Structural Damage Detection through Dual-Channel Pseudo-Supervised Learning

Abstract

Structural damage detection is crucial for maintaining the health and safety of buildings. However, achieving high accuracy in damage detection remains challenging, especially in noisy environments. To improve the accuracy and noise robustness of damage detection, this study proposes a novel method that combines the Conformer model and the dual-channel pseudo-supervised (DCPS) learning strategy for structural damage detection. The DCPS learning strategy improves the stability and accuracy of the model in noisy environments. It enables the model to input acceleration signals with different noise levels into each branch of the dual-channel network, thereby learning noise-robust features. The Conformer model, as the backbone network, integrates the advantages of convolutional neural networks (CNNs) and Transformers to effectively extract both local and global features from acceleration signals. The proposed method is validated using a four-story single-span steel-frame building model and the IASC-ASCE simulated benchmark structure. The results show that the proposed method achieves a higher classification accuracy than existing structural damage detection methods. Compared to the single Conformer-based method, this method improves the accuracy by 1.57% and 4.93% for the two validation structures, respectively. Moreover, the proposed method benefits from the DCPS learning strategy’s ability to achieve superior noise robustness compared to other methods. The proposed method holds potential value for improving the accuracy of damage detection and noise robustness in scenarios such as maintenance and extreme events.

1. Introduction

The fundamental structural components of building structures, including beams, columns, and slabs, are vulnerable to damage in a multifield coupling environment [1,2]. Such damages jeopardize the stability and safety of the building structure and may lead to engineering accidents [3]. Therefore, accurately monitoring damage in building structures has become a significant concern in the fields of civil engineering and computer applications [4]. Structural Health Monitoring (SHM) [5,6,7,8] systems play a crucial role in detecting the health status of structures. They are widely used for diagnosing and predicting the structural health of buildings such as high-rise buildings, large gymnasiums, and historical buildings [9]. Structural damage detection methods are an essential part of the SHM, especially vibration-based structural damage detection methods that have received widespread attention [10,11,12,13].

With the rapid development of artificial intelligence, many machine learning-based structural damage detection algorithms have been proposed [14,15]. These methods typically extract features manually from raw data and then establish the mapping relationship between features and structural states through a classifier. However, the classification accuracy of machine learning-based methods is affected by hand-crafted features, and it is difficult to mine deep features of the data.

In recent years, numerous structural damage detection methods based on deep learning have been proposed [16,17,18] due to the remarkable performance of deep learning in various fields. To this end, researchers focus on designing effective deep learning models to extract features related to structural damage identification in order to accurately locate and classify structural damage. These methods can be mainly categorized into those employing Convolutional Neural Networks (CNNs) [19,20,21,22,23], those utilizing a Long Short-Term Memory (LSTM) [24,25,26], and those combining both CNNs and LSTM (CNN-LSTM) [27,28,29]. For a more detailed description of structural damage detection methods, please refer to the comprehensive reviews in [12,30].

CNNs [19,20,21,22,23] can learn local features from the input signals, so the straightforward idea is to use a 1D CNN model to extract local features from the 1D signals. CNNs are a type of multilayer feedforward neural network that is extensively employed in various supervised classification tasks [31]. Zhang et al. [22] created an acceleration response database related to bridge structures for training a 1D CNN model and demonstrated that CNN was highly sensitive to small structural changes. However, it is difficult for 1D CNNs to process input signals from multiple sensors. To address this difficult, Khodabandehlou et al. [19] proposed concatenating 1D acceleration response signals from multiple sensors into a 2D matrix as inputs and applying a 2D CNN for structural damage detection. They collected acceleration response data from multiple sensors and constructed a 2D signal matrix, which was fed into a 10-layer 2D CNN for training. Although CNNs are highly effective in extracting local features, they struggle to capture global features present within acceleration response data. LSTM [24,25,26], as a representative model for capturing long-distance feature dependencies of signals, uses the output of the previous moment as the input of the current moment to form a recursive connection structure. Lin et al. [24] used LSTM to identify structural damages. They input raw acceleration response data into LSTM to learn the long-term time-series features in the data. As a result, they obtained more accurate damage detection results compared to traditional machine learning algorithms. Sony et al. [26] proposed a multi-category structural damage detection approach based on windowed LSTM. They used windowed sample sequences from signals as inputs for LSTM, enabling the detection of multiple categories and degrees of structural damage. Nevertheless, LSTM ignores the local information from the damage signal, and its performance will degrade when dealing with long-distance dependencies within response data. In recent years, some researchers have combined the local feature learning capability of CNNs with the global feature learning capability of LSTM to propose innovative structural damage detection methods based on CNN-LSTM frameworks [27,28,29]. These frameworks can not only automatically extract local features from sensor signals but also capture global feature dependencies within data, which is beneficial for improving the accuracy and robustness of models. However, these hybrid models still have difficulty robustly handling long-range dependencies in the response data.

In addition to the model architecture, the noise present in the acceleration response signals obtained from sensors also affect the performance of the model in identifying structural damage. A number of studies [32,33,34] have shown that utilizing denoised signals as the input to train deep learning models can effectively enhance the classification accuracy of the models. Bao et al. [34] employed the Random Decrement Technique (RDT) to denoise raw data and demonstrated that the performance of this model was enhanced when exposed to low levels of noise. Wang et al. [35] combined the Hilbert–Huang Transform (HHT) and a CNN to propose a novel structural damage-identification method. The research results demonstrate that this method possesses significant noise-immunity advantages. Although these works have shown that denoising preprocessing techniques can enhance the accuracy of damage detection, they require manual denoising. Nevertheless, this makes them difficult to apply in engineering practices.

