MAML Bridges the Data Gap in Deep Learning-Based Structural Health Monitoring

Abstract

Deep learning has revolutionized structural health monitoring (SHM), yet data scarcity remains a critical bottleneck limiting its deployment in real-world engineering applications. Meta-learning—an emerging paradigm enabling models to learn from limited examples—offers a compelling solution to this challenge. Herein, we systematically investigate meta-learning’s efficacy across three key SHM applications: surface damage detection, structural response prediction, and data-driven damage identification. Our experiments demonstrate that meta-learning achieves comparable performance with substantially reduced data requirements. For surface damage detection, meta-learning maintains detection accuracy while modestly decreasing sample dependency. In response prediction tasks, although the number of prediction errors increases marginally, the data efficiency gains are substantial. Similarly, damage identification shows slight accuracy trade-offs but dramatic reductions in required training samples. These findings establish meta-learning as a practical pathway for deploying deep learning in data-constrained SHM scenarios, potentially accelerating the adoption of intelligent monitoring systems in critical infrastructure. Our results suggest that the traditional data-hungry nature of deep learning need not be a barrier to advancing automated structural health assessment.

1. Introduction

Structural health monitoring (SHM) integrates advanced field sensing systems and analytical methodologies to continuously assess the operational integrity, safety, and durability of structures [1,2]. By leveraging state-of-the-art data analysis techniques, SHM enables the extraction of critical structural parameters and damage indicators, facilitates early warning through prompt alerts when predefined thresholds are surpassed, and supports comprehensive evaluation of structural performance, damage prognosis, health rating, and remaining service life prediction. This information is essential for grounding decisions regarding necessary interventions, such as repair, retrofitting, or replacement. The domain of SHM is primarily founded upon two interrelated pillars: sensing technology and data analytics. The former focuses on the development and application of diverse sensors—encompassing advances in manufacturing and sensing principles—to monitor environmental conditions, structural responses, and various physical signals (e.g., acoustic and optical) affecting the structure. The latter involves the entire data lifecycle, including collection, transmission, mining, storage, damage identification, and decision support [3,4]. Of these, robust sensing technology provides the high-quality data that form the foundation for accurate damage identification, while data analysis methods constitute the core of SHM, underpinning both the diagnosis of structural conditions and subsequent auxiliary decision-making processes.

High-quality data lie at the heart of structural health monitoring (SHM), fundamentally underpinning the accuracy and robustness of damage detection. While traditional modal-based approaches tend to overlook subtle or localized defects, data-rich image-based methods provide a pathway to overcoming these limitations. The advent of deep learning has ushered in a new era for SHM, offering advanced capabilities for automatic feature extraction from complex, noisy datasets that are ubiquitous in real-world monitoring scenarios. Unlike conventional techniques, deep learning approaches leverage the full breadth of SHM data—including images, time-series signals, and sensor arrays—to autonomously learn and distil damage-relevant features. This data-driven paradigm has yielded significant advances in a diverse spectrum of SHM tasks, such as surface damage identification, structural response prediction, and signal interpretation, marking deep learning as a highly effective and forward-looking methodology for practical structural health assessment [5,6,7].

Despite the transformative potential of deep learning for structural health monitoring, the widespread deployment of such methods remains hampered by a fundamental bottleneck—the limited scale and diversity of available SHM datasets. Deep learning models typically require vast amounts of high-quality, annotated data to achieve robust and generalizable performance. In practice, however, SHM data acquisition is expensive, labor-intensive, and often constrained by operational or environmental factors, resulting in datasets that are sparse, heterogeneous, and unbalanced. This scarcity of comprehensive datasets significantly impedes the ability of deep learning algorithms to capture the full spectrum of damage scenarios encountered in real-world structures, thus posing a formidable challenge to the large-scale practical adoption of these approaches in SHM. [8,9].

