Mechanics-informed autoencoder enables automated detection and localization of unforeseen structural damage

Structural health monitoring (SHM) is vital for ensuring the safety and reliability of engineering systems, yet real-world deployment faces challenges due to diverse structures, sensor types, and unknown damage scenarios. Early detection and localization are critical but minor or hidden damage may be hard to sense and cannot be easily identified by numerical models. Existing SHM solutions often require active measurements, detect but do not localize damage, or rely on complex and expensive technologies (e.g., guided waves and acoustic emissions). Many machine learning approaches for SHM require annotated data, which is impractical to collect at scale, and models trained with explicit supervision often fail to generalize to unseen damage. Unsupervised methods (autoencoders, PCA) exist but typically consider single-sensor data and do not exploit domain knowledge such as mechanical relations between sensor responses. The research question addressed in this paper is how to develop a scalable, passive, unsupervised SHM framework that can learn a bespoke baseline from an intact structure and then detect and localize unforeseen damage robustly and early, leveraging multiple sensors without complex, structure-specific numerical models. The authors propose MIDAS (Mechanics-Informed Damage Assessment of Structures), which integrates inexpensive passive sensors, on-device data compression, and a mechanics-informed autoencoder (MIAE). The hypothesis is that learning a compact representation of compressed multi-sensor strain responses from the undamaged state, augmented with pairwise mechanical consistency between sensors, will enhance sensitivity to subtle damage and enable earlier detection and localization compared to standard autoencoders and traditional anomaly detection baselines.

The paper surveys SHM approaches spanning active sensing (guided waves, acoustic emissions) and passive sensing with machine learning. Physics-Informed Neural Networks and Graph Neural Networks have shown promise for forward and inverse problems but require precise knowledge of governing equations, parameters, and loading—information typically unavailable for damage detection/localization in practice. Supervised ML methods (SVMs, neural networks, RNN/LSTM/GRU) have been applied to steel bridges, buildings, slabs, pavements, and frames, as well as specific components (gusset plates, bridges, highways, railways). However, these require large labeled datasets per deployment and often fail to generalize to unseen damage types. Unsupervised anomaly detection methods using autoencoders and PCA have been explored for detection, and some for localization (finite element model-based, CNNs, autoencoders), but they often operate on single-sensor data or ignore structural domain attributes and sensor placement. This motivates an unsupervised, multi-sensor approach that incorporates mechanical relationships between sensors to improve early detection and localization.

Overview (MIDAS): The framework instruments a structure with multiple passive strain sensors and collects data from its undamaged (intact) state to learn a baseline via unsupervised training of a Mechanics-Informed Autoencoder (MIAE). Raw time-series signals are compressed on-device into compact features, then the MIAE learns to reconstruct these features while enforcing pairwise mechanical consistency between sensor responses. During deployment, reconstruction errors for new data are compared against the baseline error distribution to detect anomalies (damage). Localization is achieved by computing sensor-wise error norms and interpolating scores across the structure.

Data compression: Time-series strain signals from N sensors are reduced by: (i) defining several strain thresholds based on overall response magnitudes; (ii) computing cumulative times above thresholds over segments; (iii) fitting the cumulative-time data to a Gaussian CDF to obtain parameters; (iv) using the fitted mean (μ) and standard deviation (σ) as compressed features. Seven thresholds are chosen between 0.5 and 3 times the mean strain across sensors in the intact state. Every 200 raw data points are compressed into one pair (μ, σ) per sensor. Batches are formed using a moving window (length 12, stride 2), yielding input tensors of size B × 1 × 2N (μ and σ for N sensors).

MIAE architecture and loss: A 6-layer autoencoder processes the 2N-dimensional input (concatenated μ and σ across sensors) to a compact latent representation and reconstructs the input. For 45 sensors (simulation), input/output size is 90; hidden layers are compacted to 20 units. With fewer sensors (e.g., 4), hidden layers are scaled up to maintain learning capacity. The standard autoencoder baseline shares the same architecture. The loss combines: (1) mean squared reconstruction error; and (2) a mechanics-informed pairwise consistency term. A weight matrix W (N × N) encodes relationships between sensor pairs derived directly from intact-structure strain responses (e.g., larger weights for sensors experiencing higher peak strains), capturing mechanical features such as stress concentration and adjacency effects. The mechanics term penalizes discrepancies between reconstructed responses across sensor pairs relative to intact-structure patterns. The combined loss is L = LMSE + γ LMechanics, with γ tuned to 0.05. For temperature-variation training, central sensor measurements are scaled down when computing W, and the corresponding mechanics penalty is reduced to improve robustness.

