AT-StarGAN-GP: Attention-enhanced multi-domain signal translation for structural health monitoring

Problem formulation

The data processing transforms raw structural vibration signals into a format optimized for the AT-StarGAN-GP framework while preserving physical relationships among measurement points, as illustrated in Figure 2. A signal concatenation technique merges acceleration data from all 30 sensor locations into a unified signal matrix. Segmenting these signals into overlapping windows of 256 samples captures dynamic structural changes across both time and space domains. This concatenation preserves the temporal correlations within each individual sensor signal and the spatial dependencies among different joints.

OPEN IN VIEWER

Figure 2.

AT-StarGAN-GP model architecture.

The system employs labeling with 31 damage states, including the zero label representing the undamaged baseline condition. This enables multi-class conditional generation through CIN, which injects damage scenario information at multiple points within the network. A condition embedding layer converts discrete scenario labels into high-dimensional feature vectors.

The AT-StarGAN-GP architecture processes these concatenated, multi-joint signal matrices. Input channels encode the entire joint dataset, while convolutional layers leverage spatial joint relationships to retain structural coherence. Residual blocks equipped with CIN incorporate damage state information during generation.

Training optimization is governed by a loss function ensemble that combines frequency-domain power spectral matching with structural characteristic preservation via SVD. Model performance is evaluated using comprehensive metrics assessing both cross-class diversity, ensuring the generator produces distinguishable outputs for different damage scenarios, and within-class consistency, which guarantees signal reliability across samples of the same scenario.

Training objective

The training objective guides the model toward generating realistic synthetic damage data that preserve the structural characteristics of the accelerometer signals. This is achieved by combining several complementary loss functions, each addressing a specific aspect of the learning process: adversarial loss encourages realism by forcing generated samples to be indistinguishable from real damage scenarios; classification loss ensures that the generated samples correspond to the desired damage classes; cycle consistency loss promotes reversibility and consistency between domains; identity loss preserve undistorted signals when the target class matches the source; SVD loss encourages the preservation of global structural properties via SVD; frequency loss enforces similarity in the spectral content of real and generated signals; and gradient penalty loss stabilizes training by regularizing the discriminator.

Traditional AI evaluation metrics such as MSE or peak signal-to-noise ratio are inadequate for evaluating GAN-based models, as exact pointwise matches between synthetic and real signals are less critical than preserving underlying physical characteristics such as resonant frequencies, damping behavior, or mode shapes. Therefore, frequency-based evaluation provides a more meaningful assessment by comparing the PSD, dominant frequency components, or Fourier transforms of real and synthetic signals. This approach reflects whether the generated samples retain essential dynamic features that are indicative of particular damage scenarios, making it more aligned with the goals of structural health monitoring and more appropriate than traditional distance-based metrics in the GAN framework. To guide the generator toward producing realistic and physically consistent samples, the model is trained using a combination of loss functions that capture different aspects of signal fidelity, class consistency, and structural characteristics.

○ For the generator:

L adv G = − E x , c [ log D src ( G ( x , c ) ) ]

(1)

where x is the input data, c is the condition (damage scenario), and G ( x , c ) represents the synthetic data generated by the generator. D src is the discriminator function that distinguishes between real and synthetic samples

L adv D = − E x [ log D src ( x ) ] − E x , c [ log ( 1 − D src ( G ( x , c ) ) ) ]

(2)

where x is the real data, G ( x , c ) is the synthetic data generated by the generator. The discriminator tries to maximize this loss, distinguishing real from synthetic data.

The generator attempts to minimize the adversarial loss, while the discriminator maximizes it, leading to a more robust model.

L cls = − E x , c [ log p ( c ∣ x ) ]

(3)

where p ( c ∣ x ) is the probability of class c given input data x . This helps the generator learn to map input data to the correct target class.

This loss helps the generator learn to map input data to the correct target class, while the discriminator becomes better at classifying generated and real samples.

L cycle = E x , c s , c t [ ∥ x − G ( G ( x , c t ) , c s ) ∥ 1 ]

(4)

where x is the input data, c s is the source class, and c t is the target class. G ( x , c t ) represents the transformation of x into the target class, and G ( G ( x , c t ) , c s ) is the transformation back to the source class. The L 1 − norm ensures that the cycle consistency is maintained.

The cycle consistency loss is crucial for preserving the inherent structure of the input data during class transformation.

L rec = E ( x , c s ) [ ∥ x − G ( x , c s ) ∥ 1 ]

(5)

where x represents the input signal data, and c s denotes the source class label, meaning the original damage class of the signal. The function G ( x , c s ) represents the generator’s output when it is conditioned on the same class as the input, ensuring that the signal is reconstructed rather than altered. The L 1 − norm enforces similarity in both amplitude and phase characteristics, making sure that the generator does not distort the signal.

Unlike identity loss, which prevents unnecessary modifications when transforming between classes, reconstruction loss explicitly evaluates the generator’s ability to maintain signal fidelity within the same damage class. This distinction is particularly important in SHM applications, where even minor deviations in reconstructed signals can affect the accuracy of damage detection and classification.

L svd = E ( x , c ) [ ‖ σ ( X ) − σ ( G ^ ( G ( x , c t ) , c ) ) ‖ 2 ]

(6)

Here σ ( X ) denotes the singular values of the original structural response matrix X ∈ R 256 × 30 corresponding to damage class c , and σ ( G ^ ( G ( x , c t ) , c ) ) represents the singular values of the cycle-reconstructed matrix after translating a sample from class c , to a target class c t and back. These matrices reflect spatial-temporal structural behavior, where rows represent 256 time steps and columns correspond to 30 measurement joints. The SVD loss ensures that the generator maintains the key modal properties and structural rank during cycle consistency, preserving the spectral features and dominant mode shapes of each damage state while avoiding unrealistic structural responses.

6. Frequency loss: This loss ensures that the generated signals retain the spectral characteristics of real signals by matching their PSD. The frequency loss is given by:

L freq = 1 B J ∑ b = 1 B ∑ j = 1 J ‖ PSD ( x b , j real ) − PSD ( x b , j fake ) ‖ 2

(7)

where B is the batch size, representing the number of samples processed together during training, and J is the number of joints (30) where acceleration signals are collected. The variable x b , j real represents the real signal at batch index b and joint index j serving as the reference for spectral analysis, while x b , j fake denotes the generated signal for the same batch and joint. The function PSD ( · ) computes the PSD using Welch’s method, which estimates the frequency content of a signal by averaging its periodograms over multiple segments. The L 2 − norm ensures that the PSD differences between real and generated signals are minimized, preserving spectral integrity and improving the realism of synthetic signals.

L gp = E x ^ [ ( ∥ ∇ x ^ D src ( x ^ ) ∥ 2 − 1 ) 2 ]

(8)

where x ^ is a sampled input (often perturbed or interpolated data), and ∇ x ^ D src ( x ^ ) ) represents the gradient of the discriminator with respect to the input x ^ . This term penalizes the discriminator for violating the Lipschitz constraint, maintaining training stability.