In summary, it is a challenging task to design an effective model to extract features from signals with noise for the accurate identification of structural damage. This paper presents a novel method that combines a dual-channel pseudo-supervised (DCPS) learning strategy and the Conformer model for structural damage detection. On the one hand, the existing methods rely on manual denoising to deal with the sensitivity of the model to noise in the signals, which limits their practical application in engineering. To address this issue, a DCPS learning strategy is proposed to improve the noise robustness of the model. The Cross Pseudo Supervision (CPS) method proposed in reference [36] uses two branches with the same structures but different initial weights in a dual-channel network to generate labels for the same input image separately. These generated labels are then used as supervision signals of the other branch. This method improves the noise robustness of the model. Based on this idea, the proposed DCPS introduces different levels of noise into each branch of the dual-channel network and uses the output of one branch as labels for the other branch to train the model. Through this learning process, the model adapts better to input signals with noise, consequently enhancing the stability and accuracy of structural damage detection. On the other hand, this paper introduces the Conformer model to address an issue of existing models, wherein it is difficult for the latter to robustly extract local and global features from response data. The Conformer model [37] exploits the advantages of CNNs and Transformers, and it has been widely used in speech signal processing to extract long-distance dependencies in speech signals. In contrast to LSTM, the Transformer model incorporates a self-attention mechanism and position encoding to effectively capture long-distance relationships within the input sequence. Thus, this paper explores the application of the Conformer model in the field of structural damage identification, combining the local feature extraction capability of CNNs with the long-term sequence modeling capability of Transformers to fully describe the information of the response signal. Notably, this is the first time that DCPS and Conformers have been integrated and applied to structural damage detection.

2. Methodology

2.1. The Equation of Motion

The equation that describes the motion of a linear system with n degrees of freedom (DOFs) [38] is as follows:

$$\mathit{M}\ddot{\mathit{u}}\left(t\right)+\mathit{C}\dot{\mathit{u}}\left(t\right)+\mathit{K}\mathit{u}\left(t\right)=\mathit{F}\left(t\right)$$

(1)

where M, C, and K denote $n\times n$ matrices representing mass, damping, and stiffness. Meanwhile, $\mathit{u}\left(t\right)$, $\dot{\mathit{u}}\left(t\right)$, and $\ddot{\mathit{u}}\left(t\right)$ are $n\times 1$ vectors representing displacement, velocity, and acceleration. Additionally, $\mathit{F}\left(t\right)$ is $n\times 1$ a vector representing excitation.

It is generally assumed that damage to a structure only results in a decrease in stiffness and does not cause a change in mass. Prior to damage, the stiffness matrix and flexibility matrix of the structure are denoted as ${\mathit{K}}_u$ and ${\mathit{F}}_u$, respectively. After damage, the stiffness matrix and flexibility matrix of the structure are denoted as ${\mathit{K}}_d$ and ${\mathit{F}}_d$, respectively. The subscripts d and u represent the states after damage and before damage, respectively. The change in the overall stiffness matrix of the structure, before and after damage, is denoted as $∆\mathit{K}$ [39].

$$∆\mathit{K}={\mathit{K}}_u-{\mathit{K}}_d$$

(2)

This can be further expressed as the linear superposition of elemental stiffness matrices.

$$∆\mathit{K}=\sum _{i=1}^n{a}_i{K}_u^i$$

(3)

where $K_u^i$ denotes the stiffness matrix of the i-th element in the structure, and $a_i(0\le a_i\le 1)$ represents the damage coefficient.

Structural damage detection and the acceleration response are closely related in the field of SHM. The acceleration response refers to the measurement of the acceleration generated by a structure under various loads or external forces. In the context of structural damage detection, response data are collected using acceleration sensors placed at critical points on the structure. The collected data are then analyzed to identify any abnormal patterns or deviations from the expected behavior of a healthy structure. This analysis can reveal valuable insights into the presence and location of structural damage. Different methods and algorithms, such as the modal analysis, frequency-based analysis, and time–frequency analysis, can be applied to the response data for damage detection and localization. By comparing the response data with baseline or reference data, engineers can identify changes in the structural dynamics that may indicate damages. Additionally, the amplitude and frequency characteristics of the acceleration response can provide information about the severity and type of damage, such as cracks, fractures, or deformations. Overall, the acceleration response data play a crucial role in the process of structural damage detection, enabling engineers to assess the structural integrity and make informed decisions regarding the maintenance, repair, or further investigation of the damaged structure.

This study proposes a method for detecting structural damage by combining a dual-channel pseudo-supervised learning strategy (DCPS) with a Conformer model, using structural acceleration response data. The DCPS is applied to structural damage detection, enabling the model to acquire noise immunity instead of manual denoising.

