Thermographic Reference Dataset: Experimentally simulated Gaussian-shaped internal defects in GFRP

Thermographic Reference Dataset: Experimentally simulated Gaussian-shaped internal defects in GFRP Julien LECOMPAGNON 1∗, Ali SARHADI 2, Rodrigo Q. ALBUQUERQUE 3and Martin EDER 2 1Bundesanstalt für Materialforschung und -prüfung (BAM), Division 8.3: Thermographic Methods, Berlin, Germany 2Technical University of Denmark, Department of Wind and Energy Systems, Roskilde, Denmark 3University of Bayreuth, Department of Polymer Engineering, Bayreuth, Germany Abstract We introduce a thermographic reference dataset consisting of 100 experimentally recorded temperature fields that replicate defect-like heat signatures in glass fiber reinforced polymer (GFRP) composites. Instead of relying on the fabrication of numerous damaged specimens, the dataset was generated by directly imprinting defect signatures onto an intact laminate using a near-infrared laser projector with spatial light modulation. The projected patterns are derived from parameterized Gaussian distributions, enabling systematic variation in defect size, shape, and orientation. The resulting steady-state thermal responses were captured with infrared thermography, providing high-resolution temperature distribution measurements for each case. This novel approach ensures that the heat transfer physics are preserved experimentally, while no special samples with different defects need to be manufactured to acquire datasets for different defect parameters. The dataset is ultimately designed as a resource for the benchmarking of thermographic non-destructive testing techniques, the validation of numerical heat transfer simulations, and the training of data-driven algorithms for defect detection in composite materials. 1. Motivation The characterization of fatigue damage in composite structures remains a critical challenge in the pursuit of safer and more reliable lightweight materials. Under cyclic loading, localized heating effects caused by internal defects or microcracks can provide valuable insight into the onset and progression of material degradation. Infrared thermography has thus emerged as a powerful nondestructive testing (NDT) technique for monitoring self-heating phenomena associated with cyclic fatigue, enabling the early detection of hidden defects and progressive damage before catastrophic failure occurs [1, 2]. Accurate thermal defect detection plays a dual role in this context. On one hand, it enables direct correlation between local heat generation and the underlying damage mechanisms such as fiber breakage, matrix cracking, and delamination. On the other hand, it provides essential experimental data for refining thermal models and improving predictive tools, including machine learning-based approaches, which rely heavily on high-fidelity ground truth measurements. Since ∗Corresponding author: [email protected] 1 the spatial and temporal distribution of temperature fields is highly sensitive to material-specific thermal properties, precise control and measurement of thermal responses are indispensable for advancing fatigue life assessment [3]. The present experimental work focuses on simulating defect-like thermal signatures under controlled laboratory conditions using near-infrared laser projection and infrared thermography. By generating and recording spatially structured heating patterns on composite laminates, the setup reproduces thermal responses that mimic those observed in real fatigue tests. In conventional laboratory fatigue studies [4], generating representative datasets for the detection of a wide variety of different defect shapes requires the preparation of numerous physical specimens with different defect types, sizes, and geometries — a process that is both time-consuming and costly and quickly suffers from complexity explosion. In this work, a fundamentally novel approach is applied that allows for a maximum of flexibility: by using a near-infrared (NIR) laser projector, defect-like heat signatures can be directly imprinted onto a single intact specimen. This eliminates the need for destructive specimen preparation while enabling rapid variation of defect shapes and distributions across a broad parameter space. Crucially, the laser-generated patterns reproduce the actual thermal footprints of damage without requiring intermediate thermal modeling of the heat transfer processes in the material, ensuring that the underlying physics are captured with high fidelity. Consequently, the ability to match real-world defect signatures in practical applications depends entirely on the accuracy of the thermal model used to define those signatures [5]. This combination of experimental control, repeatability, and flexibility provides a powerful pathway for producing large, diverse datasets for validation and for training advanced data-driven models in fatigue defect detection. 