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
1. School of Automobile and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410114, China;
2. Key Laboratory of Safety Design and Reliability Technology for Engineering Vehicle, Hunan Province, Changsha Hunan 410114;
3. Guangdong Provincial Key Laboratory of Intelligent Transportation System, School of Engineering, Sun Yat- sen University, Guangzhou 510275, China
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.
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