Accurate and timely detection of structural damage is essential for ensuring the safety and integrity of civil infrastructure. While Bayesian filtering has been widely adopted in structural health monitoring (SHM) for estimating system states and parameters, full-scale parameter estimation can often result in biased outcomes and significant computational costs. To overcome these limitations, this study proposes a framework toward digital twin-enabled SHM by integrating proper orthogonal decomposition (POD) with Bayesian filtering. The framework uses displacement and excitation measurements from the system to estimate states in real-time, updated proper orthogonal mode (POM) slopes, and the location and severity of damage. Structural damage localization is achieved by continuously monitoring changes in the slope of the first POM, which is updated in real time using an online singular value decomposition (SVD) algorithm. Simultaneously, the Unscented Kalman Filter (UKF) estimates system states and selectively updates stiffness parameters, focusing only on degrees of freedom identified as damaged by comparing the evolving POM slopes with a baseline reference derived from the healthy structure. This coordinated operation of online SVD and UKF enables efficient, accurate, and robust assessment of structural condition in real time. The proposed framework addresses three critical stages of SHM that is, detection, localization, and quantification. Its performance is validated through comprehensive numerical simulations on an eight-story shear frame under various damage scenarios, including adjacent-story, non-adjacent, and progressive damage cases. Furthermore, validation on a laboratory-scale three-dimensional steel frame confirms its practical applicability. The results demonstrate that the proposed approach can reliably localize and quantify multiple damage events, offering a scalable solution for real-time SHM.
GlaessgenEStargelD. The digital twin paradigm for future Nasa and US air force vehicles. In: 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference 20th AIAA/ASME/AHS adaptive structures conference 14th AIAA, 2012. p. 1818.
2.
GrievesM. Digital twin: manufacturing excellence through virtual factory replication. White Paper2014; 1(2014): 1–7.
3.
TripuraTDesaiASAdhikariS, et al. Probabilistic machine learning based predictive and interpretable digital twin for dynamical systems. Comput Struct2023; 281: 107008.
4.
CiminoCNegriEFumagalliL. Review of digital twin applications in manufacturing. Comput Industry2019; 113: 103130.
5.
SunTHeXLiZ. Digital twin in healthcare: recent updates and challenges. Digital Health2023; 9: 20552076221149651.
6.
HomaMasoumiPE SaraShirowzhanPettitCJ. City digital twins: their maturity level and differentiation from 3d city models. Big Earth Data2023; 7(1): 1–36.
7.
LehtolaVVKoevaMElberinkSO, et al. Digital twin of a city: Review of technology serving city needs. Int J Appl Earth Observation Geoinform2022; 114: 102915.
8.
WangTGanVJHuD, et al. Digital twin-enabled built environment sensing and monitoring through semantic enrichment of Bim with Sensorml. Autom Construct2022; 144: 104625.
9.
HodaMAKunchamESenS. Enhanced high-resolution structural crack detection using hybrid interacting particle-Kalman filter. In: Structures, 2024, volume 62, p. 106227. Elsevier.
10.
LaiXYangLHeX, et al. Digital twin-based structural health monitoring by combining measurement and computational data: an aircraft wing example. J Manuf Syst2023; 69: 76–90.
11.
LiuCZhangPXuX. Literature review of digital twin technologies for civil infrastructure. Journal of Infrastructure Intelligence and Resilience2023; 2(3): 100050.
12.
AstrozaRConteJPRestrepoJI, et al. Seismic response analysis and modal identification of a full-scale five-story base-isolated building tested on the nees@ ucsd shake table. Eng Struct2021; 238: 112087.
13.
MoaveniBHeXConteJP, et al. System identification study of a 7-story full-scale building slice tested on the UCSD-NEES shake table. J Struct Eng2011; 137(6): 705–717.
14.
SalawuOS. Detection of structural damage through changes in frequency: a review. Eng Struct1997; 19(9): 718–723.
15.
PandeyABiswasMSammanM. Damage detection from changes in curvature mode shapes. J Sound Vibration1991; 145(2): 321–332.
16.
WahabMADe RoeckG. Damage detection in bridges using modal curvatures: application to a real damage scenario. J Sound Vibration1999; 226(2): 217–235.
17.
FransRArfiadiYParungH. Comparative study of mode shapes curvature and damage locating vector methods for damage detection of structures. Procedia Eng2017; 171: 1263–1271.
18.
CiambellaJPauAVestroniF. Modal curvature-based damage localization in weakly damaged continuous beams. Mech Syst Signal Process2019; 121: 171–182.
19.
AvciOAbdeljaberOKiranyazS, et al. A review of vibration-based damage detection in civil structures: from traditional methods to machine learning and deep learning applications. Mech Syst Signal Process2021; 147: 107077.
20.
DessiDCamerlengoG. Damage identification techniques via modal curvature analysis: overview and comparison. Mech Syst Signal Process2015; 52: 181–205.
21.
