Quantitative risk assessment of safety-critical systems via guided simulation for rare events

Abstract

For developers of assisted or automated driving systems, gaining specific feedback and quantitative figures on the safety impact of the systems under development is crucial. However, obtaining such data from simulation of their design models is a complex and often time-consuming process. Especially when data of interest hinge on extremely rare events, an estimation of potential risks is highly desirable but a non-trivial task lacking easily applicable methods. In this paper we describe how a quantitative statement for a risk estimation involving extremely rare events can be obtained by guiding simulation based on reinforcement learning. The method draws on variance reduction and importance sampling, yet applies different optimization principles than related methods, like the cross-entropy methods against which we compare. Our rationale for optimizing differently is that in quantitative system verification, a sharper upper bound of the confidence interval is of higher relevance than the total width of the confidence interval. Our application context is deduced from advanced driver assistance system (ADAS) development. In that context virtual driver simulations are performed with the objective to generate quantitative figures for the safety impact in pre-crash situations. In order to clarify the difference of our technique to variance reduction techniques, a comparative evaluation on a simple probabilistic benchmark system is also presented.