Reliability prediction and design optimization of BGA solder joint based on multi-fidelity surrogate model
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摘要:
焊点可靠性预测研究多采用有限元仿真与单一精度近似模型相结合的模式，存在仿真时间长、效率低、准确性差等问题，为此，提出了一种基于变可信度近似模型的球栅阵列(ball grid array，BGA)焊点可靠性预测与优化方法.首先, 对不同网格细化方案进行收敛性验证，分别设计高/低精度样本点进行有限元仿真；其次，基于Co-Kriging模型融合高/低精度仿真数据进行焊点可靠性预测；最后，将预测结果与单一精度近似模型进行对比分析，并采用遗传算法优化模型获得对应结构参数.结果表明，在更少的仿真成本下，变可信度模型的预测效果更好，在同等预测精度下，变可信度模型高精度样本点数量仅为单一精度模型的1/4，相比高精度神经网络预测模型，在寻优过程中收敛更快.
Abstract:At present, the reliability prediction of solder joints is mostly based on the combination of finite element simulation and single precision surrogate model, which has some problems such as long simulation time, low efficiency and poor accuracy. Therefore, a reliability prediction method for BGA (ball grid array) solder joints based on multi-fidelity model is proposed. Firstly, the convergence of different meshing schemes was verified, and then the high and low precision sample points were designed respectively for finite element analysis (FEA). Secondly, the reliability of solder joints was predicted based on the Co-Kriging model based on multi fidelity FEA data. Finally, the prediction results were compared with the single precision surrogate model, Under the same cost constraints, the multi-fidelity model demonstrates significantly higher prediction accuracy. and NSGA(nondominated sorting genetic algorithm) was used to optimize the model to obtain the corresponding process parameters. The results show that with less simulation cost, the prediction result of multi-fidelity model is better. Under the same prediction accuracy, the number of high-precision sample points of the variable reliability model is only 1/4 of that of the single precision model. At the same time, compared with the neural network prediction model, it converges faster in the optimization process. This paper provides some reference for the research of reliability prediction of solder joint with multi-fidelity model.
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Keywords:
- solder joint reliability /
- life prediction /
- multi-fidelity model /
- NSGA
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图 4 网格划分方案
Figure 4. Grid division scheme. (a) global refinement; (b) edge refinement; (c) above and below refinement; (d) side refinement
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图 7 焊点应力寻优结果
Figure 7. Optimization results of solder joint stress. (a) neural network model; (b) multi-fidelity model
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图 8 焊点寿命寻优结果
Figure 8. Optimization results of solder joint life. (a) neural network model; (b) multi-fidelity model
表 1 焊点材料参数
Table 1 Solder joint material parameters
温度T/℃ 杨氏模量E/MPa 泊松比ν −55 47 970 0.352 −35 46 890 0.354 −15 45 790 0.357 5 44 380 0.360 20 43 250 0.363 50 41 330 0.365 75 39 450 0.370 100 36850 0.377 125 34590 0.380 
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表 2 不同模型应力和寿命测试结果
Table 2 Stress test results and life test results of different models
编号 应力相对误差δ1 寿命相对误差δ2 嵌套
Co-Kriging非嵌套
Co-Kriging高精度
神经网络高精度
Kriging嵌套
Co-Kriging非嵌套
Co-Kriging高精度
神经网络高精度
Kriging1 −0.013 9 −0.017 1 −0.060 7 0.034 3 −0.157 9 −0.005 9 1.132 5 −0.221 4 2 −0.013 4 −0.011 9 0.016 7 0.047 9 −0.039 9 0.152 3 0.159 8 −0.540 5 3 −0.051 1 −0.063 0 0.065 1 0.027 8 0.391 5 0.319 2 −0.337 4 −0.357 3 4 0.001 6 −0.011 1 −0.008 9 −0.015 2 −0.020 4 −0.309 3 0.569 4 0.015 0 5 0.008 0 0.004 8 −0.068 0 0.012 5 0.044 2 0.074 1 0.330 8 0.433 8 6 0.009 7 0.015 1 −0.020 6 −0.008 4 −0.533 7 0.094 8 0.326 0 −0.115 6 7 0.022 4 0.029 0 −0.122 7 −0.043 0 −0.251 9 −0.485 7 1.893 1 2.449 3 8 0.011 0 0.052 6 −0.105 9 −0.070 4 −1.001 0 −1.500 5 0.478 9 2.268 6 9 −0.077 0 −0.036 0 −0.016 5 −0.099 1 0.069 0 −0.090 8 −0.233 1 0.948 6 10 −0.010 6 0.056 0 −0.028 1 −0.037 6 −0.441 4 −0.151 2 1.098 2 0.712 6 11 0.015 9 −0.003 9 −0.016 1 0.042 9 0.163 9 0.091 2 0.110 7 −0.569 4 12 −0.026 1 −0.026 6 −0.024 3 0.108 7 0.180 3 0.463 5 0.204 6 −0.560 9 13 0.020 1 −0.000 1 −0.004 3 0.018 7 −0.157 9 −0.144 2 −0.017 4 −0.385 8 RMSE 0.621 8 0.709 8 1.290 0 1.16 29.010 5 36.4 7 45.23 79.32 样本组成 A B C C A B C C 仿真时长 t/min 3 250 3 250 5 000 5 000 3 250 3 250 5 000 5 000
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表 3 高精度样本点个数与应力预测效果
Table 3 Number of high-precision sample points and stress prediction performance
高精度样本点个数N 均方根误差δRMSE 20 1.1996 25 0.7638 30 0.7497 35 0.7220 40 0.6576 45 0.6344 50 0.6218
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表 4 遗传算法参数
Table 4 Parameters of genetic algorithm
初始种群
数量m最大迭代数
max精英数
n交叉
概率A函数收敛
残差δ扩展适应度
函数50 100 5 0.8 1 × 10−10 Rank
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