复合材料结构力学性能分布的多保真度数据驱动预测框架及验证
收稿日期: 2025-04-29
修回日期: 2025-06-17
录用日期: 2025-07-03
网络出版日期: 2025-07-15
A multi-fidelity data-driven framework for predicting mechanical property distributions of composite structures and its validation
Received date: 2025-04-29
Revised date: 2025-06-17
Accepted date: 2025-07-03
Online published: 2025-07-15
碳纤维增强复合材料的失效机理复杂，试验成本高昂。受限于现有理论模型，传统的有限元方法难以精确模拟复合材料失效全过程，并存在显著的累积误差，造成了其精确模拟和不确定性量化的困难。机器学习方法为解决这一问题提供了潜在途径，但其有效性通常依赖于大量数据支撑。提出了一种多保真度数据驱动预测框架，旨在通过结合少量高保真度试验数据与大量低保真度仿真数据，实现对复合材料结构力学性能分布的准确预测。该框架的有效性经过切口层合板拉伸破坏试验验证。此外，为提高小样本试验数据的统计代表性，提出了一种基于贝叶斯理论的数据扩充方法，并推导了组间变异系数的理论分布以验证其有效性。交叉验证结果表明，所提方法在预测破坏载荷分布第10百分位数时的平均绝对误差率仅为4.99%。该研究有效缓解了复合材料结构性能预测过程中数值模型与物理试验数据关联困难及试验数据稀缺的问题。
唐铠瑞 , 王喆 , 陈向明 , 崔保让 , 陈艳辉 , 陈普会 . 复合材料结构力学性能分布的多保真度数据驱动预测框架及验证[J]. 航空学报, 2025 , 46(21) : 532180 -532180 . DOI: 10.7527/S1000-6893.2025.32180
The failure mechanisms of carbon-fiber-reinforced composites are complex， and experimental tests are costly. Traditional finite element methods， limited by current theoretical models， struggle to accurately simulate the entire failure process and exhibit significant cumulative errors， complicating precise modeling and uncertainty quantification. Machine learning approaches offer a promising alternative but generally require extensive datasets to achieve satisfactory performance. We present a multi-fidelity data-driven framework that blends a small set of high-fidelity test results with an extensive collection of low-fidelity simulation data to predict the distribution of mechanical properties in composite structures. The framework is validated through tensile-failure experiments on notched laminates. To improve the statistical representativeness of the limited experimental samples， we introduce a Bayesian data-augmentation scheme and derive the theoretical distribution of the inter-group coefficient of variation to confirm its soundness. Cross-validation shows that the proposed method attains a mean absolute error of 4.99% when predicting the 10th percentile of the failure-load distribution. The study mitigates the twin challenges of scarce experimental data and weak coupling between numerical models and physical tests.
| [1] | U.S. Department of Defense. Composite materials handbook. Volume 3， Polymer matrix composites materials： Usage， design， and analysis［M］. Warrendale： SAE International， 2002. |
| [2] | U.S. Department of Defense. Composite materials handbook. Volume 1， Polymer matrix composites： Guidelines for characterization of structural materials［M］. Warrendale： SAE International， 2002. |
| [3] | CUMBO R， BARONI A， RICCIARDI A， et al. Design allowables of composite laminates： A review［J］. Journal of Composite Materials， 2022， 56（23）： 3617-3634. |
| [4] | PAPADRAKAKIS M， PAPADOPOULOS V. Robust and efficient methods for stochastic finite element analysis using Monte Carlo simulation［J］. Computer Methods in Applied Mechanics and Engineering， 1996， 134（3-4）： 325-340. |
| [5] | CAVDAR O， BAYRAKTAR A， CAVDAR A， et al. Perturbation based stochastic finite element analysis of the structural systems with composite sections under earthquake forces［J］. Steel and Composite Structures， 2008， 8（2）： 129-144. |
| [6] | GHANEM R G， SPANOS P D. Spectral stochastic finite-element formulation for reliability analysis［J］. Journal of Engineering Mechanics， 1991， 117（10）： 2351-2372. |
| [7] | STEFANOU G. The stochastic finite element method： Past， present and future［J］. Computer Methods in Applied Mechanics and Engineering， 2009， 198（9-12）： 1031-1051. |
| [8] | CHAHAR R S， MUKHOPADHYAY T. Multi-fidelity machine learning based uncertainty quantification of progressive damage in composite laminates through optimal data fusion［J］. Engineering Applications of Artificial Intelligence， 2023， 125： 106647. |
| [9] | REINER J， LINDEN N， VAZIRI R， et al. Bayesian parameter estimation for the inclusion of uncertainty in progressive damage simulation of composites［J］. Composite Structures， 2023， 321： 117257. |
| [10] | REINER J. A multi-analysis framework for uncertainty quantification and data-driven simulation of design allowables in laminated composites［J］. Composites Science and Technology， 2025， 261： 111030. |
| [11] | FURTADO C， ARTEIRO A， BESSA M A， et al. Prediction of size effects in open-hole laminates using only the Young’s modulus， the strength， and the R-curve of the 0° ply［J］. Composites Part A： Applied Science and Manufacturing， 2017， 101： 306-317. |
| [12] | VALLMAJó O， CóZAR I R， FURTADO C， et al. Virtual calculation of the B-value allowables of notched composite laminates［J］. Composite Structures， 2019， 212： 11-21. |