2.2. Data Preprocessing

To acquire acceleration response data, it is assumed that n sensors are deployed on the h-th floor of the structure, with m sensors measuring the translational acceleration in the x direction and k sensors measuring the translational acceleration in the y direction. During response data collection, the sampling frequency of each sensor is $f_s$, and the sampling time is $t_s$, resulting in the number of sampling points $S_j$ per sensor being $S_j=f_s\times t_s$. In this paper, Equation (4) was used to fuse the acceleration response data from the co-oriented sensors on the h-th floor to obtain the fused translational accelerations in the x and y directions of this floor [40]. Equation (4) is as follows:

$$\left\{\begin{array}{c}ac{c}_{x,h}={\displaystyle \frac{1}{m}}\times \left(ac{c}_{x,1,h}+ac{c}_{x,2,h}+\dots +ac{c}_{x,i,h}+\dots +ac{c}_{x,m,h}\right)\\ ac{c}_{y,h}={\displaystyle \frac{1}{k}}\times \left(ac{c}_{y,1,h}+ac{c}_{y,2,h}+\dots +ac{c}_{y,i,h}+\dots +ac{c}_{y,k,h}\right)\end{array}\right.$$

(4)

where ${acc}_{x,i,h}$ and ${acc}_{y,i,h}$, respectively, denote the translational acceleration response data collected by the i-th sensor in the x and y directions of the h-th floor, and ${acc}_{x,h}$ and ${acc}_{y,h}$ denote the fused translational acceleration in the x and y directions of the h-th floor. The variables m and k denote the number of sensors in the x and y directions of the h-th floor, respectively. All of these data are one-dimensional time series with $S_j$ data points.

Subsequently, fused translational acceleration data are sequentially divided into w nonoverlapping samples, each consisting of 128 continuous data points [41]. Each sample is then independently normalized and marked with the corresponding damage pattern label. The processed data are defined as ${acc}_{x,h}^{\prime }$ and ${acc}_{y,h}^{\prime }$. Afterward, ${acc}_{x,h}^{\prime }$ and ${acc}_{y,h}^{\prime }$ are randomly shuffled. Assuming the damage detection task includes q damage patterns, the acceleration response data under each damage pattern are processed using the aforementioned method. After processing, the response data for the x and y directions on the h-th floor under the r-th damage pattern are denoted as ${acc}_{x,h,r}^{\prime }$ and ${acc}_{y,h,r}^{\prime }$, respectively. The subsets constructed from the response data of the q damage patterns in the x and y direction of the h-th floor are, respectively, expressed as follows:

$$D_{x,h}=\left[\begin{array}{c}{acc}_{x,h,1}^{\prime }\\ {acc}_{x,h,2}^{\prime }\\ \cdots \\ {acc}_{x,h,q}^{\prime }\end{array}\right]$$

(5)

$$D_{y,h}=\left[\begin{array}{c}{acc}_{y,h,1}^{\prime }\\ {acc}_{y,h,2}^{\prime }\\ \cdots \\ {acc}_{y,h,q}^{\prime }\end{array}\right]$$

(6)

Assuming the structure has d floors, the intact translational acceleration dataset D, composed of the subsets of the response data in the x and y directions of each floor, can be denoted as follows:

$$D=\left[D_{x,1}{D}_{y,1}\cdots D_{x,h}{D}_{y,h}\cdots D_{x,d}{D}_{y,d}\right]$$

(7)

2.3. Dual-Channel Pseudo-Supervised (DCPS) Learning

To improve the noise immunity of the network model, a learning strategy based on DCPS learning is proposed in this paper. DCPS learning consists of two parallel channels whose inputs are different data-augmented versions from the same signal. In this paper, the inputs to the dual-channel network are signals with different levels of noise introduced. Subsequently, segmentation confidence maps for signals with two levels of noise are obtained through the same network architecture with different initial weights or two different network architectures, as follows:

$${\mathit{p}}_a=f\left(X_a;W_a\right)$$

(8)

$${\mathit{p}}_b=f\left(X_b;W_b\right)$$

(9)

where $X_a$ and $X_b$ denote the input signal $X$ with different levels of noise, respectively, $W_a$ and $W_b$ are the parameters of two networks, and ${\mathit{p}}_a$ and ${\mathit{p}}_b$ represent segmentation confidence maps after softmax normalization. According to the segmentation confidence maps, the predicted values ${\mathit{y}}_a$ and ${\mathit{y}}_b$ of two networks, expressed as one-hot vectors, can be further obtained. There is a supervised loss L and a DCPS loss to jointly drive model network learning to improve the noise immunity, which are defined as follows:

$$L={\displaystyle \frac{1}{\left|B\right|}}\sum _{i=0}^{\left|B\right|}\left({\mathcal{l}}_{ce}\left({\mathit{p}}_{ai},{\mathit{y}}_i^{*}\right)+{\mathcal{l}}_{ce}\left({\mathit{p}}_{bi},{\mathit{y}}_i^{*}\right)\right)$$

(10)

$$L_d={\displaystyle \frac{1}{\left|B\right|}}\sum _{i=0}^{\left|B\right|}\left({\mathcal{l}}_{ce}\left({\mathit{p}}_{ai},{\mathit{y}}_{bi}\right)+{\mathcal{l}}_{ce}\left({\mathit{p}}_{bi},{\mathit{y}}_{ai}\right)\right)$$

(11)

where $B$ is the batch size, ${\mathcal{l}}_{ce}(·)$ denotes the cross-entropy loss function, and ${\mathit{y}}_i^{*}$ indicates the ground truth. The supervised loss $L$ represents the degree of inconsistency between the network predictions and the true values corresponding to the original data in two parallel channels with different noise levels. Meanwhile, the DCPS loss $L_d$ is a manifestation of the mutual supervision and constraint of the different channels, which encourages the prediction of the same input signal at different noise levels to be consistent across channels. In this case, the one-hot predictions output from one network are used to supervise the confidence map of the other network.