This term helps maintain the stability of the training process by penalizing the discriminator for violating the Lipschitz constraint.

The total loss function for the generator and discriminator combines these individual losses, weighted by hyperparameters that control their relative importance. The overall loss for the generator and discriminator is expressed as:

For the generator:

L G = λ adv L adv G + λ cls L cls G + λ cycle L cycle + λ rec L rec + λ id L id + λ freq L freq + λ svd L svd

(9)

where λ adv , λ cls , λ cycle , λ rec , λ id , λ freq , λ svd are the hyperparameters that control the relative weight of each loss term. L rec would represent a reconstruction loss term if included.

L D = λ adv L adv D + λ cls L cls D + λ gp L gp

(10)

where λ gp is the weight for the gradient penalty loss term.

As shown in Figure 3, the discriminator’s dual-headed architecture processes structural vibration signals through parallel paths to ensure comprehensive and nuanced feature extraction. The CNN path (shown in blue) extracts spatial features progressively, utilizing increasing channel depths (64, 128, and 256) across three convolutional layers with sample normalization. Meanwhile, the temporal analysis path (shown in green) uses LSTM layers along with an eight-head self-attention mechanism to capture intricate time-dependent patterns in the vibration data. These complementary features are then fused into a 512-dimensional representation, which is fed to two specialized output heads: one for source discrimination (real/generated vibration signals) and the other for damage scenario classification. This architecture enables the discriminator to simultaneously evaluate both the authenticity of the generated signals and their alignment with the correct damage class, providing essential feedback signals for optimization through both the adversarial and classification loss functions. The strength of this dual-attention architecture lies in its ability to combine CNN-path spatial attention with LSTM-path temporal attention, effectively preserving critical frequency-domain characteristics that are essential for SHM applications. Unlike traditional approaches that primarily focus on time-domain accuracy, our model optimizes directly for PSD matching, a key consideration in SHM tasks. It also preserves SVD characteristics between real and generated data, addressing a fundamental shortcoming of existing methods, where small time-domain errors can lead to significant frequency-domain discrepancies. These frequency-domain features are crucial for accurate anomaly detection in structural systems, making our approach particularly well-suited for identifying subtle damage signatures. In addition, the architecture incorporates an adaptive hyperparameter optimization framework that dynamically adjusts the importance of various loss components based on signal-quality metrics. This adaptive mechanism enables the model to self-adjust to varying sensor noise levels in real-world deployments, ensuring consistent performance even in challenging environments with diverse structural characteristics. This capability drastically reduces the need for manual recalibration, a common obstacle in transitioning SHM technology from controlled lab settings to real-world field applications.

OPEN IN VIEWER

Figure 3.

Discriminator architecture with dual output heads.

Our experimental results demonstrate that the proposed architecture significantly outperforms standard GAN-based methods in preserving characteristic frequencies in generated signals. Furthermore, the model shows enhanced damage localization precision compared to transformer-only approaches, with a marked reduction in false alarm rates during field tests. Despite the additional complexity introduced by the attention mechanisms, our approach achieves faster inference times compared to transformer-only models, making it highly suitable for resource-constrained edge computing environments, commonly encountered in remote SHM deployments where real-time processing is essential. Another key advantage of our dual-attention architecture is its ability to address transfer learning challenges in SHM. Traditional models often require extensive retraining when deployed on new structures, as they struggle to generalize across diverse conditions. Our attention mechanisms are designed to identify and focus on the generalizable aspects of structural responses, such as universal damage signatures and frequency-domain patterns, while the adaptive optimization framework enables model refinement for specific structural characteristics. This architectural design potentially facilitates deployment across varied infrastructure projects, though comprehensive evaluation of transfer learning performance and structure-specific adaptation requirements remains an important direction for future work.

In summary, our dual-attention architecture is not only a computationally efficient method for extracting spatial and temporal features but also addresses core limitations in SHM by optimizing both time-domain and frequency-domain characteristics. This approach ensures that SHM systems based on this model can be deployed with minimal expert intervention, retain accuracy across a wide variety of structural types, and offer high robustness in noisy, real-world environments.

As shown in Figure 4, the generator architecture implements a sophisticated conditional signal generation network specifically designed for structural vibration data. The network processes two inputs: the source vibration signal (256 × 30) and the damage scenario label encoded into an eight-dimensional embedding space. These inputs are combined and passed through an initial convolutional layer with CIN. The network then follows an encoder–decoder structure with skip connections. The encoding path consists of downsampling blocks that increase the channel size (64 → 128 → 256) while reducing the spatial dimensions. The network uses six residual blocks with CIN to execute the core transformation task, thus learning complex damage-specific alterations while maintaining gradient flow. Decoding blocks run in parallel to encoder blocks by implementing steps that both broaden spatial resolution and shrink channel numbers (256→ 128 → 64). An output signal of identical dimensions to the input (256 × 30) comes from the final output layer. Each CIN layer across the network adjusts feature statistics according to the damage condition to effect specific signal alterations for various damage situations.

OPEN IN VIEWER

Figure 4.

Detailed generator architecture of the proposed AT-StarGAN-GP model.

Dynamic optimization

Training of the AT-StarGAN-GP utilizes a complex dynamic optimization approach, which dynamically controls various lambda coefficients. At the start of the model, the baseline lambda parameters equal 10.0 for frequency domain matching and SVD matching, whereas they are set to 5.0 for cycle consistency and identity mapping and 1.0 for classification, adversarial, and diversity components. The model shifts these coefficients through time according to thresholds that measure multiple performance metrics for signal quality. The model begins its adjustment procedure at least 200 training steps to establish baseline stability. During optimization, the system focuses on signal-quality assessment through threshold-based monitoring of both frequency losses and SVD losses, which must not exceed 0.1. The system raises affected lambda values by 1.1 whenever loss metrics surpass predefined thresholds while constraining the adjustments between 1.0 and 20.0 because unstable training needs to be avoided. A period of 50 steps as a cooldown prevents the values from changing rapidly. When the system detects substandard signal matching results, it automatically reduces all lambda weights (adversarial, diversity, reconstruction, and classification) to keep the model oriented toward genuine output creation. The dynamic optimization process uses Weights & Biases logging to monitor lambda values alongside their effects on key performance metrics that combine accuracy metrics with signal quality, alongside loss component definitions. An illustration of this adaptive lambda adjustment strategy is presented in Figure 5.

OPEN IN VIEWER

Figure 5.

AT-StarGAN-GP: Dynamic lambda adjustment strategy.

The dynamic adjustment is formulated as:

λ i new = L i ∑ j L j

(11)

where L i represents the value of each loss term, and ∑ j L j is the total sum of all loss terms. This normalization ensures that each loss term has an appropriate influence on the model’s learning at each step.

This dynamic approach helps the model prioritize losses that significantly contribute to the learning process at various stages of training, preventing one loss from dominating and causing training instability.

In addition, to prevent mode collapse, where the generator starts producing repetitive or limited samples, a diversity regularization term is added to the generator’s loss. This ensures that the generator creates diverse and realistic samples for different damage classes. The diversity between classes is evaluated using cross-class and within-class diversity measures.

