## 2 Methods
### Test Finite Element Analysis  
#### 2.2.1 Basic Theory and Modeling Parameters  
Multi-defect identification of concrete piles required many defect pile signals for classifier training. However, it is impossible to obtain enough signal samples, even after spending a lot of time and effort in the experiment. Therefore, in this study, the ABAQUS 2020 version/explicit method was used to solve the dynamic response of piles under high-speed dynamic loading [29] and to build the multi-defective pile database required for TC-CNN. Since the pile deformation by the excitation force during the LSPIT is small, the material parameters, Young's modulus, and density changes are also small. Therefore, the time-domain curve of foundation pile vibration velocity is directly related to the pile geometry [30]. Typical pile foundation defects are weak concrete, neck defect, bulge imperfection, crack, and broken piles. With multiple defect combinations in various forms, LSPIT quickly identifies broken piles and challenges to identifying tiny cracks [31; 32]. The situation of a double defect combination of weak concrete, a neck defect, and a bulge imperfection in a pile is the only one considered in this paper, which is the case where the original linear elastic structure remains linear after damage [30]. [PERSON], a person who has made outstanding contributions to the field of pile-soil research through the analysis of the experimental data of London clay soil, concluded that the size of shear displacement is almost negligible when the pile perimeter soil radius is about 10r\({}_{0}\); for the actual project, the pile perimeter soil radius can meet the requirements when set to 5r0-6r0 [33], so the model size of this paper is following: the pile length L is 1.2 m, the pile radius r\({}_{0}\) is 0.05 m, the pile perimeter soil size is 10r\({}_{0}\) (0.5 m), and the soil at the bottom of the pile is 10r\({}_{0}\) (0.5 m) along the axial depth of the pile. The material parameters of the model will affect the simulation effect of the velocity response curve, including the amplitude difference, the apparent degree of pile bottom reflection, and the accuracy of pile length measurement. Referring to relevant data [34], we made minor adjustments. The parameter settings of the model materials in this paper are shown in Table 1.  
The sensor replaced the historical output history in ABAQUS, and the sensor position was placed at 2/3r\({}_{0}\) to reduce the 3D effect [35]. The ascending cosine pulse shown in Equation (5) simulated the excitation force [36]. \[p(t)=\frac{I}{T_{d}}\left[1-\cos\frac{2\pi}{T_{d}}t\right]0\leq t\leq T_{d} \tag{5}\]  
where \(T_{d}\) = 0.2 ms, \(I\) = 0.0001 N\(\cdot\)s, \(t\) = 0.1 ms, achieving the simulation of the experimental excitation force in Section 2.3.2. Analysis step duration: The reflected wave must include the incident to the wave reflected from the pile bottom, and the length of the time recorded in the time-domain signal should continue not less than 5 ms after the 2L/\(c\) moment [37], and the preliminary estimate of the analysis step time is 2L/\(c\) = 0.68 ms, and the analysis step time is 1.2 ms. If the analysis step is too short, the simulation of the velocity response curve will be incomplete, affecting the data set's quality. The boundary conditions are: the soil around the pile is fixed in X and Y directions (U1 = U2 = 0), the bottom of the pile is fixed in X, Y, and Z directions (U1 = U2 = U3 = 0), and the top of the pile is not constrained. Grid division; since the model is only concerned with the displacement of the cell, the advantage of C3D8R (three-dimensional eight-node simplified integral cell) is that the results of the solution for the displacement are more accurate. According to the velocity of wave estimating grid size, bringing the pile-soil parameters into Equation (2) yields a wave velocity of 3535 m/s. The span of the impact load is more reasonable within ten cells. As \((T_{d}\times c)/10\) = 0.07 m, the cell division is 0.03 m [36].