## 3 Experimental Results and Discussions
### The Measurement Error Analysis of the Multi-Electrode Sensor System  
It can be seen from Figure 6 that serious localized corrosion also happened on WE 5 and WE 6. Tiny pits can also be observed on WE 1, WE 2, and WE 7 as well. According to the calculating results of the anodic electric charge, the corrosion depths of WE 4 and WE 5 were only 4.7 \(\times\) 10\({}^{-3}\) um and 5.9 \(\times\) 10\({}^{-3}\) um, respectively. [PERSON] [44] pointed out that the corrosion current in a corroding area on the rebar is composed of the macrocell current between the non-corroding zones and corroding zones and microcell current produced within the corroding zones. The galvanic current is not directly equal to the corrosion current. This theory well explained the measurement error of the multi-electrode system. The multi-electrode array is a more complex system. As shown in Figure 8, the corrosion current of one electrode \(I_{corr}\) can be expressed as:  
\[I_{corr}=I_{Macro}+I_{Micro}=I_{Micro}+\sum_{i=1}^{7}I_{gi} \tag{4}\]  
where \(I_{Macro}\) is the sum of the galvanic current flowing to the other electrodes, \(I_{Micro}\) is the corrosion current within the electrode. Through the ZRA, only \(I_{Macro}\) can be measured. In general studies, it is thought that the electrode will act as a cathode when the \(I_{Macro}\) is positive. However, it cannot be guaranteed the whole galvanic current (\(I_{g1}\), \(I_{g2}\),..., \(I_{g7}\)) are all positive. In other words, even if the electrode obtained an electron in the system, it cannot be determined as the pure cathodic area. In this test, during the period from 35 h to 63 h, except for the only anodic electrode WE 3, the other electrodes all acted as cathodes and a large cathodic current was flowing to these electrodes. Nevertheless, the OCP of WE 4, WE 5, and WE 6 were \(-\)283 mV, \(-\)310 mV, and \(-\)279 mV at 48 h which was much lower than the other cathodic electrodes. Meanwhile, the OCP also indicated the passive film on these electrodes which were not intact. Both \(I_{Micro}\) and anodic galvanic current should exist on the three electrodes and it will lead to underestimates of the corrosion degree on the electrodes. This phenomenon also appeared in [PERSON]'s [45] studies that serious corrosion occurred on the cathodic electrodes by using the multi-electrode array. For the pure anodic electrodes WE 3, since the OCP was the most negative, it can ensure that all the galvanic currents were negative. The measurement error caused by the galvanic current can be ignored. The \(I_{Micro}\) became the only factor for the measurement  
Figure 8: Representation of the macro current among the electrodes and microcurrent within the corroding electrode. error of the pure anodic electrode. It can be seen from Figure 8, when the pure anodic electrode was coupled with the other cathodic electrodes, the potentials of the electrodes will be polarized to the same coupling potential \(E_{couple}\)[25]. The corrosion current \(I_{corr}\) was the anodic reaction current and it can be calculated from the \(E_{couple}\) as shown in Figure 8. Meanwhile, the cathodic reaction current \(I_{c}\) also can be obtained. The corrosion current can be deduced from the diagram:  
\[I_{corr}=I_{Macro}+I_{c} \tag{5}\]  
Combined with Equation (4), it can be found that \(I_{Micro}\) is equal to the cathodic reaction current. The \(I_{corr0}\) shown in Figure 9 is the corrosion current at the OCP and it can be accurately measured by LPR method. It can be seen that \(I_{c}\) is smaller than \(I_{corr0}\). In this test, when serious localized corrosion happened on WE 3, the OCP of the WE 3 was \(-697\) mV which was close to the coupled potential of \(-650\) mV. Therefore, the \(I_{corr0}\) can be used to qualitatively estimate the \(I_{micro}\). Because the anodic polarization may impact the surface of the electrode, the measurement of the \(I_{corr0}\) was not conducted into this test to ensure the in-situ monitoring status of the sensor system.