碰撞前车速计算误差的成因及处理方法

张健; 张鑫; 李江

doi:10.3969/j.issn.0258-2724.20170562

碰撞前车速计算误差的成因及处理方法

doi: 10.3969/j.issn.0258-2724.20170562

张健^1,,
张鑫²,
李江³

基金项目: 国家自然科学基金资助项目（51178001）

详细信息

作者简介:
张健（1961—），男，教授，博士，研究方向为车辆安全，E-mail：zhjdp@126.com

中图分类号: U491.3
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- 文章访问数: 642
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- 被引次数: 2
出版历程
- 收稿日期: 2017-07-22
- 修回日期: 2018-10-17
- 网络出版日期: 2019-09-04
- 刊出日期: 2019-10-01

Origin and Solution of Pre-crash Speed Calculation Error

摘要

摘要: 为准确计算汽车碰撞事故碰撞前车速，基于动量守恒定理的汽车碰撞事故模型，在事故分析中采用反推法求解. 根据事故现场勘查信息,应用运动学公式计算碰撞后车速，再将碰撞后车速代入模型计算碰撞前车速. 以实车碰撞试验对模型计算结果进行检验后，发现用模型计算的碰撞前车速存在误差. 为此以实车碰撞试验为对象，根据模型的求解过程和误差的传递过程，研究了碰撞前车速误差的成因和处理方法，以提高交通事故分析的准确性. 首先，应用矩阵理论研究了碰撞前车速误差的形成原因；其次，应用反推迭代算法建立了碰撞前车速误差的处理方法；最后，通过实例应用验证了该方法的可行性. 研究结果和实例应用表明：用运动学公式计算碰撞后车速所产生的误差是造成碰撞前车速误差的决定性原因，只需对碰撞后车速误差进行简单的1次处理就能使应用该模型计算碰撞前车速所产生的误差归0.
- 碰撞前车速 /
- 误差 /
- 碰撞后车速 /
- 事故现场
Abstract: In accident analysis vehicle collision model based on the momentum conservation is solved by the inverse algorithm to calculate pre-crash speed accurately. Then post-crash speed is calculated by a kinematics formula with survey data from accident scene, and is used to calculate the pre-crash speed by the model. In this work, the pre-crash speed error emerges when examining the model calculation results by a car crash test. From the model solving and error propagation processes, the origin and solution of the pre-crash speed error was studied by the car crash test to improve the accuracy of traffic accident analysis. Firstly, the matrix theory was applied to study the origin of the pre-crash speed error. Secondly, the inverse iterative algorithm was applied to establish a solution of the pre-crash speed error. Finally, an example was used to verify the solution. Study results and example applications show that the error in post-crash speed calculation with the kinematics formula is the decisive to the pre-crash speed error. Thus, the pre-crash speed error can be eliminated completely by simply correcting the post-crash speed error.
- pre-crash speed /
- error /
- post-crash speed /
- accident scene

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图 1 模型坐标系

Figure 1. Coordinate systems of models

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图 2 模型1对应的试验现场

Figure 2. Trial scene of model 1

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图 3 模型2对应的试验现场

Figure 3. Trial scene of model 2

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图 4 模型1对应的方向角误差

Figure 4. Direction angle error of model 1

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图 5 模型2对应的方向角误差

Figure 5. Direction angle error of model 2

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表 1 试验数据

Table 1. Trial data

试验参数	车辆1	车辆2
m_j /kg	977	976
ρ_j /m	1.220	1.230
l_jτ（a_j）/m	−0.530 1（−0.530 1）	−0.075 2（−0.075 2）
l_jn（b_j）/m	−0.984 4（0.984 4）	0.739 4（−0.739 4）
v_jn /（m•s⁻¹）	−16.581 3（−16.581 3）	−4.378 7（−4.378 7）
v_jτ /（m•s⁻¹）	−2.284 8（2.284 8）	17.790 0（−17.790 0）
ω_j /（rad•s⁻¹）	−5.347 9（5.347 9）	−8.021 1（8.021 1）
v_j₀_n /（m•s⁻¹）	−19.598 4（−19.598 4）	0（0）
v_j₀_τ /（m•s⁻¹）	−12.246 4（12.246 4）	22.780 0（−22.780 0）
ω_j₀ /（rad•s⁻¹）	0（0）	0（0）
注：括弧中的数值对应模型2.

