Evaluation of numerical techniques for optimization of ISOCS modeled detector measurement geometries

Mathematical detector peak efficiency calibrations are often limited in accuracy by uncertain knowledge of source and shielding geometry parameters. Measured spectral peak areas from source emissions of known relative intensity determine the measured relative efficiencies. Absolute calibration accuracy may be improved by optimizing uncertain geometry parameters within specified ranges to best match calculated relative efficiencies to these measured relative efficiencies. The figure of merit (FOM) is a weighted Chi-squared measure of the difference between the measured and calculated relative efficiencies based on Canberra's ISOCS mathematical absolute efficiencies. While this FOM provides a measure of the quality of a given model, a method of efficiently improving the model must also be employed. Several numerical techniques are evaluated in this study for the automated optimization of ISOCS modeled detector measurement geometries. These include an undirected Random Search, Sequential Bracketing, Downhill Simplex, Particle Swarm, Levenberg-Marquardt and Quasi-Newton optimizations. Performance criteria include the speed of convergence and the robustness of the results, with special emphasis on speed given each ISOCS calculation may take several seconds. A variety of geometries, number of free parameters and search ranges were: used to test all of the optimization methods to evaluate their performance for this application. The results, in order of average number of FOM calculations to reach a minimum common FOM were: Quasi-Newton (9.5 ± 4.3), Simplex (22.7 ± 11.2), Swarm (43.2 ± 26.9), Sequential (58.1 ± 54.6), and Marquardt (118.5 ± 78.8).