For the characterisation of radioactive waste packages, like 200l barrels, preferably non-destructive methods like segmented gamma scanning (SGS), transmission measurement or computer tomography are used. Segmented gamma scanning allows to identify gamma-emitting isotopes and their distribution in the vessel. To determine the corresponding activities additional information on the absorption of the waste matrix is needed. In addition, supplemental information on the waste like its chemical composition, materials and nuclide vectors are frequently available.
A unified method allowing to combine data from measurements and a-priory knowledge on each waste package giving a precise result as well as robust error estimates is currently not available. A method allowing to achieve this combination is Bayesian statistics.
The application of the Bayesian approach typically requires solve integrals (marginalize), whose dimensions are determined by the number of parameters. Depending on the size of the problem, various methods to accomplish this are described in literature. Common to all of them is the need of a model to predict the outcome of the measurement given the parameters of interest like the radioactive inventory. In case of large number of parameters, the Marcov-Chain-Monte-Carlo (MCMC) algorithm is the method of choice.
The talk will focus on the modelling of the SGS measurement process using information of the matrix derived from computer tomography. In a first step the CT-data is transferred into a 3d-voxel model. The loss of photons due to absorption and scattering on their path to the detector is calculated using an adapted Box-Intersect algorithm to get the individual contribution of each voxel. In addition, the solid angle and attenuation due to the collimator are incorporated using geometric considerations. The approach allows to assign a weight to each voxel allowing to predict the photon count rate given the activity in the voxel.
The validity of the procedure has been tested using various vessels with well-known matrix and calibration standards. The results of these comparisons will be presented.
The model predicts the count rate in each segment of the scan given the radioactive inventory in each voxel, one of the key elements to run the Marcov-Chain-Monte-Carlo algorithm. Besides the model connecting the observed quantities with the parameters of interest. Further considerations are necessary to model the activity. In a straightforward manner each voxel is allowed to carry an activity determined by prior knowledge. We demonstrate that this assumption delivers good performance for a subset of problems. However once the measurement don’t constrain the spatial distribution of the radioactive inventory properly convergence problems arise. To mitigate them the activity distribution is modeled using a compositional distribution consisting of point sources and various forms of homogeneous sources. This effectively reduces the dimensionality of the posterior distribution and improves the convergence of the algorithm.