4.2.2. Relationship between Working Stress and dΔVpp

As shown in Figure 5, the gradient of the *σ*-Δ*Vpp* curve (*d*Δ*Vpp*) decreased continuously during the unloading stage. The curves of Δ*Vpp* and working stress for different diameters had similarities. When the working stress decreased gradually, one Δ*Vpp* corresponded to two different stress levels of the rebar. Therefore, in the data analysis, *d*Δ*Vpp* could be chosen as the fit variable to characterize the variation of the magnetic properties of prestressed rebar with working stress, which was recorded as Method 2. D16-P90-T2, D18-P90-T2, and D20-P90-T2 were used as examples.

As shown in Figure 9, the working stress of rebar could be uniquely determined by the *d*Δ*Vpp*. In the unloading stage, the trend between the *d*Δ*Vpp* and the working stress was basically the same. With the decrease of working stress, the *d*Δ*Vpp* decreased gradually and was linearly correlated. Therefore, to clarify the relationship between the two variables, a linear fit was made between the *d*Δ*Vpp* and working stress of the three specimens. The goodness of fit (R2) was used to indicate the linear fit of the specimens. The R2 corresponding to D16-P90-T2, D18-P90-T2, and D20-P90-T2 was 0.97112, 0.97041, and 0.91294, respectively. Therefore, it was preliminarily shown that there was a good linear relationship between the working stress and the *d*Δ*Vpp* curve. The R<sup>2</sup> of all specimens was calculated, and the results are shown in Figure 10.

**Figure 9.** The overall linear fitting of the relationship between working stress and *d*Δ*Vpp* of three diameter rebars: (**a**) D16-P90-T2; (**b**) D18-P90-T2; (**c**) D20-P90-T2.

**Figure 10.** The overall linear fit R<sup>2</sup> of the relationship between working stress and the *d*Δ*Vpp* of each group of specimens.

It can be seen from Figure 10 that the R2 of each specimen was more significant than 0.9, indicating an excellent linear fit between *d*Δ*Vpp*-*σ*. Therefore, the working stress of rebar could be determined by the linear relationship of *d*Δ*Vpp*-*σ*. Among them, the minimum R2 was 0.91293 for D20-P90-T2, and the maximum R2 was 0.99208 for D18-P50-T1. The R<sup>2</sup> for each of the three diameters was discussed by taking the average values of each specimen. The average values of R2 for Group 1 and Group 2 were similar: 0.96699 and 0.97510, respectively. The average value of the R2 of Group 3 was slightly lower, 0.94390. This was because the relative effective working area of the rebar decreased with increasing diameter due to the skin effect at a high alternating frequency.
