Stochastic approach for radionuclides quantification

Abstract

Abstract-Gamma spectrometry is a passive non-destructive assay used to quantify radionuclides present in more or less complex objects. Basic methods using empirical calibration with a standard in order to quantify the activity of nuclear materials by determining the calibration coefficient are useless on non-reproducible, complex and single nuclear objects such as waste packages. Package specifications as composition or geometry change from one package to another and involve a high variability of objects. Current quantification process uses numerical modelling of the measured scene with few available data such as geometry or composition. These data are density, material, screen, geometric shape, matrix composition, matrix and source distribution. Some of them are strongly dependent on package data knowledge and operator backgrounds. The French Commissariatà l'Energie Atomique (CEA) is developing a new methodology to quantify nuclear materials in waste packages and waste drums without operator adjustment and internal package configuration knowledge. This method suggests combining a global stochastic approach which uses, among others, surrogate models available to simulate the gamma attenuation behaviour, a Bayesian approach which considers conditional probability densities of problem inputs, and Markov Chains Monte Carlo algorithms (MCMC) which solve inverse problems, with gamma ray emission radionuclide spectrum, and outside dimensions of interest objects. The methodology is testing to quantify actinide activity in different kind of matrix, composition, and configuration of sources standard in terms of actinide masses, locations and distributions. Activity uncertainties are taken into account by this adjustment methodology.

Bayesian Approach for Multigamma Radionuclide Quantification Applied on Weakly Attenuating Nuclear Waste Drums

“…Let us assume there are N net extracted areas gathered in vector [1,N ] energies of the multi gamma-emitter radionuclide, and X ∈ Ξ D represents a D-dimension vector of inputs needed for the calculation of the absolute efficiency calibration coefficients vector (X) = { n (X), n ∈ [1, N ]} estimation.The X vector is composed of variables impacting the detection efficiency: measurement distance, cylindrical dimensions (radius, height), proportion of materials composing the cylinder (vinyl, iron, plutonium), bulk density, etc. Details are available in [6].…”

“…The calculation of the conditional PDF of m f (m|Y obs ) leads to the evaluation of the integral over X appearing in (6). When the dimension of X is relatively high, directly computing the integral given by ( 6) is hardly feasible.…”

“…Current and common calculation methods use Monte Carlo simulation codes as MCNP6 [3] to model measured scenes and approach as precisely as possible the real values of the (E) coefficient. Several years ago, new kinds of nuclear numerical quantification methods dealing with applied mathematics and stochastic approaches [6] proposed emulating outcomes of interest such as (E) to solve the inverse problem of quantification and to estimate the mass distribution of a radionuclide of interest included in objects such as nuclear waste drums. In this way, Carasco [7] proposes to couple gamma ray spectrometry and tomography in a Bayesian framework to characterize radionuclides of interest such as 239 P u in nuclear waste.…”

Group kernels for Gaussian process metamodels with categorical inputs

“…Thus, surrogate models have to be introduced to emulate the function w → (w), which is now investigated in the frame of Gaussian process regression. We refer to Clement et al [2018] for the second step, namely the treatment of the inversion problem. Model settings are now motivated by a graphical analysis.…”