面向变刚度复合材料筒壳高效屈曲分析的变保真度迁移学习模型

李增聪; 田阔; 黄蕾; 王博

doi:10.13801/j.cnki.fhclxb.20210604.001

面向变刚度复合材料筒壳高效屈曲分析的变保真度迁移学习模型

doi: 10.13801/j.cnki.fhclxb.20210604.001

李增聪¹,
田阔^{1, 2, 3, ,},
黄蕾¹,
王博^{1, 2}

1.
大连理工大学　工业装备结构分析国家重点实验室，大连 116024
2.
大连理工大学　辽宁省工业装备数字孪生重点实验室，大连 116024
3.
大连理工大学　人工智能大连研究院，大连 116024

基金项目: 国家自然科学基金(11902065；11825202)；中央高校基本科研业务费(DUT21RC(3)013)

详细信息

通讯作者:
田阔，博士，副教授，硕士生导师，研究方向为数据驱动的结构强度与优化设计　 E-mail：tiankuo@dlut.edu.cn

中图分类号: V214.4；V414.4
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出版历程
- 收稿日期: 2021-04-25
- 修回日期: 2021-05-20
- 录用日期: 2021-05-27
- 网络出版日期: 2021-06-05
- 刊出日期: 2022-03-23

Variable-fidelity transfer learning model for efficient buckling analysis of variable stiffness composite cylindrical shells

LI Zengcong¹,
TIAN Kuo^{1, 2, 3
, ,},
HUANG Lei¹,
WANG Bo^{1, 2}

1.
State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China
2.
Key Laboratory of Digital Twin for Industrial Equipment, Dalian University of Technology, Dalian 116024, China
3.
DUT Artificial Intelligence Institute, Dalian University of Technology, Dalian 116024, China

摘要

摘要: 相较于传统直线铺层设计的复合材料筒壳结构，变刚度复合材料筒壳结构通过曲线纤维路径铺层，可以极大地增加复合材料的设计空间，进而获得更优的抗屈曲能力。为了准确描述曲线纤维路径，需要针对变刚度复合材料筒壳建立精细有限元模型，因此对屈曲分析和优化效率带来了较大的挑战。本论文以变刚度复合材料筒壳结构的线性屈曲及后屈曲承载力快速预测为目标，提出了一种变保真度迁移学习模型的构建方法。首先，针对变刚度复合材料筒壳结构建立合适的高保真度、低保真度模型；然后，基于大量低保真度样本数据作为源域样本集建立并训练深度神经网络，得到预训练模型；最后，以少量高保真度样本数据作为目标域样本集对最后一层神经网络参数进行微调，训练得到变保真度迁移学习模型。变刚度复合材料筒壳线性屈曲和后屈曲算例结果表明，在达到相同的预测精度水平时，变保真度迁移学习模型比直接采用高保真度样本数据构建的代理模型分别节约了47.7%和62.3%的计算成本，验证了提出方法的高效率优势。同时，与基于桥函数构建的变保真度代理模型和Co-Kriging进行比较，所提出方法在不同高保真度、低保真度样本数据组合下均具有更优精度，验证了提出方法的高精度优势。
- 变刚度复合材料筒壳 /
- 屈曲分析 /
- 迁移学习 /
- 变保真度代理模型 /
- 深度神经网络
Abstract: Compared with the traditional design method of composite cylindrical shells with straight fiber laminate, variable stiffness composite cylindrical shells can greatly increase the design space of composite material and thus achieve higher buckling loads by means of the curved fiber laminate. To describe the curved fiber path precisely, it is necessary to establish high-fidelity detailed finite element model for variable stiffness composite cylindrical shells. Therefore, it brings great challenges to the efficiency of buckling analysis and optimization of variable stiffness composite cylindrical shells. In this paper, a variable-fidelity transfer learning model was proposed for the fast prediction of linear buckling load and post-buckling load of variable stiffness composite cylindrical shells. Firstly, the appropriate high-fidelity model and low-fidelity model of variable stiffness composite cylindrical shells were constructed. Then, the deep neural network was established and trained with a large number of low-fidelity samples as the source dataset, and the pre-trained model was obtained. Finally, the last layer was retained by fine-tuning with a small number of high-fidelity samples as the target dataset, and the variable-fidelity transfer learning model was constructed after the retraining on the pre-trained model. The example results of linear buckling and post-buckling load prediction of variable stiffness composite cylindrical shells indicate that, the computational cost of variable-fidelity transfer learning model can reduce by 47.7% and 62.3% than surrogates built by the high-fidelity samples directly when achieving similar prediction accuracy, showing the advantage of high prediction efficiency of the proposed method. Besides, compared with the variable-fidelity surrogate models built by the bridge function and Co-Kriging, the proposed method shows the best prediction accuracy with different combinations of high-fidelity and low-fidelity samples, which demonstrates the advantage of high prediction accuracy of the proposed method.
- variable stiffness composite cylindrical shell /
- buckling analysis /
- transfer learning /
- variable-fidelity surrogate model /
- deep neural network

