Indirect Structural Health Monitoring

• Indirect Structural Health Monitoring (ISHM) is defined as inferring a structure’s condition from secondary measurements, such as vibrations, thermal imaging, and wireless signals, rather than direct damage observation.
• It employs advanced signal processing, feature extraction, and probabilistic methods—including Bayesian and physics-informed models—to isolate damage signatures amidst environmental and operational variability.
• ISHM offers cost-effective and scalable monitoring through diverse sensing architectures like drive‐by inspections and autonomous platforms, while also facing challenges in noise robustness and calibration.

Indirect Structural Health Monitoring (ISHM) denotes the inference of structural condition from indirect measurements of structural responses, often under ambient or operational loads, rather than from direct observation of damage or dense direct instrumentation. In bridge monitoring, a canonical example is evaluating bridge health by monitoring vehicle responses rather than bridge-mounted sensors; more broadly, ISHM includes response-based diagnosis from vibration, acceleration, strain, thermal, LiDAR, and wireless measurements. The literature consistently frames the appeal of ISHM in terms of reduced instrumentation burden, lower deployment cost, and improved scalability, while also emphasizing that indirect signatures are entangled with environmental and operational variability, complex structural and vehicle dynamics, signal noise, and limited labeled data (Madabhushi, 2023, Hurtado et al., 1 Oct 2025, Bull et al., 2021, Bradley et al., 30 Apr 2026).

1. Conceptual scope and inferential character

ISHM is defined by how information is obtained rather than by a single sensor class or algorithm. The common feature is that structural state is inferred from secondary observables: vibration signatures, vehicle accelerations, stochastic response trajectories, temperature fields, radio localization of reference points, or latent representations learned from response histories. In that sense, the monitored quantity is not damage itself, but a response process whose statistical or dynamical properties are affected by damage.

The distinction from direct monitoring is operational as well as epistemic. Direct monitoring can be complicated and expensive, whereas indirect methods can be much cheaper and easier to conduct; at the same time, accurate results are nontrivial because the measurement channel is indirect by construction (Madabhushi, 2023). Several studies also stress that indirect methods are particularly relevant when direct diagnosis is impractical for inaccessible or remote systems, or when controlled excitation is not feasible (Rinn et al., 2012). In smart-structure settings, response-based diagnosis is used to infer internal characteristics such as delaminations or structural degradation from embedded fiber optic sensors and piezoelectric transducers rather than from direct inspection of defects (0705.3669).

A recurrent misconception is that indirect monitoring is synonymous with model-free monitoring. The literature does not support that equivalence. Baseline-comparison methods can indeed operate without a detailed analytical model, but probabilistic, Bayesian, physics-informed, and digital-twin formulations are equally central to ISHM practice [(0705.4654); (Bull et al., 2021); (Bradley et al., 30 Apr 2026); (Kaewnuratchadasorn et al., 2023)]. This suggests that ISHM is better understood as a family of inferential strategies ranging from baseline statistics to operator learning and hierarchical Bayes.

2. Measurement architectures and observed data

The sensing architectures used in ISHM are heterogeneous, but they are unified by their emphasis on response observability. One early vibration-based configuration is the Active Damage Interrogation (ADI) system, which uses an array of piezoelectric transducers attached to or embedded within a composite structure for both actuation and sensing. In the reported rotorcraft flexbeam study, 4 half-inch square PZT wafers were applied to a local area, broadband excitation was applied across a desired frequency range, and transfer functions between each actuator/sensor pair were used to characterize the vibration signature (0705.4654).

A related smart-structures line uses embedded fiber optic strain sensors and piezoelectric transducers to capture transient dynamic response. In the neural-network-based vibrational system identification study, the measured data were time-sequences of displacement or strain, and the first four natural vibration modes of a cantilevered laminated composite beam, with frequencies ranging up to approximately $54.4$ Hz, were analyzed as damage-sensitive observables (0705.3669).

