Hybrid Deflection-Damage Index (HDDI): A Physics-Informed Framework for Interpretable Structural Health Monitoring

Abstract

This paper introduces the Hybrid Deflection-Damage Index (HDDI), a practical physics-informed framework for interpretable structural health monitoring of civil infrastructure. The approach combines four key measurable indicators deflection utilization, crack severity, stiffness degradation, and load utilization into a single unified Failure Risk Index that tracks the progressive deterioration of structures. By normalizing these indicators and blending them using a transparent weighting scheme, the framework maintains clear engineering meaning while delivering a continuous measure of structural condition. A simple threshold-based system then classifies the structure into three practical states: SAFE, WARNING, and CRITICAL. This helps engineers and asset managers make informed decisions about inspections and maintenance. Designed as a grey-box model, the HDDI bridges the gap between traditional mechanics-based methods and modern data-driven techniques. Its primary contribution is a straightforward, interpretable, and easily extensible damage indexing approach that can be applied to reinforced concrete structures and other infrastructure systems. The framework aims to support more reliable and explainable structural health monitoring in safety-critical applications.

Introduction

The text discusses the need for more interpretable and practical Structural Health Monitoring (SHM) methods for reinforced concrete (RC) structures. Traditional inspection techniques are labor-intensive, subjective, and often fail to detect internal damage early, while many modern machine learning approaches function as "black boxes," making their predictions difficult for engineers to interpret.

To address these limitations, the study proposes the Hybrid Deflection-Damage Index (HDDI), a physics-informed framework that combines multiple structural indicators—deflection utilization, crack severity, stiffness degradation, and load utilization—into a single Failure Risk Index (FRI). The framework provides continuous assessment of structural deterioration and classifies structural conditions into SAFE, WARNING, and CRITICAL categories using transparent threshold-based logic.

The HDDI framework is designed around four layers:

1. Physical Observation – Collects measurable structural responses such as deflection, crack width, applied load, and stiffness changes.
2. Damage Representation – Converts raw measurements into normalized indicators representing different aspects of structural deterioration.
3. Inference – Combines these indicators into a composite Failure Risk Index using simple, explainable aggregation methods.
4. Risk Interpretation – Translates the risk index into practical condition states to support maintenance and decision-making.

Unlike conventional methods that rely on a single parameter or opaque machine learning models, HDDI adopts a grey-box approach, integrating engineering knowledge with computational techniques. The framework emphasizes physical interpretability, normalization, modularity, scalability, algorithm independence, explainability, and extensibility, making it applicable to reinforced concrete structures as well as other infrastructure systems such as bridges and steel structures.

Conclusion

This paper proposed the Hybrid Deflection-Damage Index as a physics-informed framework for interpretable structural health monitoring. The method combines normalized indicators of deflection utilization, crack severity, stiffness degradation, and load utilization into a single Failure Risk Index. A threshold-based interpretation scheme then converts the continuous index into practical condition states such as SAFE, WARNING, and CRITICAL. The result is a transparent and engineer-friendly assessment structure that preserves physical meaning while supporting decision-making[12], [13], [19], [16]. The main contribution of the framework is its ability to represent structural deterioration in a way that is both quantitative and interpretable. Unlike black-box data-driven methods, HDDI makes the role of each input variable explicit. Unlike single-response damage indices, it captures multiple aspects of deterioration within one unified formulation. This makes the approach suitable for reinforced concrete structures and potentially adaptable to other infrastructure systems. The proposed framework is not intended to replace detailed structural analysis or expert judgment. Instead, it is meant to support those processes by providing a clear and interpretable health indicator. Future work should focus on calibration, experimental validation, and extension to more complex loading and failure conditions. With these developments, HDDI has the potential to become a useful tool for practical structural monitoring and maintenance planning.

