Design of experiment in analyzing uncertainty of simulation results in accident reconstruction

Abstract

In order to obtain a more accurate interval of an accident reconstruction result, two modified experiment design methods were proposed. The first is based on the orthogonal design (OD) and it is named as the orthogonal-based design (OBD), while the other is based on the uniform design (UD) and it is named as the multi-response surface-uniform design (MUD). Furthermore, some conclusions are given according to seven numerical cases: results obtained from the Latin hypercube sampling design (LHS) are the worst, while those obtained from the UD are the last but one, and all are worse than the results obtained from the OBD and the MUD. Furthermore, some conclusions about the number of simulation runs of each design of experiment (DOE) can be given: if the second order response surface model is selected, the number of simulation runs of the LHS is the same as the UD, and all are lesser than the number of simulation runs of the OBD and the MUD in most cases. As for the OBD and the MUD, the number of simulation runs of the OBD is lesser than the number of simulation runs of the MUD, but the MUD can be applied more widely than the OBD. Finally, a true vehicle-pedestrian accident case is given, Pc-Crash was used to reconstruct the accident based on all traces provided by the police, and the interval of the impact velocity of the vehicle was calculated using the OBD, results showed that the research is meaningful in practice.

Keywords

Accident simulation Latin hypercube sampling design orthogonal design uncertainty analysis uniform design

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References

Zou

et al . A simple algorithm for analyzing uncertainty of accident reconstruction results. Forensic Sci Int 2015; 257: 229–235.

Wach

Unarski

Uncertainty of calculation results in vehicle collision analysis. Forensic Sci Int 2007; 167(2–3): 181–188.

Han

Fuzzy estimation of vehicle speed in pedestrian collision accidents. Int J Automot Technol 2013; 14(3): 385–393.

Brach

RM.

Vehicle accident analysis and reconstruction methods. Warrendale, PA: SAE International Publishier, 2005.

Wach

Structural reliability of road accidents reconstruction. Forensic Sci Int 2013; 228(1–3): 83–93.

Han

Impulse-momentum based analysis of vehicle collision accidents using Monte Carlo simulation methods. Int J Automot Technol 2015; 16(2): 253–270.

Zhang

Probabilistic inverse simulation and its application in vehicle accident reconstruction. ASME J Mech Des 2013; 135(12): 12100601–12100610.

Inverse simulation under uncertainty by optimization. J Comput Inform Sci Eng 2013; 13: 0210051–0210058.

Zou

Cai

Shu

Response surface methodology and improved interval analysis method: for analyzing uncertainty in accident reconstruction. Forensic Sci Int 2012; 222(1–3): 306–312.

10.

Cai

Zou

Luo

et al . Evaluation of simulation uncertainty in accident reconstruction via combining response surface methodology and Monte Carlo method. Transp Res Part C: Emerg Technol 2014; 48: 241–255.

11.

Zou

Cai

et al . Analyzing the uncertainty of simulation results in accident reconstruction with response surface methodology. Forensic Sci Int 2012; 216(1–3): 49–60.

12.

Bartlett

Fonda

Evaluating uncertainty in accident reconstruction with finite differences. SAE technical paper 2003-01-0489, 2003.

13.

Kim

Seong

PH.

Prediction of sever accident occurrence time using support vector machines. Nucl Eng Technol 2015; 47(1): 74–84.

14.

Abdel-Aty

Utilizing support vector machine in real-time crash risk evaluation. Accid Anal Prev 2013; 51: 252–259.

15.

Barca

Del Moro

Mascolo

et al . Gross parameters prediction of a granular attached biomass reactor through evolutionary polynomial regression. Biochem Eng J 2015; 94: 74–84.

16.

Deng

Guo

MZ.

A new co-training-style random forest for computer aided diagnosis. J Intell Inform Syst 2011; 36(3): 253–281.

17.

Tramontana

Ichii

Camps-Valls

et al . Uncertainty analysis of gross primary production upscaling using random forest, remote sensing and eddy covariance data. Remote Sens Environ 2015; 168: 360–373.

18.

Kotini

Anninos

Alpha, delta and theta rhythms in a neural net model. Comparison with MEG data. J Theor Biol 2016; 388: 11–14.

19.