Drive-by bridge inspection represents the most explicit bridge-focused form of ISHM. A laboratory study used a model bridge and a model car equipped with four uniaxial Mistras Model 5102 accelerometers, with two accelerometers on the car chassis and two on the wheel axles; no sensors were installed on the bridge (Madabhushi, 2023). A later field study developed a purpose-built autonomous electric inspection vehicle, adapted to carry four PCB-ICP393B05 accelerometers and four Honeywell Model 31 load cells, with constant, low, and customizable speeds to improve repeatability in indirect sensing (Hurtado et al., 1 Oct 2025).

Recent work broadens the sensor concept beyond acceleration and strain. Thermo-LIO fuses thermal imaging with high-resolution LiDAR and integrates the result with LiDAR-Inertial Odometry, enabling full coverage of large-scale structures and quantitative 3D representations of temperature distributions in buildings and bridges (Yang et al., 13 Jan 2026). In wireless ISHM, reconfigurable intelligent surfaces are used as monitorable reference points affixed to structural elements, while base stations and users sense RIS location through radio signals, enabling non-contact deformation sensing in three-dimensional cellular networks (Yang et al., 3 Jul 2025).

These measurement architectures cover local composite inspection, drive-by bridge monitoring, large-scale civil thermography, and non-contact radio sensing. A plausible implication is that the observable space of ISHM is expanding from classical modal signatures toward multimodal spatio-temporal fields.

3. Signal processing, feature extraction, and damage inference

The methodological core of ISHM is the transformation of response data into damage-sensitive features. In ADI, several healthy-state datasets are first collected, transfer functions $H_{ij}(f)$ are estimated for each actuator-sensor pair, and the baseline mean and standard deviation are computed for magnitude and phase at each frequency bin. Damage interrogation then computes a normalized deviation,

$$\Delta_{ij}(f)=\frac{H_{ij}^{\text{current}}(f)-\overline{H}_{ij}^{\text{baseline}}(f)}{\sigma_{ij}^{\text{baseline}}(f)},$$

followed by windowed averaging and spectral integration to form the Cumulative Average Delta,

$$\text{CAD}_{ij}=\frac{1}{N_f}\sum_{f=1}^{N_f}|\Delta_{ij}(f)|.$$

The damage index is compared to a threshold, and localization is based on the transducer with the highest index. In the MD Explorer flexbeam dataset, the system detected all induced delaminations, with 100% detection and 0% false alarms, and the damage index increased with the size of the delamination (0705.4654).

In drive-by bridge quantification, raw acceleration time series and their frequency-domain transforms are both used. One study normalized acceleration data, performed a Fast-Fourier Transform, extracted three principal components from normalized acceleration and normalized FFT data using Non-Linear Principal Component Analysis, and then trained Support Vector Regression and Gaussian Process Regression models. With 20% of the data reserved for testing and 5-fold cross-validation, the best overall result was obtained by combining acceleration and FFT principal components with a Gaussian Process Regression model using an ARD Matérn $3/2$ kernel, giving an MSE of approximately $100$ and an expected error of approximately $10$ g (Madabhushi, 2023).

A different signal-processing philosophy is used in stochastic in-situ damage analysis. Rather than relying on global spectral shifts, the method reconstructs stochastic differential equations from measured beam deflections under turbulent wind using Kramers-Moyal coefficients. The drift coefficient $D^{(1)}$ isolates deterministic restoring behavior, and the slope of the drift function near the origin is linked to stiffness. In the reported beam experiments, the drift slope decreased by approximately $6\%$ after thermal damage and approximately $28\%$ after cutting, whereas the corresponding eigenfrequency shifts were approximately $H_{ij}(f)$0 and $H_{ij}(f)$1, respectively; the reported conclusion is that drift slope analysis is several times more sensitive in noisy environments (Rinn et al., 2012).