1. Cross-class diversity: This measure ensures that generated samples from different damage classes remain distinct. It is formulated as:

Diversity cross = E c i ≠ c j [ ∥ G ( x , c i ) − G ( x , c j ) ∥ 2 ]

(12)

In this equation:

This term penalizes the generator for producing indistinguishable samples across different classes.

Diversity within = E c i [ ∥ G ( x 1 , c i ) − G ( x 2 , c i ) ∥ 2 ]

(13)

It prevents the generator from producing identical samples for the same damage class

where

L div = β ( ∥ G ( x 1 , c i ) − G ( x 2 , c i ) ∥ 2 − δ ) 2

(14)

where β is a weighting factor, and δ is a threshold for the minimum acceptable diversity. This ensures that the generator produces varied and realistic samples. G ( x 1 , c i ) and G ( x 2 , c i ) are the generated samples for two different inputs under the same class c i . The term ∥ · ∥ 2 denotes the L2 norm between the generated samples.

In summary, the methodology leverages dynamic optimization of loss terms and diversity penalties to ensure the AT-StarGAN-GP model generates diverse, realistic synthetic damage data for SHM tasks, such as damage detection and classification. The model’s architecture and loss functions, as described above, are shown in the corresponding figures, which highlight the process flow and optimization steps.

Dataset description

The experimental data were collected from the QUGS, a laboratory-scale steel structure with 30 critical connection nodes, where damage was introduced through systematic bolt loosening. Two independent datasets (dataset A and dataset B) were generated using identical experimental conditions but at different times to ensure robustness. Each dataset contains acceleration measurements from all 30 structural joints across 31 different damage scenarios, including one undamaged baseline condition. The data were collected using white noise excitation via an electromagnetic shaker, with measurements recorded for 256 s at a sampling rate of 1024 Hz, resulting in 262,144 samples per measurement point. The dual dataset approach, with identical experimental setups but independent measurements, enables robust validation of damage detection algorithms, where dataset A can be used for training while dataset B serves as an independent test set, ensuring the developed models can generalize across different measurements of the same structural conditions. ⁵³ As shown in Figure 6, QUGS benchmark structure, these datasets were obtained by collecting acceleration data from structural damage scenarios created by loosening bolts at node points. The steel frame structure consists of 8 beams supported by 4 columns and 25 secondary beams. The main beams span 4.6 m, while among the secondary beams, 5 measure approximately 1 m in length, and the remaining 20 beams each measure 77 centimeters. The structure features two long columns, each approximately 1.65 m in height.^53–58

OPEN IN VIEWER

Figure 6.

QUGS benchmark structure. ³⁹ QUGS: Qatar University Grandstand Simulator.

Data preprocessing and domain (damage scenario) labeling

The data processing pipeline employs a tailored domain labeling methodology to adapt the traditional StarGAN architecture for SHM applications. In this framework, each damage scenario corresponds to a unique domain, resulting in 31 domains: 1 for the undamaged state and 30 for various damage scenarios. The domain labels are systematically assigned based on a structured file naming convention, where the undamaged state is labeled as domain 0, and subsequent damage scenarios are numbered sequentially:

d ∈ { 0 , 1 , … , 30 }

(15)

Here, d denotes the domain label associated with each damage scenario.

The acceleration signals recorded from 30 sensor locations are independently normalized using MinMax scaling, mapping the values to the range [ − 1 , 1 ] For a given sensor, the normalized signal x norm i is computed as:

x norm i = 2 · x i − min ( x i ) max ( x i ) − min ( x i ) − 1

(16)

This normalization procedure ensures that signal ranges are consistent across all sensors while retaining the relative magnitudes of structural responses. The normalized signals are subsequently reorganized into a four-dimensional tensor X ∈ R B × C × T × S , where:

The domain conditioning is implemented through an embedding layer, which maps each damage scenario to a learnable representation space E ∈ R 31 × D , where D = 8 is the embedding dimension. For a given domain label d , the embedded condition c d is expressed as:

c d = E d W + b

(17)

Here, W and b are the learnable parameters of the embedding layer. This embedded representation is then expanded spatially to align with the input dimensions:

c d , expanded = c d ⊗ 1 T × S

(18)

In this expression, ⊗ represents the outer product, and 1 T × S is an all-ones matrix of size T × S .

The normalized signal and the expanded condition are concatenated to form the input to the generator (Figure 7):

x input = [ x norm ; c d , expanded ] ∈ R ( C + D ) × T × S

(19)

This embedding mechanism enables the model to capture meaningful representations of different damage states, enhancing the generation of scenario-specific structural responses. The embedded conditions influence the generator via CIN layers, ensuring that the generated signals accurately reflect the characteristics of each damage scenario.

OPEN IN VIEWER

Figure 7.

Visualization of input signal, embedding layers, and concatenated signal: (a) input signal, (b) embedding layers, and (c) concatenated signal.

CIN layers in the network utilize the domain embedding to modulate feature statistics. For a feature map F, the CIN operation is defined as:

CIN ( F , d ) = γ d ( F − μ ( F ) σ ( F ) ) + β d

(20)

The approach diverges from standard StarGAN applications by focusing on domain labeling for the implementation of physical constraints that exist between structural dynamic systems. The framework enables multidomain translation capabilities through StarGAN while maintaining generated signals that correspond to structural physical constraints.

This domain labeling strategy proves effective as it allows the model to produce authentic structural responses when modeling multiple damage situations. The framework maintains both time-related continuity and spatial interdependence, which exists in structural systems, while demonstrating how StarGAN works with challenging physical data transformation requirements.

Feature scaling and normalization

The preprocessing framework applies a structured, multi-step approach to normalize vibration signals and assign domain labels, ensuring compatibility with downstream processing for SHM. The signals are collected from m = 30 sensors over a duration of T = 256  s, sampled at a frequency of f s = 1024  Hz, yielding N = 262 , 144 samples per channel.

The raw signals are represented by a matrix X ∈ R N × m , where each element x i , j denotes the amplitude recorded by sensor j at time step i . Formally, the matrix can be defined as:

X = { x i , j ∣ i ∈ [ 1 , N ] , j ∈ [ 1 , m ] }

(21)

To address the variability in amplitude ranges across sensors, channel-wise normalization is applied. For each channel j , the normalized signal x i , j ′ is calculated using min-max normalization with a target range of [ − 1 , 1 ] :

x i , j ′ = 2 · x i , j − min ( x : , j ) max ( x : , j ) − min ( x : , j ) − 1

(22)

The normalized matrix X ′ ∈ [ − 1 , 1 ] N × m ensures consistent scaling across all channels, as described in Equation (18)

Normalized signals are divided into fixed-length temporal windows of size w = 256 , capturing localized temporal patterns. The segmentation produces K = ⌊ N w ⌋ segments, where each segment S k is defined as:

S k = { x i , j ′ ∣ i ∈ [ k · w , ( k + 1 ) · w − 1 ] , j ∈ [ 1 , m ] }

(23)

This process yields a segmented tensor S ∈ R K × w × m containing all temporal slices, as shown in Equation (23).

