## 3 Verification of the Clustering Algorithm on RC Prisms
### Results of the RC Prisms  
The main objective of the AE clustering is to distinguish between the corrosion process at the anode, and the concrete cracking. In previous work by the authors on small corroded mortar samples, the algorithm allowed distinguishing between corrosion and concrete cracking [29]. Two clusters were obtained and the onset of concrete cracking could be distinguished based on the number of AE events and occurrence in time of the clusters. In the current research, it was first investigated whether additional sources such as absorption of the sodium chloride solution could be distinguished with the clustering algorithm. Therefore, a set of dummy samples was tested. A first dummy sample (dummy 1) was an uncorroded RC beam subjected to a four-point bending test. Expected damage sources are micro- and macro-cracking of the concrete. A second dummy sample (dummy 2) was an older RC prism that was placed in water to investigate whether signals due to absorption could be detected. The third sample (dummy 3) was a concrete cube with an age of 28 days that was placed in dry conditions (20 \({}^{\circ}\)C, 40% RH) after being stored in a humidity chamber (20 \({}^{\circ}\)C, 95% RH). Hydration processes as well as a change in ambient humidity level could cause AE signals in this dummy sample. The final dummy sample (dummy 4) was a ribbed rebar that was subjected to accelerated corrosion by placing it in a sodium chloride solution and applying a direct current. In this way, signals related to steel corrosion could be detected. It is assumed that similar processes during the corrosion process itself (such as the formation of salt crystals in the pits, local plastic deformation of the pit, and the expansion of corrosion products [31]) are occurring during corrosion of a rebar without surrounding concrete layer as during corrosion of an RC sample. However, it should be noted that the presence of a concrete layer may influence the AE signal due to a different propagation path. Nonetheless, it was found in previous work by the authors that the AE signals are still alike [5]. A total of 1000 signals (600, 50, 150, and 200 from, respectively, dummies 1, 2, 3, and 4) were randomly selected resulting in a representative share of each damage source based on the occurrence rate of the AE signals during testing of the dummy samples and as expected during the accelerated corrosion tests. On these 1000 signals, which is in terms of order of magnitude in line with the number of AE signals detected during the corrosion tests on the RC prisms, the clustering algorithm was applied. Figure 3 shows the dendrogram (top) and peak (bottom left) and center (bottom right) frequencies of each AE event versus the ID number of the AE signal. The peak frequency of the signal is defined as the frequency with the maximum signal amplitude in the frequency domain. The center frequency or frequency centroid is defined as the center of gravity of the signal in the frequency domain. The cluster dissimilarity threshold was set in order  
Figure 2: Schematic representation of the accelerated corrosion setup and 1D AE sensor configuration with two AE sensors (S1–S2). to obtain two clusters. For the used AE setup, acquisition settings, and AE sensors, it was found in previous work of the authors that the peak and center frequency ranges of signals obtained from micro-cracking, absorption, hydration, and steel corrosion are overlapping (peak frequency between 200 and 260 kHz and center frequency between 170 and 360 kHz) [5]. The signals are characterized by higher frequencies than signals obtained from macro-cracking (peak frequency between 90 and 250 kHz and center frequency between 160 and 290 kHz) [5]. The algorithm is able to distinguish these two groups as visualized in Figure 3. Events belonging to the first cluster (blue) are found in each dummy sample.