1. Introduction

The use of concrete in buildings is increasingly widespread with the growth of the construction industry. Numerous concrete structures, such as dams, offshore buildings, and marine platforms, have either partial or complete surface exposure to environmental conditions involving water contact [1, 2]. The water permeability of the concrete structure is crucial for its durability, and it is essentially related to the concrete moisture content [3]. Therefore, the internal moisture condition of the concrete component plays a crucial role in determining its serviceability. In addition, moisture in concrete pores results in a variety of physicochemical erosion, such as chloride diffusion [4], steel reinforcement corrosion [5, 6], and alkali–aggregate reactions. Therefore, it is crucial to estimate the variation of moisture within concrete structures. For large-scale hydraulic concrete structures (e.g., dams, bridge abutments, and retaining walls), the water seepage depth is often used as a key indicator of the water content within the concrete [7].

Methods for detecting the depth of water seepage in concrete structures mainly include the capacitance method [8, 9], piezoelectric stress wave method [10, 11], hyperspectral imaging method [12], and microwave method [13], among others. While these methods demonstrate significant potential for detecting water seepage depth in concrete structures, each comes with its own set of limitations. Salt conductivity can adversely impact the capacitance method based on permittivity measurements, leading to inaccuracies in the results [14]. The piezoceramic stress wave method involves the prior installation of sensors in the structure, which may increase the cost and reduce the structural load-bearing capacity. Hyperspectral imaging methods may damage the specimen and require the involvement of specialized personnel. The accuracy of the microwave method is compromised at times due to internal scattering and diffraction arising from the heterogeneity of concrete. Hence, there is a need to identify a straightforward and cost-effective method for detecting the water seepage depth in concrete structures.

The percussion method can be utilized to gather information about potential damage by striking the surface of a test object. It is gaining prominence in nondestructive testing (NDT) due to its ease of operation, cost-effectiveness, and ability to function without sensors requiring direct contact with the object [15–18]. Researchers focusing on the percussion method were primarily concerned with the structural vibration response induced by percussion rather than the sound generated by the impact [19]. However, with the swift advancement of machine learning (ML) techniques, there is a growing interest among researchers in sounds induced by percussion. Chen et al. [20] extracted power spectrum density (PSD) energy from percussion sound signals as features and employed a support vector machine (SVM) algorithm to classify subsurface voids in CFST structures. Zheng et al. [21] converted percussion sound signals with different concrete water content into Mel-frequency cepstral coefficients (MFCCs) and classified them using the SVM algorithm. Cheng et al. [16] demonstrated the effectiveness of the percussion method for detecting pipeline deposits by employing the SVM algorithm to identify the MFCC extracted from percussion sound signals. He et al. [22] used the K-nearest neighbors (KNNs) algorithm to recognize PSD features extracted from percussion sound signals. This was applied to detect the looseness condition in underwater bolted connections. Thus, to establish the connection between structural damage (e.g., loose bolts) and percussion-induced sound signals, the mentioned percussion methods heavily depend on ML techniques. However, ML techniques require features to be manually crafted and then input into the classifier. This approach might overlook critical features in percussion-induced sound signals, resulting in suboptimal classification accuracy [23]. Furthermore, the antinoise capacity and adaptability of existing ML techniques remain unverified, thereby constraining their practical effectiveness in real-world scenarios [24].

Recently, deep learning (DL) techniques have advanced rapidly, emerging as a promising solution to tackle the aforementioned challenges. In contrast to traditional ML techniques, DL techniques can autonomously extract features from data without the need for manual feature extraction. As a typical DL algorithm, convolutional neural networks (CNNs) have gotten a lot of attention because of their superior performance. Chuang, Tsai, and Wang [25] utilized CNNs to classify Mel-frequency spectrograms obtained by transforming one-dimensional signals for water pipe leak detection. Yuan et al. [26] employed CNNs to implement bolt-loosening detection by classifying Mel spectrograms derived from one-dimensional signals. However, when traditional CNNs process one-dimensional data such as audio, it is often necessary to convert the data into two-dimensional images, which can lead to redundant computations. To address this issue, researchers have introduced one-dimensional CNNs (1D-CNNs). Abdeljaber et al. [27] realized damage detection and real-time damage localization based on vibration by fusing feature extraction and classification modules into a compact learning body using 1D-CNN. Eren [28] employed 1D-CNN for rapid identification of bearing faults. In addition, 1D-CNN has been widely studied in pipeline leakage and water deposition detection [29, 30], bolt loosening detection [31, 32], intelligent diagnosis of rotating machinery [33], etc. However, to the best of the author’s knowledge, no existing research has applied DL techniques in combination with the percussion method to detect the depth of water seepage in concrete structures.