Notwithstanding the considerable progress made in integrating deep learning with structural health monitoring (SHM), systematic evaluations of meta-learning algorithms—such as Model-Agnostic Meta-Learning (MAML) [10]—across multiple SHM tasks remain relatively scarce. In particular, the field lacks comprehensive studies that simultaneously address surface damage detection, response prediction, and signal-based damage identification within practical engineering contexts, where labeled data are exceedingly scarce. In response, this study centers on representative tasks in bridge SHM to directly confront the challenges posed by limited annotated data. The aims of this work are threefold: first, to critically review the state-of-the-art in deep learning and meta-learning applications for SHM and their unresolved limitations; second, to introduce a meta-learning framework based on MAML, adapted for application to surface defect detection (with YOLOv5 [11]), response prediction (with LSTM [12]), and signal classification (with 1DCNN); and third, to rigorously benchmark the proposed methods against conventional deep learning approaches under data-constrained conditions. Through these efforts, this research seeks to advance the practical deployment of meta-learning in SHM and to provide a robust theoretical and technical foundation for future developments in the discipline.

2. Related Work

2.1. Meta-Learning

In SHM, meta-learning has emerged as a powerful paradigm for tackling damage detection and prognosis in data-scarce, dynamic environments [13]. Entezami et al. [14] introduced an unsupervised meta-learning framework that reconstructs extensive missing data in bridge monitoring via segmentation and subspace search, whereas Xu et al. [15] devised a task-aware approach for structural damage segmentation from limited images, markedly enhancing adaptability in few-shot settings. Similarly, Che et al. [16] and Tsialiamanis et al. [17] leveraged deep meta-learning for aircraft repair decisions and population-based prognosis, underscoring knowledge transfer in multi-source SHM data integration. These developments underscore meta-learning’s strengths in bolstering SHM robustness and generalization, notably by enabling rapid task adaptation to circumvent traditional machine learning’s reliance on vast labelled datasets [18]. Yet, despite efficacy in controlled simulations, meta-learning’s deployment in SHM is hampered by key limitations, such as sensitivity to meta-task design, high computational demands impeding real-time use, and poor generalization amid noise or heterogeneous data [19]—constraints that curtail scalability in intricate engineering systems and demand enhanced robustness. Addressing these gaps, model-agnostic meta-learning [10] presents a compelling remedy: by optimizing task-independent initial parameters for swift adaptation via minimal gradient steps, MAML’s architecture-agnostic design facilitates integration across SHM frameworks, alleviating task sensitivity and computational burdens while bolstering noise-resilient generalization, thereby elevating the viability of current methodologies.

2.2. Data-Driven SHM

With the advent of advanced machine learning and deep learning techniques, the detection and localization of surface defects in civil structures have transitioned from manual feature extraction of shallow properties to automated and high-precision methods. Early studies primarily focused on low-level feature extraction from images for surface defect identification, which demonstrated limited applicability in practical engineering settings [20,21,22]. The development of object detection [23,24] and semantic segmentation algorithms [25,26], has significantly advanced automated defect detection, yielding robust results in both research and field applications. For instance, methods such as YOLO, U-Net, and Fully Convolutional Networks (FCNs) have shown substantial capabilities in identifying and localizing damage in complex structural environments [27,28,29,30].

Structural response data—such as strain, vibration, and displacement—provide essential information for damage identification, particularly in large-scale SHM systems with massive, heterogeneous datasets. However, the nonlinear and high-dimensional nature of these data poses challenges for traditional analysis methods, often resulting in limited accuracy and efficiency [31,32]. The emergence of deep learning-based approaches, including Long Short-Term Memory (LSTM) networks for sequential data prediction [33] and ensemble methods, such as XGBoost [34,35], has enabled the modeling of nonlinear damage mechanisms and improved condition diagnosis. Knowledge-enhanced models further augment data efficiency and noise resistance, enabling reliable simulation and prediction with reduced sample sizes [36,37]. Additionally, advanced sensor technologies allow for the replacement of costly measurement systems (e.g., strain gauges) with lower-cost alternatives (e.g., accelerometers) when combined with appropriate deep learning-based estimation models [38].

