## 1 Introduction  
With the rapid development of railway and highway constructions, the number of tunnels increases, nevertheless, because of the complicated geological conditions and inappropriate constructions, the tunnel diseases such as the lining cracks, tunnel leakage, vault roof slab, voids behind the lining, etc. are also increasing. Particularly, a void located behind the lining in a tunnel may cause leakage and deformation of the surrounding rocks that can significantly impair the tunnel service life. The non-destructive testing (NDT) methods commonly adopted for the investigation of a tunnel void includes ground-penetrating radar (GPR) [1, 2], ultrasonic resilience method [3], infrared photographing technology of temperature field [4], etc. Similarly, impact-echo (IE) is one another widely used NDT method to detect the piles [5] and other engineering structures [6], and it is also employed to detect the voids behind a tunnel lining. This method is especially known for locating the voids in the very early stage of evaluation whereby the stress waves get reflected between the interfaces; accordingly, the IE method is based on the analysis of the vibration response signal. [PERSON] et al. [7] assessed the quality of long drilled piles, such as the pile length, by analysing the test results in time domain and time-frequency domain. [PERSON] et al. [8] used the transfer function simulated by the IE method to analyse the bond condition of the concrete and substrate layers. The effect of the acoustic impedance and thickness of the substrate layer on the simulated transfer function was analysed in the frequency domain. [PERSON] et al. (2019) reported the effectiveness of grouting through a study that combined the time domain characteristics, spectral content, and wavelet transform. [PERSON] and [PERSON] (2010) analysed the response signals in the time-frequency domains through short-time Fourier transform (STFT) to evaluate the bonding state of tunnel shotcrete. They also studied the effects of the ground types, thickness of the shotcrete, undulating surfaces, and impact sources in both frequency and time-frequency domains ([PERSON] et al., 2012). [PERSON] et al. (2012) calculated the dynamic stiffness, mobility and damping, and peak/mean mobility ratio of the tested concrete elements to evaluate the tunnel lining grouting. [PERSON] et al. (2013) evaluated the quality of backfill material in the segmental lining of a tunnel based on the IE amplification factor (Q-factor). In a previous study, the IE method was used to study the grouting quality, the tunnel shotcrete bonding state, the material quality, etc. The response signals derived from IE method were analysed in the time, frequency, time-frequency domains using various methods such as Q-factor, dynamic stiffness, STFT, etc. The methods of analysis and the aspects of the response signal were selected based on the quality or bonding state of the material under study. Various analysis methods were used to analyse the properties of the data obtained by the IE method. They are usually compared in the situation of detecting the bonding state or the material quality. However, the tunnel structure that we studied in this article is in a complex loaded situation compared with the structure mentioned above such as the concrete slab. Accordingly, in order to study the specific aspects of the tunnel lining and to select an appropriate method of analysis to detect the void behind tunnel lining, it is necessary to apply various methods and analyse the test results. The properties and applicability of these methods should be compared. In this paper, to compare different types of signal analysis method for detection of tunnel voids, an experimental study was first performed to compare two conditions, tunnel lining with and without voids.