This paper presents a framework for detecting water seepage depth through the application of a percussion-based DL technique. The suggested DL framework is termed as the one-dimensional convolutional bidirectional gated recurrent unit network (1D-WCBGRU) with a wide first kernel. This hybrid framework combines the 1D-CNN and bidirectional gated recurrent unit (BiGRU). Unlike traditional ML/DL techniques, this framework harmonizes the potent feature extraction capability of 1D-CNN with BiGRU’s ability to capture both long-temporal and short-temporal relationships in features. This combination enhances the accuracy and robustness of predicting concrete structure water seepage depth.

This paper’s main contributions are as follows: (1) This paper establishes a finite element model to simulate the water seepage depth in concrete structures and verifies the feasibility of detecting water seepage depth using the percussion method. Additionally, a DL model is proposed, primarily for classifying percussion sound signals to achieve the detection of water seepage depth. (2) To enhance the feature extraction capability of the 1D-WCBGRU model, we designed a wide kernel convolutional block to extract more representative features from the original signal. The model also integrates a BiGRU block to bolster predictive performance, thereby improving the model’s accuracy in classifying percussion sound signals. (3) The experimental results demonstrate that the 1D-WCBGRU model exhibits strong noise immunity in noisy environments and shows powerful adaptability across various application conditions, proving the model’s potential and effectiveness in practical applications.

The rest of the paper is organized as follows. Section 2 provides an explanation of the model’s theoretical background. A detailed description of the 1D-WCBGRU model is provided in Section 3. In Section 4, the experimental setup is described in detail. In Section 5, we compare the performance of 1D-WCBGRU with other methods. Section 6 summarizes the study.

2. Theoretical Background

2.2. Gated Recurrent Unit (GRU)

Feedforward neural networks offer only a static mapping of inputs and outputs, limiting their applicability to static classification tasks. To address the requirements of temporal prediction tasks, like speech recognition and natural language processing, several studies have concentrated on the development of recurrent neural networks (RNNs). However, challenges like gradient explosion undermine the performance of RNNs in processing time series tasks. To tackle these challenges, long short-term memory (LSTM) was introduced, replacing the RNN’s hidden layer with a memory block capable of retaining past data. After that, Chung et al. [40] proposed a GRU based on LSTM. The GRU replaces the input gate, output gate, and forget gate in LSTM with reset gate and update gate. Consequently, the GRU demonstrates performance comparable to that of LSTM, while requiring fewer training parameters and offering a faster training process [41]. Figure 1 illustrates the architecture of the GRU. The mathematical expression is as follows:

$$ ()

where R_t and Z_t stand for reset gate and update gate, W_r and W_z are the weights connected to the input vector, U_r and U_z are joined to the weights of the previously hidden state, H_t−1 and H_t are the output at time t − 1 and t, and ⊙ is the product.

2.3. Numerical Simulation

Zhou et al. [17] investigated the correlation between percussion-induced vibration and percussion sound by wavelet packet decomposition and sound reconstruction techniques. Therefore, the sound produced by percussing concrete varies in response to the vibrations induced by the impact.

