## 1 Introduction  
The detection of concrete, particularly with high precision, is essential for social infrastructures such as bridges and tunnels that are easily affected by disasters and ageing [1]. In recent years, many studies have been conducted on the detection of aging infrastructure, and new technologies, such as sensors and ultrasound, have been used to process complex information, save labor, and reduce costs [2, 3]. However, some problems remain, such as high cost and heavy weight. The hammering test is a traditional method of inspection that is very effective and is widely used for the maintenance of bridges and tunnels. However, with the current shortage of skilled professionals, it is becoming increasingly difficult to rely solely on human sensory inspection methods for the prevention of bridge and tunnel deterioration accidents and the performance of large-scale, mobile and rapid detection of post-disaster infrastructure damage.  
To date, a tremendous amount of research has been conducted on damage detection and hammering tests. In the past, time series methods of damage detection based on Autoregressive Parameters, Intrinsic Mode Function and Hilbert Spectrum, and Signal Components were widely used [4]. [PERSON] et al. performed modal identification and damage detection in time-frequency analysis using an algorithm based on time-frequency analysis and power spectrum [5]. [PERSON] et al. reviewed the application of traditional methods of machine and deep learning in damage detection, demonstrating that ML-based models can be applied in damage detection [6]. In the past, hammering test applicationshave included the diagnosis of concrete structures [7; 8; 9; 10; 11], such as diagnosis systems for spalling tiles on the facades of high-rise buildings [12] and the construction of cavity and crack detection algorithms [13]. However, these applications typically limit the number of instances of damage within the detection area to a specific number. Furthermore, they consider only a single type of damage within the target detection area for each hammering point.  
However, under the influence of disasters and aging, the inspection environment becomes complex. Moreover, there are typically different types of damage in the target area, and detection is made difficult by the varying extent of their damage; for example, internal and surface cracks may be located in the target detection area of a hammering point. In this case, the simultaneous identification of the type, size, and depth of the damage means that the used qualitative and quantitative information is in the same dimension, which leads to an increased possibility that this will be misjudged.  
To obtain damage information, most existing studies have focused on acoustic data obtained from single-frequency hammering, lacking the means to increase the damage information obtained from the hammering test method. This study proposes a method of acoustic concrete damage detection based on variable-frequency hammering, which is different from the usual single-frequency hammering method, to achieve the classification of multiple categories of damage occurring in the same concrete member. The acoustic data obtained from variable-frequency hammering are combined with feature selection and feature extraction to enhance the effective usage of the data without increasing its dimensionality. Finally, a detection model is established using a support vector machine (SVM), and complex multi-class damage is successfully identified. This research focuses on the innovation of the hammering method. In fact, the ML model is used as the carrier to improve the hammering detection method itself. This provides a new and promising method for hammering detection.