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

Ruixian Fang,Dan Gabriel Cacuci

doi:10.4236/ajcm.2020.104031

Ruixian Fang, Dan Gabriel Cacuci

Open Access

https://doi.org/10.4236/ajcm.2020.104031

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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 3rd-order sensitivities can surpass the importance of the 1st- and 2nd-order sensitivities when the parameters’ uncertainties increase. In particular, for a uniform standard deviation of 10% of the microscopic total cross sections, the 3rd-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 3rd-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 3rd-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 3rd-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.

Highlights

The accompanying works [1] [2] have computed exactly and efficiently the (180)3 = 5,832,000 third-order sensitivities of the leakage response, of the OECD/NEA subcritical polyethylene-reflected plutonium metal fundamental physics benchmark [3], with respect to the benchmark’s 180 group-averaged microscopic total cross sections
For a uniform standard deviation of 10% of the microscopic total cross sections, the 3rd-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
The effects of the 3rd-order sensitivities on the polyethylene-reflected plutonium (PERP) benchmark’s leakage response distribution moments in the space of parameters will be quantified and compared with the contributions stemming from the corresponding 1st- and 2nd-order sensitivities, underscoring the importance of the 3rd-order sensitivities

Summary

Introduction

The effects of the first- and second-order sensitivities of the leakage response with respect to the microscopic total cross sections on the response’s expected value, variance and skewness have been quantified and documented in the previous works [5] [7]. The effects of the third-order sensitivities on the response’s variance and skewness are quantified by considering typical values for the standard deviations of the group-averaged microscopic total cross sections, and using these values together with the respective first-, second- and third-order sensitivities in Equations (6)-(15).

Results

Conclusion