HTML全文

图 1 罗-罗公司采用自动纤维铺放(AFP)技术制造航空发动机风扇机匣^[6]

Figure 1. Rolls-Royce aero-engine fan casing manufactured by automated fiber placement (AFP)^[6]

下载: 全尺寸图片幻灯片

图 2 变保真度迁移学习模型建立方法

Figure 2. Establishment method of variable-fidelity transfer learning model

HFM—High-fidelity model; LFM—Low-fidelity model; n, m—Number of LFM and HFM sample points

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图 3 变刚度复合材料筒壳纤维路径 (a) 与设计变量(b) 示意图

Figure 3. Schematic diagram of fiber path (a) and design variables (b) of variable stiffness composite cylindrical shell

α—Circumferential azimuth angle; θ—Fiber orientation angle; M—Moment; T₁-T₇—Continuous design variables

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图 4 变刚度复合材料筒壳高保真度模型(HFM) ((a), (b)) 与低保真度模型(LFM) ((c), (d)) 示意图

Figure 4. Schematic diagram of high-fidelity model (HFM) ((a), (b)) and low-fidelity model (LFM) ((c), (d)) for variable stiffness composite cylindrical shell

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图 5 变刚度复合材料筒壳HFM (a) 与LFM (b) 一阶屈曲模态

Figure 5. First buckling modes of HFM (a) and LFM (b) for variable stiffness composite cylindrical shell

M_cr—Critical buckling moment

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图 6 变刚度复合材料筒壳算例各代理模型回归系数 R²(a) 和相对均方根误差R_RMSE(b) 预测精度

Figure 6. Prediction accuracy of regression square R² (a) and relative root mean square error R_RMSE (b) for various surrogates of variable stiffness composite cylindrical shell

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图 7 含缺陷变刚度复合材料筒壳HFM (a)、LFM (b) 与缺陷分布示意图 (c)

Figure 7. Schematic diagram of HFM (a), LFM (b) and imperfection distribution (c) of variable-stiffness composite cylindrical shell with imperfection

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图 8 含缺陷变刚度复合材料筒壳HFM (a) 与LFM (b) 屈曲模态

Figure 8. Buckling modes of HFM (a) and LFM (b) for variable stiffness composite cylindrical shell with imperfection

P_co—Collapse load

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图 9 含缺陷变刚度复合材料筒壳算例各代理模型 R² (a) 和 R_RMSE (b) 预测精度

Figure 9. Prediction accuracy of R²(a) and R_RMSE (b) for various surrogates of variable stiffness composite cylindrical shell with imperfection

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表 1 变刚度复合材料筒壳材料属性

Table 1. Material properties of variable stiffness composite cylindrical shell

Property	Value
E₁/GPa	134
E₂/GPa	7.71
E₃/GPa	7.71
G₁₂/GPa	4.31
G₁₃/GPa	4.31
G₂₃/GPa	2.76
v₁₂	0.301
v₁₃	0.301
v₂₃	0.396
Thickness of each ply/mm	0.127
Notes: E₁, E₂, E₃—Modulus of elasticity of direction 1, direction 2 and direction 3, respectively; G₁₂, G₁₃, G₂₃—Shear elasticity of direction 12, direction 13 and direction 23, respectively; ν₁₂, ν₁₃, ν₂₃—Poisson's ratio of direction 12, direction 13 and direction 23, respectively.

