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Sampling of systematic errors to estimate likelihood weights in nuclear data uncertainty propagation
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Applied Nuclear Physics. (Nuclear Reactions)
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Applied Nuclear Physics. (Nuclear Reactions)
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Applied Nuclear Physics. IAEA. (Nuclear reaction group)
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
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2016 (English)In: Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, ISSN 0168-9002, E-ISSN 1872-9576, Vol. 807, p. 137-149Article in journal (Refereed) Published
Abstract [en]

In methodologies for nuclear data (ND) uncertainty assessment and propagation based on random sampling, likelihood weights can be used to infer experimental information into the distributions for the ND. As the included number of correlated experimental points grows large, the computational time for the matrix inversion involved in obtaining the likelihood can become a practical problem. There are also other problems related to the conventional computation of the likelihood, e.g., the assumption that all experimental uncertainties are Gaussian. In this study, a way to estimate the likelihood which avoids matrix inversion is investigated; instead, the experimental correlations are included by sampling of systematic errors. It is shown that the model underlying the sampling methodology (using univariate normal distributions for random and systematic errors) implies a multivariate Gaussian for the experimental points (i.e., the conventional model). It is also shown that the likelihood estimates obtained through sampling of systematic errors approach the likelihood obtained with matrix inversion as the sample size for the systematic errors grows large. In studied practical cases, it is seen that the estimates for the likelihood weights converge impractically slowly with the sample size, compared to matrix inversion. The computational time is estimated to be greater than for matrix inversion in cases with more experimental points, too. Hence, the sampling of systematic errors has little potential to compete with matrix inversion in cases where the latter is applicable. Nevertheless, the underlying model and the likelihood estimates can be easier to intuitively interpret than the conventional model and the likelihood function involving the inverted covariance matrix. Therefore, this work can both have pedagogical value and be used to help motivating the conventional assumption of a multivariate Gaussian for experimental data. The sampling of systematic errors could also be used in cases where the experimental uncertainties are not Gaussian, and for other purposes than to compute the likelihood, e.g., to produce random experimental data sets for a more direct use in ND evaluation.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 807, p. 137-149
Keyword [en]
Nuclear data, Uncertainty propagation, Experimental correlations, Systematic uncertainty, Total Monte Carlo
National Category
Physical Sciences
Research subject
Physics with specialization in Applied Nuclear Physics
Identifiers
URN: urn:nbn:se:uu:diva-265321DOI: 10.1016/j.nima.2015.10.024ISI: 000365596200019OAI: oai:DiVA.org:uu-265321DiVA, id: diva2:865156
Available from: 2015-10-27 Created: 2015-10-27 Last updated: 2018-04-16
In thesis
1. Experimental data and Total Monte Carlo: Towards justified, transparent and complete nuclear data uncertainties
Open this publication in new window or tab >>Experimental data and Total Monte Carlo: Towards justified, transparent and complete nuclear data uncertainties
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The applications of nuclear physics are many with one important being nuclear power, which can help decelerating the climate change. In any of these applications, so-called nuclear data (ND, numerical representations of nuclear physics) is used in computations and simulations which are necessary for, e.g., design and maintenance. The ND is not perfectly known - there are uncertainties associated with it - and this thesis concerns the quantification and propagation of these uncertainties. In particular, methods are developed to include experimental data in the Total Monte Carlo methodology (TMC). The work goes in two directions. One is to include the experimental data by giving weights to the different "random files" used in TMC. This methodology is applied to practical cases using an automatic interpretation of an experimental database, including uncertainties and correlations. The weights are shown to give a consistent implementation of Bayes' theorem, such that the obtained uncertainty estimates in theory can be correct, given the experimental data. In the practical implementation, it is more complicated. This is much due to the interpretation of experimental data, but also because of model defects - the methodology assumes that there are parameter choices such that the model of the physics reproduces reality perfectly. This assumption is not valid, and in future work, model defects should be taken into account. Experimental data should also be used to give feedback to the distribution of the parameters, and not only to provide weights at a later stage.The other direction is based on the simulation of the experimental setup as a means to analyze the experiments in a structured way, and to obtain the full joint distribution of several different data points. In practice, this methodology has been applied to the thermal (n,α), (n,p), (n,γ) and (n,tot) cross sections of 59Ni. For example, the estimated expected value and standard deviation for the (n,α) cross section is (12.87 ± 0.72) b, which can be compared to the established value of (12.3 ± 0.6) b given in the work of Mughabghab. Note that also the correlations to the other thermal cross sections as well as other aspects of the distribution are obtained in this work - and this can be important when propagating the uncertainties. The careful evaluation of the thermal cross sections is complemented by a coarse analysis of the cross sections of 59Ni at other energies. The resulting nuclear data is used to study the propagation of the uncertainties through a model describing stainless steel in the spectrum of a thermal reactor. In particular, the helium production is studied. The distribution has a large uncertainty (a standard deviation of (17 ± 3) \%), and it shows a strong asymmetry. Much of the uncertainty and its shape can be attributed to the more coarse part of the uncertainty analysis, which, therefore, shall be refined in the future.

