## 3 Verification of the Clustering Algorithm on RC Prisms
### Results of the RC Prisms
Events belonging to the second cluster (red) are mainly found in the first dummy sample which is the RC beam subjected to a four-point bending test, being the only one of the dummy samples that should indeed show concrete macro-cracking. Most of these events are characterized by high amplitudes. The cluster dissimilarity threshold was decreased in order to investigate whether other sources could be distinguished such as corrosion and absorption. The result is shown in Figure 4. When lowering this threshold, four clusters can be obtained. The pink and red cluster can still be assigned to concrete macro-cracking. However, signals belonging to the blue and green cluster still occur in four different dummy samples. Therefore, the clustering algorithm does not allow further differentiating the AE sources. This confirms previous findings that signals originating from corrosion, absorption and concrete micro-cracking are difficult to distinguish from each other [5]. Alternatives to cross-correlation may be investigated such as magnitude-squared coherence [32] or dynamic time warping [33]. However, these alternatives are computationally more demanding. A comparison of the techniques is outside the scope of the current paper. Clustering will further be applied on the accelerated corrosion tests to investigate whether the onset of concrete macro-cracking can be automatically distinguished. It was checked whether similar results were obtained using a different set of signals and this was the case. Figure 3: Results of the clustering algorithm performed on dummy samples with (**top**) dendrogram, (**bottom left**) peak frequency versus ID number of the AE signals, and (**bottom right**) center frequency versus ID number of the AE signals. The size of the dots depends on the amplitude (in dB) of the AE signal. Expected AE sources are indicated for each group of signal IDs. Figure 5 shows the clustering result of prism CL3-S which is a sample with a smooth rebar that was corroded until a target corrosion level of 10% mass loss was reached. Crack measurements were performed every week. The grey shaded area on the two bottom figures indicates the time period in which the surface crack must have occurred. This is the period between the last crack measurement where no crack was observed and the first crack measurement where the crack was observed. Figure 4: Results of the clustering algorithm performed on dummy samples with (**left**) dendrogram, and (**right**) peak frequency versus ID number of the AE signal. The size of the dots depends on the amplitude (in dB) of the AE signal. Expected AE sources are indicated for each group of signal IDs. Figure 5: Clustering result of sample CL3-S with (**top**) dendrogram, (**bottom left**) peak frequency versus time, and (**bottom right**) center frequency versus time. The period in which the surface crack occurred is indicated by the grey area. Three clusters can be observed. The blue cluster starts from the beginning of the test and contains signals with an average peak frequency of 220 kHz. The number of AE signals of the second cluster (red) increases at the onset of concrete macro-cracking which is confirmed by the grey shaded area. In addition, a decrease in the peak and center frequency can be seen, as observed from the moving average (200 datapoints), which was found to indicate the onset of macro-cracking in previous work [5]. Few AE signals are assigned to the red cluster before the crack was visually observed. As seen in Figure 3, few AE signals due to absorption, hydration and corrosion were seen as similar to the cracking signals and were assigned to the same cluster. Therefore, the early signals assigned to cluster 2 in sample CL3-S may also originate to a limited extent from absorption, hydration or corrosion. Alternatively, it may be the case that cracking started internally and that these signal represent internal cracking, predicting the occurrence of the surface crack that was later observed. The third cluster (green) represents AE signals due to electromagnetic interference.