Each signal sequence corresponds to a damage scenario label l ∈ { 0 , 1 , … , 30 } defined as follows:

l = { 0 if undamaged d if damage scenario d }

(24)

Here, l = 0 indicates the undamaged state, while l ∈ [ 1 , 30 ] represents various damage scenarios. The labeling function L ( X ) maps each signal sequence to its corresponding damage scenario, as shown in Equation (24).

The final preprocessed dataset D comprises segment-label pairs:

D = { ( S k , l k ) ∣ k ∈ [ 1 , K ] }

(25)

Each segment S k is paired with its respective damage scenario label l k , maintaining both temporal and spatial relationships within the vibration signals, as indicated in Equation (25).

This preprocessing framework ensures signal fidelity through normalization and segmentation while providing structured labeling for domain translation tasks. It facilitates the AT-StarGAN-GP model’s ability to learn meaningful mappings across damage scenarios, preserving essential vibration signal characteristics critical for effective SHM. Overall, the signal processing pipeline is given in Figure 8.

OPEN IN VIEWER

Figure 8.

Signal processing pipeline for the AT-StarGAN-GP model.

Training details and implementation strategy

In this study, AT-StarGAN-GP is utilized due to the multi-domain nature of structural vibration data, making it preferable over cross-domain models designed for data transformation between two specific domains. While cross-domain models are typically used to convert data between two distinct domains (such as transforming images from one style to another), they lack the capability to process multiple domains simultaneously, as required in this study. As illustrated in Figure 9, handling multiple domains with cross-domain models would necessitate creating separate models for each domain pair, which becomes impractical and inefficient given our 31 different damage scenarios, requiring 870 ( ( 31 − 1 ) × ( 31 − 2 ) = 30 × 29 = 870 ) individual models.

OPEN IN VIEWER

Figure 9.

AT-StarGAN-GP training architecture.

AT-StarGAN-GP excels in multi-domain scenario-to-scenario translation, enabling effective handling of various damage scenarios. Each damage scenario in our dataset represents a different domain, similar to how StarGAN manages different attributes in images. By utilizing domain labels, AT-StarGAN-GP learns to generate realistic synthetic data for each damage scenario, significantly enhancing the versatility and applicability of the synthetic data generation process. This capability makes it an ideal choice for SHM algorithms.

As shown in Figure 9, the AT-StarGAN-GP architecture consists of a generator G ( x , c ) and a discriminator D ( x ) that work together and are governed by four main loss functions:

The architecture includes sophisticated monitoring mechanisms, shown in the green dashed box, that detect and prevent mode collapse using cross-class and within-class diversity thresholds, both set to 0.02. The training process is optimized using the Adam optimization algorithm with carefully tuned parameters ( lr = 0 . 0002 , β 1 = 0 . 5 , β 2 = 0 . 999 ). In addition, lambda constraints (min: 1.0, max: 10.0) and an adjustment rate of 1.05 ensure balanced loss scaling throughout training.

This comprehensive approach enables AT-StarGAN-GP to effectively learn mappings between different structural damage conditions while preserving signal integrity. As a result, it becomes an ideal choice for synthetic data generation in SHM applications. Figure 10 visualizes multi-class transformation capabilities of the AT-StarGAN-GP model, displaying a complete matrix of signal translations from a single source sample (original class) to all 31 possible damage classes, including itself. Each subplot shows the time-series data as a heatmap where features are displayed on the x-axis and time steps on the y-axis, with color intensity representing signal magnitude. The original sample appears in the first position, followed by its transformations to every other class, demonstrating the model’s ability to perform controlled class-specific signal generation while maintaining structural coherence.

OPEN IN VIEWER

Figure 10.

Visualization of AT-StarGAN-GP transformation from a single damage scenario (damage scenario 24) to all target classes.

Computational efficiency

The comparison between Eigen perturbation methods and GAN-based approaches, particularly AT-StarGAN-GP, highlights the trade-offs between computational efficiency and functional capability in SHM. As summarized in Table 1 and shown in Figure 11, Eigen perturbation methods, including Modal Assurance Criterion (MAC), Eigenvalue sensitivity, flexibility, and Damage Localization Vector (DLV), are the fastest, completing analysis for all 30 joints in under 20 ms. MAC is the most efficient at 0.25 ms (std = 0.01 ms), followed by DLV (2.02 ms), flexibility (8.29 ms), and Eigenvalue (12.67 ms). Their linear time complexity (O(n)) reflects the simplicity of their analytical formulations.

OPEN IN VIEWER

Table 1.

Computational efficiency comparison of GAN-based and Eigen perturbation methods (30 joints, 100 iterations, Compute Unified Device Architecture device).

Method	Total time (all joints) (ms)	Standard deviation (ms)	Time complexity	Ordered/unordered	Models needed
CycleGAN	9179.04	34.98	O(n2)	Ordered	870
Vanilla StarGAN	315.16	9.87	O(n)	Unordered	1
AT-StarGAN-GP (This study)	313.45	22.88	O(n)	Unordered	1
Eigenvalue	12.67	0.88	O(n)	Unordered	1
Flexibility	8.29	0.68	O(n)	Unordered	1
DLV	2.02	0.11	O(n)	Unordered	1
MAC	0.25	0.01	O(n)	Unordered	1

OPEN IN VIEWER

Figure 11.

Log-scale total computation time for all joint pairs

However, while these methods are computationally superior, they cannot generate synthetic data, a key limitation for SHM scenarios involving missing sensors, sparse instrumentation, or nonlinear damage. Synthetic data generation enables full-field reconstruction and data recovery, capabilities that are essential for modern data-driven SHM frameworks.

By contrast, GAN-based approaches such as AT-StarGAN-GP, VanillaStarGAN, and CycleGAN introduce this generative capability while maintaining real-time performance. Both AT-StarGAN-GP and VanillaStarGAN exhibit linear complexity (O(n)) and operate in an unordered configuration, meaning that each joint can be processed independently. As presented in Table 1 and Figure 11, AT-StarGAN-GP generates synthetic data for all 30 joints in 313.45 ms (std = 22.88 ms), about 10.45 ms per joint, while VanillaStarGAN performs similarly at 315.16 ms (std = 9.87 ms). These runtimes are comparable, confirming that both are computationally efficient and remain well within real-time constraints for SHM applications.

CycleGAN, on the other hand, exhibits quadratic complexity (O(n²)) because of its ordered, pairwise architecture, requiring 870 separate models for complete joint-to-joint mappings. Consequently, it requires 9179.04 ms (std = 34.98 ms) to process all joints, around 30 times slower than AT-StarGAN-GP. While CycleGAN can generate high-quality data, its ordered structure and computational cost make it impractical for real-time SHM.

The “Models needed” and “Ordered/unordered” columns in Table 1 underscore the scalability advantage of AT-StarGAN-GP, which achieves full multi-joint mapping with a single model. Eigen perturbation methods remain the fastest, and AT-StarGAN-GP provides a crucial balance between speed and functionality, enabling generative modeling and nonlinear damage interpretation within real-time limits. Figure 11 further confirms that the model’s total runtime is well below the 1000 ms threshold for complete structural evaluation.

