Seismic Structural Health Monitoring

• Seismic Structural Health Monitoring (SSHM) is a method that applies seismic excitations and ambient noise to monitor structural integrity and detect damage.
• It employs techniques such as output-only modal identification, EEMD–HT–ANN frameworks, and diffractive optical sensing to extract modal frequencies and assess stiffness changes.
• By integrating diverse sensing architectures with advanced inference algorithms, SSHM delivers actionable insights for immediate damage detection and post-seismic recovery planning.

Seismic Structural Health Monitoring (SSHM) is the use of seismic excitation and seismic ambient noise to detect anomalies, identify damage, assess structural condition, and support post-event decision-making. In the cited literature, earthquakes are described as imparting highly non-stationary, multi-directional inertial forces to structures; under a design-level ground motion, members may enter the inelastic range, causing stiffness degradation, strength loss and permanent drift. Complementarily, seismic ambient noise is reported to provide precious information about the structural behavior of old buildings, and its use for dynamic identification and structural health monitoring initiated an emerging, cross-disciplinary field engaging seismologists, engineers, mathematicians, and computer scientists (Vazirizade et al., 2018, Carrara et al., 2022). Across the studies considered here, SSHM includes output-only modal identification, unsupervised anomaly detection, ANN-based damage onset detection and stiffness estimation, event-driven wireless sensing, diffractive optical vibration monitoring, and probabilistic quantification of resilience benefit in post-earthquake recovery (Sarwar et al., 2019, Wang et al., 3 Jun 2025, Liang et al., 14 Aug 2025).

1. Scope, objectives, and operating regimes

SSHM addresses both immediate seismic response and long-term monitoring. Under earthquake loading, early detection of the onset of damage is critical for ensuring occupant safety, preventing collapse or progressive damage under aftershocks, and validating and updating performance-based design models. Real-time SSHM is therefore framed as a mechanism for immediate detection and localization of damage, giving engineers and emergency managers actionable information (Vazirizade et al., 2018).

The literature also treats SSHM as a long-duration observational problem. In the heritage-monitoring setting, the structural response is inferred from ambient vibrations produced by anthropic and environmental sources. This extends SSHM beyond triggered strong-motion recording to continuous tracking of modal behavior, seasonal dependence, and rare anomalies. A plausible implication is that SSHM spans at least two distinct operating regimes: event-driven monitoring during strong excitation and persistent monitoring during nominal operation (Carrara et al., 2022).

The objectives differ accordingly. In one regime, the target is damage onset detection, story localization, and stiffness-loss estimation during an earthquake. In another, the target is unsupervised detection of deviations from learned normal modal dynamics. In infrastructure-recovery studies, SSHM is further treated as a source of damage information whose quality affects repair scheduling and system-level resilience (Liang et al., 14 Aug 2025).

2. Measurements, state variables, and modal representations

In the ambient-noise heritage pipeline, the measured signal at each of four instrumented heights is a tri-axial ground velocity record

$$x^{(k)}(t) = [x_1^{(k)}(t), x_2^{(k)}(t), x_3^{(k)}(t)]^{\top},$$

sampled at $f_s = 100$ Hz for $k=1\ldots 4$. All channels are stacked into a 12-dimensional vector $x(t)\in\mathbb{R}^{12}$. Over non-overlapping one-hour windows $[T_h, T_h+3600\,\mathrm{s}]$, output covariance tensors are estimated as

$$R_{\tau}=E[x(t)x(t+\tau)^{\top}], \qquad \tau=0,\ldots,N_{\mathrm{lags}}.$$

Block Hankel matrices are formed and an SVD is used to extract a state-space realization with system matrices $(A,B,C,D)$. If $\lambda_i$ denotes an eigenvalue of $A$, the $i$-th natural frequency is obtained as

$f_s = 100$0

Repeating this hourly yields $f_s = 100$1 for $f_s = 100$2, and the structural state is encoded as

$f_s = 100$3

Environmental covariates are

$f_s = 100$4

and temporal-fingerprint features are

$f_s = 100$5

These variables define the forecasting state for anomaly detection (Carrara et al., 2022).

In the earthquake-response pipeline based on Ensemble Empirical Mode Decomposition (EEMD) and Hilbert Transform (HT), each story acceleration signal is decomposed into Intrinsic Mode Functions (IMFs). An IMF $f_s = 100$6 is defined by two conditions: the number of zero crossings and extrema differ at most by one, and the local mean of the upper and lower envelopes is zero. For EEMD, white noise $f_s = 100$7 is added to form

$f_s = 100$8

each realization is decomposed by classical EMD, and the IMFs are averaged:

$f_s = 100$9

The Hilbert transform then defines the analytic signal

$k=1\ldots 4$0

from which instantaneous frequency is

$k=1\ldots 4$1

The first bending-mode frequency is identified from a histogram of instantaneous frequencies, and the first-mode shape is obtained by normalizing the instantaneous amplitude of the corresponding IMF at each story by the amplitude at the top story (Vazirizade et al., 2018).

