On the premise of taking the materials of the printed circuit board and component as orthotropic, a method based on response surface was proposed to update the finite element model(FEM) of printed circuit board assembly(PCBA). The parameters which have great influence on the modal frequencies of PCBA were screened out and taken as the updating parameters by correlation analysis. The sample points were acquired by using an appropriate experimental design according to the number of the updating parameters to construct the polynomial response surface model. The least squares method was used to determine the polynomial coefficients and then to test the fitting accuracy of response surface. The absolute value of error between the results of the calculated response surface and the actual test was taken as the objective function. The optimized parameters were obtained by iterative calculation of MOGA. The updated model was then obtained by substituting optimized parameters into the non-updated FEM.Take the PCBA of an aircraft electronic product as an example. The comparison of modal frequencies of non-updated and updated FEM shows that the relative error of modal frequencies between the updated FEM and the actual test obviously reduced and thus verifies the effectiveness of the model updating methodology suggested in the paper.
王开山1,李传日1,庞月婵1,郭恒晖1 . 基于响应面法的印制电路板组件有限元模型修正[J]. 振动与冲击, 2015, 34(22): 42-46.
WANG Kai-shan1 LI Chuan-ri1 PANG Yue-chan1 GUO Heng-hui1. The Finite Element Model Updating of Printed Circuit Board Assembly Based on Response Surface Methodology. JOURNAL OF VIBRATION AND SHOCK, 2015, 34(22): 42-46.
[1] 王红芳,赵玫.基于动态特性的印制板结构改进[J].振动与冲击,2000,19(1):49-51.
Wang Hongfang, Zhao Mei. The structure improvements based on the dynamic characteristics of the printed circuit board[J]. Journal of Vibration and Shock, 2000, 19(1): 49-51(in Chinese)
[2] 杨宇军,叶松林,游少雄,等.插板式PCB的内置式减振设计方法及其PSD动力学仿真[J].振动与冲击,2007,26(2):39-42.
Yang Yujun, Ye Songlin, You Shaoxiong, et a1. The vibration damping design method of PCB and its PSD dynamics simulation[J]. Journal of Vibration and Shock, 2007, 26(2): 39-42(in Chinese)
[3] 鲍诺,王春洁,赵军鹏等.基于响应面法的结构动力学模型修正[J].振动与冲击,2013,32(16):30-34.
[4] 费庆国,韩晓林,苏鹤玲.响应面有限元模型修正的实现与应用[J].振动、测试与诊断,2010,30(2):132-134.
Fei Qingguo, Han Xiaolin,Su Heling. The implementation and application of finite element model updating based on response surface[J]. Journal of Vibration, Measurement & Diagnosis, 2010, 30(2): 132-134(in Chinese)
[5] 常涛,郭勤涛,张保强.应用模型修正方法的印制电路板参数识别[J].振动、测试与诊断,2013,33(3):111-116.
[6] Heinonen O, Pajunen S. Optimal design of stiffened plate using metamodeling techniques[J]. Journal of Structural Mechanics, 2011, 44(3): 218-230.
[7] Friswell M I, Mottershead J E, Ahmadian H. Combining subset selection and parameter constrants in model updating[J]. Journal of Vibration and Acoustics, 1998, 120(4): 854-859.
[8] Friswell M I, Garvey S D, Penny J E T. The convergence of the iterated IRS method[J]. Journal of Sound and Vibration, 1998, 211(1): 123-132.
[9] 庄楚强.应用数理统计基础[M].4版.华南理工大学出版社,1992.
Zhuang Chuqiang. Application of mathematical statistics[M]. 4nded. South China University of Technology Press, 1992(in Chinese)
[10] Dougles C. Montgomery Design and analysis of experiments[M]. John Wiley & Sons, Tnc, 2008.
[11] 郭勤涛,张令弥,费庆国.用于确定性计算仿真的响应面法及其试验设计研究[J].航空学报,2006,27(1):55-61.
Guo Qintao, Zhang Lingmi, Fei Qingguo. Response surface method and its experimental design for deterministic computer simulation[J]. Journal of Aeronautics, 2006, 27(1): 55-61(in Chinese)
[12] 宗周红,高铭霖,夏樟华.基于健康监测的连续刚构桥有限元模型确认(I)-基于响应面法的有限元模型修正[J].土木工程学报,2011,44(2):90-98.
Zong Zhouhong, Gao Minglin, Xia Zhanghua. The finite element model validation of continuous rigid frame bridge based on health monitoring(I)-the finite element model updating based on response surface[J]. China Civil Engineering Journal, 2011, 44(2): 90-98(in Chinese)
[13] Kwon Joong-Hak, Hwang Sang-Moon, Lee ChangMin, et a1. Application of response surface methodology in microspeaker design used in mobile phones[J]. Institute of Electrical and Electronics Engineers Transactions on Magnetics, 2009, 45(10): 4550-4553.
[14] Montgomery D C. Design and analysis of experiments[M]. John Wiley & Sons, Tnc, 2008.
[15] Montgomery D C.试验设计与分析[M].北京:中国统计出版社,1998.563-575.
Montgomery D C. Design and analysis of experiments[M].
Statistics Press of China, 1998. 563-575.
[16] 费庆国,张令弥,李爱群,等.基于统计分析技术的有限元模型修正研究[J].振动与冲击,2005,24(3):23-26.
Fei Qingguo, Zhang Lingmi, Li Aiqun, et a1. The finite element model updating based on statistical analysis techniques[J]. Journal of Vibration and Shock, 2005, 24(3): 23-26(in Chinese)
[17] 费庆国,韩晓林,苏鹤玲.响应面有限元模型修正的实现与 应用[J].振动、测试与诊断,2010,30(2):132-134.
Fei Qingguo, Han Xiaolin, Su Heling. The implementation and application of finite element model updating based on response surface[J]. Journal of Vibration, Measurement & Diagnosis, 2010, 30(2): 132-134(in Chinese)