| [13] | FURTADO C， PEREIRA L F， TAVARES R P， et al. A methodology to generate design allowables of composite laminates using machine learning［J］. International Journal of Solids and Structures， 2021， 233： 111095. |
| [14] | TANG K R， CUI Y Y， CHEN P H. A deep learning method for addressing the scarcity of experimental data in composite structures： Multi-fidelity triple LSTM［J］. Thin-Walled Structures， 2025， 211： 113106. |
| [15] | YUAN M Q， ZHAO H T， XIE Y H， et al. Prediction of stiffness degradation based on machine learning： Axial elastic modulus of ［0m/90n］s composite laminates［J］. Composites Science and Technology， 2022， 218： 109186. |
| [16] | GISELLE FERNáNDEZ-GODINO M. Review of multi-fidelity models［J］. Advances in Computational Science and Engineering， 2023， 1（4）： 351-400. |
| [17] | BREVAULT L， BALESDENT M， HEBBAL A. Overview of Gaussian process based multi-fidelity techniques with variable relationship between fidelities， application to aerospace systems［J］. Aerospace Science and Technology， 2020， 107： 106339. |
| [18] | MENG X H， EM K. A composite neural network that learns from multi-fidelity data： Application to function approximation and inverse PDE problems［J］. Journal of Computational Physics， 2020， 401： 109020. |
| [19] | EGOROVA O， HAFIZI R， WOODS D C， et al. Multifidelity statistical machine learning for molecular crystal structure prediction［J］. The Journal of Physical Chemistry A， 2020， 124（39）： 8065-8078. |
| [20] | OREJUELA I P， GONZáLEZ C L， GUERRA X B， et al. Geoid undulation modeling through the Cokriging method-A case study of Guayaquil， Ecuador［J］. Geodesy and Geodynamics， 2021， 12（5）： 356-367. |
| [21] | ROUCHON J. Certification of large airplane composite structures［C］∥ICAS Congress Proceedings.1990， 2： 1439-1447. |
| [22] | MARCH A， WILLCOX K， WANG Q. Gradient-based multifidelity optimisation for aircraft design using Bayesian model calibration［J］. The Aeronautical Journal， 2011， 115（1174）： 729-738. |
| [23] | PERDIKARIS P， RAISSI M， DAMIANOU A， et al. Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling［J］. Proceedings Mathematical， Physical， and Engineering Sciences， 2017， 473（2198）： 20160751. |
| [24] | MAHMOUDABADBOZCHELOU M， CAGGIONI M， SHAHSAVARI S， et al. Data-driven physics-informed constitutive metamodeling of complex fluids： A multifidelity neural network （MFNN） framework［J］. Journal of Rheology， 2021， 65（2）： 179-198. |
| [25] | ZHANG P， YIN Z Y， JIN Y F， et al. Physics-informed multifidelity residual neural networks for hydromechanical modeling of granular soils and foundation considering internal erosion［J］. Journal of Engineering Mechanics， 2022， 148（4）： 04022015. |
| [26] | PERDIKARIS P， RAISSI M， DAMIANOU A， et al. Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling［J］. Proceedings Mathematical， Physical， and Engineering Sciences， 2017， 473（2198）： 20160751. |
| [27] | LU L， DAO M， KUMAR P， et al. Extraction of mechanical properties of materials through deep learning from instrumented indentation［J］. PNAS 2020， 117（13）： 7052-7062. |
| [28] | GREEN B G， WISNOM M R， HALLETT S R. An experimental investigation into the tensile strength scaling of notched composites［J］. Composites Part A： Applied Science and Manufacturing， 2007， 38（3）： 867-878. |
| [29] | RIDHA M， WANG C H， CHEN B Y， et al. Modelling complex progressive failure in notched composite laminates with varying sizes and stacking sequences［J］. Composites Part A： Applied Science and Manufacturing， 2014， 58： 16-23. |
| [30] | LAFFAN M， PINHO S， ROBINSON P， et al. Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part Ⅱ： Size and lay-up effects［J］. Composites Science and Technology， 2010， 70（4）： 614-621. |
| [31] | JOHNSON N L， BALAKRISHNAN N. Continuous Univariate distributions［M］. 2nd ed. New York： John Wiley & Sons Inc， 1994： 515-516. |
| [32] | METROPOLIS N， ULAM S. The Monte Carlo method［J］. Journal of the American Statistical Association， 1949， 44（247）： 335-341. |
| [33] | PARZEN E. On estimation of a probability density function and mode［J］. The Annals of Mathematical Statistics， 1962， 33（3）： 1065-1076. |
| [34] | BERGER J. The case for objective Bayesian analysis［J］. Bayesian Analysis， 2006， 1（3）： 385-402. |
| [35] | GELMAN A， CARLIN J B， STERN H S， et al. Bayesian data analysis［M］. 3rd ed. New York： Chapman and Hall/CRC， 2025： 150-151. |
| [36] | AKIBA T， SANO S， YANASE T， et al. Optuna： A next-generation hyperparameter optimization framework［C］∥Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. New York： ACM， 2019： 2623-2631. |
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