Inspired by real-world challenges in long-term bridge monitoring, researchers developed an AI system that rebuilds lost sensor data, boosting accuracy, safety, and confidence in the integrity of modern infrastructure.
Study: Spatiotemporal dependency data imputation for long-term health monitoring of concrete arch bridges. Image Credit: ThamKC/Shutterstock.com
In a recent study published in the journal Scientific Reports, researchers introduced a novel deep learning framework, the Cross-Correlation Function Bidirectional Gated Recurrent Unit (CCF-BiGRU), to impute missing data in long-term structural health monitoring (SHM) of concrete arch bridges. The goal was to address sensor data loss caused by environmental disruptions or equipment failures.
By integrating spatial correlations and temporal dependencies, CCF-BiGRU significantly enhances the accuracy and reliability of strain data recovery, improving the assessment, operational efficiency, maintenance, and safety of bridge structures.
Challenges in Structural Health Monitoring
SHM systems are essential for ensuring the safety and durability of civil infrastructure, particularly bridges. These systems utilize sensor networks to continuously record parameters such as strain, displacement, and vibration. However, in real-world applications, data loss due to sensor malfunctions, transmission errors, or environmental interference can compromise model accuracy and delay maintenance decisions.
To address these challenges, engineers have developed various data imputation techniques, including compressive sensing, statistical interpolation, and deep learning. Among these, deep learning models capable of capturing nonlinear and spatiotemporal relationships have proven effective for reconstructing missing data in SHM systems.
CCF-BiGRU: A Framework for Data Recovery
The presented CCF-BiGRU model combines the Cross-Correlation Function (CCF) algorithm with a Bidirectional Gated Recurrent Unit (BiGRU) neural network. This architecture was mainly designed to recover missing strain data in concrete arch bridges.
Unlike graph neural network (GNN) approaches, the CCF-BiGRU model autonomously determines spatial dependencies without requiring predefined adjacency matrices, enhancing adaptability to dynamic bridge conditions.
The CCF component quantifies temporal relationships among sensors via time-lagged correlations, identifying the most relevant for reconstructing missing data. It captures dynamic interactions and delayed strain propagation caused by environmental loads.
Similarly, the BiGRU module processes time-series data, enhancing the model’s ability to learn long-term dependencies and nonlinear patterns. This improves prediction accuracy in complex structural environments where strain responses evolve.
The model was validated using real-world data from the Dongjiang Bridge in Huizhou, China, an 805.73-meter concrete arch bridge with 18 spans and 222 vibrating-wire strain sensors installed at the arch crowns. Data was collected over 32 months across 971 time steps per sensor, with missing rates of 5–20 % introduced to simulate real-world conditions.
Data preprocessing involved Kalman filtering for noise reduction and normalization, followed by a sliding window technique to generate training samples. The model was trained using the Adam optimizer technique and evaluated with metrics such as Root Mean Square Error (RMSE), Correlation Coefficient (R), and Relative Accuracy (RA).
Evaluating Model Performance and Robustness
The CCF-BiGRU model consistently outperformed BiGRU, GRU, Long Short-Term Memory (LSTM), and Bidirectional LSTM (BiLSTM) across all evaluation metrics. At just a 5 % missing data rate, it achieved an average RMSE of 4.83, an R value of 0.987, and a relative accuracy of 0.42, showing strong precision in reconstructing missing strain data.
Even when the missing data rate increased to 20 %, the model’s performance remained stable, highlighting its robustness under more challenging conditions.
While the CCF-BiLSTM model delivered similar accuracy, it came with a higher computational cost. Training times were roughly 28 % longer, and inference was 40 % slower compared to CCF-BiGRU. In contrast, the proposed model struck a better balance between accuracy and efficiency, making it more suitable for large-scale or resource-constrained applications.
Computational analysis also showed that although the CCF preprocessing step increased training time by about 15 %, it led to better imputation results. Its low inference time is another key advantage, supporting real-time use in bridge monitoring systems.
It’s important to note that these experiments were conducted under the assumption of data missing completely at random (MCAR), meaning the data gaps weren’t tied to any structural conditions. Exploring how the model performs under other scenarios - like missing at random (MAR) or not missing at random (NMAR) - is a valuable direction for future research.
This research could make a real difference in how we manage and maintain concrete arch bridges and other civil structures. By filling in missing data accurately, the model helps keep monitoring systems running smoothly and catches early signs of structural issues - reducing the chances of something going wrong and supporting timely maintenance.
What’s more, the model is designed to work well even in complex, sensor-heavy environments like long-span bridges and dense urban infrastructure. And it’s not just limited to bridges, the same approach could be useful for tunnels, high-rises, and transport networks where losing sensor data can be a big problem.
Conclusion
To sum up, this study offers a practical and well-rounded approach to improving SHM. By combining spatial insights from CCF with the time-series modeling power of BiGRU, the researchers tackled a common but critical problem: how to recover missing sensor data reliably. The result is a model that’s not only accurate and robust but also efficient enough to be used in real-world systems, especially for monitoring the health of concrete arch bridges.
What makes the CCF-BiGRU model especially valuable is its ability to capture complex data patterns on its own while keeping computational costs low. This balance makes it a strong candidate for large-scale monitoring efforts, especially as infrastructure ages and cities continue to grow. Reliable, intelligent tools like this will be key to building safer and more sustainable urban environments.
That said, there’s still room to grow. Future work should look at adding environmental factors like temperature and humidity into the model and explore real-time learning to make it even more adaptable. Testing it across different types of structures and locations will also help ensure it performs well in a variety of real-world settings.
Journal Reference
Longji, Z., & et al. (2025). Spatiotemporal dependency data imputation for long-term health monitoring of concrete arch bridges. Sci Rep 15, 36218. DOI: 10.1038/s41598-025-20126-2, https://www.nature.com/articles/s41598-025-20126-2
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