In diffractive optical vibration monitoring, the state is not measured by dense contact sensors. Instead, a scalar complex illumination field $k=1\ldots 4$2 is modulated by a phase-only diffractive layer with local phase profile $k=1\ldots 4$3, yielding

$k=1\ldots 4$4

Structural vibrations modulate the layer height so that

$k=1\ldots 4$5

and shallow neural networks decode detector signals into 3D displacement spectra (Wang et al., 3 Jun 2025).

Pipeline	Measured signals	State representation
SSI-based ambient-noise monitoring	Four tri-axial ground velocity signals at 100 Hz plus environmental covariates	$k=1\ldots 4$6 from five modal frequencies
EEMD + HT + ANN	Story acceleration signals	First mode frequency $k=1\ldots 4$7 and relative first-mode shape vector $k=1\ldots 4$8
Diffractive optical monitoring	Time-series detector intensities from passive optical encoding	Reconstructed 3D displacement spectra $k=1\ldots 4$9

These state definitions illustrate that SSHM is not tied to a single sensing modality. The monitored quantity may be a modal-frequency vector, a low-order mode-shape descriptor, or a decoded spectral representation, provided that changes in that quantity correlate with structural condition.

3. Detection and inference algorithms

In the San Frediano bell tower study, the monitoring problem is framed as an unsupervised anomaly detection task. A Temporal Fusion Transformer (TFT) is trained to learn the normal dynamics of the structure and to detect anomalies from differences between predicted and observed frequencies. The architecture combines static covariate encoders for $x(t)\in\mathbb{R}^{12}$0, gated residual LSTM layers, variable selection networks, multi-head self-attention, temporal multi-head attention, and quantile output heads. The typical configuration reported is: embedding dimension 16; one encoder and one decoder LSTM layer with hidden size 64; multi-head attention with 4 heads of size 16; dropout 0.1; and 7 quantiles at 1%, 10%, 25%, 50%, 75%, 90%, and 99%. Training uses the sum of quantile losses over all output quantiles and all five frequency targets,

$x(t)\in\mathbb{R}^{12}$1

with $x(t)\in\mathbb{R}^{12}$2, Adam with learning rate $x(t)\in\mathbb{R}^{12}$3 and weight decay $x(t)\in\mathbb{R}^{12}$4, batch size 32, and 100 epochs with early stopping on validation loss. The training split is 28 Oct 2015–30 June 2016, the validation split is 1 July–13 Aug 2016, the window length is $x(t)\in\mathbb{R}^{12}$5 hours, and the horizon is $x(t)\in\mathbb{R}^{12}$6 hour (Carrara et al., 2022).

The anomaly criterion is quantile-based. If

$x(t)\in\mathbb{R}^{12}$7

then the measured frequency $x(t)\in\mathbb{R}^{12}$8 is anomalous when $x(t)\in\mathbb{R}^{12}$9 or $[T_h, T_h+3600\,\mathrm{s}]$0. The per-mode normalized anomaly score is defined piecewise:

$[T_h, T_h+3600\,\mathrm{s}]$1

and the overall score is

$[T_h, T_h+3600\,\mathrm{s}]$2

where $[T_h, T_h+3600\,\mathrm{s}]$3 is the mean of mode $[T_h, T_h+3600\,\mathrm{s}]$4 over the training set. A threshold $[T_h, T_h+3600\,\mathrm{s}]$5 such as $[T_h, T_h+3600\,\mathrm{s}]$6 may be chosen via inspection or by fixing a desired false-alarm rate on a held-out normal segment. In the reported test interval, the Amatrice earthquake on 24 Aug 2016 at 03:00 UTC caused all five modes to violate high quantiles; the Santa Croce celebrations on 13 Sep 2016 yielded a clear anomaly in the second mode driven by crowds; and weekly bell-swing peaks on Saturdays and Sundays were visible as recurring anomalies in mode 2. In this preliminary study, all known events in the test window were correctly flagged, with negligible false alarms outside celebratory weekends (Carrara et al., 2022).

