Prediction of Self-piercing Riveting Quality Based on Multi-strategy Improved Composite Sparrow Search Algorithm

doi:10.3969/j.issn.1004-132X.2026.02.022

Abstract

Abstract:

To efficiently predict the forming quality of self-piercing riveted joints， a finite element model of self-piercing riveting for AA5754 aluminum alloys was established， and the effectiveness of the simulation model was verified through experiments. Based on the simulation analysis， 176 sets of effective cross-sectional data of the joints were obtained. By integrating the sparrow search algorithm and the butterfly algorithm， a composite optimization algorithm was constructed. The algorithm's convergence speed and solution quality were improved by employing population initialization and lens reverse learning strategies. Multidirectional learning and Levy flight strategies were introduced to enhance the algorithm's ability to escape local optima， thereby improving the global search capabilities. Research indicates that the prediction results of the established model have a MAPE of less than 10%， a correlation coefficient R² higher than 0.99， and a mean square error MSE consistently less than 0.001. Therefore， the proposed improved model has high predictive accuracy and robustness.

Key words: self-piercing riveting, neural network, optimization algorithm, forming quality prediction, simulation

摘要：

为了高效预测自冲铆接头的成形质量，建立AA5754铝合金自冲铆成形有限元模型，通过实验验证仿真模型的有效性，基于仿真分析获得了176组有效接头成形截面数据集。通过整合麻雀算法和蝴蝶算法，初步构建复合优化算法。采取种群初始化和透镜反向学习策略改进算法的收敛速度和求解质量，引入多向学习和Levy飞行策略增强算法跳出局部最优，提高了全局搜索能力。研究表明所建模型预测结果的平均绝对百分比误差MAPE均在10%以下，相关系数R²均在0.99以上，均方误差MSE稳定在0.001以下，证明所提改进模型具有较高的预测精度和鲁棒性。

关键词: 自冲铆, 神经网络, 优化算法, 成形质量预测, 仿真

CLC Number:

TG938

LIU Yang, WU Qingjun, GUO Hao, QI Kaifei, ZHUANG Weimin, FU Guangsheng. Prediction of Self-piercing Riveting Quality Based on Multi-strategy Improved Composite Sparrow Search Algorithm[J]. China Mechanical Engineering, 2026, 37(2): 476-486.

刘洋, 吴庆军, 郭浩, 祁凯飞, 庄蔚敏, 伏广省. 基于多策略改进复合麻雀搜索算法的自冲铆成形质量预测[J]. 中国机械工程, 2026, 37(2): 476-486.

Figures/Tables 24

Fig.1 Flowchart for determining failure parameters of AA5754 aluminum alloy

Tab.1 Average stress triaxiality， mean lode angle parameters， fracture strain， and instability strain of AA5754 aluminum alloy

试件类型	平均应力三轴度	平均罗德角参数	断裂应变	失稳应变
圆棒试件	0.460 50	1.00	0.670 00	0.1360
缺口12 mm 的圆棒试件	0.676 93	0.97	0.548 64	0.1033
缺口4 mm 的圆棒试件	0.906 10	1.00	0.491 68	0.0720
缺口2.4 mm 的薄板试件	0.732 70	0.03	0.226 60	0.0260
剪切试件	0.084 70	0.02	0.385 20	0.0503
圆柱压缩试件R3H7.5	$-$ 0.695 90	$-$ 1.00	2.007 40	1.3457

Tab.1 Average stress triaxiality， mean lode angle parameters， fracture strain， and instability strain of AA5754 aluminum alloy

试件类型	平均应力三轴度	平均罗德角参数	断裂应变	失稳应变
圆棒试件	0.460 50	1.00	0.670 00	0.1360
缺口12 mm 的圆棒试件	0.676 93	0.97	0.548 64	0.1033
缺口4 mm 的圆棒试件	0.906 10	1.00	0.491 68	0.0720
缺口2.4 mm 的薄板试件	0.732 70	0.03	0.226 60	0.0260
剪切试件	0.084 70	0.02	0.385 20	0.0503
圆柱压缩试件R3H7.5	$-$ 0.695 90	$-$ 1.00	2.007 40	1.3457

Tab. 2 Failure parameters of material model

材料	c₁	c₂	c₃	LES值
AA5754	0.05	166	1.004	0.0383

Fig.2 Failure surface of AA5754 aluminum alloy

Tab.3 Self-piercing riveting parameters of the three groups of joints

编号	上板厚度/mm	下板厚度/mm	铆钉长度/mm	冲头位移/mm
J-1	2.0	2.0	5.0	5.1
J-2	2.0	2.5	5.5	5.6
J-3	2.5	2.0	6.0	6.1

