title: A Taylor-Affine Arithmetic for analyzing the calculation result uncertainty in accident reconstruction.
abstract: In order to analyze the uncertainty of a reconstructed result, the Interval Algorithm (IA), the Affine Arithmetic (AA) and the Modified Affine Arithmetic (MAA) were introduced firstly, and then a Taylor-Affine Arithmetic (TAA) was proposed based on the MAA and Taylor series. Steps of the TAA, especially in analyzing uncertainty of a simulation result were given. Through the preceding five numerical cases, its application was demonstrated and its feasibility was validated. Results showed that no matter other methods (The IA, AA, the Upper and Lower bound Method, the Finite Difference Method) work well or bad, the TAA work well, even under the condition that the MAA cannot work in some cases because of the division/root operation in these models. Furthermore, in order to make sure that the result obtained from the TAA can be very close to the accurate interval, a simple algorithm was proposed based on the sub-interval technique, its feasibility was validated by two other numerical cases. Finally, a vehicle-pedestrian test was given to demonstrate the application of the TAA in practice. In the vehicle-pedestrian test, the interval [35.5, 39.1]km/h of the impact velocity can be calculated according to steps of the TAA, such interval information will be more useful in accident responsibility identification than a single number. This study will provide a new alternative method for uncertainty analysis in accident reconstruction.
authors.affiliation: School of Automobile and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410004, China; Key Laboratory of Safety Design and Reliability Technology for Engineering Vehicle, Hunan Province 410004, China. Electronic address: tiefang@163.com.
authors.forename: Tiefang
authors.initials: T
authors.lastname: Zou
authors.affiliation: School of Automobile and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410004, China; Key Laboratory of Safety Design and Reliability Technology for Engineering Vehicle, Hunan Province 410004, China.
authors.forename: Haitao
authors.initials: H
authors.lastname: Peng
authors.affiliation: School of Engineering, Sun Yat-sen University, Guangzhou, Guangdong 510275, China.
authors.forename: Ming
authors.initials: M
authors.lastname: Cai
authors.affiliation: School of Automobile and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410004, China; Key Laboratory of Safety Design and Reliability Technology for Engineering Vehicle, Hunan Province 410004, China.
authors.forename: Hequan
authors.initials: H
authors.lastname: Wu
authors.affiliation: School of Automobile and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410004, China; Key Laboratory of Safety Design and Reliability Technology for Engineering Vehicle, Hunan Province 410004, China.
authors.forename: Lin
authors.initials: L
authors.lastname: Hu
keywords: Accident reconstruction; Affine arithmetic; Calculation result uncertainty; Interval; Taylor-expansion