The EEMD–HT–ANN framework uses two sequential ANN tasks. The first is an emulator network for damage onset detection. Under undamaged conditions, each story’s acceleration time-history is assumed predictable from past values. A feed-forward multilayer perceptron or radial-basis-function network takes accelerations at times $[T_h, T_h+3600\,\mathrm{s}]$7 from the target story and its immediate neighbors and predicts $[T_h, T_h+3600\,\mathrm{s}]$8. The loss is mean-square error,

$[T_h, T_h+3600\,\mathrm{s}]$9

and the damage-onset indicator is

$$R_{\tau}=E[x(t)x(t+\tau)^{\top}], \qquad \tau=0,\ldots,N_{\mathrm{lags}}.$$0

with declaration when $$R_{\tau}=E[x(t)x(t+\tau)^{\top}], \qquad \tau=0,\ldots,N_{\mathrm{lags}}.$$1 exceeds a threshold such as three times the baseline standard deviation. The second ANN estimates the story stiffness vector $$R_{\tau}=E[x(t)x(t+\tau)^{\top}], \qquad \tau=0,\ldots,N_{\mathrm{lags}}.$$2 from the input vector $$R_{\tau}=E[x(t)x(t+\tau)^{\top}], \qquad \tau=0,\ldots,N_{\mathrm{lags}}.$$3. In the 3-story nonlinear steel frame case study, the FEM baseline first-mode frequency was $$R_{\tau}=E[x(t)x(t+\tau)^{\top}], \qquad \tau=0,\ldots,N_{\mathrm{lags}}.$$4 Hz with mode shape $$R_{\tau}=E[x(t)x(t+\tau)^{\top}], \qquad \tau=0,\ldots,N_{\mathrm{lags}}.$$5, while EEMD + HT gave $$R_{\tau}=E[x(t)x(t+\tau)^{\top}], \qquad \tau=0,\ldots,N_{\mathrm{lags}}.$$6 Hz with error $$R_{\tau}=E[x(t)x(t+\tau)^{\top}], \qquad \tau=0,\ldots,N_{\mathrm{lags}}.$$7 and $$R_{\tau}=E[x(t)x(t+\tau)^{\top}], \qquad \tau=0,\ldots,N_{\mathrm{lags}}.$$8 with maximum error $$R_{\tau}=E[x(t)x(t+\tau)^{\top}], \qquad \tau=0,\ldots,N_{\mathrm{lags}}.$$9. The first-story prediction error spiked sharply at the two damage instants, approximately $(A,B,C,D)$0 s and $(A,B,C,D)$1 s, correctly identifying the damage times and location. After detection, an ANN trained on 100 synthetic patterns estimated reduced first-story stiffness: FEM true damaged stiffness $(A,B,C,D)$2 MPa and ANN estimate $(A,B,C,D)$3 MPa, with error $(A,B,C,D)$4 (Vazirizade et al., 2018).

Taken together, these algorithms separate at least three inference problems: forecasting normal modal behavior, detecting abrupt response inconsistency, and solving an inverse mapping from modal parameters to stiffness reduction. A common misunderstanding is to treat these as interchangeable. The cited studies keep them distinct.

4. Sensing architectures and deployment configurations

The San Frediano long-term deployment used four tri-axial velocimeters, a 24-bit SARA digitizer, and continuous sampling at 100 Hz. Environmental covariates were obtained from three local weather stations and included air temperature, relative humidity, rainfall, average wind speed, peak wind speed, and wind direction. Data were packaged hourly; 13 months of data corresponded to approximately 9,600 hourly samples; the full monitoring period was Oct 2015–Nov 2017, approximately 25 months; and the anomaly-detection test interval was 19 Aug 2016–16 Oct 2016, approximately 1,800 hours (Carrara et al., 2022).

For long-term wireless operation, an event-based sensing system design is built around the ATtiny85 ultra-low-power MCU and three independent trigger modules: vibration, strain, and time. The hardware stack includes the ADXL362 MEMS accelerometer, a Wheatstone bridge with INA2128 instrumentation amplifier, first-order RC low-pass filter and LPV7215 comparator for strain detection, a TPL5111 nanopower timer, a DS1342 real-time clock, a MAX5479 digital potentiometer, and SN74AUP1G07 low-power logic aggregation. All modules operate on a dedicated 3.2 V rail. When any trigger line goes high, the ATtiny85 exits power-down, asserts the OR gate, and latches the main sensor platform power gate for high-fidelity data capture. The reported current consumption is approximately $(A,B,C,D)$5 mA inactive and $(A,B,C,D)$6 mA active. In laboratory validation, an 80 mg vibration threshold produced triggering with 0.95 s latency, a strain threshold of $(A,B,C,D)$7 also produced 0.95 s latency, and a 24-hour mixed test yielded 20 events with correct event classification and time-stamping. For the comparison shown, always-on Xnode operation consumed 170 mA and 544 mW with approximately 59 h uptime for a 10 Ah battery, whereas EDS-driven sensing at 1% events consumed 2.6 mA and 8.3 mW with approximately 3054 h uptime (Sarwar et al., 2019).