Next, the supervised loss $L$ and the DCPS loss $L_d$ are combined to form the complete loss function:

$$LOSS=\alpha L+\left(1-\alpha \right)L_d$$

(12)

where $\alpha$ denotes a linearly decreasing parameter ranging from 0 to 1. It determines the weight of the supervised loss $L$ and the DCPS loss $L_d$. As the number of training iterations increases, the weight of the supervised loss $L$ decreases, while the weight of the DCPS loss $L_d$ increases. This adjustment is made to reflect the increasing stability of DCPS learning during the later stages of training.

2.4. Conformer Module

One of the key factors contributing to the successful application of the CNN-LSTM architecture in structural damage detection methods is its capability to capture both the local and global features of signals. Recent studies [42] have shown that Transformers based on self-attention mechanisms have a better ability to capture global features than LSTMs. Based on this, we investigated and studied a Transformer model that includes CNNs and self-attention mechanisms and introduced it into structural damage detection methods to extract more effective local and global features. As shown in Figure 1, the Conformer contains multiple Conformer blocks, each of which is mainly composed of a feedforward module, a self-attention module, and a convolutional module. By alternately extracting features through convolution modules and self-attention modules, local and global features in the signal are effectively extracted.

Unlike the absolute position encoding of classical Transformer networks, in order to enable the model to effectively capture long-distance dependencies, relative position encoding [43] is incorporated into the self-attention module. Also, the self-attention module employs a multi-head self-attention mechanism, and H attention heads perform self-attention on the sequence and then concatenate the results of the H heads. The calculation for each attention head is as follows:

$$Att\left(A,V\right)=softmax\left(A\right)V$$

(13)

$$A_{ij}=Q_i^T{K}_j+Q_i^T{W}_R{R}_{ij}+u^T{K}_j+v^T{W}_R{R}_{ij}$$

(14)

$$[Q,K,V]=E_x\left[W_Q,W_K,W_V\right]$$

(15)

where $softmax(·)$ represents the softmax function; $E_x$ denotes the token-embedding lookup or the output of the upper level Conformer, and $W_Q$, $W_K$, $W_V$, $W_R\in {\mathbb{R}}^{d_{model}\times d_{head}}$, $u$, and $v\in {\mathbb{R}}^{d_{head}}$ are learnable parameters. $d_{model}=H\times d_{head}$, $d_{head}$ denotes the dimension of each attention head, and $R_{ij}$ denotes a sinusoidal encoding matrix [42].

Assuming $x_i$ is defined as the input and output of the i-th Conformer module, and the output $y_i$ is calculated as follows:

$$x_i^{ffn}=x_i+{\displaystyle \frac{1}{2}}{f}_{FFN}\left(x_i\right)$$

(16)

$$x_i^{sa}=x_i^{ffn}+f_{SA}\left(x_i^{ffn}\right)$$

(17)

$$x_i^{conv}=x_i^{sa}+f_{Conv}\left(x_i^{sa}\right)$$

(18)

$$y_i=f_{Layernorm}\left(x_i^{conv}+{\displaystyle \frac{1}{2}}{f}_{FFN}\left(x_i^{conv}\right)\right)$$

(19)

where $f_{FFN}(·)$, $f_{SA}(·)$, and $f_{Conv}(·)$ represent the feedforward module, the self-attention module, and the convolution module, respectively, and $f_{Layernorm}(·)$ denotes the layer normalization. This sandwich structure was proposed by reference [44].

2.5. The Process of the Algorithm

Figure 2 illustrates the pipeline of the proposed model that combines the DCPS learning strategy and Conformers for detecting structural damage. Initially, the raw data from various acceleration response signals undergo different noise-addition processes and are then input into dual-channel networks. Two Conformer networks, having the same architecture but different randomly initialized weights, are used to predict the segmentation confidence maps of the two signals and obtain one-hot labels. In the next step, one network utilizes the output of the other network as a label and applies a cross-entropy loss for cross-channel learning and network training.

The procedures are summarized as follows. Step 1: Data Collection and Preprocessing—collect structural acceleration response data related to structural damage preprocess and process it. Step 2: Data Partitioning and Annotation—divide the dataset into training, validation, and testing sets, and each dataset is annotated with its impairment category. Step 3: Model Building and Training—train a DCPS learning and Conformer model using the training and validation data. Step 4: Model Evaluation—evaluate the trained model using the testing set. Step 5: Application—Deploy the trained model into practical applications for the real-time identification and monitoring of structural damage. This can involve integrating the model into existing systems or creating a new application for this purpose.

3. Validation by a Numerical Model

3.1. IASC-ASCE SHM Benchmark Dataset

The IASC-ASCE SHM research group established the IASC-ASCE SHM simulated benchmark structure [45] in 2003. This benchmark structure aimed to create a standardized platform for evaluating structural damage detection methods. It enables researchers to compare and analyze different structural damage detection methods. In this section, we used its numerical model for testing and evaluation.

As shown in Figure 3, the IASC-ASCE SHM benchmark model is a four-story, 2 × 2-span, steel-frame model with a floor height of 0.9 m and a plan size of 2.5 m × 2.5 m and which is 1.25 m per span. The model has 9 steel columns on each floor and is set up with 8 diagonal supports. More information about this benchmark model can be found in reference [45].

