Improvement to Ill-Conditioned Two-Dimensional Vehicle Collision Models
-
摘要: 为消除二维汽车碰撞模型的病态性,利用矩阵扰动理论分析了模型病态性的实质.结果表明,病态性的根本原因在于模型中某些方程间存在严重的线性相关现象.通过数学变换消除了线性相关现象.用变换后的新方程替代原始模型中存在线性相关现象的方程,建立了重组模型,与原始模型共同组成了新的二维汽车碰撞模型.对汽车碰撞实例的分析结果表明,当两车质量比处于特定范围且碰撞点坐标存在5%误差时,选择合适的重组模型,相对误差由原始模型的71.91%降为16.4%.Abstract: Matrix perturbation theory was applied to analyzing the ill-conditioned two-dimensional vehicle collision model.The analysis shows that the ill-condition is caused by the linear correlation between some equations in the model.The linear correlation was solved by a mathematical transform to get new equations free of ill-condition,and reconstructed models composed of the new equations were obtained.The reconstructed models and the original one formed a new model.The calculated result of a real collision case shows that the new model reduces the relative error from 71.91% to 16.4% compared with that by the original model when the mass ratio of the two vehicles involved falls into a specific range and there is 5% error in the measured coordinates of the colliding point on the two vehicles.
-
Key words:
- two-dimensional vehicle collision /
- model /
- ill-conditioned equation /
- linear correlation
-
李江.交通事故力学[M].北京:机械工业出版社,2000:119-128.[2] 裴剑平,李一兵,吴卫东.事故再现典型碰撞模型的参数敏感度分析[J].公路交通科技,2002,19(4):130-131.[3] CHAN S H,PHOON K K,LEE F H.A modified Jacobi preconditioner for solving ill-conditioned Biot's consolidation equations using symmetric quasi-minimal residual method[J].International Journal for Numerical and Analytical Methods in Geomechanics,2001,25(10):1001-1025.[4] 李亚兰,秦世伦.对有限元计算中某些病态问题的研究[J].四川大学学报(工程科学版),2002,34(3):38-40.LI Yalan,QIN Shilun.Research of some ill problems by the computing method of FEM[J].Journal of Sichuan University:Engineering Science Edition,2002,34(3):38-40.[5] 张建,李江,倪行达,等.汽车碰撞事故再现模型病态问题处理方法研究[J].汽车工程,2007,29(1):59-62.ZHANG Jian,LI Jiang,NI Xingda,et al.A study on the solution to ill-conditioned problem in vehicle crash accident reconstruction model[J].Automotive Eng.,2007,29(1):59-62.[6] 姜家辉.矩阵理论基础[M].大连:大连理工大学出版社,1997:32-33.[7] 魏朗,陈荫三,石川,等.车辆碰撞过程的试验分析研究[J].汽车工程,2000,22(4):256-261.WEI Lang,CHENG Yinsan,SHI Chuan.et al.An experiment research on the car-to-car collision[J].Automotive Eng.,2000,22(4):256-261.[8] 王志中,邵苇敏.方程病态程度的估计——病态准则[J].上海交通大学学报,1988,22(5):68-73.WANG Zhizhong,SHAO Weimin.Estimators of ill-conditioned degree of equations-ill-condition criteria[J].Journal of Shanghai Jiaotong University,1988,22(5):68-73.
点击查看大图
计量
- 文章访问数: 1410
- HTML全文浏览量: 66
- PDF下载量: 324
- 被引次数: 0