Section: New Results

Reliability

Participants : Yves Auffray, Gilles Celeux, Rémy Fouchereau, Patrick Pamphile.

Since 2011, in the framework of a CIFRE convention with Snecma-SAFRAN Rémy Fouchereau has started a thesis on the modeling of fatigue lifetime supervised by Gilles Celeux and Patrick Pamphile. In aircraft, space and nuclear industry, fatigue test is the main basic tool for analyzing fatigue lifetime of a given material, component, or structure. A sample of the material is subjected to cyclic loading $S$ (stress, force, strain, etc.), by a testing machine which counts $N$, the number of cycles to failure. Fatigue test results are plotted on a SN-curve. A probabilistic model for the construction of SN-curve is proposed. In general, fatigue test results are widely scattered for High Cycle Fatigue region and "duplex" SN-curves appears for Very High Cycle region. That is why classic models from mechanic of rupture theory on one hand, probability theory on the other hand, do not fit SN-curve on the whole range of cycles. We have proposed a probabilistic model, based on a fracture mechanic approach: few parameters are required and they are easily interpreted by mechanic or material engineers.This model has been applied to both simulated and real fatigue test data sets. The SN-curves have been well fitted on the whole range of cycles. The parameters have been estimated using the EM algorithm, combining Newton-Raphson optimisation method and Monte Carlo integral estimations. Recently, the model has been improved taking into account production process information, thanks to a clustering approach. Thus, we have provided engineers with a probabilistic tool for reliability design of mechanical parts, but also with a diagnostic tool for material elaboration.

Since 2013, Gilles Celeux and Patrick Pamphile supervise, in the framework of a collaboration with CEA not yet finalized, a thesis on the modeling of battery State Of Charge for electrical vehicles. Electrical battery is an electrochemical device that converts stored chemical energy into electrical energy. This conversion is reversible and can be repeated during charge/discharge cycles. In an electric vehicle, the battery State Of Charge (SOC) gives the driver indication of how long he can drive without recharging the battery. Unfortunately the complex nature of electrochemical reactions does not allow to measure the SOC directly. Different methods of estimation exist, but they are not robust to various environment conditions (temperature, vehicle driving,...) and to the battery ageing. We propose to estimate the SOC from an Markov-switching model : the measurement equation specifies how the SOC depends of an unobservable Markov chain and physical data (temperature, voltage and current intensity,...). Moreover, the SOC estimation is included in the Battery Management System, and therefore estimations must be done online, i.e. with minimum information.

A collaboration has started in 2013 with Dassault Aviation on modal analysis of mechanical structures, which aims at identifying the vibration behavior of structures under dynamic excitations. From algorithmic view point, modal analysis amounts to estimation in parametric models on the basis of measured excitations and structural responses data. As it appears from literature and existing implementations, the model selection problem attached to this estimation is currently treated by a rather heavy and very heuristic procedure. The model selection via penalization tools are intended to be tested on this model selection problem.