DoeblingSWFarrarCRPrimeMB, et al. Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review. Technical report, Los Alamos National Lab. (LANL), Los Alamos, NM, USA, 1996.
22.
DoeblingSWFarrarCRPrimeMB, et al. A summary review of vibration-based damage identification methods. Shock Vibration Digest1998; 30(2): 91–105.
23.
GharehbaghiVRNoroozinejad FarsangiENooriM, et al. A critical review on structural health monitoring: definitions, methods, and perspectives. Arch Comput Methods Eng2022; 29(4): 2209–2235.
24.
CaoMRadzieńskiMXuW, et al. Identification of multiple damage in beams based on robust curvature mode shapes. Mech Syst Signal Process2014; 46(2): 468–480.
25.
DahakMTouatNKharoubiM. Damage detection in beam through change in measured frequency and undamaged curvature mode shape. Inverse Problems Sci Eng2019; 27(1): 89–114.
26.
WahabMA. Effect of modal curvatures on damage detection using model updating. Mech Syst Signal Process2001; 15(2): 439–445.
27.
RoyKRay-ChaudhuriS. Fundamental mode shape and its derivatives in structural damage localization. J Sound Vibration2013; 332(21): 5584–5593.
28.
QiaoPLuKLestariW, et al. Curvature mode shape-based damage detection in composite laminated plates. Composite Struct2007; 80(3): 409–428.
29.
RucevskisSJaneliukstisRAkishinP, et al. Mode shape-based damage detection in plate structure without baseline data. Struct Control Health Monit2016; 23(9): 1180–1193.
30.
ChaYJBuyukozturkO. Structural damage detection using modal strain energy and hybrid multiobjective optimization. Comput Aided Civil Infrastruct Eng2015; 30(5): 347–358.
31.
RoyK. Structural damage identification using mode shape slope and curvature. J Eng Mechs2017; 143(9): 04017110.
32.
RoyK. Structural damage quantification in shear buildings using mode shape slope ratio. Struct Health Monit2023; 22(4): 2346–2359.
33.
CruzPJSalgadoR. Performance of vibration-based damage detection methods in bridges. Comput Aid Civil Infrastruct Eng2009; 24(1): 62–79.
34.
IezziFSpinaDValenteC. Damage assessment through changes in mode shapes due to non-proportional damping. In: Journal of physics: conference series, 2015, volume 628, p. 012019. IOP Publishing.
WangDXiangWZengP, et al. Damage identification in shear-type structures using a proper orthogonal decomposition approach. J Sound Vibration2015; 355: 135–149.
37.
ShaneCJhaR. Proper orthogonal decomposition based algorithm for detecting damage location and severity in composite beams. Mech Syst Signal Process2011; 25(3): 1062–1072.
38.
HodaMAMazzantiAShojaiiJ, et al. Unsupervised machine learning for bridge SHM using FPGA: proof of concept via full-scale experiments. Measurement2025; 256: 118717.
39.
ZhouWXuY. Damage identification for beam-like structures based on proper orthogonal modes of guided wavefields. Mech Syst Signal Process2023; 189: 110052.
40.
LeeETEunHC. Damage identification based on the proper orthogonal mode energy curvature. J Vibration Acoust2015; 137(4): 041018.
41.
Eftekhar AzamSRagehALinzellD. Damage detection in structural systems utilizing artificial neural networks and proper orthogonal decomposition. Struct Control Health Monit2019; 26(2): e2288.
42.
HodaSBhattacharyyaB. Prediction of physical space parameters for dynamical systems: a Pod-ANN approach. Comput Struct2025; 316: 107891.
43.
KimMSongJKimCW. Near-real-time damage identification under vehicle loads using dynamic graph neural network based on proper orthogonal decomposition. Mech Syst Signal Process2025; 224: 112175.
44.
GodsillS. Particle filtering: the first 25 years and beyond. In: ICASSP 2019-2019 IEEE International conference on acoustics, speech and signal processing (ICASSP), 2019, pp. 7760–7764. IEEE.
45.
KunchamEHodaMASenS. Identifying the cracks in beam structures using a simplified substructure technique. In: SidhardhSPrakashSSAnnabattulaRK, et al. (eds.) Advances in structural integrity for mechanical, civil, and aerospace applications. Singapore: Springer Nature Singapore, 2025, pp. 43–51.
46.
KalmanRE. A new approach to linear filtering and prediction problems. J Basic Eng1960; 82(1): 35–45.
47.
BeidesHMHeydtGT. Dynamic state estimation of power system harmonics using Kalman filter methodology. IEEE Trans Power Delivery1991; 6(4): 1663–1670.
48.
PengZCheJQiY. Interval response reconstruction based on Kalman filter. In: Structures, 2025, volume 75, p. 108621. Elsevier.
49.
YuKKWatsonNArrillagaJ. An adaptive Kalman filter for dynamic harmonic state estimation and harmonic injection tracking. IEEE Trans Power Delivery2005; 20(2): 1577–1584.
50.
