Dynamic estimation of heat source distribution during solidification of composite materials under sparse monitoring samples

doi:10.11996/JG.j.2095-302X.2024020388

Abstract

Abstract:

Carbon fiber reinforced polymer (CFRP) has excellent properties and has become the material of choice for reducing weight and enhancing efficiency in high-end aerospace equipment. Curing is a critical process in achieving the forming and load-bearing of a composite member. The temperature field of the component in the curing process directly determines the curing quality and mechanical properties of the component. Accurately and dynamically reversing the heat source distribution on the surface of the composite member is the key to realizing the accurate control of the temperature field. However, in the actual curing process, auxiliary materials such as breathable felt and vacuum bags are attached to the surface of the composite, making it difficult to directly monitor the surface temperature field. Only several optical fiber temperature measurement points can be introduced to obtain sparse temperature samples, posing challenges to the reconstruction of the high-dimensional scalar field of heat source distribution. Therefore, a dynamic estimation method of heat source distribution in the curing process based on Gaussian mixture distribution model (GMM) was proposed, which introduced the physical a priori equivalence of Gaussian fuzzy and in-plane heat diffusion, established a Gaussian fuzzy-based temperature field evolution model, and then use multiple Gaussian distributions in the GMM to characterize heat source distribution in the curing process, which transformed the difficult problem of high-dimensional field reconstruction into an optimization problem of solving several Gaussian distribution parameters. The feasibility and effectiveness of this method were verified by simulation experiments, demonstrating that it can achieve accurate dynamic estimation of heat source distribution during solidification.

Key words: composite solidification, temperature field, heat source estimation, GMM, global optimization

CLC Number:

TP391

WANG Shixin, XU Ke. Dynamic estimation of heat source distribution during solidification of composite materials under sparse monitoring samples[J]. Journal of Graphics, 2024, 45(2): 388-398.

Figures/Tables 19

Fig. 1 A dynamic estimation method of heat source distribution for curing composites based on GMM

Fig. 2 Relationship between in-plane heat transfer diffusion and Gaussian Blurring

Fig. 3 Evaluation of heat transfer model accuracy

Fig. 4 Common interpolation methods ((a) Nearest neighbor interpolation; (b) Linear interpolation; (c) Natural neighbor interpolation; (d) Biharmonic spline interpolation)

Fig. 5 Validation of GMM reconstruction algorithm ((a) Original temperature difference data; (b) Fitting GMM surfaces; (c) The corresponding value of the sampling point on the fitted surface)

Fig. 6 Pseudocode of reconstruction of internal heat source

Fig. 7 Pseudocode of iteration refresh of internal heat source

Fig. 8 A Simulation verification and preset heat source distribution based on COMSOL ((a) Simulation heating device; (b) Grayscale image of boundary heat source; (c) Simulated heat source distribution; (d) CFRP surface temperature field)

Fig. 9 Heat source distribution reconstruction iterative optimization process

Fig. 10 Reconstruction of heat source distribution ((a) Temperature field distribution at 1 000 s; (b) Temperature field at 1 100 s as predicted; (c) Surfaces fitted by temperature difference; (d) Heat source distribution for final reconstruction)

Fig. 11 Heat source distribution reconstruction results ((a) Predefined heat sources; (b) Reconstructed heat source)

Fig. 12 Heat source distribution updating dynamically

Fig. 13 Comparison of error values at sampling points

Fig. 14 Comparison of reconstruction results ((a) Linear interpolation; (b) Biharmonic spline interpolation; (c) ART iterative reconstruction; (d) GMM-based reconstruction)

Table 1 Comparison of reconstruction error

重建方法	SSIM	PSNR	Corr2
线性插值	0.34	10.94	0.49
双调和样条插值	0.36	10.67	0.72
ART算法^[27]	0.32	9.23	0.59
本文算法	0.43	15.18	0.85

Fig. 15 The influence of the number of sampling points on the accuracy of reconstruction results

Fig. 16 Reconstruction results of heat source distribution in Case2 ((a) Preset heat source distribution; (b) Reconstructed heat source distribution; (c) Residual)

Fig. 17 Reconstruction results of heat source distribution in Case3 ((a) Preset heat source distribution; (b) Reconstructed heat source distribution; (c) Residual)

Fig. 18 The effectiveness of this method is verified ((a) Reconstruction of heat source distribution; (b) Prediction of the temperature field at 800 s; (c) COMSOL simulation of 800 s temperature field)

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