Unsupervised sequence models have also entered ISHM. For rail infrastructure, an incremental synthetic benchmark introduces speed variation, multi-channel inputs, noise changes, high-frequency local noise, and periodic impulses. Within that benchmark, an Attention-Focused Transformer uses reconstruction training but derives anomaly scores mainly from deviations in learned attention weights. The reported finding is that transformer-based models generally outperform other unsupervised baselines as complexity rises, but all tested models remain vulnerable to high-frequency localized noise, which causes the major performance drop (Ma et al., 8 Oct 2025).

4. Probabilistic, Bayesian, and physics-informed formulations

Probabilistic inference is a natural fit for ISHM because the measured signals are noisy, incomplete, and frequently unlabeled. A review of probabilistic learning modes in SHM emphasizes semi-supervised learning, active learning, Dirichlet Process mixture models, and multi-task learning as mechanisms for dealing with missing labels, streaming data, and unknown operational or damage states. The cited case studies include a semi-supervised Gaussian Mixture Model on the Gnat aircraft wing dataset, active learning and nonparametric clustering on the Z24 bridge, and Kernelized Bayesian Transfer Learning on simulated and experimental shear-building structures (Bull et al., 2021).

Hierarchical Bayes extends this logic to populations of similar structures. In ship hull monitoring, a hierarchical Bayesian model is used to infer the distributions of out-of-plane deflection amplitudes for a population of plate elements. At the plate level,

$H_{ij}(f)$2

while the plate-specific parameters are drawn from population-level distributions with Gamma hyperpriors, and the observed strain is modeled through an FE-based surrogate likelihood,

$H_{ij}(f)$3

The reported comparison with an independent model shows that, under data sparsity conditions, the hierarchical model yields narrower posteriors and more robust uncertainty quantification for the data-scarce plate (Aravanis et al., 18 Oct 2025).

Physics-informed machine learning introduces another layer of structure by embedding prior physical knowledge into the regression model. A Gaussian-process study compares a purely data-driven Squared Exponential kernel,

$H_{ij}(f)$4

with grey-box variants that multiply it by a periodic kernel,

$H_{ij}(f)$5

In the toy example, the data coverage required to reach the NMSE threshold was $H_{ij}(f)$6 for Black-1, $H_{ij}(f)$7 for Grey-1, and $H_{ij}(f)$8 for Grey-2, with estimated emissions of $H_{ij}(f)$9, $$\Delta_{ij}(f)=\frac{H_{ij}^{\text{current}}(f)-\overline{H}_{ij}^{\text{baseline}}(f)}{\sigma_{ij}^{\text{baseline}}(f)},$$0, and $$\Delta_{ij}(f)=\frac{H_{ij}^{\text{current}}(f)-\overline{H}_{ij}^{\text{baseline}}(f)}{\sigma_{ij}^{\text{baseline}}(f)},$$1 $$\Delta_{ij}(f)=\frac{H_{ij}^{\text{current}}(f)-\overline{H}_{ij}^{\text{baseline}}(f)}{\sigma_{ij}^{\text{baseline}}(f)},$$2, respectively. In the GARTEUR case, grey-box models again needed less coverage, but the carbon advantage was not uniform for small datasets because extra hyperparameters increase runtime; in the upsampled setting, Grey-2 required $$\Delta_{ij}(f)=\frac{H_{ij}^{\text{current}}(f)-\overline{H}_{ij}^{\text{baseline}}(f)}{\sigma_{ij}^{\text{baseline}}(f)},$$3 coverage and $$\Delta_{ij}(f)=\frac{H_{ij}^{\text{current}}(f)-\overline{H}_{ij}^{\text{baseline}}(f)}{\sigma_{ij}^{\text{baseline}}(f)},$$4 $$\Delta_{ij}(f)=\frac{H_{ij}^{\text{current}}(f)-\overline{H}_{ij}^{\text{baseline}}(f)}{\sigma_{ij}^{\text{baseline}}(f)},$$5, compared with $$\Delta_{ij}(f)=\frac{H_{ij}^{\text{current}}(f)-\overline{H}_{ij}^{\text{baseline}}(f)}{\sigma_{ij}^{\text{baseline}}(f)},$$6 coverage and $$\Delta_{ij}(f)=\frac{H_{ij}^{\text{current}}(f)-\overline{H}_{ij}^{\text{baseline}}(f)}{\sigma_{ij}^{\text{baseline}}(f)},$$7 $$\Delta_{ij}(f)=\frac{H_{ij}^{\text{current}}(f)-\overline{H}_{ij}^{\text{baseline}}(f)}{\sigma_{ij}^{\text{baseline}}(f)},$$8 for Black-1 (Bradley et al., 30 Apr 2026).

