基于WOA-BP-LSTM自编码器的CFRP薄壁C柱轴压响应预测

doi:10.7527/S1000-6893.2025.32349

Abstract

Abstract:

To predict the force-displacement responses of Carbon Fiber Reinforced Plastic （CFRP） thin-walled C-columns in the aircraft sub-cargo area under quasi-static axial crushing， an intelligent prediction model （WOA-BP-LSTM autoencoder model） integrating the Whale Optimization Algorithm （WOA）， Back Propagation （BP） neural network， and Long Short-Term Memory （LSTM） autoencoder was proposed. The reliability of the finite element model of CFRP thin-walled C-columns was validated through quasi-static axial crushing tests， with axial crushing response evaluation indicators showing errors within 10%. A dataset comprising 700 force-displacement response samples with variable cross-sectional geometric parameters was constructed based on the model. The LSTM autoencoder was employed for dimensionality reduction and reconstruction of the force-displacement responses. Subsequently， the BP neural network was used for force-displacement responses prediction， with WOA optimizing the neural network parameters. The results show that the LSTM autoencoder achieved high-precision reconstruction of force-displacement responses， where the errors for initial peak crushing force and energy absorption in the test set were both less than 3%， and 80% of the samples had errors within 1%. The optimized prediction model significantly improved prediction accuracy， reducing the test set’s Mean Absolute Error （MAE） by 17.55%， Mean Squared Error （MSE） by 31.77%， and Root Mean Squared Error （RMSE） by 17.47%. Prediction errors for the initial peak crushing force and energy absorption were both less than 8%， with 80% of samples showing errors within 5%. This model enables rapid and accurate prediction of axial crushing responses for variable cross-section CFRP thin-walled C-columns while reducing computational costs， providing an efficient parameter-performance mapping tool for the study of its axial crushing response.

Key words: CFRP thin-walled C-columns, axial crushing response, LSTM autoencoder, whale optimization algorithm, BP neural network

CLC Number:

V229

Haolei MOU, Jia ZHANG, Zhenyu FENG, Chunyu BAI. Prediction of axial crushing response for CFRP thin-walled C-columns based on WOA-BP-LSTM autoencoder[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(4): 232349.

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参数	数值
密度/（t·mm^-3）	1.5×10^-9
轴向弹性模量/MPa	134 000
横向弹性模量/MPa	9 000
泊松比ν12	0.3
12方向剪切模量/MPa	4 300
13方向剪切模量/MPa	4 300
23方向剪切模量/MPa	4 300
轴向拉伸失效应力/MPa	2 158
轴向压缩失效应力/MPa	1 000
横向拉伸失效应力/MPa	42
横向压缩失效应力/MPa	172
轴向剪切失效应力/MPa	75
横向剪切失效应力/MPa	75

铺层方式		IPCF/kN	EA/J	SEA/（kJ·kg^-1）	MCF/kN
［±45/90/0₂/90/0₂］_s	试验	33.27	1 256.39	15.67	38.35
	仿真	33.26	1 236.53	15.43	37.18
	误差/%	0.03	1.58	1.53	3.05
［0/90］_{4 s}	试验	28.96	993.14	12.36	30.10
	仿真	26.12	1 074.58	13.37	32.31
	误差/%	9.81	8.20	8.17	7.34

a/mm	b/mm	c/mm	d/mm
0，20，40，60，80	0，20，40，60，80	10	10
		15	15，10
		20	20，15，10
		25	25，20，15，10
		30	30，25，20，15，10
		35	35，30，25，20，15，10
		40	40，35，30，25，20，15，10

样本	IPCF/kN			EA/J
样本	真实值	重建值	误差/%	真实值	重建值	误差/%
1	32.75	33.00	0.77	1 396.33	1 388.91	0.53
2	27.08	27.82	2.72	1 124.41	1 133.20	0.78
3	27.51	27.62	0.42	1 092.41	1 098.68	0.57
4	46.61	46.64	0.06	1 505.54	1 488.62	1.12
5	29.70	29.94	0.81	1 162.46	1 171.61	0.79
6	22.85	22.68	0.73	478.99	474.58	0.92
7	29.29	29.15	0.49	1 122.19	1 096.37	2.30
8	41.95	42.19	0.57	1 430.47	1 434.60	0.29
9	33.26	33.48	0.68	1 237.73	1 241.88	0.34
10	21.58	21.99	1.89	1 097.71	1 094.41	0.30
11	34.65	34.69	0.13	1 286.87	1 311.65	1.93
12	20.23	20.31	0.35	511.62	509.47	0.42

样本	IPCF/kN					EA/J
样本	真实值	BP-LSTM自编码器预测值	误差/%	WOA-BP-LSTM自编码器预测值	误差/%	真实值	BP-LSTM自编码器预测值	误差/%	WOA-BP-LSTM自编码器预测值	误差/%
1	33.26	33.53	0.83	33.52	0.80	1 237.73	1 278.03	3.26	1 256.6	1.53
2	23.89	22.31	6.61	22.88	4.21	1 009.58	808.18	19.95	1 021.43	1.17
3	28.66	26.60	7.16	27.17	5.18	1 154.32	1 120.60	2.92	1 143.83	0.91
4	22.94	24.68	7.60	23.71	3.34	1 157.65	1 172.38	1.27	1 154.17	0.30
5	33.04	34.31	3.84	33.55	1.56	1 289.85	1 306.47	1.29	1 299.45	0.74
6	27.51	26.31	4.36	26.81	2.54	1 092.41	1 099.62	0.66	1 090.98	0.13
7	33.05	33.94	2.70	33.54	1.47	1 341.59	1 332.72	0.66	1 342.94	0.10
8	20.23	20.15	0.43	21.76	7.53	511.62	586.77	14.69	534.66	4.50
9	46.61	45.49	2.42	45.68	2.02	1 505.54	1 511.12	0.37	1 509.78	0.28
10	24.68	22.47	8.97	22.99	6.86	450.82	526.26	16.73	453.79	0.66
11	34.07	33.69	1.10	33.86	0.61	1 323.26	1 310.19	0.99	1 302.55	1.56
12	41.95	43.45	3.56	43.02	2.53	1 430.47	1 438.79	0.58	1 435.12	0.32

Prediction of axial crushing response for CFRP thin-walled C-columns based on WOA-BP-LSTM autoencoder

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