Improving Bayesian radiological profiling of waste drums using Dirichlet priors, Gaussian process priors, and hierarchical modeling.

We present three methodological improvements of our recently proposed approach for Bayesian inference of the radionuclide inventory in radioactive waste drums, from radiological measurements. First we resort to the Dirichlet distribution for the prior distribution of the isotopic vector. The Dirichlet distribution possesses the attractive property that the elements of its vector samples sum up to 1. Second, we demonstrate that such Dirichlet priors can be incorporated within an hierarchical modeling of the prior uncertainty in the isotopic vector, when prior information about isotopic composition is available. Our used Bayesian hierarchical modeling framework makes use of this available information but also acknowledges its uncertainty by letting to a controlled extent the information content of the indirect measurement data (i.e., gamma and neutron counts) shape the actual prior distribution of the isotopic vector. Third, we propose to regularize the Bayesian inversion by using Gaussian process (GP) prior modeling when inferring 1D spatially-distributed mass or, equivalently, activity distributions. As of uncertainty in the efficiencies, we keep using the same stylized drum modeling approach as proposed in our previous work to account for the source distribution uncertainty across the vertical direction of the drum. A series of synthetic tests followed by application to a real waste drum show that combining hierarchical modeling of the prior isotopic composition uncertainty together with GP prior modeling of the vertical Pu profile across the drum works well. We also find that our GP prior can handles both cases with and without spatial correlation. Of course, our GP prior modeling framework only makes sense in the context of spatial inference. Furthermore, the computational times involved by our approach are on the order of a few hours, say about 2, to provide uncertainty estimates for all variables of interest in the considered inverse problem. This warrants further investigations to speed up the inference.

Estimation of soil radioactivity-depth profiles using Bayesian inversion of borehole gamma spectrometry data.

Inversion of in situ borehole gamma spectrometry data is a faster and relatively less laborious method for calculating the vertical distribution of radioactivity in soil than conventional soil sampling method. However, the efficiency calculation of a detector for such measurements is a challenging task due to spatial and temporal variation of the soil properties and other measurement parameters. In this study, the sensitivity of different soil characteristics and measurement parameters on simulated efficiencies for a 662 keV photon peak were investigated. In addition, a Bayesian data inversion with a Gaussian process model was used to calculate the activity concentration of 137Cs and its uncertainty considering the sources of uncertainty identified during the sensitivity analysis, including soil density, borehole radius, and the uncertainty in detector position in the borehole. Several soil samples were also collected from the borehole and surrounding area, and 137Cs activity concentration was measured to compare with the inversion results. The calculated 137Cs activity concentrations agree well with those obtained from soil samples. Therefore, it can be concluded that the vertical radioactivity distribution can be calculated using the probabilistic method using in situ gamma spectrometric measurements.

2D inversion of in situ gamma-ray spectrometric measurements of 137Cs for site characterization.

Environmental contamination by radioactive materials can be characterized by in situ gamma surface measurements. During such measurements, the field of view of a gamma detector can be tens of meters wide, resulting in a count rate that integrates the signal over a large measurement support volume/area. The contribution of a specific point to the signal depends on various parameters, such as the height of the detector above the ground surface, the gamma energy and the detector properties, etc. To improve the spatial resolution of the activity concentration, contributions of a radionuclide from nearby areas to the count rate of a single measurement should be disentangled. The experiments described in this paper, deployed 2D inversion of in situ gamma spectrometric measurements using a non-negative least squares-based Tikhonov regularization method. Data were acquired using a portable LaBr3 gamma detector. The detector response as a function of the distance of the radioactive source, required for the inversion process, was simulated using the Monte Carlo N-Particle (MCNP) transport code. The uncertainty on activity concentration was calculated using the Monte Carlo error propagation method. The 2D inversion methodology was first satisfactorily assessed for 133Ba and 137Cs source activity distributions using reference pads. Secondly, this method was applied on a 137Cs contaminated site, making use of above-ground in-situ gamma spectrometry measurements, conducted on a regular grid. The inversion process results were compared with the results from in-situ borehole measurements and laboratory analyses of soil samples. The calculated 137Cs activity concentration levels were compared against the activity concentration value for exemption or clearance of materials which can be applied by default to any amount and any type of solid material. Using the 2D inversion and the Monte Carlo error propagation method, a high spatial resolution classification of the site, in terms of exceeding the exemption limit, could be made. The 137Cs activity concentrations obtained using the inversion process agreed well with the results from the in-situ borehole measurements and those from the soil samples, showing that the 2D inversion is a convenient approach to deconvolute the contribution of radioactive sources from nearby areas within a detector's field of view, and increases the resolution of spatial contamination mapping.

Soil radioactivity-depth profiles from regularized inversion of borehole gamma spectrometry data.

