二维汽车碰撞模型病态性的处理

Improvement to Ill-Conditioned Two-Dimensional Vehicle Collision Models

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%.

Matrix perturbation theory was applied to analyzing the ill-conditioned two-dimensional vehicle collision model. The analysis shows that the iU-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.