RibeiroMI. Kalman and extended Kalman filters: concept, derivation and properties. Institute Syst Robotics2004; 43(46): 3736–3741.
51.
KunchamESenSKumarPPathakH. An online model-based fatigue life prediction approach using extended Kalman filter. Theor Appl Fract Mech2022; 117: 103143.
52.
RoffelANarasimhanS. Extended Kalman filter for modal identification of structures equipped with a pendulum tuned mass damper. J Sound Vibration2014; 333(23): 6038–6056.
53.
ChatziENSmythAW. The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing. Struct Control Health Monit2009, 16(1): 99–123.
WanEAVan Der MerweR. The unscented Kalman filter for nonlinear estimation. In: Proceedings of the IEEE 2000 adaptive systems for signal processing, communications, and control symposium (Cat. No. 00EX373), 2000, pp. 153–158. IEEE.
56.
WangJMoreiraJCaoY, et al. Time-variant digital twin modeling through the Kalman-generalized sparse identification of nonlinear dynamics. In: 2022 American Control Conference (ACC), 2022, pp. 5217–5222. IEEE.
57.
FengHGomesCLarsenPG. Model-based monitoring and state estimation for digital twins: the Kalman filter. arXiv preprint arXiv:2305.00252, 2023.
58.
DidykMMHassanabadiMENasimiR, et al. Towards digital twinning: Input-state-parameter estimation through extended MVU filter for systems without direct feedthrough using computer vision. Mech Syst Signal Process2025; 230: 112557.
59.
TatsisKEAgathosKChatziE, et al. A hierarchical output-only Bayesian approach for online vibration-based crack detection using parametric reduced-order models. Mech Syst Signal Process2022; 167: 108558.
60.
TchemodanovaSPTatsisKSanayeiM, et al. State estimation for prediction of fatigue life for a rollercoaster connection subjected to operational multiaxial nonproportional loading. J Struct Eng2021; 147(5): 04021041.
61.
BilbaoJLourensEMSchulzeA, et al. Virtual sensing in an onshore wind turbine tower using a Gaussian process latent force model. Data-Centric Eng2022; 3: e35.
62.
AzamSE. Online damage detection in structural systems: applications of proper orthogonal decomposition, and Kalman and particle filters. Springer Science & Business Media, 2014.
63.
Eftekhar AzamSMarianiSAttariN. Online damage detection via a synergy of proper orthogonal decomposition and recursive Bayesian filters. Nonlinear Dynamics2017; 89: 1489–1511.
64.
HodaSBhattacharyyaB. A reduced order model for damage detection of dynamic problems. Struct Eng Conven2023; 460: 165–173.
65.
BhattacharyyaB. Uncertainty quantification of dynamical systems by a POD–Kriging surrogate model. J Comput Sci2022; 60: 101602.
66.
BhattacharyyaBJacquelinEBrizardD. Stochastic analysis of a crash box under impact loading by an adaptive POD-PCE model. Struct Multidisciplinary Optimiz2022; 65(8): 229.
67.
JacquelinEBaldanziniNBhattacharyyaB, et al. Random dynamical system in time domain: a POD-PC model. Mech Syst Signal Process2019; 133: 106251.
68.
TatsisKOuYDertimanisVK, et al. Vibration-based monitoring of a small-scale wind turbine blade under varying climate and operational conditions. part II: a numerical benchmark. Struct Control Health Monit2021; 28(6): e2734.
69.
BrandM. Incremental singular value decomposition of uncertain data with missing values. In: Computer Vision—ECCV 2002: 7th European conference on computer vision Copenhagen, Denmark, May 28–31, 2002 Proceedings, Part I 7, pp. 707–720. Springer.
70.
FareedHSinglerJRZhangY, et al. Incremental proper orthogonal decomposition for PDE simulation data. Comput Mathematics Appl2018; 75(6): 1942–1960.
71.
KühlNFischerHHinzeM, et al. An incremental singular value decomposition approach for large-scale spatially parallel & distributed but temporally serial data–applied to technical flows. Comput Phys Commun2024; 296: 109022.
72.
LiXHulshoffSHickelS. An enhanced algorithm for online proper orthogonal decomposition and its parallelization for unsteady simulations. Comput Mathematics Appl2022; 126: 43–59.
73.
LiuZHassanabadiMEAbolghasemiS, et al. A recursive nonlinear virtual sensing method for joint input-state-parameter estimation of partially measured structures. Eng Struct2025; 330: 119828.
74.
De CallafonRAMoaveniBConteJP, et al. General realization algorithm for modal identification of linear dynamic systems. J Eng Mechs2008; 134(9): 712–722.
75.
AnjneyaKRoyK. Acceleration time history dataset for a 3d miniature model of a shear building with structural damage. Data Brief2021; 38: 107377.
76.
KumarARoyK. Acceleration time history data for experimental shear building model (Kumar Anjneya & Koushik Roy). Mendeley Data, V2, 2021. DOI:10.17632/ snmz587nvb.2.