Furthermore, numerous factors (e.g., density and properties of interfacial transition zones.) influence the elastic modulus of concrete, given that it is an inhomogeneous multiphase material [42]. Liu et al. [43] investigated the relationship between the elastic modulus of concrete and water content. The results showed that the modulus of elasticity was positively correlated with water content. The formula for the interaction between the two was presented as follows:

$$ ()

where E denotes the modulus of elasticity (MPa) and M represents the moisture content (%). In addition, Kolluru, Popovics, and Shah [44] experimentally demonstrated a good correlation between resonance frequency and elastic modulus.

Luo and Yang [45] conducted experiments demonstrating that changes in the natural frequency of a structure influence its vibrational characteristics, resulting in distinct percussion sounds. Thus, numerical simulations were conducted for six concrete specimens with varying water seepage depths using the commercial finite element software Abaqus in this study. An example finite element model of a concrete specimen with dimensions 100 mm × 100 mm × 400 mm is illustrated in Figure 2. In this paper, the impact of water seepage depth on resonance frequency was simulated by adjusting the modulus of elasticity of concrete at different heights (0 mm, 80 mm, 160 mm, 240 mm, 320 mm, and 400 mm). All parameters were held constant except for the varying of the modulus of elasticity.

2.3.1. Concrete Constitutive Model

The concrete damage plasticity (CDP) constitutive model [46] was used to simulate the concrete in this paper. To characterize the yield function and plastic flow properties of concrete, the following parameters were set: dilation angle of 30°, eccentricity of 0.1, f_b0/f_c0 of 1.16, K of 0.6667, and viscosity parameter of 0.0005. The elastic modulus was calculated based on equation (10). Following the Chinese standard GB50010-2010 [47], equations (7)–(11) were used in this paper to represent the uniaxial compression principal model of concrete.

$$ ()

$$ ()

$$ ()

$$ ()

$$ ()

where σ is the compressive stress; d_c represents the damage parameter under uniaxial compressive stresses; E₀ denotes the elastic modulus between the peak point and the origin; ε and ε₀ indicate the compressive strain and the compressive strain at the peak point, respectively; f_c represents the axial compressive strength; ρ_C represents the ratio of compressive strength to E_c multiplied by ε₀; n and α_c represent the parameters of the ascending and descending phases of concrete under uniaxial compressive stress, respectively; and x represents the ratio of ε to ε₀.

2.3.2. Boundary Conditions and Mesh Sizes

The model simulates a portion of a mass hydraulic concrete structure with column top displacements (U_x, U_y, and U_Z) and column bottom displacements (U_x, U_y, and U_Z) in all three directions constrained to 0. At the same time, the rotational degrees of freedom (UR_x, UR_y, and UR_z) of the column was 0. The concrete mesh size was set to 5 mm.

The concrete model was subjected to modal analysis to validate the effect of seepage depth on the natural frequency of concrete. Table 1 illustrates the first three orders of natural frequency for concrete specimens at different water seepage depths. The results indicate that the increase in the depth of water seepage leads to a gradual increase in the first three orders of the natural frequency of the concrete specimens. Thus, with other conditions held constant, the sound generated from percussion is influenced by the water seepage depth, confirming the feasibility of using percussion sound to identify the water seepage depth in concrete structures.

Table 1. Natural frequency of concrete specimens.

Water seepage depth (mm)	First mode frequency (Hz)	Second mode frequency (Hz)	Third mode frequency (Hz)
0	1627.4	2492.1	3597.1
80	1646.1	2523.8	3633.8
160	1652.6	2538.2	3656.2
240	1662.6	2539.6	3671.8
320	1669.6	2552.5	3694.0
400	1688.8	2586.1	3732.8