2. Thermographic Defect model Typical defects in glass fiber reinforced polymer (GFRP) composite materials that are prone to dissipating mechanical energy can manifest themselves in a wide variety of ways, especially as delaminations, debondings, or inclusions/voids. In a first-order approximation, especially when taking the low-pass spatial filtering effects of thermal diffusion into account, the resulting heat signature qualitatively appears as a 2D-Gaussian ellipsoid. As such, it can be described by a single symmetrical 2×2matrix, defining its extension in width and height, as well as its distortion/rotation. Translating these parameters into a corresponding heat signature wnwith entries wn i,j for the n-th simulated defect (cf., Section 3), the following constraints need to be fulfilled: Constraint 1: Xwn i,j ≡1Heat signatures are normalized to contain equal energy. Constraint 2: wn i,j < wth ∀i, j Heat signatures should not be too narrow and spread their energy over a large area. Constraint 3: max ij wn i,j ≡wth ∀nExperimental constraint to maximize power output for heating (cf., Section 4). 2 3. Data Point Generation To generate the individual data points N= 1×105points were sampled from a bi-variate Gaussian distribution as a function of the sample point vector x= [xk, yk]T, defined by yk=1 2π|Σ|−1/2exp −1 2(xk−µ)TΣ−1(xk−µ),1≤k≤N∈N.(1) In the first step, a symmetric and positive definite co-variance tensor Σ2×2as defined in Eq.2 was selected and the mean vector µwas set to µ= [0,0]T. Σ=σ2 xr σxσy r σxσyσ2 y=S11 S12 S21 S22,with S12 =S21 (2) After that, the resulting 2D point cloud was binned inside a 16 pixel ×10 pixel rectangular grid. One pixel spans approximately an area with a side length of ∆≈3.2 mm. The indices (i, j)for any resulting pixel bin Pij pertaining to each sample point xcan then be calculated as follows: i, j=xk−Xmin ∆,yk−Ymin ∆,(3) where Xmin and Ymin are the lower bounds of the grid coordinates. Finally, a matrix of weights 0≤wij <1∈Rwas calculated by summing all points in each bin and normalizing it with the number of total samples Nas follows: wij =1 N N X k= 1 xkwhere xk=(1if xk∈Pij 0else (4) Equation 4 strictly fulfills Constraint 1 that Xwij ≡1. The additional constraints are fulfilled by rejecting all datasets for which any of the weights exceeded the threshold value wij > wth, wth = 0.1 (Constraint 2) and where wth −max wij wth >10% (Constraint 3). Following this procedure, a total of 100 valid data points were generated. Ideally, the dataset should cover the entire parameter space of the covariance matrix Σas uniformly as possible, while the constituent parameters S11,S12, and S22 should be mutually uncorrelated. However, due to the constraints imposed on the heat signatures, this is not entirely feasible. The final distribution of the parameters and their mutual correlations are shown in Figure 1. It can be seen that the parameters S11 and S22 are slightly correlated, which is a direct consequence of Constraint 2. The parameter S12, on the other hand, is largely uncorrelated with the other two parameters. 4. Experimental Setup The experimental investigations were carried out using a fiber-coupled NIR diode laser operated at a fixed output power of 50 W. Beam shaping was achieved with a DLP-based spatial light modulator equipped with a digital micromirror device (DMD) chip (Texas Instruments DLP650LNIR, 1280 pixel ×800 pixel). By applying pulse-width modulation (PWM) at a frequency of 256 Hz, the individual micromirrors were switched to define the spatial intensity distribution of the laser 3 30 40 50 S11 r= 0.056 r=−0.738 −20 0 20 S12 r=−0.028 30 40 50 S11 20 30 S22 −20 0 20 S12 20 30 S22 Correlation matrix Figure 1: Parameter distribution and correlations beam, which was then directed onto the rear surface of the test specimen. The specimen itself was a square plate of 260 mm ×260 mm, manufactured as a [+45◦/−45◦]sHM glass fiber–epoxy biax laminate with a thickness of 3.4 mm. The thermophysical properties of this material system are listed in Table 1. To reduce the resolution of the modulator to a manageable scale for heat patterning, groups of 80 ×80 pixels were combined into macro-pixels. In this way, any 16 pixel ×10 pixel heating distribution could be formed and projected. The corresponding illuminated area covered roughly 51.15 mm ×31.97 mm, centered on the specimen, with each projected heating pixel corresponding to about 3.2 mm in size. In order to suppress parasitic heat fluxes into the surroundings, the specimen was suspended in front of the laser beam by means of thin threads attached to its upper corners. Both front and back surfaces were spray-coated with a thin layer of high-emissivity black paint to ensure uniform absorption of the laser power, eliminate optical transmission through the laminate, and provide a well-characterized emissivity for the infrared measurements. The complete arrangement is shown in Figure 2. Each heating