Bertrand Bouriquet

Stabilization of (G)EIM in presence of measurement noise: application to nuclear reactor physics

The Empirical Interpolation Method (EIM) and its generalized version (GEIM) can be used to approximate a physical system by combining data measured from the system itself and a reduced model representing the underlying physics. In presence of noise, the good properties of the approach are blurred in the sense that the approximation error no longer converges but even diverges. We propose to address this issue by a least-squares projection with constrains involving a some a priori knowledge of the geometry of the manifold formed by all the possible physical states of the system. The efficiency of the approach, which we will call Constrained Stabilized GEIM (CS-GEIM), is illustrated by numerical experiments dealing with the reconstruction of the neutron flux in nuclear reactors. A theoretical justification of the procedure will be presented in future works.

Variational assimilation for xenon dynamical forecasts in neutronic using advanced background error covariance matrix modelling

Data assimilation method consists in combining all available pieces of information about a system to obtain optimal estimates of initial states. The different sources of information are weighted according to their accuracy by the means of error covariance matrices. Our purpose here is to evaluate the efficiency of variational data assimilation for the xenon induced oscillations forecasts in nuclear cores. In this paper we focus on the comparison between 3DVAR schemes with optimised background error covariance matrix B and a 4DVAR scheme. Tests were made in twin experiments using a simulation code which implements a mono-dimensional coupled model of xenon dynamics, thermal, and thermal–hydraulic processes. We enlighten the very good efficiency of the 4DVAR scheme as well as good results with the 3DVAR one using a careful multivariate modelling of B.

Best Linear Unbiased Estimation of the nuclear masses

Abstract This paper presents methods to provide an optimal evaluation of the nuclear masses. The techniques used for this purpose come from data assimilation that allows combining, in an optimal and consistent way, information coming from experiment and from numerical model. Using all the available information, it leads to improve not only masses evaluations, but also to decrease uncertainties. Each newly evaluated mass value is associated with some accuracy that is sensibly reduced with respect to the values given in tables, especially in the case of the less well-known masses. In this paper, we first introduce a useful tool of data assimilation, the Best Linear Unbiased Estimation (BLUE). This BLUE method is applied to nuclear mass tables and some results of improvement are shown.

Sensor placement in nuclear reactors based on the generalized empirical interpolation method

In this paper, we apply the so-called generalized empirical interpolation method (GEIM) to address the problem of sensor placement in nuclear reactors. This task is challenging due to the accumulation of a number of difficulties like the complexity of the underlying physics and the constraints in the admissible sensor locations and their number. As a result, the placement, still today, strongly relies on the know-how and experience of engineers from different areas of expertise. The present methodology contributes to making this process become more systematic and, in turn, simplify and accelerate the procedure.

Reconstruction by Data Assimilation of the Inner Temperature Field From Outer Measurement in Thick Pipe

The detailed knowledge of the inner skin temperature behavior is very important to evaluate and manage the aging of large pipes in cooling systems. We describe here a method to obtain this information as a function of outer skin temperature measurements, in space and time. This goal is achieved by mixing fine simulations and numerical methods such as impulse response and data assimilation. Demonstration is done on loads representing extreme transient stratification or thermal shocks. From a numerical point of view, the results of the reconstruction are outstanding, with a mean accuracy of the order of less than a half percent of the temperature values of the thermal transient.