Detection: After training on intact data, the distribution of reconstruction errors serves as the baseline. For test windows, per-sensor reconstruction errors are compared to adaptive thresholds derived from training false positive rates. A test sample (across N sensors) is labeled as damaged if the number of anomalous sensors exceeds a ratio qN. Class imbalance in evaluation is handled by SMOTEENN. Metrics reported include accuracy, precision, recall, F1-score, and AUROC.

Localization: Sensor-wise norm errors (along the temporal dimension) are computed to summarize deviations. For each sensor and feature type (μ or σ), relative changes in norm errors with respect to the intact baseline produce intermediate terms, which are then combined into a scalar damage score p per sensor using a mixing coefficient λ (set to 0.5). Damage maps are generated by interpolating p across the structure; with few sensors, a weighted centroid (weights = p) estimates peak location. Scores less than 1 indicate baseline; higher values indicate potential damage near that sensor. For SPIRIT (incremental PCA) comparisons, distances in the first two principal coordinates define analogous error and score measures.

Numerical simulation (gusset plate): A polygon-shaped steel gusset plate (thickness 1.2 cm) is modeled in ABAQUS using 3D elements (C3D8R), with clamped-clamped boundary conditions at the bottom edge. Material properties: Poisson’s ratio 0.32, Young’s modulus 200 GPa. Random traffic-like loads (periodic sums of sinusoids with random phase/frequency/amplitude) are applied on top edges in x and y directions. The intact model runs at a 0.025 s timestep for multiple load realizations to generate training data. Damage is introduced as cracks of varying location, length (0.4–6 cm), width (0.1–0.5 cm), and angle (0, 30, 45, 60, 90 degrees), with refined meshing near cracks (0.2 cm) and 1 cm elsewhere. Strains (y-direction) are averaged over 45 sensor regions. Temperature analyses set thermal expansion to 11×10^-6 per °C; training spans 5–30 °C, and tests include 10 and 13 °C. Noise robustness is assessed by adding 0.5% Gaussian noise to raw strains (before compression) for selected four-sensor configurations.

Laboratory experiments (gusset plate): A steel plate (~45×36 cm) with 27 vertically oriented strain gauges (1-LY11-6/350) spaced at 6.5 cm was tested under random traffic-like loading (3 hours intact for training). Two damage types were introduced sequentially: (i) a 4 cm × 0.5 cm crack on the plate’s middle-right region; (ii) boundary condition variation by progressively loosening a lower bolt connection during loading. Data acquisition used NI-9236 and LabVIEW; loading via MTS frame; time step 0.1 s. Compression thresholds spanned 30–175 microstrain with 24 microstrain increments.

Laboratory experiments (beam-column): A W4×13 A992 steel beam connected to a W4×13 A992 column via L4×4×1/2 web cleats and A325 bolts, with a support prop (W4×7.7). The beam length from column face to end is 40 inches; load applied at 30 inches from the column face (3/4 span). The column base plate is welded and anchored; the prop is welded at the top. Displacement-controlled loading to ~0.23 inches (~2000 lb). Strain sensors placed on support/beam/column. Damage introduced as progressive bolt loosening near sensor S4: D0 (intact, 80 lb·ft) to D1–D3 (~60 lb·ft). Data were compressed and used for training/evaluation similarly to the plate.

