汽车多元动态系统仿真模型响应分析方法*
雷正保1 邢欢1 陈小勇2 ( 1.长沙理工大学,大型结构碰撞实验室,长沙 410114;2.长沙理工大学,公路工程教育部重点实验室,长沙 410114)【摘要】针对动态系统仿真模型有效性验证中输出响应间存在强相关性的问题,基于误差评分法和主成分分析法,提出了一种既能全面分析动态系统输出响应间曲线特征差异,又能解决输出响应间相关性问题的多元响应分析( MRA)方法,并结合具体实例对MRA方法进行了验证。结果表明,该方法能够实现多元数据的降维并对具有强相关性的数据进行评分,提高了验证效率和鲁棒性。主题词:车辆安全技术 动态系统 模型验证 主成分分析U467 A 10.19620/j.cnki.1000-3703.20191036中图分类号: 文献标识码: DOI:
Response Analysis Method of Automobile Multi-Element Dynamic System Simulation Model
Lei Zhengbao1, Xing Huan1, Chen Xiaoyong2 1. Large Structural Impact Laboratory, Changsha University of Science and Technology, Changsha 410114; 2. Key ( Laboratory of Highway Engineering of Ministry of Education, Changsha University of Science and Technology, Changsha 410114) Abstract To solve the problem of strong correlation between output responses in the validation of dynamic system【 】simulation model, a Multivariate Response Analysis (MRA) method is proposed, which can comprehensively analyze the difference of curve characteristics between output responses of dynamic systems and solve the correlation between output responses based on principal component analysis and error scoring. The MRA method is verified by practical cases. The results show that this method can effectively achieve dimensionality reduction of multivariate data, and score the data with strong correlation, and improve the verification efficiency and robustness. Key words: Vehicle safety technology, Dynamic system, Model verification, Principal component analysis
1 前言
模型仿真技术在一定程度上已经取代物理样机试验成为汽车碰撞安全性能的主要研究工具[1- 3],但仿真模型同实际物理对象始终存在一定差距,因此,对其进行验证十分必要。动态系统的高度非线性及复杂性使得模型验证较为困难,主要表现在:动态系统的输出响应数据具有高度的时间相关性和时变性,其相位、幅度及频率等曲线特征差异都需要纳入监控范围,这要求模型验证方法能够全面分析输出响应间的曲线特征差异;
复杂动态系统通常包含多个输出响应,且响应间存在着很强的相关性[4],这要求模型验证方法能够有效解决输出响应间的相关性问题;模型验证工作涉及的验证方法较多,实施起来较为繁琐。
针对上述问题,本文基于误差评分法和主成分分析法对动态系统仿真模型的验证方法展开研究。
2 误差评分法
全局误差为时域内每个时间步长具有相同权重时, Error完整的曲线特征误差。时间响应误差评估(