Signal-based SHM methods leverage various types of data—including vibration, optical, and ultrasonic signals—to assess structural integrity. While classical signal processing techniques like Fourier and wavelet transforms remain widely used, their robustness is compromised in noisy or complex environments. Data-driven approaches, particularly deep learning models, offer improved feature fusion and nonlinear pattern recognition, enabling more accurate and automated signal interpretation [39,40,41,42]. Typical examples include direct liquid level estimation from raw guided wave signals using convolutional autoencoders and LSTM networks [43], machine learning-based Lamb wave damage identification [44], and convolutional neural network (CNN)-based fatigue crack detection from guided wave diagnostic indices [45].

3. Methodology

Model-Agnostic Meta-Learning (MAML) is a meta-learning approach that significantly reduces data dependency by enabling models to rapidly adapt to new tasks with only a handful of samples. Unlike traditional deep learning methods that require large labelled datasets, MAML employs a bi-level optimization: the inner loop fine-tunes model parameters on small task-specific datasets, while the outer loop seeks an initialization that generalizes across diverse tasks. This framework promotes effective knowledge transfer and mitigates overfitting in low-data regimes. In structural health monitoring, for example, MAML empowers models such as YOLOv5 to achieve near full-data performance for crack detection using only 10–20 local samples after meta-training, thus reducing the practical burden of data collection by over 90%. While MAML requires diverse training tasks and has higher optimization costs, its inference efficiency remains comparable to conventional models

MAML

MAML is a model- and task-agnostic algorithm for meta-learning that trains the parameters of a model in such a way that a small number of gradient updates will lead to fast learning of a new task. The flowchart is shown in Figure 1. Within the meta-learning framework, we denote the predictive model as $f_{\theta }$ with parameters $\theta$ When adapting to a new task $T_i$, the model parameters $\theta$ become ${\theta }_i^{\prime }$. Using MAML, the updated parameter vector ${\theta }_i^{\prime }, T_i$ is computed using one or more gradient descent updates to the task; e.g., when using one gradient update, we have the following:

$${\theta }_i^{\prime }=\theta -\alpha {\nabla }_{\theta }{\mathcal{L}}_{T_i}\left(f_{\theta }\right)$$

(1)

The step size $\alpha$ may be fixed as a hyperparameter or meta-learned. The model parameters are trained by optimizing the performance of $f_{{\theta }_i}^{\prime }$ with respect to $\theta$ across tasks sampled from $p\left(T_i\right)$. More concretely, the meta-objective is as follows:

$$\underset{\theta }{\mathrm{m}\mathrm{i}\mathrm{n}}\sum _{T_{i~p}\left(T\right)}{\mathcal{L}}_{T_i}\left(f_{{\theta }_i}^{\prime }\right)=\sum _{T_{i~p}\left(T\right)}{\mathcal{L}}_{T_i}\left(f_{\theta -\alpha {\nabla }_{\theta }{\mathcal{L}}_i\left(f\theta \right)}\right)$$

(2)

Note that the meta-optimization is performed $\theta$ on the model parameters, while the goal is ${\theta }^{\prime }$ computed using the updated model parameters. In fact, MAML aims to optimize the model parameters in such a way that one or a small number of gradient steps on a new task will yield the most efficient behavior on that task. Cross-task meta-optimization is performed using stochastic gradient descent (SGD) such that the model parameters $\theta$ are updated as follows:

$$\theta \leftarrow \theta -\beta {\nabla }_{\theta }\sum _{T_i~p\left(T\right)}{\mathcal{L}}_{T_i}\left(f_{{\theta }_i^{\prime }}\right)$$

(3)

where $\beta$ is the meta step size.

4. Experimental Design

All experiments in this study were implemented using the PyTorch 1.10 deep learning framework, with model training executed on an NVIDIA RTX 2080 GPU. All models were trained in batch mode, and the training, validation, and test sets were split in a ratio of 0.8:0.1:0.1. Evaluation metrics were standardized across tasks. The detailed settings of training hyperparameters are provided in

Table 1. Comparison of model training strategies.