distribution from the dataset was projected for a duration of 12 min to allow the specimen to reach thermal steady-state conditions. The film coefficient governing the convective heat loss was determined using a Bayesian Optimization approach to be h= 5.78 W/(m2K) [6], while the average temperature of the lab environment was measured to be 21.4◦C. The whole experimental campaign was conducted over a span of several days as the total measurement duration of all 100 patterns amounted to 20 h net. At the end of each heating cycle, the temperature field on the front side — denoted here as the thermal image (TI) — was captured by a cooled mid-wave infrared (MWIR) camera with a 4 Table 1: Thermal parameters of the constituents — glass fiber and epoxy matrix polymer — and the combined parameters for the glass-epoxy biax laminate. Composite values are calculated from the constituents by the rule of mixture. Parameter name Symbol Value Ref. Fiber volume fraction vf0.51 Fiber density ρf2610 kg/m3 Matrix density ρm1160 kg/m3 Composite density ρc1906 kg/m3 Fiber conductivity kf1.30 W/(m K) Matrix conductivity km0.23 W/(m K) Composite conductivity (long.) kcl 0.54 W/(m K) Composite conductivity (trans.) kct 0.40 W/(m K) [6] Fiber heat capacity cf810 J/(kg K) Matrix heat capacity cm1100 J/(kg K) Composite heat capacity cc950 J/(kg K) IR-camera GFRP-panel Laser projector Figure 2: Experimental setup: A DLP-based laser projector (right) is used to project spatially structured heating patterns onto the rear side of a GFRP panel (middle), while the resulting temperature distribution on the front side is captured with a high-resolution mid-wave infrared (MWIR) camera (left). 5 resolution of 1280 pixel ×1024 pixel, a thermal noise floor of NETD ≤30 mK and an effective projected pixel size of 82 µm. For every TI, 200 frames were acquired at a frame rate of 40 Hz and subsequently averaged to suppress measurement noise. To ensure comparability across all projected patterns, the duty cycle of the modulated pixels was individually adjusted such that each distribution yielded the same total heating power ˙ Q. Due to the discrete switching characteristics of the DMD, variations in pixel duty cycles, and the fact that the patterns do not completely fill the projection window, the time-averaged heating power amounted to ˙ Q= (0.359 ±0.004) W. This heating power level was sufficient to raise the surface temperature to an average maximum of 39 ◦Cacross all patterns. The resulting temperature rise was taken as a realistic reference for hotspot magnitudes typically encountered in fatigue testing of biax composite laminates. 5. Dataset Description The complete dataset [7] contains three main folders: Patterns, Measured_Data, and Plots, as well as this PDF file with a detailed description of the dataset. Each folder contains 100 files corresponding to the 100 different heating patterns. The following naming convention was adopted for the files: DESCRIPTOR_XXX-S11_YY.YY-S12_ZZ.ZZ-S22_WW.WW.EXT where DESCRIPTOR is a file name descriptor, XXX is the pattern index, YY.YY,ZZ.ZZ and WW.WW are the constituent parameters of the covariance matrix Σas defined in Eq. 2 rounded to two decimal places, and EXT is the file extension which can be either .txt,.h5 or .png depending on the folder. The structure of the whole dataset is illustrated in Figure 3. . 01_Patterns Pattern_001-S11_38.73-S12_5.40-S22_25.07.txt Pattern_010-S11_37.75-S12_12.00-S22_26.52.txt . . . Pattern_189-S11_36.28-S12_9.90-S22_27.10.txt 02_Measured_Data Meas_data_pattern_001-S11_38.73-S12_5.40-S22_25.07.h5 Meas_data_pattern_010-S11_37.75-S12_12.00-S22_26.52.h5 . . . Meas_data_pattern_189-S11_36.28-S12_9.90-S22_27.10.h5 03_Plots Meas_data_pattern_001-S11_38.73-S12_5.40-S22_25.07.png Meas_data_pattern_010-S11_37.75-S12_12.00-S22_26.52.png . . . Meas_data_pattern_189-S11_36.28-S12_9.90-S22_27.10.png Dataset_description.pdf Figure 3: Structure of the dataset. 6 Folder: 01_Patterns This folder contains all the target patterns used for the experiments, which were determined according to the algorithm described in Section 3. Each file is a plain text file containing a 16 pixel ×10 pixel matrix of floating-point numbers between 0 and 1, representing the normalized weights wij of the corresponding pattern. The matrix is saved in row-major order with 18-digit fixed precision, a separator of one space character, and a line break at the end of each row. Folder: 02_Measured_Data The measured data is stored in HDF5 format [8], which can be easily accessed with most modern numerical-analysis software (like MATLAB and Python). Each file contains the following datasets displayed in Table 2. Table 2: Content description of the HDF5 files in Folder 02_Measured_Data. Dataset name Type Unit Description BAM_pattern_projected_mean float-array (10 ×16)[-] Realized pattern weights using PWM. DTU_pattern_data float-array (10 ×16)[-] Target pattern weights. (same as in