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表 2 力学参数

Table 2. Mechanical parameter

μ	k	ε_n	ε_τ
−3.651 293	−0.736 506	−0.508 759	−0.892 757

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表 3 碰撞前车速误差的处理过程

Table 3. Correction process of pre -crash speed

模型	力学参数	算法	碰撞后车速	碰撞后车速误差	碰撞前车速	试验结果	碰撞前车速误差
1	μ=−3.651 293 k=−0.736 506	反推法	${ {{v} }_1} = \left[ {\begin{array}{*{20}{c} } { - 16.581\;3} \\ { - 2.284\;8} \\ { - 4.378\;7} \\ {17.790\;0} \\ { - 5.347\;9} \\ { - 8.021\;1} \end{array} } \right]$	$\begin{aligned}& { {{v} }_1} - { {{v} }_{11} } = \\& \left[ {\begin{array}{*{20}{c} } {1.470\;7} \\ {15.608\;0} \\ { - 2.830\;7} \\ { - 10.642\;2} \\ { - 9.633\;1} \\ { - 10.706\;6} \end{array} } \right]\end{aligned}$	${ {{v} }_{01} } = \left[ {\begin{array}{*{20}{c} } { - 18.127\;7} \\ {3.361\;6} \\ { - 2.830\;7} \\ {12.137\;8} \\ { - 9.633\;1} \\ { - 10.706\;6} \end{array} } \right]$	$\begin{aligned}& { {{v} }_{01{\rm{T} } } } = \\& \left[ {\begin{array}{*{20}{c} } { - 19.598\;4} \\ { - 12.246\;4} \\ 0 \\ {22.780\;0} \\ 0 \\ 0 \end{array} } \right]\end{aligned}$	${ {{v} }_{01} } - { {{v} }_{01{\rm{T} } } } = \left[ {\begin{array}{*{20}{c} } {1.470\;7} \\ {15.608\;0} \\ { - 2.830\;7} \\ { - 10.642\;2} \\ { - 9.633\;1} \\ { - 10.706\;6} \end{array} } \right]$
1	μ=−3.651 293 k=−0.736 506	处理	${ {{v} }_{11} } = \left[ {\begin{array}{*{20}{c} } { - 18.052\;0} \\ { - 17.892\;8} \\ { - 1.548\;0} \\ {28.432\;2} \\ {4.285\;2} \\ {2.685\;5} \end{array} } \right]$		${ {{v} }_{011} } = \left[ {\begin{array}{*{20}{c} } { - 19.598\;4} \\ { - 12.246\;4} \\ 0 \\ {22.780\;0} \\ 0 \\ 0 \end{array} } \right]$		${{{v}}_{011}} - {{{v}}_{01{\rm{T}}}} = \left[ {\begin{array}{*{20}{c}} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{array}} \right]$
2	ε_n= −0.508 759 ε_τ= −0.892 757	反推法	${ {{v} }_2} = \left[ {\begin{array}{*{20}{c} } { - 16.581\;3} \\ {2.284\;8} \\ { - 4.378\;7} \\ { - 17.790\;0} \\ {5.347\;9} \\ {8.021\;1} \end{array} } \right]$	$\begin{aligned}& { {{v} }_2} - { {{v} }_{21} } = \\& \left[ {\begin{array}{*{20}{c} } { - 1.619\;3} \\ { - 8.232\;5} \\ {0.262\;4} \\ {3.259\;1} \\ {4.840\;2} \\ {9.097\;7} \end{array} } \right]\end{aligned}$	${ {{v} }_{02} } = \left[ {\begin{array}{*{20}{c} } { - 21.217\;7} \\ {4.013\;9} \\ {0.262\;4} \\ { - 19.520\;9} \\ {4.840\;2} \\ {9.097\;7} \end{array} } \right]$	$\begin{aligned}& { {{v} }_{02{\rm{T} } } } = \\& \left[ {\begin{array}{*{20}{c} } { - 19.598\;4} \\ {12.246\;4} \\ 0 \\ { - 22.780\;0} \\ 0 \\ 0 \end{array} } \right]\end{aligned}$	${ {{v} }_{02} } - { {{v} }_{21{\rm{T} } } } = \left[ {\begin{array}{*{20}{c} } { - 1.619\;3} \\ { - 8.232\;5} \\ {0.262\;4} \\ {3.259\;1} \\ {4.840\;2} \\ {9.097\;7} \end{array} } \right]$
	ε_n= −0.508 759 ε_τ= −0.892 757	处理 1	${ {{v} }_{21} } = \left[ {\begin{array}{*{20}{c} } { - 14.962\;0} \\ {10.517\;3} \\ { - 4.641\;1} \\ { - 21.049\;1} \\ {0.507\;7} \\ { - 1.076\;6} \end{array} } \right]$		${ {{v} }_{021} } = \left[ {\begin{array}{*{20}{c} } { - 19.598\;3} \\ {12.246\;4} \\ 0 \\ { - 22.780\;0} \\ {0.000\;1} \\ 0 \end{array} } \right]$		${ {{v} }_{021} } - { {{v} }_{02{\rm{T} } } } = \left[ {\begin{array}{*{20}{c} } {0.000\;1} \\ 0 \\ 0 \\ 0 \\ 0.000\;1 \\ 0 \end{array} } \right]$
	ε_n₁= −0.508 756 ε_τ₁= −0.892 759	处理 2	${ {{v} }_{21} } = \left[ {\begin{array}{*{20}{c} } { - 14.962\;0} \\ {10.517\;3} \\ { - 4.641\;1} \\ { - 21.049\;1} \\ {0.507\;7} \\ { - 1.076\;6} \end{array} } \right]$		${ {{v} }_{022} } = \left[ {\begin{array}{*{20}{c} } { - 19.598\;4} \\ {12.246\;4} \\ 0 \\ { - 22.780\;0} \\ 0 \\ 0 \end{array} } \right]$		${{{v}}_{022}} - {{{v}}_{02{\rm{T}}}} = \left[ {\begin{array}{*{20}{c}} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \end{array}} \right]$

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表 4 力学参数误差

Table 4. Mechanical parameter error

力学参数	原始值	准确值	相对误差/%
μ	−3.651 293	−3.651 293	0
k	−0.736 506	−0.736 506	0
ε_n	−0.508 759	−0.508 756	0.000 511
ε_τ	−0.892 757	−0.892 759	0.000 224

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