## 6 Conclusions and Future Work  
In this study, valid information was obtained without increasing dimensionality to accurately classify multiple types of damage occurring in the same concrete component. A detection method based on the acoustic features of variable-frequency hammering was proposed. Variable-frequency hammering MFCCs are generated from acoustic data obtained by variable-frequency hammering through feature selection and extraction; they are used as the main feature of SVM classification for multi-category damage classification.  
The acoustic features obtained by single-frequency hammering were used as classification features and compared with those generated by variable-frequency hammering. The results showed that the SVM models based on both single-frequency hammering and variable-frequency hammering can accurately detect both two- and four-category concrete damage occurring in the same specimen. However, the classification model based on variable-frequency hammering showed a higher accuracy of 97.8% than that based on  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Kernel Type** & **2 Hz** & **5 Hz** & **10 Hz** \\ \hline Linear & 77.1\% & 82.2\% & 79.4\% \\ Quadratic & 88.9\% & 93.0\% & 91.1\% \\ Gaussian & 85.7\% & 96.5\% & 85.7\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Accuracy of each single-frequency hammering in the four-category classification.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Kernel Type** & **2 Hz** & **5 Hz** & **10 Hz** \\ \hline Linear & 84.1\% & 82.% & 83.1\% \\ Quadratic & 91.7\% & 94.0\% & 90.8\% \\ Gaussian & 86.3\% & 96.8\% & 86.3\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Accuracy of each single-frequency hammering in the two-category classification.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Kernel Type** & **Two Categories** & **Four Categories** \\ \hline Linear & 84.1\% & 89.2\% \\ Quadratic & 94.0\% & 96.2\% \\ Gaussian & 97.5\% & 97.8\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Accuracy of each variable-frequency hammering in the two-category and four-category classifications.  
single-frequency hammering, which indicates that variable-frequency hammering is more suitable as a feature for multi-category damage classification than single-frequency hammering. In addition, the experimental results of PSD analysis and feature selection showed that variable-frequency hammering contains more effective information than single-frequency hammering. Furthermore, variable-frequency hammering can compensate for the lack of information of single hammering from common single-frequency hammering methods. Variable-frequency hammering can be combined with machine learning to detect concrete damage more accurately without causing a dimensional disaster. Simultaneously, the experimental results proved that different types of damage have different sensitivities to different hammering frequencies. However, the tests are still at the research laboratory stage and may not solve existing engineering problems in the field, such as detecting damage in noisy and topographically complex environments. In the future, we will improve the detection method such that hammering and signal processing can be performed automatically using hammering equipment and micro-phones, and the hammering frequency can be adjusted intelligently for different dam-ages to develop an intelligent frequency-hammering robot with great potential in the field of inspection.  
Conceptualization, H.H.; Methodology, X.H.; Validation, X.H.; Formal analysis, X.H.; Investigation, X.H.; Data curation, X.H.; Writing--original draft, X.H.; Writing--review & editing, H.H. and Z.W.; Supervision, H.H. and Z.W.; Project administration, Z.W. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Key Research and Development Program of China (Grant number: 2019 YFC1511103). The authors declare no conflict of interest.