An in situ borehole gamma logging method using a LaBr3 gamma detector has been developed to characterize a137Cs contaminated site. The activity-depth distribution of 137Cs was derived by inversion of the in situ measurement data using two different least squares methods, (i) Least squares optimization (LSO) and (ii) Tikhonov regularization. The regularization parameter (λ) of the Tikhonov regularization method was estimated using three different methods i.e. the L-curve, Generalized Cross Validation (GCV) and a prior information based method (PIBM). The considered inversion method variants were first validated for a137Cs contaminated pipe, and in most of the cases, the calculated activity of 137Cs was found to be within the acceptable range. The calculated 137Cs activity-depth profiles from in situ measurements were also in good agreement with the ones obtained from soil sample analysis, with an R2 ranging from 0.76 to 0.82. The GCV method for estimating λ appeared to perform better than the two other methods in terms of R2 and root mean squared error (RMSE). The L-curve method resulted in higher RMSE than the other Tikhonov regularization methods. Instability was observed in the activity concentration depth profile obtained from the LSO method. Therefore, we recommend the Tikhonov regularization with GCV for estimating λ for estimating the activity concentration-depth profile. The site studied showed 137Cs activity concentrations above the exemption limit down to depths of 0.50-0.90 m.

Bayesian inference of 1D activity profiles from segmented gamma scanning of a heterogeneous radioactive waste drum.

We present a Bayesian approach to probabilistically infer vertical activity profiles within a radioactive waste drum from segmented gamma scanning (SGS) measurements. Our approach resorts to Markov chain Monte Carlo (MCMC) sampling using the state-of-the-art Hamiltonian Monte Carlo (HMC) technique and accounts for two important sources of uncertainty: the measurement uncertainty and the uncertainty in the source distribution within the drum. In addition, our efficiency model simulates the contributions of all considered segments to each count measurement. Our approach is first demonstrated with a synthetic example, after which it is used to resolve the vertical activity distribution of 5 nuclides in a real waste package.

Nested multiresolution hierarchical simulated annealing algorithm for porous media reconstruction.

Microstructure strongly influences flow and transport properties of porous media. Flow and transport simulations within porous media, therefore, requires accurate three-dimensional (3D) models of the pore and solid phase structure. To date, no imaging method can resolve all relevant heterogeneities from the nano- to the centimeter scale within complex heterogeneous materials such as clay, reservoir rocks (e.g., travertine, chalk, ...), hardened cement paste, and concrete. To reconstruct these porous materials it is thus necessary to merge information from different 2D and potentially 3D imaging methods. One porous media reconstruction methodology that has been around for at least two decades is simulated annealing (SA). However, realizations with SA typically suffer an artificially reduced long-range connectivity, while multiphase reconstructions are not feasible in most cases because of a prohibitive computational burden. To solve these problems we propose a hierarchical multiresolution and multiphase simulated annealing algorithm. To decrease the computational cost of multiphase simulation, our algorithm sequentially simulates one phase after another, in a hierarchical way, which enables handling multimodal distributions and topological relations. Building upon recent work, our algorithm improves long-range connectivity and CPU efficiency by simulating larger particles using a coarser resolution that is subsequently refined compared to standard SA; our proposed extension not only offers the possibility to perform multiphase reconstruction but also allows us (i) to improve binary reconstruction quality, as quantified, e.g., by multiple-point histograms by up to one order of magnitude and (ii) to achieve an overall speed-up. The proposed algorithm is also shown to outperform the direct sampling multiple-point statistics method for the generation of cement paste microstructure with respect to both generation time and quality.

Metrology for decommissioning nuclear facilities: Partial outcomes of joint research project within the European Metrology Research Program.

Decommissioning of nuclear facilities incurs high costs regarding the accurate characterisation and correct disposal of the decommissioned materials. Therefore, there is a need for the implementation of new and traceable measurement technologies to select the appropriate release or disposal route of radioactive wastes. This paper addresses some of the innovative outcomes of the project "Metrology for Decommissioning Nuclear Facilities" related to mapping of contamination inside nuclear facilities, waste clearance measurement, Raman distributed temperature sensing for long term repository integrity monitoring and validation of radiochemical procedures.

Model-based classification of CPT data and automated lithostratigraphic mapping for high-resolution characterization of a heterogeneous sedimentary aquifer.

Cone penetration testing (CPT) is one of the most efficient and versatile methods currently available for geotechnical, lithostratigraphic and hydrogeological site characterization. Currently available methods for soil behaviour type classification (SBT) of CPT data however have severe limitations, often restricting their application to a local scale. For parameterization of regional groundwater flow or geotechnical models, and delineation of regional hydro- or lithostratigraphy, regional SBT classification would be very useful. This paper investigates the use of model-based clustering for SBT classification, and the influence of different clustering approaches on the properties and spatial distribution of the obtained soil classes. We additionally propose a methodology for automated lithostratigraphic mapping of regionally occurring sedimentary units using SBT classification. The methodology is applied to a large CPT dataset, covering a groundwater basin of ~60 km2 with predominantly unconsolidated sandy sediments in northern Belgium. Results show that the model-based approach is superior in detecting the true lithological classes when compared to more frequently applied unsupervised classification approaches or literature classification diagrams. We demonstrate that automated mapping of lithostratigraphic units using advanced SBT classification techniques can provide a large gain in efficiency, compared to more time-consuming manual approaches and yields at least equally accurate results.

Determination of 137Cs contamination depth distribution in building structures using geostatistical modeling of ISOCS measurements.

Decommissioning of nuclear building structures usually leads to large amounts of low level radioactive waste. Using a reliable method to determine the contamination depth is indispensable prior to the start of decontamination works and also for minimizing the radioactive waste volume and the total workload. The method described in this paper is based on geostatistical modeling of in situ gamma-ray spectroscopy measurements using the multiple photo peak method. The method has been tested on the floor of the waste gas surge tank room within the BR3 (Belgian Reactor 3) decommissioning project and has delivered adequate results.