• MIAE consistently outperformed standard autoencoders and classical unsupervised baselines (Isolation Forest, OCSVM, LODA, SPIRIT) across accuracy, precision, recall, F1-score, and AUROC for damage detection on simulated gusset plates, especially for small cracks (<2 cm).
• Reconstruction error distributions for damaged states shifted right relative to intact baselines, with separations increasing with crack length (e.g., 0.8 cm small overlap; 2 cm clear separation; 4 cm large shift), enabling detection with as few as 20 anomaly samples per case.
• Damage localization on simulated plates showed earlier and more accurate localization with MIAE. MIAE achieved about 35% higher localization success for medium cracks (1.5–3 cm) than a standard autoencoder and substantially outperformed SPIRIT, which failed for small-to-medium cracks.
• Sensor-budget studies (simulation) demonstrated that methods operating per-sensor (Isolation Forest, OCSVM, LODA) did not improve with more sensors, whereas autoencoder and MIAE improved as sensors increased. Importantly, MIAE achieved the best detection performance even with only four sensors and improved further with additional sensors.
• With four sensors, MIAE localized cracks more accurately than a standard autoencoder (peak scores closer to true crack); SPIRIT failed with four sensors. Across crack lengths, MIAE delivered roughly 10–35% higher localization rates than baselines in four-sensor setups.
• Environmental robustness: With 0.5% Gaussian noise in raw strains (four-sensor setup), MIAE maintained superior undamaged accuracy and strong detection for large cracks (and for smaller cracks when more sensors were available). Under temperature variation, models trained from 5–30 °C and tested at 10 and 13 °C showed MIAE detecting damage where standard autoencoders failed; LODA/Isolation Forest had higher recall but poor undamaged accuracy, making them unreliable.
• Gusset-plate experiments: For a significant crack and for boundary-condition variation, MIAE matched or exceeded autoencoder detection performance and localized damage more precisely. With 27 sensors, MIAE produced strong peaks near crack tips (stress concentration) and accurately identified boundary loosening at the bottom right early in loading. With only 4 sensors, MIAE retained the best localization among methods.
• Early localization: For boundary-condition variation on the plate, MIAE localized damage within about 2–2.5 minutes of loading, while autoencoder and SPIRIT localized much later (e.g., after ~20 minutes).
• Damage-type differentiation: Using separate score maps from μ and σ, μ was more sensitive to boundary condition changes (global stiffness reduction and strain attenuation), while σ was more sensitive to cracks (localized strain variability near crack tips), enabling differentiation without supervised labels.
• Beam-column experiments: MIAE achieved the highest intact-state accuracy and detected early damage (D1–D2) better than baselines. For localization using eight sensors, MIAE accurately localized near S4 at D2–D3 (autoencoder localized only at D3; SPIRIT failed). With only four sensors on beam/support, localization at D2 degraded, illustrating the benefit of additional sensors on other components. Overall, MIAE detected and localized small damage earlier and more reliably than baseline methods.
• Across studies, incorporating mechanics-informed constraints improved early detection and localization, with reported up to 35% improvement in localization of minor damages over standard autoencoders and effective operation after learning from approximately 3 hours of intact data.

The study addresses the challenge of passive, unsupervised detection and localization of unforeseen structural damage by learning a bespoke baseline from intact-state multi-sensor strain responses and leveraging mechanical relationships between sensors. By compressing data into μ and σ features, MIDAS reduces sensitivity to environmental and loading fluctuations and enables efficient edge computation. The mechanics-informed loss enforces pairwise consistency reflective of structural mechanics (e.g., stress concentrations), increasing sensitivity to subtle deviations caused by early-stage damage. The results across simulations and two laboratory structures demonstrate that this integration yields superior performance to standard autoencoders and classical anomaly detectors, particularly for small or evolving damage. MIAE’s sensor-fusion and mechanics constraints allow it to benefit from additional sensors (even on non-local components), improving early localization on complex assemblies (beam-column). Robustness to noise and temperature variations further supports practical deployment. The findings confirm the central hypothesis that incorporating mechanics-informed sensor relations into an unsupervised multi-sensor autoencoder enhances early detection and localization without relying on labeled damage data or detailed governing equations, aligning with the goal of deploy-and-forget SHM.

The paper introduces MIDAS, a near-real-time SHM framework that combines passive sensing, on-device data compression, and a mechanics-informed autoencoder for automated detection, localization, and differentiation of unforeseen damage. Trained solely on intact-state data, MIAE leverages pairwise mechanical relations between sensors to enhance sensitivity to subtle anomalies, outperforming standard autoencoders and classical baselines across detection and localization metrics. Experiments on a gusset plate and a beam-column structure validate early detection/localization, robustness to noise and temperature, and the ability to distinguish damage types via μ and σ features. The approach reduces reliance on human intervention and costly inspections and is compatible with inexpensive wireless sensors, making it practical for field deployment. Future work includes scaling to larger systems (entire bridges/buildings), optimizing sensor placement, integrating heterogeneous sensor modalities, and adapting mechanics correlations for broader geometries and materials.

• Requires an initial period of intact-state data (e.g., ~3 hours) to establish the baseline; performance depends on the representativeness of this baseline under typical environmental and loading conditions.
• Localization accuracy and detection sensitivity degrade with very few sensors or suboptimal placement; additional sensors on other structural components were shown to improve performance (e.g., beam-column D2 localization required eight sensors for best results).
• While robust to moderate noise and temperature variations, model performance still depends on proper computation of the mechanics weight matrix W and tuning of loss coefficients (e.g., γ, λ) and thresholds; temperature robustness used specific scaling heuristics during W computation.
• Magnitude of the damage score p does not consistently correlate with severity for very small damages, limiting straightforward severity quantification in the earliest stages.
• The method currently focuses on strain sensing and requires retraining or transfer of baselines for different structures; generalization without intact data per structure is not demonstrated.