151. A comparison between Bayesian and ordinary kriging based on validation criteria: application to radiological characterisation
- Author
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Wieskotten, Martin, Crozet, Marielle, Iooss, Bertrand, Lacaux, Céline, Marrel, Amandine, EA2151 Laboratoire de Mathématiques d'Avignon (LMA), Avignon Université (AU), Institut des Sciences et technologies pour une Economie Circulaire des énergies bas carbone (ISEC), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Commission des méthodes d'analyse du CEA (CETAMA), Département de recherche sur les procédés pour la mine et le recyclage du combustible (DMRC), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation (EDF R&D PRISME), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Méthodes d'Analyse Stochastique des Codes et Traitements Numériques (GdR MASCOT-NUM), Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut de recherche sur les systèmes nucléaires pour la production d'énergie bas carbone (IRESNE), and Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3)
- Subjects
Methodology (stat.ME) ,FOS: Computer and information sciences ,model validation ,[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] ,FOS: Mathematics ,Mathematics - Statistics Theory ,kriging ,geostatistics ,Statistics Theory (math.ST) ,uncertainty ,Statistics - Methodology - Abstract
In decommissioning projects of nuclear facilities, the radiological characterisation step aims to estimate the quantity and spatial distribution of different radionuclides. To carry out the estimation, measurements are performed on site to obtain preliminary information. The usual industrial practice consists in applying spatial interpolation tools (as the ordinary kriging method) on these data to predict the value of interest for the contamination (radionuclide concentration, radioactivity, etc.) at unobserved positions. This paper questions the ordinary kriging tool on the well-known problem of the overoptimistic prediction variances due to not taking into account uncertainties on the estimation of the kriging parameters (variance and range). To overcome this issue, the practical use of the Bayesian kriging method, where the model parameters are considered as random variables, is deepened. The usefulness of Bayesian kriging, whilst comparing its performance to that of ordinary kriging, is demonstrated in the small data context (which is often the case in decommissioning projects). This result is obtained via several numerical tests on different toy models, and using complementary validation criteria: the predictivity coefficient (Q${}^2$), the Predictive Variance Adequacy (PVA), the $\alpha$-Confidence Interval plot (and its associated Mean Squared Error alpha (MSEalpha)), and the Predictive Interval Adequacy (PIA). The latter is a new criterion adapted to the Bayesian kriging results. Finally, the same comparison is performed on a real dataset coming from the decommissioning project of the CEA Marcoule G3 reactor. It illustrates the practical interest of Bayesian kriging in industrial radiological characterisation.
- Published
- 2023