Inverse problems occurring in uncertainty analysis

Abstract : This thesis provides a probabilistic solution to inverse problems through Bayesian techniques.The inverse problem considered here is to estimate the distribution of a non-observed random variable X from some noisy observed data Y explained by a time-consuming physical model H. In general, such inverse problems are encountered when treating uncertainty in industrial applications. Bayesian inference is favored as it accounts for prior expert knowledge on Xin a small sample size setting. A Metropolis-Hastings-within-Gibbs algorithm is proposed to compute the posterior distribution of the parameters of X through a data augmentation process. Since it requires a high number of calls to the expensive function H, the modelis replaced by a kriging meta-model. This approach involves several errors of different natures and we focus on measuring and reducing the possible impact of those errors. A DAC criterion has been proposed to assess the relevance of the numerical design of experiments and the prior assumption, taking into account the observed data. Another contribution is the construction of adaptive designs of experiments adapted to our particular purpose in the Bayesian framework. The main methodology presented in this thesis has been applied to areal hydraulic engineering case-study.
Document type :
Theses
Complete list of metadatas

Cited literature [111 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00766341
Contributor : Shuai Fu <>
Submitted on : Tuesday, December 18, 2012 - 10:47:05 AM
Last modification on : Friday, May 17, 2019 - 10:50:31 AM
Long-term archiving on : Tuesday, March 19, 2013 - 3:55:12 AM

Identifiers

  • HAL Id : tel-00766341, version 1

Collections

Citation

Shuai Fu. Inverse problems occurring in uncertainty analysis. General Mathematics [math.GM]. Université Paris Sud - Paris XI, 2012. English. ⟨NNT : 2012PA112208⟩. ⟨tel-00766341⟩

Share

Metrics

Record views

812

Files downloads

762