Gaussian white noise is a common method for simulating environmental excitation [46,47]. In this paper, Gaussian white noise was used as the excitation signal to induce structural vibrations. This noise excitation was generated through a random process following a normal distribution. As a result, it has a flat power spectral density across the frequency domain and uniform energy distributions across all frequencies. Its power spectral density can be expressed as follows:

$$S(f)={\displaystyle \frac{N_0}{2}}$$

(20)

where $S\left(f\right)$ is the power spectral density at frequency $f$, and $N_0$ is the noise power spectral density. With an equal amount of energy in each frequency component, this noise signal effectively excites various vibrational modes within the structure, providing comprehensive excitation for accurately assessing the structure’s dynamic response under various conditions.

To evaluate the effects of noise on the proposed damage detection method, a series of Gaussian random pulses was introduced into the numerically calculated acceleration response data of the IASC-ASCE SHM benchmark structure [45].

$${\tilde{x}}_i=x_i+\left\{{\displaystyle \frac{e}{100}}\times {RMS}_{max}\times v_i\right\}$$

(21)

where ${\tilde{x}}_i$ and $x_i$ denote the acceleration responses of the i-th sensor with added noise and without noise, respectively. The variable e represents the noise percentage, for example, e = 20 means that 20% of the noise is considered. ${RMS}_{max}$ is the maximum value of the root mean square (RMS) of the acceleration responses measured by all sensors on the structure. $v_i$ denotes a set of Gaussian random variables generated using the MATLAB 2022b routine ‘randon’, with a mean value of zero and a standard deviation of one. In this study, three distinct levels of noise were taken into account, which were 0%, 20%, and 50%, respectively.

As shown in

Table 1. The D.P.0, D.P.1, D.P.2, and D.P.4 damage patterns, as defined in the IASC-ASCE SHM benchmark structure.

Damage Mode	Mode Description
D.P.0	No damage
D.P.1	No stiffness in the braces of the first story
D.P.2	No stiffness in any of the braces of the first and third stories
D.P.4	No stiffness in one brace in the first story+No stiffness in one brace in the third story

, this study focuses on the four damage patterns of D.P.0, D.P.1, D.P.2, and D.P.4 defined in case 4 of the IASC-ASCE SHM benchmark. Figure 4 shows model diagrams of the three damage patterns of D.P.1, D.P.2, and D.P.4, and D.P.0 is shown in Figure 3.

As shown in Figure 5, four acceleration sensors were deployed on each floor of the IASC-ASCE SHM simulated benchmark structure. Each sensor recorded 800 s of acceleration data at a sampling frequency of 250 Hz under the noise levels of 0%, 20%, and 50%, respectively. This resulted in each sensor collecting 200,000 data points for each damage pattern. The collected response data were preprocessed according to the methods described in Section 2.2. At every noise level, the subset with four damage patterns in any direction on a single floor consisted of 6248 samples. Of these, 4000 samples were allocated to the training set, 1000 samples to the validation set, and 1248 samples to the testing set. These datasets served as inputs for the model. The model was presented using data from one of the floors in one direction, denoted as $X\in R^{n\times d}$, where n represents the number of time steps in the sequence, and d denotes the dimensionality of the feature vector at each time step. In the practical implementations, each floor was set up with the same network model in each direction to obtain its damage detection output separately.

3.2. Network Models and Settings

Baseline models. To evaluate the effectiveness of the proposed model on a structural damage detection task, we used a 1D CNN, LSTM, and multi-head CNN as baseline models. Among these, 1D CNN and LSTM are classical CNN and RNN architecture models, respectively, commonly used in structural damage detection research. The multi-head CNN is a variant of the CNN model. The details of the baseline models are described as follows:

• One-dimensional CNN: This model can be used to process acceleration response data, where the convolution layer can capture the local features of the signal. In this paper, two convolutional kernels of size 5 were used for convolution operations.
• LSTM: The LSTM model can capture long-range dependencies in sequence data through the gate-control mechanism, enabling the learning of crucial long-range dependency features. This model was constructed as a two-layer bidirectional LSTM with the dimension of 128 in this paper.
• Multi-head CNN: By introducing multiple parallel convolutional branches (heads), this model can learn features at different scales. Each branch focuses on different time- or frequency-domain information, and the multiple branches are eventually fused to provide a comprehensive description of the structural damage.

To further validate the effectiveness of integrating local and global features for structural damage detection and to assess the efficacy of combining CNNs and the self-attention mechanism in the Conformer network, we also included CNN-LSTM and Transformers as additional baseline models. The details of the Transformer and CNN-LSTM models are presented as follows:

• CNN-LSTM: This model, in this paper, first used a 1D CNN with a convolutional kernel of 15 to extract spatial features. Then, a two-layer LSTM model with 256 dimensions was used for long-sequence modeling.
• Transformers: Through the self-attention mechanism, the transformer model can effectively capture global dependencies in sequences. In structural damage detection, it models the acceleration response data collected by sensors to learn features related to identifying damage. In this paper, we constructed a four-layer Transformer block with 8 heads and with a dimension of 512.

Furthermore, to evaluate the performance of DCPS learning, in addition to Conformer+Conformer, we compared the combinations of CNN+CNN and CNN+Conformer, as shown in Figure 6. Finally, we conducted tests at multiple noise levels to demonstrate the improvement of model noise immunity through DCPS learning and its robustness.

Hyperparameters: For the Conformer model and models in DCPS learning, the Adam optimizer was used for a gradient descent, and the learning rate was 0.0001. The batch size was set to 32, and a total of 300 epochs were used for training and validation. In addition, we used 4 Conformer blocks and set 2 heads in the multi-head self-attention layer, with a dropout of 0.4 for the self-attention module and a dropout of 0.1.