3. Proposal Method

This paper introduces a novel deep neural network designed to address the classification of percussion sounds corresponding to different water seepage depths. Figure 3 illustrates the proposed 1D-WCBGRU architecture, which mainly consists of an input block, a wide kernel convolutional block, a BiGRU block, and an output block. The detailed parameters of the 1D-WCBGRU are shown in Table 2. The fundamental mechanism involves feeding percussion sound signals from various water seepage depths into the 1D-WCBGRU. First, a wide convolutional kernel (kernel size = 256) extracts local features from the audio signals. To reduce the computational complexity and dimensionality of the feature maps, the output of the convolutional layer is subjected to max pooling operation. Subsequently, a smaller convolutional kernel (kernel size = 2) is employed for a secondary convolution operation to further extract features from the audio signals. Concurrently, to enhance the model’s training stability and generalization capability, layer normalization (LN) is introduced, thereby improving the model’s adaptability to different input distributions. Following this, BiGRU is incorporated to more effectively capture contextual information within audio sequences. After passing through this layer, the model uses a global average pooling (GAP) layer to map audio sequences of varying lengths to a fixed-length vector. This operation enables the model to better handle audio inputs of different lengths, reduces the number of model parameters, and mitigates the risk of overfitting. Finally, the model employs an FC layer to map audio features to the output layer. The Softmax function is employed to provide for probabilistic output across six categories, achieving accurate classification of different types of damage. The model effectively captures multilevel information from audio signals, thereby enhancing the model’s classification performance and robustness. The theoretical background of each module is described in the following section.

3.2. Bidirectional GRU

While GRU performs well in handling sequence problems with long-term dependencies, many sequence modeling tasks benefit from accessing both future and past contexts. Researchers [49] introduced a reverse structure layer to the GRU, resulting in the design of BiGRU, as illustrated in Figure 4. In BiGRU, the outputs of the two networks are merged at each step, enabling the structure to offer complete contextual information. The computational procedure of BiGRU is as follows:

$$ ()

where GRU_fw and GRU_bw, respectively, represent the mapping relationship of forward GRUs and backward GRUs. In this study, the BiGRU block is connected after the wide kernel convolutional block to capture information that may be overlooked by GRU blocks.

4. Experimental Setup

Three concrete prismatic specimens, each with dimensions of 100 mm × 100 mm × 400 mm were fabricated and tested in a laboratory setting to validate the proposed method. The concrete was designed to have a compressive strength of 30 MPa. The mix ratio for achieving this strength is presented in Table 3.

Following a curing period of 28 days under standardized conditions, the concrete specimens were subsequently dried in an oven at 105°C for 48 h, ensuring that their mass reached a constant value. Once the concrete had cooled completely, the specimens were immersed in pure water at the specified depth for about 4 h. After that, the concrete specimens were taken out of the water and dried with a cloth until no water droplets remained on the surface, after which the percussion test was conducted. Given the short duration of the percussion experiments, it was assumed that water seepage depth inside the concrete remained constant. Figure 5(a) illustrates the experimental samples and equipment.

A total of six different damage conditions were set up for the experiment, and each damage condition was assigned a label value from 0 to 5, as shown in Table 4. The apparatus used for the hammering experiment comprised an impact hammer and a smartphone. Throughout the experiment, the specimen was secured at both ends using the fixture to prevent disturbances caused by the concrete shaking during percussion. As depicted in Figure 5(b), the fixture was in contact with the concrete specimen and applied no force. Concrete was percussed at specified locations 100 times with uniform force to produce an audio signal. Simultaneously, the audio signal was captured at a sampling rate of 48 kHz by a smartphone situated 100 mm from the percussion point, as depicted in Figure 5(b). The experiment was performed in a quiet laboratory to minimize noise disturbance. Afterward, the audio signal was preprocessed by converting the dual-channel raw audio to a single channel with a sampling time set to 0.1 s (i.e., a sample length of 4800). Peak points are sample points in the waveform where the amplitude exceeds a predefined threshold of 15,000. These peak points serve as the starting point for each percussion signal. To ensure an accurate separation of each individual knock sample, a minimum gap was introduced between two consecutive peak points, allowing only one peak point to be selected within this gap. Finally, the individual percussion raw signals were normalized and used as inputs to the model. Figure 6 illustrates a portion of the percussion sound signals waveform captured at various water seepage depths.