Diffractive optical SSHM replaces dense sensor arrays with passive optical encoding and shallow neural decoding. In the millimeter-wave proof-of-concept, the source is a continuous wave at $(A,B,C,D)$8 mm (100 GHz), the diffractive layer is attached to a 4-story laboratory model of total height approximately 10 cm, the shake table operates over 0–200 Hz with white noise and single-tone excitations in the 8–12 Hz band, detector sampling is 50 Hz with four single-pixel receivers at 1.62 cm pitch, and ground truth is provided by laser rangefinders at 256 Hz with 0.1 mm resolution. In the 9–11 Hz band, jointly optimized diffractive layers yielded spectral MSE values of $(A,B,C,D)$9 to $\lambda_i$0 for backend sizes of approximately 0.85k, 1.75k, and 2.98k parameters, whereas separately optimized diffractive layers, Fresnel lens arrays, and random diffusers produced substantially larger MSE ranges. The jointly trained encoder gave more than 10-fold lower spectral MSE than any baseline optics. Each 100-sample window of 2 s incurred less than 1 ms of network inference on a 32-bit microcontroller with CPU load below 1%, and the estimated per-node cost was below \$30 (Wang et al., 3 Jun 2025).

Architecture	Configuration	Reported outcome
Heritage tower monitoring	Four tri-axial velocimeters, 24-bit SARA digitizer, 100 Hz continuous acquisition	All known events in the test window were correctly flagged
Event-driven wireless node	ATtiny85 with vibration, strain, and timer triggers; inactive 0.85 mA, active 7.43 mA	Approximately 3054 h uptime for EDS-driven sensing at 1% events
Diffractive optical node	Four single-pixel receivers, 50 Hz sampling, 2 s windows	More than 10-fold lower spectral MSE than baseline optics

These deployments show that SSHM instrumentation can be continuous and contact-based, threshold-triggered and wireless, or remote and optically encoded. The studies do not present these as interchangeable; rather, they target different trade-offs among power, latency, spatial coverage, and downstream inference complexity.

5. Recovery modeling, resilience metrics, and the value of damage information

One strand of SSHM research evaluates monitoring not only by detection quality but by its effect on system recovery. In the electric power network study, the infrastructure is modeled as an undirected graph $\lambda_i$1. The case study uses the IEEE 24-bus Reliability Test System with 24 buses, 38 lines, 10 generators, 17 loads, and 5 substations, and a pre-event total capacity of 2,850 MW. Seismic hazard intensity is represented by a spatially correlated field of peak ground accelerations generated through

$\lambda_i$2

and damage states are sampled from log-normal fragility curves

$\lambda_i$3

Once a component damage state is assigned, it is mapped to a fractional functionality $\lambda_i$4; buses are binary with $\lambda_i$5–$\lambda_i$6 and $\lambda_i$7, while generators, loads, and substations degrade progressively, for example $\lambda_i$8, $\lambda_i$9, $A$0, and $A$1 (Liang et al., 14 Aug 2025).

Recovery is simulated with three identical repair crews, fixed transfer time of 0.25 days, and repair durations sampled from normal distributions truncated below 0.2 days. SSHM affects the quality and timeliness of perceived damage information through tri-diagonal confusion matrices. The matrix for SSHM uses correct-classification probability $A$2 with no delay, whereas manual inspection uses $A$3 with a 2-day delay; in partial-SSHM scenarios only a fraction $A$4 of components uses the SSHM matrix. Repair scheduling prioritizes component type in the order buses, generators, loads, substations, and within each type by descending capacity. At each completion event, system functionality is re-evaluated: damaged nodes with $A$5 are removed, islands are identified by breadth-first search, islands without a generator–load pairing are discarded, and a DC optimal power flow is solved on each viable island. Total system functionality is the served load

$A$6

and resilience loss is measured by

$A$7

with units of MW·day (Liang et al., 14 Aug 2025).