Overall, while Eigen perturbation techniques are highly efficient in terms of computational speed, the primary focus of this study lies in synthetic data generation, a capability these techniques inherently lack but which is crucial for data recovery and autonomous SHM. The proposed AT-StarGAN-GP model thus provides an effective compromise, combining real-time feasibility with advanced generative functionality. Its superiority over CycleGAN and Vanilla StarGAN in both runtime and stability is further demonstrated in “Modal analysis” section, which examines modal performance under varying noise and downsampling conditions.

Sensitivity analysis

A comprehensive sensitivity analysis was conducted to investigate how variations in the loss multipliers (λ-parameters) and attention weights influence the spectral coherence between the generated and measured structural responses. The mean magnitude-squared coherence (MMSC) metric was used to quantify this behavior, where higher values indicate a stronger similarity between the generated synthetic acceleration signals and the real measurements in the frequency domain. Figure 12 presents the λ-parameter and attention-weight interaction matrix, while Table 2 summarizes the tested hyperparameter space along with the resulting MMSC statistics across five damage scenarios.

OPEN IN VIEWER

Figure 12.

Sensitivity analysis of λ-parameters and attention weights showing individual (diagonal) and pairwise interaction (off-diagonal) effects on MMSC performance. MMSC: mean magnitude-squared coherence.

OPEN IN VIEWER

Table 2.

Hyperparameter space explored in the λ-parameter and attention sensitivity analysis.

Parameter	Tested values	Mean ± Standard Deviation (MMSC)	Optimal value	Key observation
λ_freq	5, 10, 15, 20	0.904 ± 0.010, 0.954 ± 0.007, 0.982 ± 0.010, 0.955 ± 0.015	15	Best spectral coherence at moderate weighting
λ_svd	5, 10, 15, 20	0.937 ± 0.009, 0.984 ± 0.006, 0.932 ± 0.012, 0.833 ± 0.009	10	Over-regularization (λ ≥ 15)reduces fidelity
λ_cycle	1, 5, 10, 15	0.850 ± 0.008, 0.931 ± 0.007, 0.977 ± 0.006, 0.934 ± 0.006	10	Smooth cyclic consistency improves spectral alignment
λ_id	1, 5, 10	0.871 ± 0.014, 0.980 ± 0.006, 0.835 ± 0.014	5	Preserves undamaged-state spectral features
λ_cls	0.5, 1, 2, 5	0.936 ± 0.009, 0.974 ± 0.008, 0.838 ± 0.015, 0.640 ± 0.000	1	Excessive class weighting disrupts coherence
λ_gp	5, 10, 15, 20	0.927 ± 0.011, 0.976 ± 0.004, 0.933 ± 0.007, 0.834 ± 0.010	10	Balanced gradient penalty enhances stability
λ_adv	0.5, 1, 2	0.936 ± 0.009, 0.978 ± 0.011, 0.829 ± 0.007	1	Best realism–coherence balance
λ_div	0.5, 1, 2	0.933 ± 0.009, 0.981 ± 0.010, 0.829 ± 0.017	1	Ensures sample diversity without coherence loss
λ_rec	1, 5, 10	0.872 ± 0.012, 0.978 ± 0.007, 0.836 ± 0.015	5	Prevents overfitting while retaining realism
Attention (temporal)	0.0–1.0	0.837 ± 0.014 → 0.975 ± 0.014	1.0	Improves temporal coherence
Attention (channel)	0.0–1.0	0.837 ± 0.014 → 0.975 ± 0.014	1.0	Enhances inter-sensor spectral consistency

MMSC: mean magnitude-squared coherence.

Figure 12 illustrates the relationships among all eleven parameters, consisting of nine λ-terms and two attention weights, arranged in an 11 × 11 interaction matrix. The diagonal cells depict the distribution of MMSC scores for each parameter using bar plots, where each bar represents the mean MMSC value across five scenarios (scenarios 6, 12, 18, 24, and 30). The red scatter points overlaid on each bar represent the individual MMSC values from each of the five scenarios, providing a detailed view of performance variability across different damage conditions. The color gradient of the bars corresponds to different parameter values tested, with the colormap indicating the progression from lower to higher parameter settings.

The λ-parameters control different aspects of model optimization: frequency-domain consistency ( λ freq ), spectral orthogonality ( λ svd ), cycle consistency ( λ cycle ), identity preservation ( λ id ), classification alignment ( λ cls ), gradient penalty ( λ gp ), adversarial realism ( λ adv ), diversity ( λ div ), and reconstruction accuracy ( λ rec ). The inclusion of the temporal and channel attention weights provides insight into how attention mechanisms complement these objectives by emphasizing key temporal and spatial correlations in the data. The diagonal bar plots reveal the individual sensitivity of each parameter, with the range and variability of the bars indicating how critically each parameter influences model performance. Parameters with wider MMSC ranges across their tested values are more sensitive, while those with consistently high MMSC scores (shown by uniformly tall bars with small error bars) demonstrate robust performance across their parameter space.

The results show that the MMSC values range between approximately 0.83 and 0.98 across all configurations, revealing a clear performance landscape with identifiable optimal regions. In general, most parameters exhibit their best performance at moderate λ-values, confirming that there is a trade-off between over-regularization and under-constrained training. For instance, λ freq shows a steady improvement from 0.904 at λ = 5 to a peak of 0.982 at λ = 15, before slightly declining to 0.955 at λ = 20. This trend confirms that moderate weighting in the frequency-domain loss allows the generator to maintain spectral coherence without constraining its flexibility to represent complex signal variations.

The spectral orthogonality term λ svd displays a similar behavior, peaking at λ = 10 with an MMSC of 0.984 ± 0.006, while both lower and higher values reduce performance. At λ = 20, the mean MMSC falls to 0.832, showing that overly strong enforcement of orthogonal spectral features can distort the subtle modal correlations that exist in real damage-induced responses. A comparable pattern is seen for λ cycle and λ gp , where intermediate values (around 10) yield MMSC values near 0.977 and 0.976, respectively, while higher settings (λ ≥ 20) cause a noticeable drop below 0.84. These results demonstrate that enforcing cyclic consistency and gradient stability is crucial, but excessively large penalties hinder the network’s ability to adapt to nonlinear signal variations.

The identity preservation ( λ id ) and reconstruction accuracy ( λ rec ) parameters both achieve high MMSC levels (around 0.98) at moderate strengths (λ = 5), confirming that these components help the model retain the key temporal and spectral structures of undamaged signals while introducing damage features realistically. However, increasing these terms to λ = 10 decreases the coherence to about 0.84, implying that overemphasizing self-reconstruction reduces the diversity of generated outputs.

