## 1 Introduction  
A cost-effective civil engineering material that is frequently utilized in nuclear power plants, dams, and bridges is prestressed concrete (PSC) [1]. PSC ensures the stability of the structure by employing a tendon to provide pre-tension and post-tension to address the issue of concrete that is susceptible to tensile stress. The PSC bridge is a construction that makes the greatest use of the PSC technique (post-tension) and guarantees structural stability when developing a lengthy bridge [2]. A duct (also known as a sheath) is a tube that is used in the post-tensioning technique to apply tensile stress afterwards. To put it another way, when the duct has been installed, a tendon is put inside it to generate tensile tension, and then concrete is poured to fix it. As a result, tendons are essential to the security of buildings. The tendon, however, experiences defects such as rust when it is exposed to air, which is why it is placed within the duct before concrete is poured. A defect such as rust might result in an abrupt structural collapse [2]. However, the following two restrictions apply to the tendon. First, the duct's inner diameter is quite small. Second, the duct is mounted in a curved construction. For this reason, even a small mistake might result in a void within the duct. Because of this, it is crucial to assess the duct's inside condition, which calls for great precision. A proposed technique for exploring the inside of concrete structures is non-destructive testing (NDT). It measures the signals produced by ultrasonic waves, radiation, magnetic fields, and the impact-echo (IE) method to explore the internal condition of the concrete structure [3; 4; 5; 6; 7; 8]. However, this method requires the hiring of experts for complex and academic interpretation and it is a challenge to interpret accurately due to the complicated internal structure of the PSC bridge and the lack of suitable NDT. Another way is to use expensive NDT equipment such as ultrasonic wave-based equipment, but problems such as equipment size or budget still exist. For this reason, in most cases, it has been confirmed for safety by direct drilling based on experience. To interpret the voids that exist inside the ducts of PSC bridges, additional useful and economical methodologies are therefore required. In the early studies, the IE method was widely used to identify voids in concrete structures [9; 10; 11]. It analyzes the frequency spectrum extracted by Fourier transform. However, because there is a strong likelihood that multiple peaks may occur as a reason for vibration or something similar, it has been challenging to correctly interpret this frequency spectrum by experts [12]. To address this issue, many studies try to use time-frequency analysis such as wavelet transform (WT), short-time Fourier transform (STFT), empirical mode decomposition (EMD), and Hilbert-Huang transform (HHT), a signal processing-based approach [12; 13; 14; 15]. When [16] compared various time-frequency analyses, it was discovered that WT was the most useful for interpreting the IE method. On the other hand, machine learning-based approaches concentrate on assessing the condition of specific concrete components or entire concrete structures. Most of studies have used image-based crack detection or structural health monitoring (SHM) [17; 18]. Some studies have tried to detect defects that occur inside concrete structures. After applying WT to the IE data, [19] used the extreme learning machine (ELM) [20] approach to assess the overall condition of the concrete structure, and its good performance demonstrated the promise of machine learning. The authors of [21; 22] used a convolutional neural network (CNN) [23] and long short-term memory (LSTM) [24] approach to assess the bridge deck's internal defects and confirmed their potential. According to this trend, efforts have recently been made to provide a gold-standard measurement using the IE method [25].