The reported results quantify the value of SSHM in recovery terms. Under perfect information, a single damage scenario recovered in 12.43 days with $A$8 MW·day. With SSHM-assisted perception at $A$9, recovery took approximately 13.0 days and $i$0 MW·day, the minor degradation being attributed to two false alarms. Inspection-only recovery at $i$1 required 19.13 days and $i$2 MW·day. Over 250 Monte Carlo runs on a single damage realization, mean $i$3 decreased from $i$4 without SSHM to $i$5 with SSHM, a reduction of $i$6 MW·day or 23.7%. Over 10,000 simulations spanning 100 damage scenarios with 100 runs each, mean $i$7 decreased from $i$8 MW·day to $i$9 MW·day, a reduction of $f_s = 100$00 MW·day or 21.0%. Sensitivity studies showed that increasing accuracy from $f_s = 100$01 at 50% coverage reduced mean $f_s = 100$02 from $f_s = 100$03 to $f_s = 100$04 MW·day, while increasing coverage from $f_s = 100$05 at $f_s = 100$06 reduced mean $f_s = 100$07 from $f_s = 100$08 to $f_s = 100$09 MW·day. With $f_s = 100$10 USD/MWh and SSHM system cost of approximately \$f_s = 100$11a=0.85$f_s = 100$12$f_s = 100$13$f_s = 100$14p\approx30\%$f_s = 100$15a=0.95$ (Liang et al., 14 Aug 2025).

This body of work makes SSHM a decision-support variable rather than only a sensing variable. A plausible implication is that monitoring quality should be evaluated jointly with repair logistics and network functionality, not only by detector-level performance.

6. Limitations, misconceptions, and research directions

Several limitations recur across the cited SSHM frameworks. In the TFT-based ambient-noise pipeline, anomaly detection relies on the assumption that training data are fully healthy. The anomalies are only global modal changes, with no localization of local damage, and environmental factors may mask low-magnitude structural changes. Proposed extensions include comparison against classical statistical control charts or ML baselines such as the LSTM-Autoencoder, clustering the TFT’s internal attention patterns to distinguish seismic and anthropic anomalies, incorporating spatially resolved sensor networks and higher-order modal shapes for damage localization, and evaluating sensitivity on simulated damage through FE-model perturbations to assess minimum detectable stiffness loss (Carrara et al., 2022).

In the EEMD–HT–ANN framework, performance depends on tuning the EEMD noise level, ensemble size, ANN architecture, and damage-detection thresholds. The emulator requires an initial healthy dataset, and large deviations in loading patterns may require retraining. The method also assumes that damage manifests mainly in changes to the first bending mode, so higher-mode damage signatures are not exploited. Suggested future work includes extension to taller buildings and 3D frames with torsional modes, adaptive selection of EEMD parameters based on real-time noise estimation, hybrid model-based and data-driven frameworks embedding analytical mode-shape sensitivities into the ANN, and field deployment on instrumented test structures under real earthquake records (Vazirizade et al., 2018).

Low-power event-driven sensing introduces a different set of constraints. The reported startup latency is 0.95 s; the paper notes that this may be trimmed by pre-arming the ADC or using faster MCU clocks, at the cost of higher sleep current. False alarms under wind or traffic loads may be reduced by multi-axis or pack-statistical triggers or adaptive thresholds derived from ambient noise estimators. Synchronization of wake-events across a dense network may require a low-power wake-radio, and energy harvesting is presented as a route to replenishing the multi-year battery budget (Sarwar et al., 2019).

Diffractive optical SSHM remains limited by the need for active illumination, environmental calibration, and currently coarse spatial sampling with a single tile per node. The adaptation roadmap includes longer microwave wavelengths for sub-centimeter to centimeter seismic displacements, tiled apertures over 0.5–2 m² panels, placement at modal-hotspot locations determined by finite-element models, multi-wavelength multiplexing, longer temporal windows for sub-0.1 Hz spectral resolution, compensation networks for thermal and humidity-induced drift, extension to visible or near-IR wavelengths for millimeter-scale crack monitoring, and on-site continual learning for non-stationary structural changes (Wang et al., 3 Jun 2025).

A common misconception is that improved SSHM value is identical to dense deployment. The recovery-simulation results indicate otherwise: high sensing accuracy is reported to be more valuable than instrumenting every component at lower fidelity, and moderate coverage of 20–40% with high-quality sensors delivers most of the resilience benefit, approximately 80% of full-deployment value of information, at a fraction of cost. Another misconception is that anomaly flags alone constitute damage localization. The cited methods distinguish anomaly scoring, onset detection, stiffness estimation, and recovery prioritization as separate tasks with separate assumptions (Liang et al., 14 Aug 2025).

Taken together, the literature presents SSHM as a layered discipline: sensing, modal representation, inference, deployment, and decision support are all explicit design variables. This suggests that future SSHM systems will be judged not only by whether they detect abnormal structural behavior, but by how precisely they characterize it, how efficiently they can operate in the field, and how much they improve post-earthquake actions under uncertainty.