3.3. Comparative Experimental Results

The testing results in the x direction on the initial floor of simulated data from the IASC-ASCE SHM benchmark structure were utilized for a comparative analysis, and classification accuracy (ACC) was used as an indicator to measure the performance of each model. The training set experienced 5% and 20% noise augmentations. This involves directing the training data into two distinct channels within the DCPS architecture, facilitating the acquisition of noise-robust features by the proposed model.

Table 2. Detection accuracy (%) results and inference time (s) of baseline models for tests conducted on the IASC-ASCE SHM benchmark simulated dataset.

Model	1D CNN	LSTM	Multi-Head CNN	CNN-LSTM	Transformer	Conformer
ACC	89.10	88.22	92.39	92.55	94.07	95.19
Time(s)	0.57 × 10−3	3.2 × 10−3	1.0 × 10−3	2.9 × 10−3	1.0 × 10−3	1.6 × 10−3

presents the accuracy performance and inference time of different models on the IASC-ASCE SHM benchmark dataset. Table 2 shows that the CNN-LSTM and Conformer models, which extracted both local and global features, achieved higher accuracy than the CNN and multi-head CNN models, which only extracted local features, and the LSTM model, which only extracted global features. Since the Conformer model has the local information representation ability of CNNs and also inherits the long-sequence temporal modeling ability of Transformers, it achieved the best classification accuracy, reaching 95.19%. The classification performance of the Conformer was 2.64% higher than that of CNN-LSTM, which considers both local and global features; 6.09% higher than that of 1D CNN, which only considers local features; and 6.97% higher than that of LSTM, which only considers global features. The Conformer model achieves the highest prediction performance among the compared models. Moreover, it has a very low computational cost, requiring only about three times the computational resources of the fastest CNN model, which has the lowest accuracy. This indicates that the proposed model effectively balances performance and computational efficiency.

To verify the effectiveness of the DCPS learning strategy,

Table 3. Detection accuracy (%) of different network combinations for tests conducted on the IASC-ASCE SHM benchmark simulated data.

Model	1D CNN	Conformer	CNN+CNN	CNN+Conformer	Conformer+Conformer
ACC	89.10	95.19	94.23	95.99	96.96

presents the gains achieved using the different network combinations (i.e., CNN+CNN, CNN+Conformer, and Conformer+Conformer). These tests were conducted on the IASC-ASCE SHM benchmark simulated dataset. In Table 3, “+” means the network architecture of each branch of the DCPS. Figure 6 intuitively shows the different network combinations used in the DCPS learning strategy. From Table 3, it can be seen that the performances of the single CNN model and the Conformer model are 89.1% and 95.19%, respectively. The models utilizing DCPS learning generally exhibited superior performance compared to those without it. In particular, the performances of CNN+CNN and Conformer+Conformer were 5.13% and 1.77% higher than those of the single CNN and Conformer model, respectively. Since the DCPS learning strategy took different levels of noise signals as the input, the classification results of the same network architecture with different initialization weights were used as the target to perform cross-channel learning. Driven by a DCPS learning strategy, this network was robust to different levels of noise signals. Finally, a more accurate classification performance was obtained. In addition, we used a different network architecture (i.e., CNN+Conformer) for DCPS learning and also achieved performance improvements relative to the single CNN or Conformer model. This means that this DCPS learning strategy can generalize to different models. Note that the two-channel pseudo-supervised learning strategy is performed during training, so it does not increase the computational cost of the model during testing.

3.4. Ablation Study

To demonstrate the advantage of the DCPS learning strategy in improving noise robustness, the noise augmentation step was omitted for the training set, as outlined in the preceding subsection. Specifically, the training set within the input DCPS architecture was exempt from noise addition. The results are presented in

Table 4. Detection accuracy (%) with and without noise augmentation using the DCPS learning strategy. ‘Noisy’ indicates that the noise augmentation step of the training set is used, and ‘Noiseless’ means that the noise augmentation step is omitted.

Model	CNN+CNN		CNN+Conformer		Conformer+Conformer
Noise handling of the training set	Noisy	Noiseless	Noisy	Noiseless	Noisy	Noiseless
ACC	94.23	93.43	95.99	95.91	96.96	96.88

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The ACC results of the CNN+CNN, CNN+Conformer, and Conformer+Conformer models with the training noise removed, exhibited a simultaneous decrease. This observation suggests that the DCPS strategy, which includes noise addition in the training, plays a crucial role in training the models to achieve a better noise-robust performance. This indicates that the DCPS strategy is capable of maintaining high performance in feature learning and task classification even in highly noisy environments. The proposed model, with its ability to accurately extract noise-robust and comprehensive features, demonstrates its effectiveness in dealing with noise and achieving a robust performance.

3.5. Comparative Analysis at Different Noise Levels

Lastly, the accuracy results of different models were compared using the complete IASC-ASCE SHM benchmark simulated data for in-depth research and a comprehensive analysis. This evaluation encompassed the entire dataset across different noise levels. Through this study, the aim is to demonstrate the exceptional capabilities of the proposed model in environments characterized by high levels of noise, thereby reaffirming its noise robustness.

Table 5. Accuracy results (%) of different models for tests conducted on the complete IASC-ASCE SHM benchmark simulated data at different noise levels. Average results are bolded to emphasize the average performance of each model at each noise level.