Fig.3 Finite element model of self-piercing riveting

Tab.4 Mechanical property parameters of AA5754 aluminum alloy and rivets

名称

密度/

（kg·m $- 3$ ）

Tab.4 Mechanical property parameters of AA5754 aluminum alloy and rivets

名称

密度/

（kg·m $- 3$ ）

弹性模量/GPa

泊松比

屈服强度/MPa

抗拉强度/MPa

铆钉

7800

210

0.3

885.6

1170.6

AA5754

2700

0.3

162.1

244.1

Fig.4 Evaluation indicators for the forming quality of self-piercing riveted joint

Fig.5 Comparison of joint forming sections obtained by experiments and simulations

Tab.5 Prediction errors of cross-section geometric parameters of the joints

接头	钉脚张开度			残余底厚			下板中心厚度
接头	实验值/mm	仿真值/mm	误差/%	实验值/mm	仿真值/mm	误差/%	实验值/mm	仿真值/mm	误差/%
J-1	0.448	0.401	10.49	0.690	0.631	8.55	1.483	1.552	4.65
J-2	0.491	0.473	3.67	0.755	0.714	5.43	1.962	1.891	3.62
J-3	0.359	0.371	3.34	0.344	0.364	5.81	1.563	1.661	6.27

Fig.6 Schematic diagram of five input process parameters

Tab.6 Design of full factorial process parameters for five factors at three levels

因素	范围	水平
因素	范围	1	2	3
上板厚度/mm	1.5~2.5	1.5	2.0	2.5
下板厚度/mm	1.5~2.5	1.5	2.0	2.5
铆钉长度/mm	5.0~6.0	5.0	5.5	6.0
凸台高度/mm	0.0~1.8	0.0	1.0	1.8
凹槽深度/mm	1.8~2.2	1.8	2.0	2.2

Fig.7 Structure diagram of a BP neural network

Fig.8 RMSE of model validation sets with varying numbers of neurons in hidden layers

Fig.9 Schematic of lens imaging principle

Fig.10 Flowchart of MIC_SSA optimized neural network prediction model

Fig.11 Fitness variation curve of the MIC_SSA_BP model

Fig.12 Comparison of model predicted values and true values in the test set

Fig.13 Comparison of prediction errors among various models

Tab.7 Computational data for error evaluation metrics of prediction results from various models

	指标	BP模型	GA_BP 模型	MIC_SSA_BP模型
钉脚张开度	RMSE/10 $- 2$	8.524	5.792	1.950
	MAE/10 $- 2$	7.258	5.650	1.756
	MAPE/%	18.445	15.771	4.884
残余底厚	RMSE/10 $- 2$	18.106	12.348	2.385
	MAE/10 $- 2$	12.062	10.027	2.103
	MAPE/%	13.680	13.239	3.300
下板中心厚度	RMSE/10 $- 2$	20.519	13.654	2.600
	MAE/10 $- 2$	14.729	12.167	2.418
	MAPE/%	21.415	16.228	3.740

Tab.7 Computational data for error evaluation metrics of prediction results from various models

	指标	BP模型	GA_BP 模型	MIC_SSA_BP模型
钉脚张开度	RMSE/10 $- 2$	8.524	5.792	1.950
	MAE/10 $- 2$	7.258	5.650	1.756
	MAPE/%	18.445	15.771	4.884
残余底厚	RMSE/10 $- 2$	18.106	12.348	2.385
	MAE/10 $- 2$	12.062	10.027	2.103
	MAPE/%	13.680	13.239	3.300
下板中心厚度	RMSE/10 $- 2$	20.519	13.654	2.600
	MAE/10 $- 2$	14.729	12.167	2.418
	MAPE/%	21.415	16.228	3.740

Fig.14 Error evaluation metrics for the prediction results of each model

Tab.8 R2 and MSE values of prediction results for each model

	指标	BP	GA_BP	MIC_SSA_BP
钉脚张开度	R²	0.856 04	0.933 53	0.992 46
钉脚张开度	MSE/10 $- 3$	7.265 00	3.354 00	0.380 00
残余底厚	R²	0.849 65	0.930 07	0.997 39
残余底厚	MSE/10 $- 3$	32.782 00	15.246 00	0.569 00
下板中心厚度	R²	0.830 97	0.925 16	0.997 28
下板中心厚度	MSE/10 $- 3$	42.103 00	18.642 00	0.676 00

Tab.8 R2 and MSE values of prediction results for each model

	指标	BP	GA_BP	MIC_SSA_BP
钉脚张开度	R²	0.856 04	0.933 53	0.992 46
钉脚张开度	MSE/10 $- 3$	7.265 00	3.354 00	0.380 00
残余底厚	R²	0.849 65	0.930 07	0.997 39
残余底厚	MSE/10 $- 3$	32.782 00	15.246 00	0.569 00
下板中心厚度	R²	0.830 97	0.925 16	0.997 28
下板中心厚度	MSE/10 $- 3$	42.103 00	18.642 00	0.676 00

Fig.15 Comparison of prediction accuracy among various models in the test set

Fig.16 Comparison of joint cross-sectional geometric parameters between experimental and predicted data

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