为了解决汽车碰撞事故典型模型的病态问题,以线性空间与内积空间理论为基础,建立了模型病态问题的处理方法。应用该方法分析了模型病态问题的实质,利用数学变换消除了导致模型病态问题的线性相关现象,通过重组原始模型彻底解决了病态问题。实例计算证明:重组模型大大降低了计算结果的误差,提高了汽车碰撞事故模型的计算精度,拓展了解决模型病态问题的方法。

Analysis and Improvement of Ill-conditioned Problem in Typical Impact ModelsZHANG Jian1,3,ZHANG Xin2,LI Jiang3(1.School of Traffic and Construction Engineering,Beihua University,Jilin 132013,China;2.School of Traffic and Transportaption,Beijing Jiaotong University,Beijing 100044,China;3.School of Transportation,Jilin University,Changchun 130025,China)In order to solve the ill-conditioned problem in vehicle accidental typical collision impact models,a improvement method was established on the basis of the Linear Zone and the Interior Product Zone theory.The ill-conditioned problem nature was analyzed by this method,which showed that the ill-conditioned problem was caused by the serious linear interrelation between some equations in the models.The authors of this paper eliminated the linear interrelation by the equality shift,then solved thorough the ill-conditioned problem by constituting the model anew.The calculation results of an application show that the reconstructed models accuracy overtakes obviously the models by reducing the calculation result error large,it will give a new method for solving the model ill-conditioned problem.vehicle impact accidental models;ill-conditioned problem;reconstructed models