Inverse Berru Predictive Modeling Of Radiation Transport In The Presence Of Counting Uncertainties
Using a paradigm 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 Chapter presents an investigation of 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 Chapter also presents a comparison of the results produced by such traditional methods with the results produced by applying the BERRU methodology, for optically thin and thick slabs. For optically thin slabs, the results presented in this Chapter show that both the traditional chi-square-minimization method and the BERRU methodology predict the slab’s thickness accurately. However, the BERRU methodology is considerably more efficient computationally, and a single application of the BERRU 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 BERRU methodology were ten times less accurate than the ones used for the traditional chi-square-minimization method. For optically thick slabs, however, the results presented in this Chapter show that:
(i) The traditional inverse-problem methods based on the minimization of chi-square-type functionals fail to predict the slab’s thickness.
(ii) The BERRU methodology under-predicts the slab’s actual physical thickness when imprecise experimental results are assimilated, even though the predicted responses agrees within the imposed error criterion with the experimental results; (iii) The BERRU 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.
(iv) The BERRU methodology is vastly more efficient computationally, while yielding significantly more accurate results, than the traditional chi-square-minimization methodology.
(v) The accuracy of the results predicted by using the BERRU methodology in the “inverse predictive” mode is limited more by the precision of the measurements, rather than by the BERRU methodology’s underlying computational algorithm.
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