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表 2 不同网格数量下变刚度复合材料筒壳结构屈曲载荷与计算耗时

Table 2. Buckling load and computational cost with different number of elements of variable stiffness composite cylindrical shell

Number of elements	Buckling load/(kN∙m)	CPU time/s
600	97.30	28
840	95.46	37
1000	94.46	45
1800	93.78	65
3600	93.22	120
6000	93.12	190
7500	93.09	230
—	93.10 (Rouhi^[40])	—
Note: CPU—Central processing unit.

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表 3 变刚度复合材料筒壳算例各代理模型预测精度与计算耗时

Table 3. Prediction accuracy and computational cost of various surrogates for variable stiffness composite cylindrical shell

	Kriging		RBF-VFSM		Co-Kriging		Proposed method		CPU time/min
	R²	R_RMSE	R²	R_RMSE	R²	R_RMSE	R²	R_RMSE	CPU time/min
30HFM	0.272	0.849	—	—	—	—	—	—	95.0
90HFM	0.691	0.548	—	—	—	—	—	—	285.0
180HFM	0.850	0.380	—	—	—	—	—	—	570.0
200LFM	0.549	0.661	—	—	—	—	—	—	93.3
300LFM	0.542	0.668	—	—	—	—	—	—	140.0
30HFM+300LFM	—	—	0.529	0.691	0.780	0.481	0.823	0.418	235.0
50HFM+300LFM	—	—	0.661	0.580	0.838	0.393	0.871	0.360	298.3
Notes: R²—Regression square; R_RMSE—Relative root mean square error; RBF-VFSM—BRF-based variable-fidelity surrogate model.

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表 4 含缺陷变刚度复合材料筒壳材料属性

Table 4. Material properties of variable stiffness composite cylindrical shell with imperfection

Property	Value
E₁/GPa	124.4
E₂/GPa	8.69
E₃/GPa	8.69
G₁₂/GPa	4.83
G₁₃/GPa	4.83
G₂₃/GPa	4.83
v	0.347
Thickness of each ply/mm	0.124

下载: 导出CSV

表 5 不同网格数量下含缺陷变刚度复合材料筒壳后屈曲载荷与计算耗时

Table 5. Post-buckling load and computational cost with different number of elements for variable stiffness composite cylindrical shell with imperfection

Number of elements	Buckling load/(kN∙m)	CPU time/s
2600	75.69	72
4000	75.27	104
7000	74.98	176
9600	74.65	267
15000	73.96	505
21600	73.50	895
28560	71.30	1423
—	71.20 ^[42]	—

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表 6 含缺陷变刚度复合材料筒壳算例各代理模型预测精度与计算耗时

Table 6. Prediction accuracy and computational cost of various surrogates for variable stiffness composite cylindrical shell with imperfection

	Kriging		RBF-VFSM		Co-Kriging		Proposed method		CPU time/min
	R²	R_RMSE	R²	R_RMSE	R²	R_RMSE	R²	R_RMSE	CPU time/min
5HFM	0.744	0.503	—	—	—	—	—	—	118.6
10HFM	0.915	0.290	—	—	—	—	—	—	237.2
20HFM	0.959	0.201	—	—	—	—	—	—	474.3
50LFM	0.843	0.395	—	—	—	—	—	—	60.0
100LFM	0.842	0.395	—	—	—	—	—	—	120.0
5HFM+50LFM	—	—	0.933	0.257	0.932	0.260	0.961	0.196	178.6
10HFM+50LFM	—	—	0.946	0.231	0.956	0.208	0.972	0.167	297.2

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