Probabilistic design approach. Uncertainty quantification and approximation methods

The designer's art is to propose a technical solution that satisfies functional requirements and guarantees safety for goods, people and the environment. Functional requirements must ensure that the systems in question operate correctly, and among these is reliability, i.e. the ability of a device to perform a required function under given conditions, for a given period of time. The designer's role is to optimize sizing by justifying sufficient reliability in terms of risk, i.e. the consequences of an undesirable event: absolute reliability cannot exist, and there is always the possibility of failure. Today, we can say that the precautionary principle only consists in demonstrating that all current knowledge has been applied to ensure that the gain obtained by the success of the device is sufficient to accept the cost of the possible failure due to its malfunction. These few lines set out the framework of the approach: it proposes an approach to the theoretical reliability of mechanical systems, but it should be noted that it can be applied in many other fields. By theoretical reliability, we mean everything that can be simulated by modeling to predict possible behaviors. It complements practical reliability, which is assimilated to the quality approach: theoretical reliability is conditioned by practical reliability, by quality assurance. Designing a mechanical system and calculating its parameters is a search for a dimensioning whose reliability must be justified. The article [BM 5 003] introduced the concept of theoretical reliability and implemented the solution by Monte-Carlo simulation. This article looks at approximation-based solutions, which enable more economical implementation of the calculations. It successively introduces the – constrained resistance method, then the approximation and mechano-fiabilistic coupling methods, and finally the products of the analysis: i.e. the quantities of interest made available to the designer to help his decisions. Finally, it opens up a number of perspectives. As the same conductive example is repeated, it is essential to first read the article [BM 5 003] .