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Section: New Results

Optimization of test case generation for ADAS via Gibbs sampling algorithms

Participant : Guy Fayolle.

Validating Advanced Driver Assistance Systems (ADAS) is a strategic issue, since such systems are becoming increasingly widespread in the automotive field.

But ADAS validation is a complex issue, particularly for camera based systems, because these functions may be facing a very high number of situations that can be considered as infinite. Building at a low cost level a sufficiently detailed campaign is thus very difficult. Indeed, test case generation faces the crucial question of inherent combinatorial explosion. An important constraint is to generate almost all situations in the most economical way. This task can be considered from two points of view: deterministic via binary search trees, or stochastic via Markov chain Monte Carlo (MCMC) sampling. We choose the latter probabilistic approach described below, which in our opinion seems to be the most efficient one. Typically, the problem is to produce samples of large random vectors, the components of which are possibly dependent and take a finite number of values with some given probabilities.The following flowchart is proposed.

  1. In a first step, starting from the simulation graph generated by the toolboxes of MATLAB, we construct a so-called Markov Random Field (MRF). When the parameters are locally dependent, this can be achieved from the user's specifications and by a systematic application of Bayes' formula.

  2. Then, to cope with the combinatorial explosion, test cases are produced by implementing (and comparing) various Gibbs samplers, which are fruitfully employed for large systems encountered in physics. In particular, we strive to make a compromise between the convergence rate toward equilibrium, the percentage of generated duplicates and the path coverage, keeping in mind that the speed of convergence is exponential, a classical property deduced from the general theory of Markov chains.

  3. The generation of rare events by mixing Gibbs samplers, large deviation techniques (LDT) and cross-entropy method is a work in progress.

The French car manufacturer Groupe PSA shows a great interest in these methods and has established a contractual collaboration involving ARMINES-Mines ParisTech (Guy Fayolle as associate researcher) and Can Tho University in Vietnam (Pr. Van Ly Tran).