## 1 Introduction  
As the foundation of bearing track structure and train, the performance of subgrade is critical to the stability and safety of train operation. With increasing train speeds and axle loads of high-speed trains in China, railroad subgrade is required to have higher strength, stiffness, stability and uniformity. In order to meet these requirements, the main technical measure is that the compaction of railroad subgrade has successful quality control and quality assurance [1; 2; 3]. In recent years, researchers have done a lot to control the compaction quality of railroad subgrade. The method of quality control has developed from conventional methods to the Intelligent Compaction (IC) [4; 5; 6]. The IC method can monitor the compaction process through a vibratory roller equipped with accelerometers, and feedback compaction information to the control system in real-time. By analyzing the vibration characteristics of vibratory roller and filling materials, several compaction values that can reflect the compaction quality were proposed [7]. For instance, Compaction Meter Value (CMV) [8; 9], which is the amplitude ratio of the first harmonic wave to the fundamental wave obtained through spectral analysis of the measured vertical acceleration, was applied to control the compaction quality of subgrade and dam. On the basis of CMV, Compaction Control Value (CCV) [10], which further considers the influence of half-order harmonics and higher-order harmonics, was proposed. Total Harmonic Distortion (THD) [11] and Resonant Meter Value (RMV) [6] are similar to CCV. In addition, Machine Drive Power (MDP) [12] is calculated by analyzing the energy needed to overcome the resistance of the vibratory roller when it moves, and it is often used in combination with CMV in some projects [4; 13]. The application of these compaction measurement values avoided over- or under-compaction of filling materials, and improved the efficiency of subgrade compaction [6; 14; 15]. However, the vibration wave is very complicated and its transmission and evolution mechanism is not clear enough [16; 17], especially in the construction field, which leads to that CMV can only be used to roughly estimate the compaction quality of subgrade and the above-mentioned other (CCV, THD, RMV and MDP) compaction measurement values also had some problems in practical applications [18; 19; 20; 21]. Therefore, it is very necessary to study the transmission and evolution characteristics of the vibration signal from the vibratory roller to filling materials in the compaction process. In exploring the transmission and evolution characteristics of the vibration signal, two approaches have been used: (1) analyses were performed in the time domain, but only vibration time-history responses were obtained [8; 22; 23; 24]; (2) analyses were performed in the frequency, but only Fourier spectrums and energy spectrums are obtained [25; 26; 27; 28; 29]. However, the vibration wave is a complicated nonlinear non-stationary signal and its vibration frequency and amplitude are constantly changing in the compaction progress. Its order of harmonics cannot be predicted, which will affect the analysis accuracy if it is calculated from the time domain or the frequency domain alone [30; 31; 32]. Therefore, the jointed time-frequency domain will be a better approach for studying the transmission and evolution characteristics of the vibration signal from the vibratory roller to filling materials in the compaction process. Few studies have been done by using the jointed time-frequency domain to study the transmission and evolution characteristics of the vibration signal. At the same time, a lot of research mainly relies on numerical simulation, theoretical analysis and laboratory tests [33; 34; 35], and few field prototypes tests have been done because of its high cost, long period and so on.