Model	Data Split	Training Settings and Platform	Evaluation Metrics
YOLOV5	923 images	Batch size = 16, epochs = 500, lr = 0.001, momentum = 0.9, weight decay = 0.0005, optimizer: SGD	Precision, Recall, mAP@0.5
MAML + YOLOV5	VOC2012	3-way 3-shot; parameter tuning ≈ 5–10 times	Precision, Recall, mAP@0.5
LSTM	50k samples	Batch size = 500, epochs = 200, dropout = 0.2, lr = 0.001	MAE
MAML + LSTM	10 tasks	500 samples/task, 24 steps input, 2 output steps	MAE
1DCNN	1k/class	lr = 0.003, Adam optimizer, activation: tanh	Accuracy
MAML + 1DCNN	MaFaulDa	6-way 6-shot, parameter tuning ≈ 3 times	Accuracy

. For meta-learning (MAML) experiments, an N-way K-shot episodic training protocol was adopted, with dedicated meta-train and meta-test splits as well as a separate validation set, thereby ensuring the reproducibility and scientific rigor of the experimental results.

4.1. Experiment 1: Bridge Steel Structure Damage Detection

(1) Pascal VOC2012 dataset [46]: Pascal VOC2012 has been used several times as one of the benchmark datasets in object detection, image segmentation network comparison experiments, and model effectiveness evaluation. It contains 17,125 samples in 20 classes.

(2) Bridge steel surface defects dataset: This dataset was taken at the bridge on the campus of Dalian University of Technology and contains three defects: corrosion, crack, and defect [47,48]. There is a total of 923 images in the dataset, with a size of 400 × 400. Samples are shown in Figure 2.

4.2. Experiment 2: Bridge Strain Response Prediction

(1) DJI stock price dataset: This dataset contains DJI’s stock prices for the 2006/1 to 2020/11 period, which spans 14 years and 10 months and includes the opening price, closing price, highest price, and lowest price.

(2) Songhua River Bridge Structural response dataset: This bridge is located in Tonghe County, Heilongjiang Province. The total length of the bridge is 2578.28 m. The main bridge structure is a prestressed concrete continuous box girder divided into two links. Each link span arrangement is (63 m + 4 × 110 m + 63 m), and the total length is 1132 m. A total of 54 sensors were placed on the bridge, and the strain response was monitored for 5 months. The sensor layout is shown in Figure 3.

4.3. Experiment 3: Guided Wave Signal Classification

(1) MaFaulDa [49]: In this study, the MaFaulDa (Machinery Fault Database) dataset is employed as a representative source of non-civil engineering vibration signals to evaluate the cross-domain transferability and generalization ability of the proposed meta-learning approach. MaFaulDa is a publicly available dataset extensively used in the field of machine fault diagnosis. It comprises multi-channel vibration signals collected from a machinery fault simulator under a variety of operating conditions, including different speeds and loads, and a wide range of typical mechanical faults, such as unbalance, misalignment, and inner and outer bearing defects. By utilizing MaFaulDa, this research simulates scenarios where knowledge learned from mechanical equipment can be transferred to structural health monitoring (SHM) tasks under small-sample conditions. The diversity and complexity of MaFaulDa’s time-series data make it an ideal benchmark for testing the robustness and adaptability of meta-learning models in SHM, especially when labeled data are limited and domains are heterogeneous.

(2) Aluminum plate damage detection: This dataset is acquired for the detection of damage on six aluminum plates with longitudinal wave velocity cL = 5115 m/s and transverse wave velocity cS = 3123 m/s; the size of the aluminum plates is 200 mm × 100 mm × 6 mm; the aluminum plate was prefabricated with damage of 5 mm in height and 2 mm to 7 mm in width. The PZT is on both sides of the aluminum plate, and the detection method is pitch-catch. The sampling frequency was set at 5 MHz. The sampling length was set to 1000 for each group of testing experiments. The signal is generated by a function generator (33220A, Agilent, USA) and received by an oscilloscope (MDO3022, Tektronix, USA). The sampling rate was set at 1 MHz, and the sampling length is 2.5 K. The number of samples sampled for each defect is 1000. The guided wave experimental equipment is shown in Figure 4 and Figure 5.

