearity parameters, and evaluate concrete samples with alkali-silica reaction (ASR) damage. They found that the damaged concrete samples showed higher sensitivity to temperature than the control samples. In their study, CWI was used to determine the relative wave-velocity change with temperature. [PERSON] [33] reported that the temperature dependence of wave velocity is different for P wave and S wave. Because the relative contributions of P and S waves vary with time window positions in a signal, the CWI analysis results also vary with window positions. This section presents the application of the stretching technique to different parts of signals and the results are compared. Similar to the test setup in Section 2, two PZT discs (10 \(\times\) 2 mm) were attached to the opposite flat ends of a concrete cylinder at a distance of 200 mm. The P wave velocity of the concrete cylinder was measured at 4600 m/s, and the compressive strength was 48 MPa. Ultrasonic signals of 1.8 ms duration were acquired every 2 min. Another concrete cylinder containing a surface and an internal thermocouple was used to monitor the temperature changes during the measurement. These two concrete cylinders were placed in an environmental chamber for heating at a temperature-change rate of 1 \({}^{\circ}\)C/h to avoid a large thermal gradient. Figure 7 shows two ultrasonic signals acquired at 27 \({}^{\circ}\)C and 29 \({}^{\circ}\)C. It can be seen that the latter part shows larger time shifts than the early part of the signal. The stretching technique was applied to the following signal window positions: P wave part, S wave part, full-length signal, and moving time windows. Determination of P and S wave parts still follows the same procedure as in the early-age concrete test. Figure 8 presents the relative velocity change vs. temperature variation using different time windows. It should be noted that the calculated slope values \(\alpha\) in Figure 8 include the thermal expansion effect. The relative time shift \(dt/t\) or velocity change \(dV/V\) calculated using the stretching technique method includes two components: temperature-induced velocity change and length change caused by thermal expansion. The actual temperature-induced relative velocity change is \(dV/V-\alpha T\Delta T\), after correction of thermal expansion induced length change (thermal strain), where \(\alpha_{T}\) is the coefficient of thermal expansion. The stretching analyses on the full-length signal and the S wave part give very close results, which is consistent with the theory that CWI is more sensitive to perturbations on the S wave velocity than on the P wave velocity [6]. [PERSON] also showed that the relative velocity change of the coda wave is the weighted average of the P and S velocity perturbation given by  
\[\frac{dV}{V}=0.09\frac{dV_{p}}{V_{p}}+0.91\frac{dV_{s}}{V_{s}} \tag{6}\]  
Figure 7: Two ultrasonic signals collected at 27 \({}^{\circ}\)C and 29 \({}^{\circ}\)C. Three zoomed insets show the time shifts at different window locations. Figure 9 shows the calculated \(\alpha=dV/V/\Delta T\) for different time window positions. A time window of 0.2 ms wide moved from 0.2 ms to 1.6 ms (center) with a step of 0.1 ms.