## 5 Experimental Results and Discussion  
### Power Spectral Density Analysis  
The sound signals recorded during the experiment were used for the PSD analysis. In this study, an automatic hammering device was used to hammer the area at three preset hammering frequencies under four different conditions for a total of 12 datasets. A typical acoustic wave was selected for each dataset. It was used to observe changes in the distribution and magnitude of the acoustic wave power at different hammering frequencies. The acoustic differences between variable-frequency hammering and single-frequency hammering were compared.  
The PSD of the selected signal under different conditions was obtained for the frequency-domain analysis. As shown in Figure 10, the power was concentrated at 0-2000 Hz for the healthy category shown in Condition 1. Under different hammering frequencies, the power distribution did not change significantly with the hammering frequencies. In Condition 2, the shallow cracks (surface damage) were concentrated in  
Figure 8: Schematic diagram of the concrete damage area for the two-category classification.  
Figure 7: Schematic diagram of concrete specimen and four-point bending test.  
Figure 9: Schematic diagram of the concrete damage area for the four-category classification.  
the range of 0-4000 Hz. Under different hammering frequencies, the distribution of the power size with hammering frequency change was not obvious. At the crack extension of Condition 3 (internal damage), the power was concentrated at 0-3000 Hz and 4000-5000 Hz, and the variation in power magnitude was evident under different hammering frequencies. At the compound damage of Condition 4 (internal damage + surface damage), the power was concentrated at 0-3000 Hz, and the variation in power magnitude was evident under different hammering frequencies. Four different types of damage with different power distributions in the same component can be easily distinguished by vertical observation. However, for Condition 3 at crack propagation and Condition 4 at composite damage, the power of these two adjacent damages under the same fixed hammering is concentrated in the same frequency distribution. As a result of using variable-frequency hammering, the power change in Condition 3 in the frequency distribution was significantly different from that of Condition 4. The change in Condition 3 was significant at 0-1000 Hz, and that of Condition 4 was significant at 2000-4000 Hz. The frequency distribution of the power changes in Condition 3 was significantly different from that of those in Condition 4. Condition 3 showed a significant change at 0-1000 Hz, while Condition 4 showed a significant change at 2000-4000 Hz. With single-frequency hammering, the difference was more pronounced for the two categories of health and damage. However, acoustic signals obtained by hammering at different frequencies can differentiate between two or more similar damage classifications.  
Figure 10: _Cont_.  
The experimental results demonstrated that variable-frequency hammering contains more information than single-frequency hammering, particularly for compound damage with two types of damage within 20 mm, which is challenging to identify using single-frequency hammering alone. In actual detection, the hammering frequency is not guaranteed to correspond to the hammering frequency that can be effectively identified; therefore, variable-frequency hammering is required.