5. Results and Discussion

5.1. The Model Training

The 1800 audio data generated by percussion under six work conditions were categorized into a 7:3 ratio for training and test sets, respectively. Subsequently, the 1D-WCBGRU was trained and tested. Before training, the audio signal was normalized to the range [0, 1]. The cross-entropy loss was chosen as the loss function of the model, which is defined as follows:

$$ ()

where N is the sample size and C represents the number of categories. y_i,j and $$ denote the true and predicted label of the j-th category of the i-th sample, respectively. The model is trained for a total of 500 epochs using the Adam algorithm with a 0.0005 learning rate and a batch size of 32. The model was trained using PyTorch (Version 2.0.1) in Python (Version 3.11.4) on a computer equipped with an Intel core i5-13500HX and an Nvidia GeForce RTX4050.

The accuracy and loss curves stabilize after small fluctuations during 500 epochs of training, as shown in Figure 7. Throughout the training process, the close alignment of the training and test curves indicates that the model has strong generalization ability. The model achieves 100% training accuracy and 100% test accuracy after 500 epochs of training. This confirms the sensitivity of the 1D-WCBGRU to water seepage depth in concrete structures, showcasing its effective feature extraction and learning capabilities during training. Simultaneously, the 1D-WCBGRU has superior performance on unseen datasets.

5.2. Methodology Comparison

To demonstrate the superior performance of the 1D-WCBGRU model, it was compared against two common ML-based methods, (1) PSD + DT [51] and (2) MFCC + SVM [16], along with three DL-technology–based methods: (3) MFCC + CNN [52], (4) 1D-WDCNN [48], and (5) 1D-ResNet [29]. In the ML-based methods, (1) PSD values were extracted from 10 frequency ranges (i.e., 0 Hz to 10 kHz) of the original data to train the decision tree (DT). (2) Spectrograms containing 12 MFCC coefficients were extracted and used as input to the SVM. For the DL-based model, (3) spectrograms of the 16 MFCC were extracted from the original audio. Subsequently, these spectrograms were processed using CNNs with convolutional kernel sizes of 9 × 9, 7 × 7, and 5 × 5. In method (4), a 1D-CNN with five convolutional layers was constructed. The first convolutional layer has a kernel size of 64 × 1, while the subsequent layers have a kernel size of 3 × 1. Method (5) used three residual layers (including two convolutional layers with a convolutional kernel size of 3 and a skip-joining group) to learn the residual information after extracting the features using convolutional layers. The training and testing experiments for all six models were conducted in the same computing environment on the same computer. To comprehensively compare the performance of each method, accuracy, precision, recall, and F1-score were calculated. These metrics are defined as follows:

$$ ()

where TP, FP, FN, and TN represent the number of true-positive, false-positive, false-negative, and true-negative outcomes, respectively. The classification performance of each model for the concrete structures water seepage depth task is presented in Table 5. Figure 8 illustrates the classification results of the different methods. The analysis of the results reveals that the 1D-WCBGRU achieves a classification accuracy, precision, recall, and F1-score of 100%. This indicates that the 1D-WCBGRU exhibits outstanding performance in the task of detecting water seepage depth in concrete structures when compared to other methods. Furthermore, it is evident from the results that the DL-based methods (MFCC + CNN, 1D-WDCNN, 1D-ResNet, and 1D-WCBGRU) outperform the ML-based methods. The results also demonstrate that manually extracting features leads to redundant computation, thus reducing accuracy.

Table 5. Performance comparison of different methods.

Method	PSD + DT	MFCC + SVM	MFCC + CNN	1D-WDCNN	1D-ResNet	1D-WCBGRU
Accuracy	0.7926	0.9722	0.9815	0.9907	0.9926	1.0000
Precision	0.7967	0.9730	0.9815	0.9909	0.9928	1.0000
Recall	0.7926	0.9722	0.9815	0.9907	0.9926	1.0000
F1-score	0.7932	0.9730	0.9815	0.9906	0.9926	1.0000

