区间痕迹下事故再现结果不确定性分析的改进仿射法

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (16) : 68-72.

论文

邹铁方1,2，彭海涛1,2，肖璟1,2 蔡铭3 李华1,2

作者信息 +

A Modified Affine Arithmetic for Analyzing Uncertainty of Reconstructed Results in Traffic Accidents with Interval Traces

Tiefang Zou1,2, Haitao Peng1,2, Jing Xiao1,2 Ming Cai3 Hua Li1,2

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文章历史 +

摘要

区间痕迹下事故再现结果亦为区间，当采用仿射算法分析再现结果不确定性时，因再现模型的非线性而会导致分析结果偏离真值。为提高不确定性分析的精度，借助泰勒展开式对仿射法进行改进。改进仿射法首先对事故再现模型进行标准化处理，然后再对模型进行泰勒展开，得到理想的泰勒展开式；接着对泰勒展开式内的变量进行仿射转换，并用矩阵形式表达；最后用区间多项式上下界公式计算出事故再现结果的取值区间。进一步，给出了分析仿真再现结果不确定性的改进仿射法步骤，并用3个数值算例和一个真实案例验证所提出的方法，结果表明改进方法能提高计算结果精度，且实用范围广，表明其能用于实践中。

Abstract

The reconstructed result in a traffic accident with interval traces is an interval, the result obtained from the affine arithmetic is not so accurate because of the nonlinear of the accident reconstruction model. In order to enhance the accuracy of a reconstructed result, the affine arithmetic was modified by combining the Taylor series. In the modified method, the accident reconstruction model is standardized and expanded as Taylor series firstly, and then the Taylor expansion is converted to its affine form and recorded as a matrix, the interval of the reconstructed result can be calculated by the upper and lower bounds formula finally. Furthermore, steps of the modified method in analyzing uncertainty of a simulation result was given, three numerical cases and a real accident case were given, results shown that results obtained from the modified affine arithmetic are all accurate and the method can work under any conditions, which shown that the modified method is practical.

导出引用

邹铁方1,2，彭海涛1,2，肖璟1,2 蔡铭3 李华1,2. 区间痕迹下事故再现结果不确定性分析的改进仿射法[J]. 振动与冲击, 2017, 36(16): 68-72

Tiefang Zou1,2, Haitao Peng1,2, Jing Xiao1,2 Ming Cai3 Hua Li1,2. A Modified Affine Arithmetic for Analyzing Uncertainty of Reconstructed Results in Traffic Accidents with Interval Traces[J]. Journal of Vibration and Shock, 2017, 36(16): 68-72

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