Across these formulations, the common theme is uncertainty-aware inference under partial observability. This suggests that advanced ISHM is increasingly defined not just by indirect sensing, but by explicit treatment of epistemic and aleatory uncertainty.

5. Drive-by bridges, digital twins, and autonomous systems

Bridge monitoring has become the most active testbed for contemporary ISHM. The drive-by paradigm is no longer restricted to laboratory proof-of-concept studies; it now includes field validation on full-scale bridges, autonomous scanning platforms, and learned digital twins.

A central development is the Vehicle-bridge Interaction Neural Operator (VINO), built on the Fourier Neural Operator paradigm and trained to learn mappings between structural response fields and damage fields. The numerical VBI-FE dataset contains 1,200 parametric finite element simulations, with 1,000 used for training and 200 for testing, while the experimental VBI-EXP dataset contains four scenarios: INT, DMG1, DMG2, and DMG3. After pre-training on VBI-FE and fine-tuning only on healthy-state experimental data, forward VINO predicted structural responses more accurately than the FE model, and inverse VINO detected, localized, and quantified damage in all scenarios. The reported inference speed was over 19 times faster than FE after training, and the estimated damage-field errors were at most $$\Delta_{ij}(f)=\frac{H_{ij}^{\text{current}}(f)-\overline{H}_{ij}^{\text{baseline}}(f)}{\sigma_{ij}^{\text{baseline}}(f)},$$9 relative to true damage magnitudes greater than $$\text{CAD}_{ij}=\frac{1}{N_f}\sum_{f=1}^{N_f}|\Delta_{ij}(f)|.$$0 (Kaewnuratchadasorn et al., 2023).

Field-scale bridge inspection has also been advanced through a fully customised electric inspection vehicle. The autonomous platform was tested on the 17 m UNSW Pedestrian Bridge and the 23.9 m Bulli Colliery Bridge, with Frequency Domain Decomposition used to identify both vehicle and bridge modal properties. The vehicle driving frequency $$\text{CAD}_{ij}=\frac{1}{N_f}\sum_{f=1}^{N_f}|\Delta_{ij}(f)|.$$1 was found to be around $$\text{CAD}_{ij}=\frac{1}{N_f}\sum_{f=1}^{N_f}|\Delta_{ij}(f)|.$$2 Hz, and the indirectly identified bridge natural frequencies were approximately $$\text{CAD}_{ij}=\frac{1}{N_f}\sum_{f=1}^{N_f}|\Delta_{ij}(f)|.$$3 Hz for the UNSW bridge and approximately $$\text{CAD}_{ij}=\frac{1}{N_f}\sum_{f=1}^{N_f}|\Delta_{ij}(f)|.$$4 Hz for the Bulli bridge. Under simulated damage on the UNSW bridge, implemented as localized mass addition by 5 people at midspan, both the Adversarial Autoencoder and the Matrix Profile framework detected the induced state change, with the AAE achieving perfect separation between nominal and damaged samples; on the Bulli bridge, both frameworks confirmed a consistent healthy state with minimal to no false alarms (Hurtado et al., 1 Oct 2025).

