Third Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: III. Response Moments

Abstract

The (180) 3 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections have been computed in accompanying works [1] [2]. This work quantifies the contributions of these (180) 3 third-order mixed sensitivities to the PERP benchmark’s leakage response distribution moments (expected value, variance and skewness) and compares these contributions to those stemming from the corresponding first- and second-order sensitivities of the PERP benchmark’s leakage response with respect to the total cross sections. The numerical results obtained in this work reveal that the importance of the 3 rd -order sensitivities can surpass the importance of the 1 st - and 2 nd -order sensitivities when the parameters’ uncertainties increase. In particular, for a uniform standard deviation of 10% of the microscopic total cross sections, the 3 rd -order sensitivities contribute 80% to the response variance, whereas the contribution stemming from the 1st- and 2nd-order sensitivities amount only to 2% and 18%, respectively. Consequently, neglecting the 3 rd -order sensitivities could cause a very large non-conservative error by under-reporting the response variance by a factor of 506%. The results obtained in this work also indicate that the effects of the 3 rd -order sensitivities are to reduce the response’s skewness in parameter space, rendering the distribution of the leakage response more symmetric about its expected value. The results obtained in this work are the first such results ever published in reactor physics. Since correlations among the group-averaged microscopic total cross sections are not available, only the effects of typical standard deviations for these cross sections could be considered. Due to this lack of correlations among the cross sections, the effects of the mixed 3 rd -order sensitivities could not be quantified exactly at this time. These effects could be quantified only when correlations among the group-averaged microscopic total cross sections would be obtained experimentally by the nuclear physics community.