Folder 01_Patterns) S11 float [-] Constituent parameters of Σ(cf., Eq. 2). S12 float [-] S22 float [-] T_meas float-array (1280 ×1023)[◦C]Measured temperature distribution. calculated_output_power_watt float [W]Calculated average heating power of the pattern. measured_max_pro_output_power_watt float [W] Measured heating power after laser projector for fully activated (white) image. pattern_number int [-] Pattern index. pixel_size_on_sample_mm float [mm] Projected side length of a camera pixel on the panel surface. (Fixed at 0.084 mm) NOTE: – The pattern indices function as arbitrary unique IDs and are not consecutive. – The covariance matrix parameters S11,S12, and S22 are given to the scale of the initial bivariate Gaussian distribution before binning (cf., Eq. 2). – The measured temperature distribution T_meas has already been flipped horizontally to match the orientation of the projected patterns and undo the mirroring effect of heating and measuring from different sides. 7 Folder: 03_Plots This folder contains a .png image file for each pattern, showing the measured temperature distribution as a false-color plot. The color map is fixed for all images and ranges from 20 ◦Cto 40 ◦C. An example of such an image is shown in Figure 4. 6. Summary This dataset aims to provide thermographic reference data for the evaluation and benchmarking of thermal defect signatures in GFRP composite materials of typical defects that dissipate mechanical energy under cyclic loading. The dataset contains 100 different heating patterns, each described by a set of three parameters that define a bi-variate Gaussian distribution modeling ellipsoidal defect signature shapes. Each heating pattern has been applied to the backside of a GFRP panel using a DLP-based laser projector, while the resulting temperature distribution in thermal steadystate on the front side was captured with a high-resolution MWIR camera. This whole process is illustrated in Figure 4. 0 2 4 6 8 10 12 14 16 x-coordinate [px] 0 2 4 6 8 10 y-coordinate [px] sum = 0.356 W Projected pattern 0 500 1000 x-coordinate [px] 0 200 400 600 800 1000 1200 y-coordinate [px] Measured temperature profile 20 25 30 35 40 App. temperature [◦C] 0 5 10 15 20 Power per pixel [mW] Dataset #11: S11 = 46.08,S12 =−13.80,S22 = 25.07 Figure 4: Exemplary dataset: From the co-variance parameters (top), the weights of a heating pattern are derived (left) that is used to excite the backside of a GFRP panel, and produce a corresponding temperature distribution on the front side (right). Data availability This dataset is publicly available under a Creative Commons Attribution 4.0 International (CC BY 4.0) license at [7]. If you use this dataset in your research, please cite this dataset as follows: Julien Lecompagnon, Ali Sarhadi, Rodrigo Q. Albuquerque, and Martin Alexander Eder. Thermographic Reference Dataset: Experimentally simulated Gaussian-shaped internal defects in GFRP. Zenodo, Oct. 2025. doi:10.5281/zenodo.17378682 8 References [1] Mark. A. Rumsey and Walt Musial. “Application of Infrared Thermography Nondestructive Testing during Wind Turbine Blade Tests”. In: Journal of Solar Energy Engineering 123.4 (Nov. 2001), pp. 271–271. doi:10.1115/1.1409560. [2] Seyed Sina Samareh-Mousavi, Xiao Chen, Malcolm McGugan, Sergei Semenov, Peter Berring, Kim Branner, and Niels Ludwig. “Monitoring fatigue delamination growth in a wind turbine blade using passive thermography and acoustic emission”. In: Structural Health Monitoring 23.5 (Jan. 2024), pp. 2906–2921. doi:10.1177/14759217231217179. [3] Xiao Chen, Rims Janeliukstis, and Ali Sarhadi. “Thermographic data analytics-based damage characterization in a large-scale composite structure under cyclic loading”. In: Composite Structures 290 (June 2022), p. 115525. doi:10.1016/j.compstruct.2022.115525. [4] Joseph N. Zalameda and William P. Winfree. “Passive Thermography Measurement of Damage Depth During Composites Load Testing”. In: Frontiers in Mechanical Engineering 7 (Apr. 2021). doi:10.3389/fmech.2021.651149. [5] Jefri Bale, Emmanuel Valot, Olivier Polit, Claude Bathias, Martine Monin, and Tresna Soemardi. “Thermal phenomenon of glass fibre composite under tensile static and fatigue loading”. In: Journal of Mechanical Engineering and Sciences 11.2 (June 2017), pp. 2755–2769. doi:10.15282/jmes.11.2.2017.16.0250. [6] Rodrigo Q. Albuquerque, Julien Lecompagnon, Ali Sarhadi, Holger Ruckdäschel, and Martin A. Eder. “Advancing IR laser thermography in composites via thermal analysis informed machine learning”. submitted to: Elsevier: Composites Science and Technology. Oct. 2025. [7] Julien Lecompagnon, Ali Sarhadi, Rodrigo Q. Albuquerque, and Martin Alexander Eder. Thermographic Reference Dataset: Experimentally simulated Gaussian-shaped internal defects in GFRP. Zenodo, Oct. 2025. doi:10.5281/zenodo.17378682. [8] The HDF Group. Hierarchical Data Format, version 5.url:https:/ /github. com/ HDFGroup/hdf5. 9