Automation is also being pushed into workflow orchestration. SHM-Agents combines LLMs with specialized SHM algorithms in a generalist-specialist agent system capable of end-to-end execution of tasks such as data anomaly diagnosis and recovery, signal processing, statistical analysis, modal identification, damage identification, finite element model updating, vehicle load modeling, response calculation, reliability assessment, fatigue estimation, and bridge knowledge Q{data}A. In the reported cable-stayed bridge experiments, the system processed data from 11 acceleration sensors at 50 Hz and a WIM system, produced modal estimates such as $$\text{CAD}_{ij}=\frac{1}{N_f}\sum_{f=1}^{N_f}|\Delta_{ij}(f)|.$$5 Hz, $$\text{CAD}_{ij}=\frac{1}{N_f}\sum_{f=1}^{N_f}|\Delta_{ij}(f)|.$$6 Hz, and $$\text{CAD}_{ij}=\frac{1}{N_f}\sum_{f=1}^{N_f}|\Delta_{ij}(f)|.$$7 Hz for the first three orders, and reported reliability of $$\text{CAD}_{ij}=\frac{1}{N_f}\sum_{f=1}^{N_f}|\Delta_{ij}(f)|.$$8, failure probability of $$\text{CAD}_{ij}=\frac{1}{N_f}\sum_{f=1}^{N_f}|\Delta_{ij}(f)|.$$9, and reliability index $3/2$0 in a model-updating and reliability-analysis workflow (Bao et al., 13 May 2026).

6. Limitations, controversies, and emerging directions

The principal limitation of ISHM is not sensing alone but identifiability under confounding variability. In vibration-based baseline methods, changes in the vibration signature can be caused by factors other than damage, including environmental and operational variations; temperature, humidity, and static loading were specifically identified as factors requiring further study and calibration in the composite ADI work (0705.4654). In drive-by bridge monitoring, real-world effectiveness remains to be established beyond laboratory-scale tests, and representative training data remain critical for robust regression (Madabhushi, 2023).

Noise robustness is a particularly sharp issue for unsupervised deep learning. In the rail benchmark, all models exhibited significant vulnerability to high-frequency localized noise; the reported AUC for the proposed transformer dropped from approximately $3/2$1 to $3/2$2, while LSTM and CNN autoencoder baselines dropped to $3/2$3 and $3/2$4, respectively. For 6-channel data evaluated on 3000 sequences with batch size 32, the reported inference times were $3/2$5 s for the proposed model, $3/2$6 s for the Anomaly Transformer, and $3/2$7 s for MSCRED, so efficiency gains do not eliminate the unresolved noise bottleneck (Ma et al., 8 Oct 2025).

Wireless ISHM introduces a different controversy: whether radio sensing can meet the ultra-high precision required for slow and subtle structural changes. The RIS-aided cooperative ISAC framework addresses this through dynamic RIS phase switching, Fisher-information-based design, and Bayesian inference for structural state detection. The reported theoretical and numerical analyses indicate that increasing observation time, adding collaborating receivers, optimizing RIS phases, and refining collaborative node selection can reduce the Position Error Bound to millimeter-level or sub-millimeter scales, with detection probability approaching or exceeding $3/2$8 under feasible configurations (Yang et al., 3 Jul 2025). The significance is substantial, but the framework remains explicitly theoretical and numerical.

Multimodal civil inspection systems broaden coverage but do not remove practical constraints. Thermo-LIO demonstrates real-time 3D temperature-mapped point clouds and improved defect localization in a bridge and a hall building, yet the reported limitations include restricted handheld resolution for very fine or distant defects and nighttime thermal sensor noise due to automatic illumination (Yang et al., 13 Jan 2026). A plausible implication is that future ISHM will rely increasingly on sensor fusion, but that calibration, synchronization, and platform stability will remain first-order methodological concerns.

Taken together, the literature presents ISHM as a mature but still contested research area. Its strengths lie in non-invasive deployment, scalability, uncertainty-aware inference, and the ability to learn from operational data. Its unresolved issues lie in confounder disentanglement, domain shift, high-frequency noise robustness, field validation, and the translation of increasingly sophisticated models into reliable decision support under real operating conditions.