| Implicit optimization methods for solving the inverse transport problems of interface location identification, source isotope weight fraction identification, shield material identification, and material mass density identification are explored. Among these optimization methods are the Schwinger inverse method, Levenberg-Marquardt method, and evolutionary algorithms. Inverse problems are studied in one-dimensional spherical and two-dimensional cylindrical geometries. The scalar fluxes of unscattered gamma-ray lines, leakages of neutron-induced gamma-ray lines, and/or neutron multiplication in the system are assumed to be measured. Each optimization method is studied on numerical test problems in which the measured data is simulated using the same deterministic transport code used in the optimization process (assuming perfectly consistent measurements) and using a Monte Carlo code (assuming less-consistent, more realistic measurements). The Schwinger inverse method and Levenberg-Marquardt methods are found to be successful for problems with relatively few (i.e. 4 or fewer) unknown parameters, with the former being the best for unknown isotope problems and the latter being more adept at interface location, unknown material mass density, and mixed parameter problems. A study of a variety of evolutionary algorithms indicates that the differential evolution method is the best for inverse transport problems, and outperforms the Levenberg-Marquardt method on problems with large numbers of unknowns. An algorithm created by combining different variants of the differential evolution method is shown to be highly successful on spherical problems with unscattered gamma-ray lines, while a basic differential evolution approach is more useful for problems with scattering and in cylindrical geometries. A hybrid differential evolution/Levenberg-Marquardt algorithm also was found to show promise for fast and robust solution of inverse problems. |