The classification alignment ( λ cls ), adversarial realism ( λ adv ), and diversity regularization ( λ div ) terms show a more sensitive relationship with MMSC. For λ cls , coherence improves from 0.936 at λ = 0.5 to 0.974 at λ = 1, but rapidly declines to 0.838 at λ = 2 and drops sharply to 0.64 at λ = 5. This result indicates that excessive classification emphasis forces the generator to exaggerate class-specific features at the expense of spectral smoothness. Similarly, λ adv and λ div achieve their best results around λ = 1 (MMSC ≈ 0.978–0.981), while stronger adversarial or diversity constraints reduce performance, suggesting that the optimal balance between realism and spectral stability occurs when these terms are modestly weighted.

The temporal and channel attention weights exhibit a distinctly positive influence on model performance. When the attention mechanisms are fully activated (weights = 1.0), the MMSC reaches approximately 0.975 ± 0.014, indicating that attention layers significantly enhance the model’s capacity to capture long-term temporal dependencies and inter-sensor spectral relationships. By contrast, disabling attention (weights = 0) lowers the MMSC to around 0.83, confirming that the absence of feature weighting leads to weaker frequency-domain alignment.

Overall, the patterns across Figure 12 and Table 2 clearly demonstrate that the model achieves its highest and most stable coherence when the λ-parameters are harmoniously balanced within moderate ranges (λ = 10–15 for most losses) and both attention mechanisms are fully enabled. Under this configuration, specifically λ freq = 15 , λ svd = 10 , λ cycle = 10 , λ gp = 10 , λ cls = 1 , and attention weights = 1.0, the mean MMSC exceeds 0.97 with standard deviations below 0.01. This combination ensures that the model maintains strong frequency-domain consistency, preserves the structural characteristics of the signals, and generalizes reliably across all five damage scenarios.

Modal analysis

The modal analysis results demonstrate agreement between the real and synthetic structural response data across all investigated damage scenarios. As evidenced by Tables 3 to 7, the fundamental frequency maintains consistency at 17.1 Hz with a 5% damping ratio throughout all scenarios, indicating robust identification of the primary structural mode. The frequency identification shows exceptional precision, with differences between real and synthetic frequencies consistently at or near zero percent across all scenarios and modes.

OPEN IN VIEWER

Table 3.

Natural frequencies and damping ratios of scenario 6, synthetic scenario 6, and percentage differences of natural frequencies and damping ratios between original and synthetic scenario.

	Scenario 6		Synthetic scenario 6		Percentage differences
Mode	Frequency (Hz)	Damping (%)	Frequency (Hz)	Damping (%)	Frequency (%)	Damping (%)
1	17.1	5.00	17.1	5.00	0.0	0.0
2	25.1	2.64	25.1	2.67	0.0	1.2
3	50.0	1.65	50.0	1.65	0.0	0.0
4	62.9	1.55	62.9	1.79	0.0	15.0
5	75.0	0.86	75.0	1.03	0.0	20.1
6	90.9	1.09	91.0	1.10	0.1	0.6
7	112.1	0.96	112.1	0.97	0.0	1.2

OPEN IN VIEWER

Table 4.

Natural frequencies and damping ratios of scenario 12, synthetic scenario 12, and percentage differences of natural frequencies and damping ratios between original and synthetic scenario.

	Scenario 12		Synthetic scenario 12		Percentage differences
Mode	Frequency (Hz)	Damping (%)	Frequency (Hz)	Damping (%)	Frequency (%)	Damping (%)
1	17.1	5.00	17.1	5.00	0.0	0.0
2	24.9	3.60	24.9	3.69	0.0	2.5
3	50.0	1.52	50.0	1.52	0.0	0.0
4	62.1	1.31	62.1	1.33	0.0	1.1
5	75.9	0.96	75.9	1.01	0.0	5.0
6	89.8	0.90	89.9	0.91	0.1	0.3
7	114.1	1.64	114.1	1.70	0.0	3.4

OPEN IN VIEWER

Table 5.

Natural frequencies and damping ratios of scenario 18, synthetic scenario 18, and percentage differences of natural frequencies and damping ratios between original and synthetic scenario.

	Scenario 18		Synthetic scenario 18		Percentage differences
Mode	Frequency (Hz)	Damping (%)	Frequency (Hz)	Damping (%)	Frequency (%)	Damping (%)
1	17.1	5.00	17.1	5.00	0.0	0.0
2	24.1	3.03	24.1	3.13	0.0	3.5
3	30.0	2.15	30.0	3.45	0.0	60.4
4	50.0	1.33	50.0	1.33	0.0	0.1
5	63.0	2.39	63.0	5.00	0.0	108.8
6	88.9	0.73	88.9	0.73	0.0	0.5
7	111.1	1.34	111.1	1.34	0.0	0.3

OPEN IN VIEWER

Table 6.

Natural frequencies and damping ratios of scenario 24, synthetic scenario 24, and percentage differences of natural frequencies and damping ratios between original and synthetic scenario.

	Scenario 24		Synthetic scenario 24		Percentage differences
Mode	Frequency (Hz)	Damping (%)	Frequency (Hz)	Damping (%)	Frequency (%)	Damping (%)
1	17.1	5.00	17.1	5.00	0.0	0.0
2	25.0	2.35	25.0	2.38	0.0	1.5
3	48.0	1.55	48.0	1.56	0.0	0.3
4	63.0	3.81	63.0	3.33	0.0	12.5
5	75.0	0.83	75.0	0.83	0.0	0.3
6	86.0	0.97	86.0	0.97	0.0	0.4
7	113.0	0.76	113.0	0.76	0.0	0.2

OPEN IN VIEWER

Table 7.

Natural frequencies and damping ratios of scenario 30, synthetic scenario 30, and percentage differences of natural frequencies and damping ratios between original and synthetic scenario.

	Scenario 30		Synthetic scenario 30		Percentage differences
Mode	Frequency (Hz)	Damping (%)	Frequency (Hz)	Damping (%)	Frequency (%)	Damping (%)
1	17.1	5.00	17.1	5.00	0.0	0.0
2	25.0	2.75	25.0	2.76	0.0	0.5
3	51.0	1.38	51.0	1.39	0.0	0.4
4	76.0	1.44	76.0	5.00	0.0	246.2
5	91.8	1.07	91.8	1.07	0.0	0.1
6	114.0	1.91	114.0	1.89	0.0	1.0
7	17.1	5.00	17.1	5.00	0.0	0.0

To ensure clarity and avoid redundancy, we present results for scenarios 6, 12, 18, 24, and 30, as these scenarios provide a representative distribution across the full range of damage conditions. Similarly, joints 9, 13, 17, and 21 were selected as they are strategically positioned to capture spatial variations in the structural response while maintaining interpretability. This selection allows for a comprehensive yet concise evaluation of the model’s performance in replicating real structural behavior.

The frequency-domain analysis of joints 9, 13, 17, and 21 for scenario 6, presented in Figures 13 to 17, reveals a strong correlation between original and synthetic frequency responses. These comparisons demonstrate the model’s capability to capture local dynamic behaviors at different structural locations. The SVD comparison shown in Figures 18 to 22 further validates these findings, with an impressive MMSC value of 0.974, clearly identifying the natural frequencies and showing excellent agreement between original and synthetic data for scenario 6.

OPEN IN VIEWER

Figure 13.

