基于响应面法的印制电路板组件有限元模型修正

王开山，李传日，庞月婵，郭恒晖

(北京航空航天大学可靠性与系统工程学院，北京100191)

摘要：在将印制电路板及元器件材料视为正交各向异性前提下，提出基于响应面法的印制电路板组件(Printed Circuit Board Assembly，PCBA)有限元模型修正法。利用相关性分析筛选出对PCBA模态频率影响较大参数作为修正参数；据修正参数数目选择合适的试验设计获取样本点，构造多项式响应面模型；通过最小二乘法确定多项式系数并检验响应面拟合精度；用响应面计算结果与模态试验结果误差绝对值构造目标函数；通过多目标遗传算法(MOGA)迭代计算获得优化修正参数并代入有限元模型获得修正模型。以某航空电子产品某PCBA为案例，对比修正前后各阶模态频率与试验值误差。结果表明，修正后模型各阶模态频率与试验值相对误差均明显减小，验证该方法对PCBA模型修正的有效性。

关键词：各向异性；印制电路板组件；模型修正；相关性分析；响应面法；优化求解

中图分类号:V414；TB330.1；TH113文献标志码：A

基金项目：国家自然科学基金资助项目(51175086)；福建省自然科学

收稿日期：2014-08-19修改稿收到日期：2014-10-23

Finite element model updating of printed circuit board assembly based on response surface methodology

WANGKai-shan,LIChuan-ri,PANGYue-chan,GUOHeng-hui(Beijing University of Aeronautics and Astronautics, School of Reliability and Systems Engineering，Beijing 100191, China)

Abstract:On the premise of taking the materials of the printed circuit board and its components 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 a 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 result of the calculated response surface and that of an actual test was taken as an objective function. The optimized parameters were obtained taking advantage of the iterative calculation of the multiple objectives genetic algorithm (MOGA). The updated model was then obtained by substituting the optimized parameters into the non-updated FEM. Taking the PCBA of an aircraft electronic product as an example, the comparison between the modal frequencies of non-updated and updated FEM shows that the relative error of modal frequencies of the updated FEM to the actual test is obviously reduced and thus verifies the effectiveness of the model updating methodology suggested.

Key words:orthotropic; printed circuit board assembly(PCBA); model updating; correlation analysis; response surface methodology; optimization

振动会造成电子产品发生故障，尤其对机载电子产品，在寿命周期内需经受严酷的动力学环境，致故障更严重。为提高电子产品可靠性，须增强其抗振能力。有限元仿真因周期短、成本低等优势已成为产品动力学分析的重要方法。对产品进行有限元仿真前需进行实物模态试验作为仿真结果检验及模型修正标准。……