Place, publisher, year, edition, pages
Uppsala universitet, 2015
National Category
Physical Sciences
Research subject
Physics with specialization in Applied Nuclear Physics
Identifiers
urn:nbn:se:uu:diva-265330 (URN)
Presentation
2015-10-13, Polhemssalen, Ångströmslaboratoriet, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2015-11-04 Created: 2015-10-27 Last updated: 2015-11-04Bibliographically approved
2. Approaching well-founded comprehensive nuclear data uncertainties: Fitting imperfect models to imperfect data
Open this publication in new window or tab >>Approaching well-founded comprehensive nuclear data uncertainties: Fitting imperfect models to imperfect data
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Nuclear physics has a wide range of applications; e.g., low-carbon energy production, medical treatments, and non-proliferation of nuclear weapons. Nuclear data (ND) constitute necessary input to computations needed within all these applications.

This thesis considers uncertainties in ND and their propagation to applications such as ma- terial damage in nuclear reactors. TENDL is today the most comprehensive library of evaluated ND (a combination of experimental ND and physical models), and it contains uncertainty estimates for all nuclides it contains; however, TENDL relies on an automatized process which, so far, includes a few practical remedies which are not statistically well-founded. A longterm goal of the thesis is to provide methods which make these comprehensive uncertainties well-founded. One of the main topics of the thesis is an automatic construction of experimental covariances; at first by attempting to complete the available uncertainty information using a set of simple rules. The thesis also investigates using the distribution of the data; this yields promising results, and the two approaches may be combined in future work.

In one of the papers underlying the thesis, there are also manual analyses of experiments, for the thermal cross sections of Ni-59 (important for material damage). Based on this, uncertainty components in the experiments are sampled, resulting in a distribution of thermal cross sections. After being combined with other types of ND in a novel way, the distribution is propagated both to an application, and to an evaluated ND file, now part of the ND library JEFF 3.3.

The thesis also compares a set of different techniques used to fit models in ND evaluation. For example, it is quantified how sensitive different techniques are to a model defect, i.e., the inability of the model to reproduce the truth underlying the data. All techniques are affected, but techniques fitting model parameters directly (such as the primary method used for TENDL) are more sensitive to model defects. There are also advantages with these methods, such as physical consistency and the possibility to build up a framework such as that of TENDL.

The treatment of these model defects is another main topic of the thesis. To this end, two ways of using Gaussian processes (GPs) are studied, applied to quite different situations. First, the addition of a GP to the model is used to enable the fitting of arbitrarily shaped peaks in a histogram of data. This is shown to give a substantial improvement compared to if the peaks are assumed to be Gaussian (when they are not), both using synthetic and authentic data.

The other approach uses GPs to fit smoothly energy-dependent model parameters in an ND evaluation context. Such an approach would be relatively easy to incorporate into the TENDL framework, and ensures a certain level of physical consistency. It is used on a TALYS-like model with synthetic data, and clearly outperforms fits without the energy-dependent model parameters, showing that the method can provide a viable route to improved ND evaluation. As a proof of concept, it is also used with authentic TALYS, and with authentic data.

To conclude, the thesis takes significant steps towards well-founded comprehensive ND un- certainties.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2018. p. 119
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1669
Keyword
Evaluated nuclear data, uncertainty propagation, uncertainty quantification, model defects, Gaussian processes, TALYS, TENDL, covariances.
National Category
Subatomic Physics
Research subject
Physics with specialization in Applied Nuclear Physics
Identifiers
urn:nbn:se:uu:diva-348553 (URN)978-91-513-0334-5 (ISBN)
Public defence
2018-06-08, Häggsalen, Ångströmslaboratoriet, Lägerhyddsv. 1, Uppsala, 09:15 (English)
Opponent
Supervisors
Available from: 2018-05-17 Created: 2018-04-16 Last updated: 2018-05-17

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Helgesson, PetterSjöstrand, HenrikRydén, JesperAlhassan, ErwinPomp, Stephan

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