Speaker
Description
Monte Carlo (MC) simulation models implemented as computer codes are widely used for computing the full-energy peak (FEP) efficiency of gamma spectrometry (GS) systems. Their calibration is an important step in obtaining the traceability of GS measurements that employ computed values of the FEP efficiency. The input of MC models consist of model variables (e.g. photon energy) X=〖(x_1,....,x_d)〗^T and model parameters (e.g. crystal radius) θ=〖(θ_1,....,θ_m)〗^T. The design points for measurements are {X_1,...X_n }, and measured responses are Y={y_1,..,y_n }. Because computer models are always imperfect, a commonly used statistical model is y_i=y_m (X_i,θ^ )+δ(X_i )+e_i, where y_m (X,θ^) is the model output, δ(X_i) is the discrepancy function that accounts for the difference between the model and the GS system, θ^ contains optimal model parameters, e_i is y_i error. (Kennedy and O'Hagan, 2001).The goal of the model calibration is to estimate θ^ and δ(X) so that the model outputs match the measured responses.
The calibration of MC models is known as detector characterization. Previous studies showed that the discrepancy function is small for these models in the photon energy range of 60-2000 keV. In this case, it was proved that the least squares calibration is consistent and efficient (Tuo and Wu, 2015). MC codes are computationally expensive and therefore surrogate models must be built. A linear surrogate model was developed using the first order Taylor approximation of the Gespecor FEP efficiency. A nonlinear surrogate model was developed for large intervals of the detector parameters, which well approximates the Gespecor FEP efficiency using grid-based interpolation.
In this work a methodology for calibrating the Gespecor model is described and applied in practice using a GS system equipped with a p-type coaxial HPGe detector model B20214. The geometrical model of the model contains fifteen parameters but many of them are either known accurately or insensitive. Consequently, five parameters (crystal radius and length, face and side dead-layer thickness, side holder thickness) were taken as free parameters. Firstly, a set of values of the FEP efficiency of the B20214 detector was determined experimentally for different point source positions and different photon energies. Secondly, the optimal parameters for the detector B20214 were computed making use of the data obtained in the first step and employing linear and nonlinear least squares methods and surrogate models mentioned above.
The optimal model for the p-type HPGe detector B20214 was verified in the energy range of 60-2000 keV by measuring the FEP efficiency for point and cylindrical sources located at different positions above the end cap. The discrepancies between measured and computed values were smaller than 3 % for point sources and 5 % for cylindrical sources.
Kennedy, M. C. and O'Hagan, A, 2001. Journal of the Royal Statistical Society B, 63.
Tuo R. and Wu C.F.J., 2015. The Annals of Statistics, 45.
