## Section: Application Domains

### Fatigue aided-design

This is a Cifre PhD in collaboration with PSA.

The digitalization of design is at the heart of the processes of automotive manufacturers departments, to enable them to reduce costs and development time. This also applies to reliability studies of certain components of the chassis of a vehicle, and the will is to drastically reduce the number of physical tests to tend towards an almost entirely digital design having only one phase of validation. Deterministic models, although developed from detailed design drawings, can predict behaviors different from those observed on the structure during testing. These deviations can be due to the more or less faithful discretization of the geometry, the uncertainties on some parameters of the model (such as the properties of the materials, the boundary conditions), or the random loadings undergone by the structure (Beck and Katafygiotis, 1998). It is important to make available new methods in addition to the classical finite element (FE) deterministic modeling, to enable the exploitation of the accumulated data over the years for all the projects: computation results, measurements and test data.

One of the objectives of this project is to propose a probabilistic modeling of the behavior of a structure starting from a FE model, taking into account the non assignable fluctuations of the model, in order to define a probabilistic criterion of rupture and its margins of confidence. The following three steps are envisaged: (1) Define relevant prior information using business experience feedback (REX) and use a Bayesian estimation to calibrate the parameters. This REX is consequent and will require advanced statistical processing of machine learning, and in particular in clustering to identify similarities or similar patterns among several models. The estimation will use Bayesian non-iterative methods (Celeux and Pamphile, 2019), which are less expensive and less unstable than conventional methods. This will test their effectiveness in this context. (2) Select important parameters (physical or modeling). (3) Define a probabilistic criterion of coaxial fatigue taking into account both the random behavior of the structure and the material (Fouchereau et al., 2014) extending the existing deterministic criteria (Dang-Van, 1993).