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Stochastic data modeling methods: application to the reconstruction of non-regular data

​Léticia Buslig had defended her thesis on 6th October 2014 in Marseille (France).

Document type > *Mémoire/HDR/Thesis

Keywords >

Research Unit > IRSN/PSN-RES/SA2I/LIE

Authors > BUSLIG Léticia

Publication Date > 06/10/2014

Summary

​Modelling methods naturally arise in risk analysis. Indeed, the data to analyse are often discrete since they come from measurements over a territory or from numerical simulations with computer codes for example. Among classical approaches, kriging has been proven to be an efficient alternative. However, due to economical or computational time reasons, the amount of available data (called design of experiments) to build the Kriging model is not substantial and adaptive strategies are necessary to locally refine the information in regions of interest such as where the data exceed a given threshold or exhibit non stationarities.


This thesis is therefore devoted to the development of new numerical techniques to construct design of experiments. A generic criterion to derive adaptive designs is first introduced, it is based on an extension of the previous work of Picheny et al. (2010). Two numerical topics are then considered. The first one is related to computational time reduction associated with the optimization step of the criterion. It is achieved by the introduction of two strategies combining MSE and IMSE. The second one concerns the lack of stability of the underlying Kriging interpolation when the number of points in the design increases. To circumvent such a limitation, a new approach based on multiscale preconditionning using subdivision schemes is proposed. For classical covariance functions, the preconditionners are obtained directly from their Fourier transform or from their quasi-diagonal representation. These methodological developments are finally applied, in the frame of IRSN projects, to measurement mapping for environmental monitoring and to the reconstruction of non stationnary mechanical data for uncertainty quantification. It appears that each study can be performed with an affordable computational cost, which is not the case with classical approaches.

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