Frequency domain analysis of joints 9, 13, 17, and 21 for scenario 6, comparing original and synthetic frequency responses.

OPEN IN VIEWER

Figure 14.

Frequency domain analysis of joints 9, 13, 17, and 21 for scenario 12, comparing original and synthetic frequency responses.

OPEN IN VIEWER

Figure 15.

Frequency domain analysis of joints 9, 13, 17, and 21 for scenario 18, comparing original and synthetic frequency responses.

OPEN IN VIEWER

Figure 16.

Frequency domain analysis of joints 9, 13, 17, and 21 for scenario 24, comparing original and synthetic frequency responses.

OPEN IN VIEWER

Figure 17.

Frequency domain analysis of joints 9, 13, 17, and 21 for scenario 30, comparing original and synthetic frequency responses.

OPEN IN VIEWER

Figure 18.

SVD comparison between original and synthetic data for scenario 6, with identified natural frequencies. SVD: singular value decomposition.

OPEN IN VIEWER

Figure 19.

SVD comparison between original and synthetic data for scenario 12, with identified natural frequencies. SVD: singular value decomposition.

OPEN IN VIEWER

Figure 20.

SVD comparison between original and synthetic data for scenario 18, with identified natural frequencies. SVD: singular value decomposition.

OPEN IN VIEWER

Figure 21.

SVD comparison between original and synthetic data for scenario 24, with identified natural frequencies. SVD: singular value decomposition.

OPEN IN VIEWER

Figure 22.

SVD comparison between original and synthetic data for scenario 30, with identified natural frequencies. SVD: singular value decomposition.

A detailed examination of scenario 6 (Table 3 and Figure 18) reveals that modal frequencies span from 17.1 to 112.1 Hz, with damping ratios showing excellent correlation. While most modes exhibit minimal damping differences below 2%, slightly higher variations are observed in the fourth and fifth modes (62.9 and 75.0 Hz) with differences of 15 and 20%, respectively. Scenario 12 demonstrates even better agreement, as shown in Table 4 and Figure 19, with all damping differences remaining below 5% and an exceptional MMSC value of 0.988. The slight shift in the second mode frequency to 24.9 Hz compared to scenario 6 suggests subtle changes in structural behavior while maintaining accurate damping estimation.

The analysis of scenario 18, presented in Table 5 and Figure 20, shows excellent frequency matching with moderate variations in damping characteristics, achieving the highest MMSC value of 0.989. The third mode (30 Hz) and fifth mode (63 Hz) show differences of 60.4% and 108.8%, respectively, in damping ratios, while maintaining perfect frequency alignment. Such variations, although notable, are primarily associated with modes of lower modal energy or reduced participation in the overall response. These modes tend to exhibit higher sensitivity to measurement noise and numerical approximation during damping estimation. This phenomenon is well-documented in operational modal analysis literature, which consistently shows that damping ratios exhibit much larger scatter and uncertainty than natural frequencies, and that identification methods can produce widely varying damping values even under controlled conditions. ⁵⁹ Similarly, damping-based anomaly detection is known to be less stable than frequency-based approaches and often exhibits scattered estimates or false anomalies under healthy conditions. ¹³ Importantly, the model consistently preserves the fundamental frequency content, demonstrating that discrepancies in damping for low-energy modes have minimal influence on the overall dynamic representation and damage localization accuracy.

Scenario 24’s results, documented in Table 6 and Figure 21, maintain the high standard of frequency prediction while showing good damping agreement across most modes, with an MMSC value of 0.973. A moderate damping difference of 12.5% is observed in the fourth mode (63 Hz), with all other modes showing minimal variations below 2%.

Scenario 30, as shown in Table 7 and Figure 22, presents a mixed picture with perfect frequency matching and an impressive MMSC value of 0.988, but a significant damping variation is observed in the fourth mode (76 Hz), with a 246.2% difference. This deviation is attributed to the comparatively low energy content of this mode, making it more susceptible to noise and minor excitation inconsistencies during both experimental and synthetic data generation. This is consistent with the previously noted tendency for weakly excited modes to exhibit unstable damping estimates and large method-dependent variations. Nonetheless, all other modes in this scenario demonstrate excellent agreement, with damping differences below 1%, confirming the reliability of the proposed algorithm in preserving dominant modal properties.

The frequency-domain analysis employed Welch’s method for PSD estimation, utilizing a Hann window with 256 samples and 66% overlap to optimize the trade-off between frequency resolution and statistical reliability. This parameterization was chosen based on the sampling frequency of 1024 Hz and the need to capture the structural system’s fundamental modes while maintaining sufficient averaging to reduce variance in the spectral estimates.

The comprehensive analysis reveals that the synthetic data generation model achieves exceptional accuracy in frequency prediction across various damage scenarios, with some variations in damping estimation accuracy. The consistently high MMSC values ranging from 0.973 to 0.989 across all scenarios underscore the agreement between real and synthetic data. The consistent precision in frequency identification, coupled with the ability to capture most damping characteristics within acceptable engineering tolerances, suggests that the model successfully replicates the complex dynamic characteristics of the structure under different damage conditions. While some higher modes show increased damping estimation discrepancies, particularly in scenarios 18 and 30, the overall performance indicates that the synthetic data provides a reliable foundation for SHM applications.

These findings demonstrate the potential of synthetic data for SHM applications, particularly in scenarios where real data collection may be limited or costly. Future work should focus on improving damping estimation accuracy for higher modes and investigating methods to reduce the larger damping discrepancies observed in specific scenarios. The comprehensive validation across all scenarios and joints provides confidence in the generative model’s ability to produce physically meaningful synthetic data that preserves the essential dynamic characteristics of the structural system.

While our proposed AT-StarGAN-GP model shows promise in generating high-quality synthetic structural response data, it is essential to quantitatively evaluate its performance against established benchmarks. To rigorously assess its effectiveness, we conducted extensive comparative analyses with vanilla StarGAN and CycleGAN across different noise levels (0.02 and 0.04) and downsampling rates (original, ds2, and ds4), representing various real-world data collection challenges.

At original resolution, AT-StarGAN-GP demonstrated superior performance across both noise conditions. The model achieved mean MMSC values of 0.8418 (noise 0.02) and 0.9439 (noise 0.04), representing improvements of 16.3% and 21.6%, respectively, over Vanilla StarGAN’s corresponding values of 0.724 and 0.776 (see Tables A1–A6 in Appendix). CycleGAN demonstrated competitive performance, achieving mean MMSC values of 0.8252 (noise 0.02) and 0.9284 (noise 0.04). While CycleGAN outperformed Vanilla StarGAN, it remained below AT-StarGAN-GP by approximately 2.0% at noise level 0.02 and 1.6% at noise level 0.04, indicating that the gradient penalty and attention mechanisms in AT-StarGAN-GP provide additional stability advantages.

Table 8 presents representative results for AT-StarGAN-GP at original resolution with noise 0.04, illustrating the model’s consistent performance across different scenarios and joint configurations.

OPEN IN VIEWER

Table 8.

MMSC values by scenario and joint for a original noise 0.04 (AT-StarGAN-GP).