References

[1] Azimi, M., Dadras Eslamlou, A., & Pekcan, G. (2020). Data-driven structural health monitoring and damage detection through deep learning: State-of-the-art review. Sensors, 20(10), 2778. https://doi.org/10.3390/s20102778 [2] Malekloo, A., Ozer, E., AlHamaydeh, M., & Girolami, M. (2022). Machine learning and structural health monitoring overview with emerging technology and high-dimensional data source highlights. Structural Health Monitoring, 21(4). https://doi.org/10.1177/14759217211036880 [3] Gomez-Cabrera, A., & Escamilla-Ambrosio, P. J. (2022). Review of machine-learning techniques applied to structural health monitoring systems for building and bridge structures. Applied Sciences, 12(21), 10754. https://doi.org/10.3390/app122110754 [4] Gordan, M., Sabbagh-Yazdi, S. R., Ismail, Z., Ghaedi, K., Carroll, P., McCrum, D., & Samali, B. (2022). State-of-the-art review on advancements of data mining in structural health monitoring. Measurement, 196, 110939. https://doi.org/10.1016/j.measurement.2022.110939 [5] Fan, X., Li, J., & Hao, H. (2021). Review of piezoelectric impedance based structural health monitoring: Physics-based and data-driven methods. Structural Health Monitoring, 24(16). https://doi.org/10.1177/13694332211038444 [6] Luleci, F., & Catbas, F. N. (2023). A brief introductory review to deep generative models for civil structural health monitoring. AI in Civil Engineering, 2, Article 9. [7] Cha, Y.-J., Ali, R., Lewis, J., & Büyüköztürk, O. (2024). Deep learning-based structural health monitoring. Automation in Construction, 161, 105328 [8] Dadras Eslamlou, A., & Huang, S. (2022). Artificial neural network-based surrogate models for structural health monitoring of civil structures: A literature review. Buildings, 12(12), 2067. [9] American Concrete Institute (ACI). (2019). Building Code Requirements for Structural Concrete and Commentary (ACI 318-19). American Concrete Institute, Farmington Hills, MI. [10] European Committee for Standardization (CEN). (2004). Eurocode 2: Design of Concrete Structures—Part 1-1: General Rules and Rules for Buildings (EN 1992-1-1:2004). Brussels, Belgium. [11] Park, R., & Ang, A. H.-S. (1985). Mechanistic seismic damage model for reinforced concrete. Journal of Structural Engineering, 111(4), 722–739. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:4(722) [12] Sohn, H., Farrar, C. R., Hemez, F. M., Shunk, D. D., Stinemates, D. W., Nadler, B. R., & Czarnecki, J. J. (2004). A Review of Structural Health Monitoring Literature: 1996–2001. Los Alamos National Laboratory Report LA-13976-MS. [13] Brownjohn, J. M. W. (2007). Structural health monitoring of civil infrastructure. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 365(1851), 589–622. https://doi.org/10.1098/rsta.2006.1925 [14] Kodur, V. K. R., & Naser, M. Z. (2021). Structural fire engineering: Recent advances and future directions. Journal of Structural Engineering, 147(12), 03121001. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003158 [15] Nagarajaiah, S., & Narasimhan, S. (2006). Smart base isolated buildings with variable friction dampers: H? and passivity-based robust control studies. Earthquake Engineering & Structural Dynamics, 35(7), 821–839. https://doi.org/10.1002/eqe.569 [16] Worden, K., & Dulieu-Barton, J. M. (2004). An overview of intelligent fault detection in systems and structures. Structural Health Monitoring, 3(1), 85–98. https://doi.org/10.1177/1475921704041866 [17] Yuen, K.-V., & Kuok, S.-C. (2010). Bayesian methods for updating dynamic models using ambient monitoring data. Probabilistic Engineering Mechanics, 25(1), 154–160. https://doi.org/10.1016/j.probengmech.2009.08.001 [18] Inaudi, D., & Glisic, B. (2010). Long-range monitoring of structures by multiplexed fiber optic systems. Journal of Intelligent Material Systems and Structures, 11(6), 446–456. https://doi.org/10.1106/8BFB-GC8P-XQ47-YDJ8 [19] Totten, G. E., & MacLoughlin, T. R. (Eds.). (2009). Advances in the Use of Structural Health Monitoring Data for the Inspection and Maintenance of Bridge Infrastructure. Transportation Research Board.

Copyright

Copyright © 2026 Jemima Gifta S., Dr. M. Mohamed Younus. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.