Noise Level (%)	Direction	Floor	CNN	Multi-Head CNN	Conformer	CNN+Conformer *	Conformer+Conformer *
0	x	1	89.10	92.39	95.19	95.99	96.96
0	x	2	84.62	94.15	96.79	97.04	97.68
0	x	3	86.30	93.83	95.99	97.76	98.16
0	x	4	68.19	92.63	96.15	96.07	97.12
0	y	1	86.70	94.47	95.99	95.99	96.39
0	y	2	75.80	96.15	96.88	97.52	97.68
0	y	3	75.64	94.55	95.43	96.23	97.36
0	y	4	67.87	96.31	97.04	97.44	97.60
Average ACC at 0% noise level			79.28	94.31	96.18	96.76	97.37
20	x	1	85.02	90.79	92.55	94.23	95.11
20	x	2	81.89	94.15	96.39	96.63	97.44
20	x	3	85.18	92.95	94.23	95.35	96.71
20	x	4	71.07	91.99	95.51	96.23	97.12
20	y	1	81.89	94.63	94.47	96.07	96.47
20	y	2	67.71	95.19	96.63	96.88	97.36
20	y	3	68.67	93.59	95.19	95.51	96.31
20	y	4	67.63	96.31	97.04	97.52	97.84
Average ACC at 20% noise level			76.13	93.70	95.25	96.05	96.80
50	x	1	75.72	85.98	86.54	88.94	90.87
50	x	2	70.51	91.19	93.27	94.87	95.27
50	x	3	72.92	90.06	92.39	93.75	94.31
50	x	4	64.74	90.14	94.39	94.55	95.35
50	y	1	74.28	91.51	91.59	93.35	93.75
50	y	2	60.02	89.82	92.63	93.19	94.39
50	y	3	60.58	89.66	92.39	92.79	93.59
50	y	4	61.30	95.03	95.35	96.15	96.79
Average ACC at 50% noise level			67.51	90.42	92.32	93.45	94.29
Average			74.31	92.81	94.58	95.42	96.15

* represents structural damage identification methods that combine the conformer model and the DCPS learning strategy.

provides the detailed results. Some conclusions were obtained. First, the single CNN, the Conformer, or the multi-head CNN model had a higher classification accuracy in low-noise signals. As the noise level increases, the classification accuracy also dropped significantly. Secondly, it can be seen that there was a smaller gap in the performance of the different noise levels when using a DCPS training model (i.e., CNN+Conformer and Conformer+Conformer). This means that the noise robustness of the model is improved after DCPS training. Note that DCPS learning was of great significance in practical applications for the noise robustness brought by the model, since the noise in the acceleration response signal was more complex. Finally, the proposed models (i.e., CNN+Conformer and Conformer+Conformer) achieved an average accuracy of 95.42% and 96.15%, respectively, surpassing all existing traditional models.

To intuitively demonstrate the classification accuracy of the Conformer+Conformer model under different noise levels, the confusion matrices of the Conformer+Conformer model under two high-noise-level conditions are presented in Figure 7. As can be seen from Figure 7, D.P.0 and D.P.4 are occasionally confused. This phenomenon was mainly attributed to intra-class differences in D.P.4 (or D.P.0), which led to the collected training data not fully covering all instances of damage in this pattern. But overall, the classification accuracy of Conformer+Conformer was close to 1.

These aforementioned results unequivocally showcase the effectiveness of the proposed model in the field of structural damage detection. The model exhibited remarkable performance improvements across various noise levels for the IASC-ASCE SHM benchmark simulated dataset. Furthermore, the compatibility and transferability of the DCPS strategy were evident, as networks with both identical and distinct structures consistently achieved superior performance.

4. Experimental Verification on a Four-Story Steel-Frame Structure

The previous section validated the proposed method in this paper using the numerical model of the IASC-ASCE SHM benchmark structure. This section uses an experimental study based on a laboratory four-story steel-frame structure to verify the effectiveness of the proposed method and its applicability in different applicational scenarios.

4.1. Experimental Description

In Figure 8, the experimental model is a four-story single-span steel-frame structure. The model is 320 mm × 260 mm in plan size, with an overall height of 672 mm. The height of each floor is 168 mm. All floor slabs in the model are constructed from 16 mm-thick steel plates, while the columns are made of solid round steel with a height of 152 mm and a cross-sectional diameter of 16 mm. All structural elements are made of Q235 steel, with a nominal yield stress of 235 MPa. To induce structural vibrations, a Donghua DH40100 (DongHua Testing Technology Co., Ltd., Jingjiang, China) electrodynamic exciter was used to apply white Gaussian noise excitation along the southeast–northwest diagonal on the first floor of the model, and the duration of the excitation was 800 s. The structural response was measured by the Donghua 1A401E acceleration sensors, and these sensors were instrumented at midspan positions on each of the four edges of each floor plate. The acceleration data were acquired using the Donghua DH8303 data acquisition system. In this study, Gaussian white noise excitation was used as the excitation signal to induce structural vibrations, and the resulting acceleration response of the structure served as the measured signal.

In this study, three types of columns with different cross-sectional diameters were employed, as depicted in Figure 9. The structural damage was achieved by replacing original columns at the southeast corner of one or more floors with columns that have a cross-sectional diameter of 14 mm or 12 mm. We simulated a total of six different damage scenarios, which are fully listed in

Table 6. Damage scenarios as specified in the experimental structure.