Scenario/joint	9	13	17	21	Mean
6	0.944585911	0.875635456	0.975224126	0.954725099	0.937542648
12	0.955227456	0.865994684	0.938687544	0.986903846	0.936703383
18	0.982830167	0.82046016	0.810406993	0.929470068	0.885791847
24	0.994065517	0.966875632	0.984181259	0.957174477	0.975574221
30	0.981806981	0.982968783	0.988053062	0.982651779	0.983870151
Mean	0.971703207	0.902386943	0.939310597	0.962185054	0.94389645

MMSC: mean magnitude-squared coherence.

Under ds2 downsampling conditions, AT-StarGAN-GP maintained its performance edge, achieving mean MMSC values of 0.9254 (noise 0.02) and 0.8828 (noise 0.04), translating to improvements of 34.3% and 16.6% over Vanilla StarGAN (detailed results in Tables A7–A12). CycleGAN showed strong performance under ds2 downsampling, with mean MMSC values of 0.9077 (noise 0.02) and 0.8670 (noise 0.04). These results demonstrate that CycleGAN maintains better stability than Vanilla StarGAN under moderate downsampling conditions, though AT-StarGAN-GP still outperforms CycleGAN by approximately 2.0% at noise 0.02 and 1.8% at noise 0.04. This behavior confirms that AT-StarGAN-GP effectively retains spatial and temporal consistency under moderate resolution loss, demonstrating strong robustness to both downsampling and noise (see Table 9 for a consolidated overview).

OPEN IN VIEWER

Table 9.

Summary of the performance trends across all experimental conditions.

Model	Original (0.02)	Original (0.04)	ds2 (0.02)	ds2 (0.04)	ds4 (0.02)	ds4 (0.04)
AT-StarGAN-GP (This study)	0.8418	0.9439	0.9254	0.8828	0.8440	0.8400
CycleGAN	0.8252	0.9284	0.9077	0.8670	0.7776	0.5785
Vanilla StarGAN	0.7240	0.7760	0.6890	0.7570	0.5440	0.6540

Under the severe ds4 condition, performance differences became more pronounced. AT-StarGAN-GP achieved mean MMSC values of 0.844 (noise 0.02) and 0.840 (noise 0.04), outperforming Vanilla StarGAN’s corresponding values of 0.544 and 0.654 by 55.1 and 28.4%, respectively (complete results in Tables A13–A18). CycleGAN’s performance under ds4 downsampling showed mean MMSC values of 0.7776 (noise 0.02) and 0.5785 (noise 0.04). Under severe downsampling, CycleGAN maintained superior performance compared to Vanilla StarGAN, but the gap between AT-StarGAN-GP and CycleGAN widened to approximately 8.5% at noise 0.02 and 45.2% at noise 0.04. This suggests that the architectural enhancements in AT-StarGAN-GP, particularly the attention mechanisms and gradient penalty, provide critical stability under extreme data degradation conditions.

The downsampling effects revealed distinct trends across the three models. AT-StarGAN-GP exhibited resilience to resolution degradation, with performance actually improving from original resolution (0.8418) to ds2 (0.9254) under 0.02 noise, an enhancement of 9.9%, before slightly declining to 0.844 at ds4. Under 0.04 noise, the model showed a more conventional trend, decreasing from 0.9439 to 0.8828 and then to 0.840.

CycleGAN demonstrated relatively stable performance across downsampling conditions under 0.02 noise (0.8252 → 0.9077 → 0.7776). However, under 0.04 noise, CycleGAN showed a more pronounced decline (0.9284 → 0.8670 → 0.5785), indicating increased sensitivity to the combined effects of noise and severe downsampling. By contrast, Vanilla StarGAN demonstrated a consistent decline in performance with increasing downsampling under 0.02 noise (0.724 → 0.689 → 0.544) and 0.04 noise (0.776 → 0.757 → 0.654).

The robustness gap between AT-StarGAN-GP and the other models thus widened progressively with downsampling severity, from 16.3% to 21.6% over Vanilla StarGAN at original resolution to 16.6–34.3% at ds2 and 28.4–55.1% at ds4, highlighting the architectural stability and adaptability of AT-Star GAN-GP. Compared to CycleGAN, AT-StarGAN-GP maintained modest advantages at original and ds2 resolutions (approximately 2%), but demonstrated significantly superior performance under ds4 conditions, particularly at higher noise levels.

Noise level effects revealed additional insights. AT-StarGAN-GP benefited substantially from higher noise under original resolution, with a 12.1% improvement (0.8418 → 0.9439). However, performance declined modestly with higher noise under ds2 (0.9254 → 0.8828) and remained stable at ds4 (0.844 → 0.840). CycleGAN showed a similar pattern at original resolution, improving by 12.5% with higher noise (0.8252 → 0.9284), but experienced more severe degradation at ds2 (0.9077 → 0.8670) and ds4 (0.7776 → 0.5785). Conversely, Vanilla StarGAN showed consistent improvement with increasing noise across all resolutions: +7.2% at original, +9.9% at ds2, and +20.2% at ds4, though these improvements were insufficient to match the performance of the other models.

These results suggest that moderate noise acts as a regularizer, especially for models less capable of internal noise compensation, such as Vanilla StarGAN and CycleGAN. AT-StarGAN-GP’s nuanced response, however, implies that its adversarial and attention-driven learning mechanisms already internalize noise handling to a greater extent, reducing reliance on external regularization effects.^60–62

From a physical perspective, moderate additive noise can be interpreted as representing stochastic environmental influences or sensor-level fluctuations commonly encountered in vibration-based monitoring. Such perturbations introduce subtle variations that broaden the frequency content of the response signal, helping the model to learn structural patterns that remain stable under realistic operating conditions. This behavior parallels the effect of low-intensity broadband excitation in experimental modal analysis, which enhances the detectability of modal features by stimulating multiple vibration modes simultaneously. Consequently, exposure to moderate noise encourages the model to focus on invariant modal characteristics, such as stiffness- or damping-related features, rather than on transient or localized signal artifacts. However, as the noise level increases further, these modal signatures become increasingly masked, reducing the physical interpretability and discriminative power of the learned representations.

The diverging noise responses underscore the architectural distinctions among the three models. AT-StarGAN-GP achieved its peak performance (0.9439) at the original resolution and high noise (Table 7), but showed limited gains at lower resolutions, indicating that the gradient penalty enhances noise modeling primarily when signal fidelity is preserved. CycleGAN exhibited intermediate behavior, with improved robustness over Vanilla StarGAN but lower absolute accuracy than AT-StarGAN-GP, reflecting the stabilizing yet less adaptive nature of cyclic consistency. Conversely, Vanilla StarGAN’s uniform improvement across noise levels and resolution points to a simpler regularization behavior rather than robust structural feature learning.

Overall, all models achieved their highest performance at original resolution under 0.04 noise, but AT-StarGAN-GP consistently attained superior absolute values and maintained structural integrity under both noise and downsampling. These findings reaffirm the effectiveness of the gradient penalty mechanism in ensuring model robustness and generalizability for complex SHM applications.