Machine learning techniques have established sophisticated relationships between long-span bridge responses and environmental and operational variations (EOVs) for structural health monitoring (SHM) systems. Enhancing the interpretability of the machine learning models can significantly improve the reliability and trustworthiness of the SHM systems. This article proposes an interpretable machine learning framework designed to quantify the impacts of EOVs—specifically temperature variations, temperature gradients, and vehicle loads—on structural responses. Six linear and nonlinear machine learning models were evaluated to identify the most accurate and efficient model. Additionally, three interpretability techniques—regression coefficients, Permutation feature importance, and SHapley Additive exPlanations—were compared to determine the importance rankings of input temperature and vehicle load features on structural responses. The proposed framework was assessed using 21 months of continuous health monitoring data from a cable-stayed bridge. This research advances the application of interpretable machine learning in structural health monitoring.
SohnH.Effects of environmental and operational variability on structural health monitoring. Philos Trans R Soc Math Phys Eng Sci2006; 365: 539–560.
2.
CrossEJWordenKChenQ.Cointegration: a novel approach for the removal of environmental trends in structural health monitoring data. Proc R Soc Math Phys Eng Sci2011; 467: 2712–2732.
3.
FarrarCRWordenK. Structural health monitoring: a machine learning perspective. 1st ed. Chichester, West Sussex, UK: John Wiley & Sons Ltd, 2012 .
4.
DengYDingYLiA.Structural condition assessment of long-span suspension bridges using long-term monitoring data. Earthq Eng Eng Vib2010; 9: 123–131.
KimC-YJungD-SKimN-S, et al. Effect of vehicle weight on natural frequencies of bridges measured from traffic-induced vibration. Earthq Eng Eng Vib2003; 2: 109–115.
7.
ZhuJMengQ.Effective and fine analysis for temperature effect of bridges in natural environments. J Bridge Eng2017; 22: 04017017.
8.
ZhouYSunL.Insights into temperature effects on structural deformation of a cable-stayed bridge based on structural health monitoring. Struct Health Monit2019; 18: 778–791.
9.
ZhouYSunLFuZ, et al. General formulas for estimating temperature-induced mid-span vertical displacement of cable-stayed bridges. Eng Struct2020; 221: 111012.
10.
ShanYLiLXiaQ, et al. Temperature behavior of cable-stayed bridges. Part I—Global 3D temperature distribution by integrating heat-transfer analysis and field monitoring data. Adv Struct Eng2023; 26: 1579–1599.
11.
ShanYJingQLiL, et al. Temperature behavior of cable-stayed bridges. Part II—temperature actions by using unified analysis. Adv Struct Eng2023; 26: 1600–1620.
12.
ChaY-JAliRLewisJ, et al. Deep learning-based structural health monitoring. Autom Constr2024; 161: 105328.
13.
KarampinisIBantilasKEKavvadiasIE, et al. Machine learning algorithms for the prediction of the seismic response of rigid rocking blocks. Appl Sci2024; 14: 341.
14.
LazaridisPCKavvadiasIEDemertzisK, et al. Interpretable machine learning for assessing the cumulative damage of a reinforced concrete frame induced by seismic sequences. Sustainability2023; 15: 12768.
15.
WenJChenCYanX. Based on BP neural network forecast bridge temperature field and its effect on the behavior of bridge deflection. In: Proceedings 2011 International Conference on Transportation, Mechanical, and Electrical Engineering (TMEE). Changchun, China, 16–18 December 2011, pp.1333–1336. New York, NY, USA: IEEE.
16.
OhBKParkHSGlisicB.Prediction of long-term strain in concrete structure using convolutional neural networks, air temperature and time stamp of measurements. Autom Constr2021; 126: 103665.
17.
JesusABrommerPWestgateR, et al. Bayesian structural identification of a long suspension bridge considering temperature and traffic load effects. Struct Health Monit2019; 18: 1310–1323.
18.
HeHWangWZhangX.Frequency modification of continuous beam bridge based on co-integration analysis considering the effect of temperature and humidity. Struct Health Monit2019; 18: 376–389.
19.
XuYLChenBNgCL, et al. Monitoring temperature effect on a long suspension bridge. Struct Control Health Monit2009; 17(6): 632–653.
MangalathuSKarthikeyanKFengD-C, et al. Machine-learning interpretability techniques for seismic performance assessment of infrastructure systems. Eng Struct2022; 250: 112883.
22.
NaserMZ.An engineer’s guide to eXplainable artificial intelligence and interpretable machine learning: Navigating causality, forced goodness, and the false perception of inference. Autom Constr2021; 129: 103821.
23.
XiaoTHongYXuJ, et al. Performance evaluation of cable-stayed bridge expansion joints based on Lasso dimensionality reduction and temperature-displacement-correlation model. Adv Struct Eng2024; 27: 981–994.
24.
HastieTTibshiraniRFriedmanJ.The elements of statistical learning. SpringerNew York, 2009.
ChenTGuestrinC.XGBoost: a scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA, 13–17 August 2016, pp.785–794. New York, NY: Association for Computing Machinery.
29.
KeGMengQFinleyR, et al. LightGBM: a highly efficient gradient boosting decision tree. In: Proceedings of the 31st International Conference on Neural Information Processing Systems. Long Beach, CA, USA, 3–9 December 2017, pp.3149–3157. Red Hook, NY: Curran Associates Inc.
30.
ProkhorenkovaLGusevGVorobevA, et al. CatBoost: unbiased boosting with categorical features. Adv Neural Inf Process Syst. 2018, 31.
31.
FeurerMSpringenbergJTHutterF. Using meta-learning to initialize bayesian optimization of hyperparameters. In: Proceedings of the 2014 International Conference on Meta-Learning and Algorithm Selection, Prague, Czech Republic, 19 August 2014, vol. 1201, pp.3–10. Aachen, DEU, Germany: CEUR-WS.org.
RaschkaS. Model evaluation, model selection, and algorithm selection in machine learning. arXiv preprint, arXiv:1811.12808, 2018.
34.
FisherARudinCDominiciF.All models are wrong, but many are useful: learning a variable’s importance by studying an entire class of prediction models simultaneously. J Mach Learn Res2019; 20: 1–81.
