稀疏监测样本下的复合材料固化过程热源分布动态估计

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

图学学报 ›› 2024, Vol. 45 ›› Issue (2): 388-398.DOI: 10.11996/JG.j.2095-302X.2024020388

• 数字化设计与制造专刊 • 上一篇下一篇

稀疏监测样本下的复合材料固化过程热源分布动态估计

王士心(), 许可()

南京航空航天大学机电学院，江苏南京 210016

收稿日期:2023-10-01 修回日期:2023-12-11 出版日期:2024-04-30 发布日期:2024-04-30
通讯作者: 许可(1989-)，男，副教授，博士。主要研究方向为数字化制造与智能制造。E-mail：nuaa_xk@nuaa.edu.cn
作者简介:王士心(1999-)，男，硕士研究生。主要研究方向为复合材料制造工艺整体优化。E-mail：wsx051730404@nuaa.edu.cn
基金资助:
国家自然科学基金项目(52175466)

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

WANG Shixin(), XU Ke()

School of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing Jiangsu 210016, China

Received:2023-10-01 Revised:2023-12-11 Online:2024-04-30 Published:2024-04-30
Contact: XU Ke (1989-), associate professor, Ph.D. His main research interests cover digital and intelligent manufacturing. E-mail：nuaa_xk@nuaa.edu.cn
About author:WANG Shixin (1999-), master student. His main research interests cover manufacturing process optimization of composite materials. E-mail：wsx051730404@nuaa.edu.cn
Supported by:
National Natural Science Foundation of China(52175466)

摘要/Abstract

摘要：

碳纤维增强树脂基复合材料(CFRP)具有优异的综合性能，已成为航空航天高端装备减重增效的优选材料。固化是实现复材构件成形承载的关键工艺环节，固化过程中的构件温度场直接决定了构件的成形质量与力学性能，如何精确、动态的反求复材构件表面的热源分布，是实现温度场精准调控的基础。然而实际的固化工艺需在构件表面贴附透气毡、真空袋等辅助材料，难以直接监测构件表面的温度场，仅能引入若干个光纤测温点获取稀疏的温度样本，给热源分布这一高维标量场的重构带来挑战。为此，提出一种基于高斯混合分布模型(GMM)的固化过程热源分布动态估计方法，引入高斯模糊与面内热扩散等效性这一物理先验，建立了基于高斯模糊的温度场演变模型，进而利用GMM中的多个高斯分布表征固化过程中的热源分布，将高维场重构难题转化为若干高斯分布参数的优化求解问题。通过仿真实验验证了本文方法的可行性与有效性，能够实现固化过程中热源分布的精确动态估计。

关键词: 复合材料固化, 温度场, 热源估计, GMM, 整体优化

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

中图分类号:

TP391

王士心, 许可. 稀疏监测样本下的复合材料固化过程热源分布动态估计[J]. 图学学报, 2024, 45(2): 388-398.

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.

图/表 19

图1 基于GMM的复材构件固化热源分布动态估计方法

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

图2 面内传热扩散与高斯模糊的关系

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

图3 传热模型精确性评估

Fig. 3 Evaluation of heat transfer model accuracy

图4 常见的插值方法((a)最近邻点插值；(b)线性插值；(c)自然邻点插值；(d)双调和样条插值)

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

图5 GMM重构算法有效性验证((a)原始温差数据；(b)拟合GMM曲面；(c)采样点在拟合曲面对应值)

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)

图6 内部热源的重构算法流程图

Fig. 6 Pseudocode of reconstruction of internal heat source

图7 内部热源动态迭代更新算法流程图

Fig. 7 Pseudocode of iteration refresh of internal heat source

图8 基于COMSOL的仿真验证及预设热源分布((a)仿真加热装置；(b)边界热源灰度图像；(c)仿真热源分布；(d) CFRP表面温度场)

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)

图9 热源分布重构迭代更新过程

Fig. 9 Heat source distribution reconstruction iterative optimization process

图10 热源分布重构((a) 1 000 s时的温度场分布；(b)预测的第1 100 s时的温度场；(c)通过温差拟合的曲面；(d)最终重构的热源分布)

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)

图11 热源分布重构结果((a)预设热源；(b)重构热源)

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

图12 热源分布动态更新至收敛过程

Fig. 12 Heat source distribution updating dynamically

图13 采样点处误差值对比

Fig. 13 Comparison of error values at sampling points

图14 重建结果对比((a)线性插值方法；(b)双调和样条插值方法；(c) ART迭代重构方法；(d)基于GMM的重构方法)

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

表1 重建结果误差指标对比

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

图15 采样点数量对重构结果精度的影响

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

图16 Case2中的热源分布重构结果((a)预设热源分布；(b)重构热源分布；(c)二者残差)

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

图17 Case3中的热源分布重构结果((a)预设热源分布；(b)重构热源分布；(c)二者残差)

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

图18 本文方法有效性验证((a)重构热源分布；(b)预测800 s时的温度场；(c) COMSOL仿真800 s的温度场)

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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稀疏监测样本下的复合材料固化过程热源分布动态估计

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

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