Carpenter

Barthelemy

JFM

. A comparison of polynomial approximations and artificial neural nets as response surface. Tech Pap 1993; 5(3): 166–174.

20.

Qin

Zhang

Fang

KT.

Constructing uniform designs with two- or three-level. Acta Math Sci 2006; 26(3): 451–459.

21.

Shields

Zhang

The generalization of Latin hypercube sampling. Reliab Eng Syst Saf 2016; 148: 96–108.

22.

Fang

KT.

The uniform design: application of number-theoretic methods in experimental design. Acta Math Appl Sin 1980; 3: 363–372.

23.

Wang

Fang

KT.

A note on uniform distribution and experimental design. KeXue TongBao 1981; 26: 485–489.

24.

Song

Quan

et al . Uniform design for the optimization of Al₂O₃ nanofilms produced by electrophoretic deposition. Surf Coat Technol 2016; 286: 268–278.

25.

Chen

Zhou

Constructing uniform designs under mixture discrepancy. Stat Probab Lett 2015; 97: 76–82.

26.

Talke

Borkowski

JJ.

Generation of space-filling uniform designs in unit hypercubes. J Stat Plan Inference 2012; 142(12): 3189–3200.

27.

Tang

An effective construction method for multi-level uniform designs. J Stat Plan Inference 2013; 143(9): 1583–1589.

28.

McKay

Beckman

Conover

WJ.

A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 1979; 21: 239–245.

29.

Fang

KT.

Theory, methods and application of the uniform design: historical review. SHU LI TONG JI YU GUAN LI 2004; 23(3): 69–80. (In Chinese)

30.

Owen

AB.

Controlling correlations in Latin hypercube samples. J Am Stat Assoc 1994; 89(428): 1517–1522.

31.

Kalgnanam

Diwekar

UM.

An efficient sampling technique for off-line quality control. Technometrics 1997; 39(3): 308–319.

32.

Liefvendahl

Stocki

A study on algorithms for optimization of Latin hypercubes. J Stat Plan Inference 2006; 136(9): 3231–3247.

33.

Wang

Diwekar

Gregoire Padro

CE.

Efficient sampling techniques for uncertainties in risk analysis. Environ Prog 2004; 23(2): 141–157.

34.

Roshanian

Ebrahimi

Latin hypercube sampling applied to reliability-based multidisciplinary design optimization of a launch vehicle. Aerosp Sci Technol 2013; 28(1): 297–304.

35.

Park

Lee

Kim

et al . Numerical analysis of a dual fueled CI (compression ignition) engine using Latin hypercube sampling and multi-objective Pareto optimization. Energy 2014; 70: 278–287.

36.

Helton

Davis

FJ.

Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab Eng Syst Saf 2003; 81(1): 23–69.

37.

Hess

Train

Polak

JW.

On the use of a Modified Latin Hypercube Sampling (MLHS) method in the estimation of a Mixed Logit model for vehicle choice. Transp Res Part B: Methodol 2006; 40(2): 147–163.

38.

Dean

Voss

Design and analysis of experiments. Beijing, China: Beijing World Publishing Corporation, 2010.

39.

Zhang

Wang

et al . Identifying main factors of capacity fading in lithium ion cells using orthogonal design of experiments. Appl Energy 2016; 163: 201–210.

40.

Liu

Xiang

Liu

et al . Synthesis of aqueous and hydroxyl-terminated polyurethanes: impacts of formulation parameters by orthogonal matrix design. Prog Org Coat 2016; 90: 1–9.

41.

Liu

et al . Application of orthogonal experimental design in synthesis of mesoporous bioactive glass. Microporous Mesoporous Mater 2014; 184: 122–126.

42.

Shang

et al . Simulative investigation on head injury of electric self-balancing scooter riders subject to ground impact. Accid Anal Prev 2016; 89: 128–141.

43.

Yang

Review of injury biomechanics in car-pedestrian collisions. Int J Veh Saf 2005; 1(1–3): 100–117.

44.

Weng

Jin

Zhao

et al . Car-to-pedestrian collision reconstruction with injury as an evaluation index. Accid Anal Prev 2010; 42(4): 1320–1325.

45.

Nyquist

Cheng

EI-Bohy

et al . Tibia bending: strength and response. SAE technical paper 851728, 1985.