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Self-driving cars and advanced driver-assistance systems are perceived as a game-changer in the future of road transportation. However, their validation is mandatory before industrialization; testing every component should be assessed intensively in order to mitigate potential failures and avoid unwanted problems on the road. In order to cover all possible scenarios, virtual simulations are used to complement real-test driving and aid in the validation process. This paper focuses on the validation of the command law during realistic virtual simulations. Its aim is to detect the maximum amount of failures while exploring the input search space of the scenarios. A key industrial restriction, however, is to launch simulations as little as possible in order to minimize computing power needed. Thus, a reduced model based on a random forest model helps in decreasing the number of simulations launched. It accompanies the algorithm in detecting the maximum amount of faulty scenarios everywhere in the search space. The methodology is tested on a tracking vehicle use case, which produces highly effective results.

The Alienor method, based on α ‐dense curves, has been developed by Yves Cherruault and collaborators, to solve optimization problems. It can be coupled with the decomposition method of Adomian to solve optima control problems also. But α ‐dense curves can be used in many other problems. Gives an application of α ‐dense curves for calculating multiple integrals by means of simple integrals.

This paper is intended to provide a numerical method for computing integrals of several variables. The method is based on a intuitive geometric idea relative to the meaning of densifying a domain in Rn+1(n≥1) by a curve h(t), contained in that domain, say K, with a very small density α (this must be interpreted as the following property: for any point of K there exists a point of the curve at distance less or equal than α).Thus, the method states that any area, volume, etc, can be computed as the limit of the length of a certain curve, densifying that domain, multiplied by a power of its density. Therefore, the computation of a multiple integral of a nonnegative continuous function can be approached by a simple integral corresponding to the length of the curve h(t) and certain power of its density.