5. Experimental Results and Analysis

5.1. Experiment 1

As shown in Figure 6, from the detection results, all three types of damage were detected. Among them, the corrosion part has a poor detection effect, some pixels are not detected, and the confidence of the target frame is low. The defect part is best detected, and all defects are correctly identified with a high confidence level of the target frame.

As shown in Figure 7 and Figure 8, after 500 iterations, YOLOV5 began to converge, and the three indicators of precision, recall, and mAP were 85.2%, 89.1%, and 90.0% when converging; after 10 parameter adjustments, MAML-YOLOV5 based on MAML-optimized parameters began to converge, and the three indicators of precision, recall, and mAP are 92.3%, 96.2%, and 93.0% when converging, which indicates that the detection effect of MAML-YOLOV5 is better than that of ordinary YOLOV5. From the convergence situation, it can be seen that YOLOV5 has not converged well. At the end of training, the three indicator curves of the model are still jittering, while MAML-YOLOV5 has already converged before the fifth parameter adjustment, and the values of all indicators are all higher than YOLOV5; thus, in the surface damage detection task, MAML’s parameter optimization for YOLOV5 can improve its detection effect and reduce the number of samples.

5.2. Experiment 2

As shown in Figure 9, both types of methods can successfully predict the structural response. As shown in Figure 10, the mean value of the absolute error of the LSTM is 1.532 $\mu \epsilon$ at 1000 time units. The MAML-LSTM-based method has a mean value of absolute error of 2.108 $\mu \epsilon$ at 1000 time units. As shown in Figure 11, the 95% confidence interval (CI) of the prediction error based on LSTM is (−4.525, 3.779), and the 95% confidence interval of the prediction error based on MAML-LSTM is (−6.123, 4.846). Combined with the above experimental results, the findings show that the LSTM with MAML-optimized parameters does not perform as well as the traditional LSTM on the structural response prediction task.

As shown in Figure 12, the RSME of the MAML-LSTM after one adjustment of the parameters has dropped to 0.906, at which point the model has the basic predictive ability, and after 10 adjustments of the parameters, the RSME of the model has dropped to 0.623, which is close to the RSME of the traditional LSTM at 30 convergences and is close to the RSME of the LSTM at 200 convergences of 0.082, which is close to the RSME of the traditional LSTM at 30 times convergence and still shows a difference from the RSME of LSTM at 200 times convergence. These results show that in the structural response task, the detection effect of the LSTM based on the MAML optimization parameters is slightly lower than that of the ordinary training LSTM, but the number of samples is reduced.

5.3. Experiment 3

As shown in Figure 13, the ordinary 1DCNN classification accuracy is 95.17%, and the 1DCNN accuracy based on MAML-optimized parameters is 92.33%, which is lower than the former; these findings indicate that the MAML algorithm does not improve the accuracy of the model on the classification task after parameter optimization of the 1DCNN. As shown in Figure 14, the MAML-1DCNN basically reaches convergence after three parameter adjustments and achieves an accuracy of 89.5%, which is equal to the accuracy of the 1DCNN at 33 iterations, while the 1DCNN reaches a stable accuracy of approximately 95.1% only after 100 iterations. These findings show that in the signal classification task, the classification effect of the LSTM based on the MAML optimization parameters is slightly lower than that of the ordinary training 1DCNN, but the number of samples is reduced.

6. Discussion

After three experiments, through the analysis of the experimental results and evaluation criteria, the role of MAML in the following three areas was determined, and the statistical results are shown in

Table 2. Experimental results and evaluation.