The t-distributed stochastic neighbor embedding (t-SNE) technique is employed to generate a 2D visual representation of the feature mapping. This approach enhances the understanding of the features learned by the model and facilitates the analysis of the model’s representation in the data space. The 2D visualization results of the feature mapping for the input layer, convolutional layer, BiGRU layer, and FC layer of the 1D-WCBGRU are obtained using t-SNE, as illustrated in Figure 9. In this figure, each point represents a data sample, and the six different colored points correspond to the six categories of water seepage depths. The 2D visualization results from the input layer indicated a significant superposition of data points from different categories, making it challenging to differentiate the feature information of the original data. In the convolutional layer, while no clear clustering of points is observed for each category, their distribution becomes progressively more structured and organized. In contrast, features are more distinguishable after the BiGRU layer, with only a few instances of misclassification. This is evidence that the BiGRU layer enhances feature distinguishability. Ultimately, the features are perfectly classified after the FC layer. Overall, the coordinated interaction of the individual blocks significantly enhances the feature extraction capability of the 1D-WCBGRU model.

5.3. Adaptability Test

Despite the outstanding performance exhibited by the 1D-WCBGRU in the aforementioned experiments, certain challenges persist in practical applications. For this reason, two experiments were designed in this section to test the adaptability of the 1D-WCBGRU.

5.3.1. Effect of Percussion Position

Liu et al. [53] investigated the correlation between the location of percussion and detection effectiveness. The detection accuracy decreases as the percussion position moves farther away from the bolt. This could be attributed to the further distance between the percussion positions and the defect, which introduces greater physical separation and structural differences. As a result, more irrelevant information is captured, leading to a decrease in detection accuracy. In practice, it is difficult to determine the approximate range of water seepage depth to select the appropriate percussion position. Therefore, the experiment was designed with different percussion positions (120 mm and 280 mm) to assess the adaptability of the 1D-WCBGRU. Table 6 depicts the accuracy of each model in classifying the water seepage depth at different percussion positions. The results demonstrate the superiority of the proposed 1D-WCBGRU model compared to the other methods.

Table 6. The accuracy of different methods on different percussion positions.

Percussion position (mm)	Methods
	PSD + DT	MFCC + SVM	MFCC + CNN	1D-WDCNN	1D-ResNet	1D-WCBGRU
120	0.6944	0.9593	0.9889	0.9851	0.9833	0.9981
280	0.7360	0.9644	0.9850	0.9925	0.9831	1.0000

5.3.2. Cross-Dataset Performance Evaluation

As concrete is an inhomogeneous multiphase composite material, the audio features captured through the percussion method may vary even for concrete with identical mix ratios, due to differences in the manufacturing process. Consequently, additional investigations into the adaptability of the proposed model are warranted. For this purpose, the two datasets are merged into a training set, and the other dataset is used as a test set. This indicates that the training and test sets were derived from separate concrete samples, ensuring no overlap between the datasets. Table 7 demonstrates the accuracy of each method. Figure 10 depicts the classification results for the 1D-WCBGRU across different percussion positions in the cross-dataset. It is worth noting that when considering cross-dataset, the accuracy of all methods tends to decrease. However, the 1D-WCBGRU consistently outperforms the other methods.

Table 7. The accuracy of different methods on cross-datasets with different percussion positions.

Percussion position (mm)	Methods
	PSD + DT	MFCC + SVM	MFCC + CNN	1D-WDCNN	1D-ResNet	1D-WCBGRU
120	0.2883	0.3967	0.3967	0.6717	0.4800	0.9450
200	0.2450	0.4117	0.3817	0.6417	0.5450	0.9767
280	0.3650	0.4617	0.2217	0.5600	0.6783	0.9617

In real-world scenarios, the depth of water seepage in concrete structures is constantly changing and may differ from the preset depths used in this experiment, potentially making detection more challenging. To address this concern, the confusion matrix depicted in Figure 10 was simplified in Figure 11 by focusing solely on the relative position of the water seepage depth to the percussion positions. In Figure 11, the label “0” represents instances where the water level height is below the percussion positions, while the label “1” indicates instances where the water level height is above the percussion positions. The accuracy of the 1D-WCBGRU at percussion positions of 120 mm, 200 mm, and 280 mm is 99.50%, 99.17%, and 99.67%, respectively. This demonstrates that the 1D-WCBGRU achieves high accuracy when the relative position of the percussion to the water seepage depth is the primary consideration.

