Accurate through-thickness measurement of subsurface delamination depth in Carbon Fiber Reinforced Polymer (CFRP) is important for structural assessment because defect location determines affected load-bearing layers. Optical pulsed thermography (OPT) provides a two-dimensional thermal video rather than volumetric measurements, so depth must be inferred from temporal heat-diffusion responses. A challenge is spatial dataset bias: when calibration defects follow regular grids, regression models may memorize their geometry instead of learning physical relationship between thermal decay and depth. This work introduces a spatio-temporal decoupling architecture that separates spatial defect localization from temporal depth measurement. Defect regions are first localized using segmentation methods, after which thermal responses are spatially averaged and converted into sixteen physics-informed temporal, energy, statistical, and geometric features. These features expose the one-dimensional heat-conduction relationship while withholding pixel coordinates from the depth model. Four regression models are evaluated using specimen-level cross-validation: Random Forest (RF), Gradient Boosting Machine (GBM), Advanced Multi-Layer Perceptron (Adv-MLP), and XGBoost. Unregularized trees and over-parameterized Adv-MLP exhibit calibration collapse under geometric shifts, with errors exceeding 0.5 mm. In contrast, regularized XGBoost with L1/L2 penalties and column sampling maintains cross-specimen calibration, achieving a mean absolute error (MAE) of 0.056 mm and root mean square error (RMSE) of 0.085 mm. Predicted depths are merged with masks to generate Delaunay-triangulated three-dimensional defect models in three to five seconds per specimen. Results show that mathematical regularization and spatio-temporal decoupling reduce spatial memorization in thermal-video depth regression.
Figures & tables
Fig. 1: Spatio-temporal decoupling architecture for depth estimation from thermographic video. The pipeline separates spatial localization from temporal measurement to avoid geometric memorization.
Fig. 2: Predicted binary defect masks for the six CFRP specimens obtained from the best segmentation architecture. Square and circular defects are reliably detected, providing spatial support for subsequent temporal measurement.
Fig. 3: Mean thermal responses after spatial averaging. Deeper defects exhibit delayed peak times and lower amplitudes, confirming that temporal features encode depth information.
Category
Feature
Formula
Physical / measurement interpretation
Temporal
tpk
argmaxtTk(t)
Peak time; primary depth-related temporal measurement through ( 1 ).
τr
tpk−tonset
Rise duration associated with the transient response.
Tmax
maxtTk(t)
Maximum surface temperature within the response window.
T˙max
maxtΔTk(t)/Δt
Maximum thermal change rate.
drel
tpk
Linearized depth proxy derived from ( 1 ).
Energy
Aauc
∑t=1TTk(t)Δt
Integrated thermal response over the acquisition window.
TABLE I: Sixteen Physics-Informed Features Used for Depth Regression
Fig. 4: Pearson correlation matrix for the sixteen features and depth. Temporal features exhibit the strongest correlation, confirming the physics-informed design.
Fig. 5: Scatter plots of actual versus predicted depth across the three specimen-level cross-validation folds. Fold 1 (a) displays the calibration of the Gradient Boosting control, while Fold 2 (b) and Fold 3 (c) demonstrate the robust generalization of the regularized XGBoost model under distribution shifts from rigid square grids to columnless circular layouts.
Fold
Test
RF
GBM
XGBoost
Adv-MLP
MAE
RMSE
R2
MAE
RMSE
R2
MAE
RMSE
R2
MAE
RMSE
R2
1
SQ_03
0.0102
0.0171
0.996
0.0125
0.0184
0.996
0.0099
0.0169
0.996
0.1458
0.1725
0.628
CI_03
0.0647
0.1021
−0.042
0.0400
0.0861
0.259
0.1154
0.1309
−0.714
0.3385
0.3665
−12.43
Overall
0.0207
0.0475
0.995
0.0178
0.0413
0.996
0.0303
0.0596
0.992
0.1831
0.2236
0.880
2
SQ_02
0.0120
0.0158
0.997
0.0162
0.0199
0.995
0.0359
0.0461
0.973
0.5221
0.5730
−3.103
CI_02
0.5209
0.5326
−27.37
0.6834
0.7232
−51.29
0.0756
0.0967
0.066
0.1370
0.1622
−1.632
TABLE III: Depth Regression Results Across All Folds
Fig. 6: Three-dimensional structural reconstructions from XGBoost depth predictions. Green surfaces denote the true delamination boundaries, while red surfaces represent the computational predictions, demonstrating accurate spatial registration and clear resolution of closely spaced layers.
CI3 Lab, Department of Civil Engineering, The University of Hong Kong, Hong Kong SAR, China · Commonwealth Scientific and Industrial Research Organisation (CSIRO), Canberra, ACT, Australia