# A case-oriented approach for analyzing the uncertainty of a reconstructed result based on the evidence theory

## Abstract

Uncertainty analysis is an effective methodology to improve the reliability of an accident reconstruction result. Many existing methods can be employed in this field, which can confuse a practicing engineer who does not know these methods well. To make the selection easier, a case-oriented approach was proposed based on the evidence theory. Users only need to input uncertain traces and a selected accident reconstruction model to calculate the uncertainty of reconstructed results using the proposed approach. Three basic steps of the case-oriented approach are as follows: first, all types of input traces should be transformed into their evidence form; then, focal elements of the reconstructed result and their corresponding basic probability assignment (BPA) need to be calculated; finally, the belief function (*Bel*) and plausibility function (*Pl*) of the reconstructed results are calculated. Three common conditions, which are accidents with all interval traces, accidents with all probabilistic traces, and accidents with interval and probabilistic traces, were discussed based on the basic steps of the case-oriented approach. Furthermore, methods for how to transform different traces to their evidence form, how to calculate the interval of the response efficiently, and how to fuse high conflict evidence were presented. Numerical cases showed that the approach worked well in all conditions. Finally, a vehicle collisions accident case was presented to demonstrate the application of the proposed approach in practice.

## Keywords

Accident reconstruction Uncertainty Evidence theory Interval traces Probabilistic traces## Notes

### Acknowledgements

This work was supported by the National Natural Science Foundation of China (51775056), the Science and Technology Planning Project of Guangzhou City, China (No. 201704020142), the Natural Science Foundation of Hunan Province (2018JJ3544), and the China Scholarship Council (CSC).

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