To further evaluate the performance of the 1D-WCBGRU on unseen datasets, additional experiments were conducted based on the water seepage depth and the relative positions of percussion. The data labels “0,” “2,” “3,” and “5” in the training set were used to generate a new training set, and the data labels “1” and “4” in the test set were used to generate a new test set. In the new training set, data labeled “0” and “2” were combined into label “0,” while data labeled “3” and “5” were consolidated into label “1.” In the new test set, “0” and “1” correspond to labels “1” and “4” in the original test set, respectively. It should be noted that only the data from the 200-mm percussion position have been selected for the purpose of balancing the data. The classification accuracy is shown in Table 8. Notably, the 1D-WCBGRU still has high classification accuracy cross-dataset for uncollected water seepage depth signals.

Table 8. The accuracy comparison of different methods.

Methods	PSD + DT	MFCC + SVM	MFCC + CNN	1D-WDCNN	1D-ResNet	1D-WCBGRU
Accuracy	0.8000	0.5700	0.5300	0.6900	0.6350	0.9550

5.4. Model Performance in Noisy Environment

While all the raw audio data were collected in a quiet experimental environment in this study, the presence of noise in actual environments complicates obtaining a pure audio signal through the percussion method. Hence, it is essential to ensure the model’s noise immunity. To assess this, the robustness of the 1D-WCBGRU was tested in noisy environments by introducing Gaussian white noise with varying signal-to-noise ratios (SNR) into the cross-dataset data. The mathematical expression for the SNR is as follows:

$$ ()

where P_signal and P_noise represent the power of the signal and noise, respectively. This paper considers six SNR classes ranging from 0 dB to 10 dB in 2 dB increments. Figure 12 illustrates the audio waveforms at various SNR levels. The introduction of Gaussian white noise almost masks the waveform characteristics of the original audio, which makes it challenging to visually distinguish the original audio waveform from the noisy audio waveform.

Figure 13 provides a visualization of the classification accuracy in a noisy environment for different percussion positions cross-dataset. The combined analysis shows that the accuracy of all methods decreases in noisy environments, underscoring the general adverse effect of noise on model performance. Three feature extraction methods (PSD + DT, MFCC + SVM, and MFCC + CNN) perform poorly in noisy environments. However, the three methods (1D-WDCNN, 1D-ResNet, and 1D-WCBGRU) that directly take 1D audio signals as inputs show better performance. This indicates that the direct use of 1D signals as input facilitates the capture and retention of key features in the audio data. Notably, the 1D-WCBGRU has better noise immunity.

In addition, it can be observed from the figure that the accuracy of some models instead increases after adding Gaussian white noise. For instance, 1D-ResNet’s classification accuracy increased by 3.83% after introducing Gaussian white noise with an SNR of 8 to the data collected at a 120-mm percussion position, compared to using noiseless data. This phenomenon may result from the model overfitting specific features in the training set that were absent in the test set. When noise was introduced into the data, these overfitted features were masked by the noise, making the model rely on more general and robust features. However, the 1D-WCBGRU model does not suffer from this problem, indicating that the model has been effective in avoiding the overfitting problem in the absence of noise.

6. Conclusion

Overall, the 1D-WCBGRU shows promise as a reliable method for water seepage depth detection, given its superior performance demonstrated in the task of water seepage depth detection.

Conflicts of Interest

The authors declare no conflicts of interest.

Author Contributions

Wenjie Huang: conceptualization, methodology, writing–original draft preparation. Kai Zhou: formal analysis, writing–original draft preparation, funding acquisition. Jicheng Zhang: investigation, resources, writing–original draft preparation. Longguang Peng: investigation, resources, software, data curation. Guofeng Du: methodology, writing–review and editing, funding acquisition. Zezhong Zheng: conceptualization, methodology, writing–review and editing.

Funding

This research was financially supported by the National Natural Science Foundation of China (Grant No. 52078052 and 12302164).