## 1 Introduction  
Pile foundations are widely used in essential structures of highways, ports, bridges, and buildings because of their high load-bearing capacity, wide applications, and ability to adapt to various complex engineering address conditions. However, the influence of the construction process, geological conditions, and human factors lead to different types and degrees of defects in some pile foundations, which affects the bearing capacity of pile foundations. Currently, most of the research is about single-defect piles, and there are few studies on identifying multi-defect piles. Therefore, it is of guiding significance for formulating a pile foundation repair plan to accurately identify the type of multi-defect pile and complete the integrity test of the pile foundation. At present, [PERSON] et al. summarized various non-destructive testing methods, their advantages and disadvantages, and the latest progress, which is very enlightening for researchers who study and improve non-destructive testing technology [1]. LSPIT is widely accepted and used to evaluate the integrity of piles because of its simplicity, reliability, speed, and non-destructive characteristics [2]. The integrity test of more than 1800 bored piles was completed by a pile foundation non-destructive testing method at the light rail construction site in Nursultan city, of which LSPIT tested 55% [3]. The test using this method requiresthe application of an excitation force to the top of the pile, which generates an elastic wave propagating downward along the pile body. The presence of defects in the pile body causes a change in the cross-sectional impedance and generates a reflected wave. The velocity-time domain curve reflecting the pile defects can be obtained from the sensor placed on top of the pile [4]. However, when there are multiple defects in the pile foundation, the elastic wave will generate multiple reflections. It is more challenging to identify the type of multi-defect pile only by the velocity-time domain curve than the single-defect pile. [PERSON] has successfully applied deep learning technology to identify cast-in-place piles, effectively reducing the human and material resources required for monitoring [5]. However, there are still some limitations in some aspects. [PERSON] et al. extracted features from the wavelet transform components of the time-domain signal as the input to an artificial neural network, which enabled the diagnosis of the location and extent of foundation pile defects [6]. However, the signal data were not denoised, and there was feature loss. [PERSON] used wavelet analysis to denoise the signal, extracted features from the wavelet-packet-transformed components of the foundation pile dynamic measurement signal, and finally input these features into the artificial neural network for training and classification [7]. However, losing features during data processing leads to a long training time. [PERSON] et al. proposed an artificial neural network model for pile foundation fault diagnosis using the response records of actual piles [8]. However, the training data set is too small to generalize. [PERSON] extracted the power spectrum features of the time-domain signal using the fast Fourier transform (FFT), which was then fed into a BP neural network for defect-type detection [9]. [PERSON] et al. proposed to use the signal spectrum feature points as input to an artificial neural network classifier to automatically interpret the results obtained from low-strain integrity tests [10]. Regarding the differentiation of defective features, it is vital to corroborate each other in the time and frequency domains [11]. However, the input data set of these methods only considers the time domain or frequency domain characteristics in a single way, which cannot fully reflect the defective characteristics of the pile for the multi-defective pile where the data set is already tiny. The joint time-frequency analysis method is better than the traditional single-domain analysis in explaining pile integrity [12].