Damage Case	Description
D.P.0	Without damage (the columns at the southeast corner of floors 1–4 all have a diameter of 16 mm).
D.P.1	Replaced the column on the first floor with a 14 mm-diameter column.
D.P.2	Replaced the column on the second floor with a 14 mm-diameter column.
D.P.3	Replaced the column on the third floor with a 14 mm-diameter column.
D.P.4	Replaced the column on the fourth floor with a 14 mm-diameter column.
D.P.5	Replaced the columns on the first and second floors with 14 mm- and 12 mm-diameter columns, respectively.

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4.2. Experimental Procedure

The experimental structure was vibrated by the exciter. Next, acceleration data from all sensors were collected at a sampling frequency of 250 Hz for an acquisition duration of 800s. This resulted in 200,000 data points being collected in each scenario. Figure 10a,b illustrates the acceleration response time histories in the y direction on the fourth floor under the undamaged state. Subsequently, all collected data were processed using the data-processing method described in Section 2.2. Each processed dataset consisted of 9372 samples. Among these, 6000 samples were assigned to the training set, 1500 to the validation set, and 1872 to the testing set. Ultimately, eight classifiers were trained using training sets (4 stories × 2 translational directions).

4.3. Experimental Results

To accurately assess the effectiveness and generalizability of the proposed method in this paper, we conducted a comparative analysis of the detection accuracy among five different deep learning models, namely, the CNN, LSTM, multi-head CNN, CNN-LSTM, Transformer, Conformer, CNN+Conformer, and Conformer+Conformer models, using a four-story single-span steel-frame structure. The damage detection accuracy results are summarized in

Table 7. Damage detection accuracy across different floors and directions (%).

Floor/ Direction	CNN	LSTM	Multi-Head CNN	CNN-LSTM	Transformer	Conformer	CNN+Conformer	Conformer+Conformer
First floor, x direction.	80.98	84.45	87.44	89.36	89.52	91.18	93.53	94.33
First floor, y direction.	77.78	82.10	85.73	83.17	87.01	93.37	94.28	98.93
Second floor, x direction.	76.01	86.59	84.45	83.49	86.43	91.93	92.41	94.12
Second floor, y direction.	82.05	84.93	88.46	88.35	87.23	93.48	94.92	99.57
Third floor, x direction.	81.20	83.60	84.72	84.82	84.61	88.67	89.63	92.84
Third floor, y direction.	76.33	86.37	84.50	87.60	85.95	91.72	92.78	98.77
Fourth floor, x direction.	74.47	79.22	82.63	86.53	88.19	91.93	94.28	95.56
Fourth floor, y direction.	78.63	84.13	88.40	89.74	91.82	91.40	92.57	98.98
Average	78.43	83.92	85.79	86.63	87.60	91.71	93.05	96.64

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As shown in Table 7, hybrid models (i.e., CNN+Conformer and Conformer+Conformer) achieve average accuracies of 93.05% and 96.64%, significantly surpassing the Conformer (91.71%), Transformer (87.60%), CNN-LSTM (86.63%), multi-head CNN (85.79%), LSTM (83.92%), and CNN (78.43%) models. Notably, the hybrid models consistently outperformed the single models in all directions at each floor. This consistent high accuracy suggests that the DCPS learning strategy significantly improved the model’s performance. Furthermore, the superior performance of hybrid models highlights the benefits of combining advanced network architectures with the DCPS learning strategy.

5. Conclusions and Discussion

In conclusion, this study introduces a novel method for structural damage detection, combining the DCPS learning strategy and the Conformer network. The DCPS learning strategy ensures consistent classification results for the same input signal at different noise levels. By utilizing parallel channels at varying noise levels to supervise each other, this novel learning strategy enhances the learning of noise-robust features. The Conformer network, which merges the advantages of CNN and Transformer networks, captures both local and global characteristics of acceleration response signals. The effectiveness of the proposed method was validated by using the IASC-ASCE SHM benchmark structure numerical model and a four-story single-span steel-frame experiment. Notably, this is the first successful application of combining the DCPS learning strategy with the Conformer model for structural damage detection. The following conclusions can be drawn:

• Existing methods focus on either local information [19,20,21,22,23] or global information [24,25,26]. Although some works combine the advantages of CNNs and LSTM [27,28,29], the weak performance of LSTM in processing long-term dependencies of signals is still inevitable. The proposed model uses a Conformer as the backbone network, effectively combining the local feature extraction capability of CNNs with the long-term sequence modeling capability of Transformers to fully describe the local and global information of the response signal.
• The proposed model uses the DCPS learning strategy to make the model learn the consistency of different noise signals. Compared with the manual denoising method [34,35], the proposed model improves the noise robustness of the model and is more suitable for engineering practices.
• The proposed models, CNN+Conformer and Conformer+Conformer, achieve average identification accuracies of 95.42% and 96.15% in numerical simulations and 93.05% and 96.64% in laboratory experiments, markedly outperforming baseline models. This high accuracy underscores the potential of the proposed model as an effective solution for structural damage detection and demonstrates its robust to different scenarios.
• The proposed method achieves average accuracies of 96.3% and 93.0% at 20% and 50% noise levels, respectively, significantly outperforming baseline models. These results demonstrate the ability of the proposed model to learn noise-robust features without manual denoising. This method greatly simplifies the application process and improves detection accuracy in noisy environments.

In future work, to improve the understanding and representation of node features by the model and to learn more robust node representations, we will explore how to model the correlations between nodes of different structures through graph neural networks.