Coordinateurs du projet
Context
The optimal design of MRE structures requires modeling several coupled phenomena across the entire structure. This makes numerical simulation complex and costly, especially since it must be performed in a stochastic framework where uncertainties are modeled by random fields or variables. Furthermore, compared to other sectors (aviation, shipbuilding), relatively little feedback is available for MRE structures. It is therefore important to master all stages of the design process and to extract as much information as possible from in situ measurement campaigns.
Scientific breakthroughs and innovation
- Taking into account various errors (model errors, numerical resolution errors) in failure probability calculations.
- Developing methodologies that enable spatial and temporal zooming in on critical locations or moments for reliability analysis.
- Updating models based on measurements to increase simulation accuracy.
Expected technical and economic impact
- Develop digital tools that enable coupled phenomena to be considered in a stochastic framework (mechanical loading by wind and waves, variability in material properties, etc.) on complex structures (e.g., wind turbine foundations).
- Use these tools for reliability analysis and to assist in the positioning of sensors for structure surveillance and monitoring.
Results
A parametric study on a two-dimensional mechanical problem with random elastic material parameters showed the influence of mesh size on the estimation of failure probability. The discretization error may not be negligible.
A calculation strategy was developed to adapt the discretization of the finite element problem when calculating failure probability using multi-fidelity kriging. By using a posteriori discretization error estimators, it is possible to optimize the construction of the meta-model by performing simulations close to the limit state on fine meshes (and guaranteeing high accuracy) and far from the limit state on coarse meshes (sufficiently informative to capture a trend and inexpensive). A second approach, based on the use of a priori discretization error estimators, makes it possible to construct a multi-fidelity meta-model from which it is possible to calculate the probability of failure without the pollution caused by discretization error. These two approaches have been applied to two-dimensional mechanical problems with one or two random variables.
In the context of fatigue in offshore structures, local stress (calculated or measured) is subject to error and can be framed between two extreme values. A process for constructing a stress signal that maximizes and minimizes the damage calculated by Rainflow counting and exploitation of S-N curves has been developed. This makes it possible to frame the actual damage.
Finally, based on synthetic data, a stochastic model of fatigue damage evolution based on a cumulative Gamma process has been developed. Its use allows the estimation of failure probability, conditional probabilities, and the generation of future damage trajectories.