Inverse Predictive Modeling of Radiation Transport Through Optically Thick Media in the Presence of Counting Uncertainties

Abstract

Using the problem of inverse prediction from detector responses in the presence of counting uncertainties of the thickness of a homogeneous slab of material containing uniformly distributed gamma-emitting sources, this work investigates the possible reasons for the apparent failure of the traditional inverse-problem methods based on the minimization of chi-square-type functionals to predict accurate results for optically thick slabs. This work also compares the results produced by such methods with the results produced by applying the Predictive Modeling of Coupled Multi-Physics Systems (PM-CMPS) methodology for optically thin and thick slabs. For optically thin slabs, this work shows that both the traditional chi-square-minimization method and the PM-CMPS methodology predict the slab’s thickness accurately. However, the PM-CMPS methodology is considerably more efficient computationally, and a single application of the PM-CMPS methodology predicts the thin slab’s thickness at least as precisely as the traditional chi-square-minimization method, even though the measurements used in the PM-CMPS methodology were ten times less accurate than the ones used for the traditional chi-square-minimization method. For optically thick slabs, the results obtained in this work show that: (1) the traditional inverse-problem methods based on the minimization of chi-square-type functionals fail to predict the slab’s thickness; (2) the PM-CMPS methodology underpredicts the slab’s actual physical thickness when imprecise experimental results are assimilated, even though the predicted responses agree within the imposed error criterion with the experimental results; (3) the PM-CMPS methodology correctly predicts the slab’s actual physical thickness when precise experimental results are assimilated, while also predicting the physically correct response within the selected precision criterion; and (4) the PM-CMPS methodology is computational vastly more efficient while yielding significantly more accurate results than the traditional chi-square-minimization methodology.

Keywords:

• Inverse radiation transport
• chi-square minimization
• predictive modeling of coupled multi-physics systems

Acknowledgments

The author gratefully acknowledges illuminating discussions with J. K. Mattingly (North Carolina State University), who provided the basic software which was used by M. Badea (University of South Carolina) to produce the results depicted in Figs. 2 through 8. The author also acknowledges gratefully various computational results provided by M. Badea.