Experiment	Training Method	Number of Samples	Result Evaluation
Bridge steel structure surface damage detection	YOLOV5	300/class	Precision: 85.2% Recall: 89.1% mAP: 90.0%
	MAML- YOLOV5	100/class	Precision: 92.3% Recall: 96.2% mAP: 93.0%
Bridge strain response prediction	LSTM	50,000	Mean value of absolute error: 1.532 $\mu \epsilon$
	MAML- YOLOV5	1000	Mean value of absolute error: 2.108 $\mu \epsilon$
Guided wave signal classification	1DCNN	1000/class	Accuracy: 95.17
	MAML-1DCNN	80/class	Accuracy: 92.33

.

In the task of bridge steel structure surface damage detection, MAML can improve the detection effect of the damage detection model by a small margin and substantially reduce the number of samples. Based on a comprehensive comparison of the three tests of precision, recall, and mAP, MAML has an approximately 5% improvement on the damage detection model, and the required sample size requires only five parameter adjustments for approximately 100 images per category of damage, while the damage detection model trained using the common method requires 300 images per category of damage. The reason for this phenomenon is the quality and quantity of the dataset. Based on the convergence curve of YOLOV5, it can be seen that the model jittered throughout the training cycle, and the jitter decreased at the end of the training but did not completely level off. However, this situation is also in line with the engineering reality that the steel part of the bridge is usually located in a higher position, which requires the use of unmanned aerial vehicles to collect damage images, and the acquisition is so difficult that it is impossible to obtain a high-quality dataset.

In the task of bridge strain response prediction, the prediction accuracy of the deep learning model with optimized parameters of MAML is substantially lower than that of the ordinary structural response prediction model, but the number of samples is substantially reduced. As observed from the error level, the average error of the structural response prediction model with MAML-optimized parameters is 137.6% of that of the ordinary model, and the 95 CI of the error is 132.1% of the former. In terms of the sample size, the prediction model of MAML basically converged after three parameter adjustments, requiring approximately 1000 samples, while the prediction model trained using the ordinary method consumed 50,000 sample points.

In the task of guided wave signal classification, the classification accuracy of the signal classification model with optimized parameters of MAML is slightly lower than that of the ordinary signal classification model, but the number of samples is substantially reduced. In terms of the accuracy of signal classification, the accuracy of the signal classification model with MAML-optimized parameters is 2.84 lower than that of the ordinary signal classification model. In terms of the number of samples, the classification model of MAML basically converges after three parameter adjustments, requiring approximately 80 signal samples for each class of defects, while the ordinary signal classification model requires approximately 1000 signal samples.

7. Conclusions

This study provides a comprehensive summary of deep learning applications in structural health monitoring, focusing on three primary domains: structural surface damage detection, structural response prediction, and data-driven damage recognition. A major challenge across these applications lies in the acquisition of high-quality, large-scale datasets, which constrains the practical deployment of data-driven methodologies in this field. With the recent emergence of meta-learning as a prominent research direction in artificial intelligence, notable for its efficacy in small-sample scenarios, we conducted targeted experiments using Model-Agnostic Meta-Learning (MAML), a representative meta-learning algorithm, to evaluate its potential across key tasks in structural health monitoring.

Our findings indicate that meta-learning holds significant promise for alleviating data scarcity by enabling deep learning models to achieve competitive or superior performance with a fraction of the data required by conventional approaches, although this advantage varies among different detection and prediction tasks. It is important to note, however, that our results are exploratory in nature and subject to several limitations. Specifically, while the meta-learning algorithms and deep learning models employed are widely recognized, they do not represent the most advanced methodologies currently available, and future work with state-of-the-art models may yield further improvements. Additionally, the real-world, self-collected dataset used in our experiments, while valuable, does not fully match the scale or quality of widely used open-source datasets, potentially influencing the generalizability of our results.

In summary, our analysis suggests that meta-learning algorithms have the capacity to substantially relax data requirements and mitigate dataset limitations in structural health monitoring, offering a compelling direction for advancing practical engineering applications where annotated data remain scarce.