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Approaching well-founded comprehensive nuclear data uncertainties: Fitting imperfect models to imperfect data
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Applied Nuclear Physics. (Nuclear Reactions)
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
Keywords [en]
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: urn:nbn:se:uu:diva-348553ISBN: 978-91-513-0334-5 (print)OAI: oai:DiVA.org:uu-348553DiVA, id: diva2:1197900
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: 2018-10-08
List of papers
1. Incorporating Experimental Information in the Total Monte Carlo Methodology Using File Weights
Open this publication in new window or tab >>Incorporating Experimental Information in the Total Monte Carlo Methodology Using File Weights
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2015 (English)In: Nuclear Data Sheets, ISSN 0090-3752, E-ISSN 1095-9904, Vol. 123, no SI, p. 214-219Article in journal (Refereed) Published
Abstract [en]

Some criticism has been directed towards the Total Monte Carlo method because experimental information has not been taken into account in a statistically well-founded manner. In this work, a Bayesian calibration method is implemented by assigning weights to the random nuclear data files and the method is illustratively applied to a few applications. In some considered cases, the estimated nuclear data uncertainties are significantly reduced and the central values are significantly shifted. The study suggests that the method can be applied both to estimate uncertainties in a more justified way and in the search for better central values. Some improvements are however necessary; for example, the treatment of outliers and cross-experimental correlations should be more rigorous and random files that are intended to be prior files should be generated.

National Category
Physical Sciences
Research subject
Physics with specialization in Applied Nuclear Physics
Identifiers
urn:nbn:se:uu:diva-224670 (URN)10.1016/j.nds.2014.12.037 (DOI)000348490700039 ()
Available from: 2014-05-16 Created: 2014-05-16 Last updated: 2018-04-16Bibliographically approved
2. Combining Total Monte Carlo and Unified Monte Carlo: Bayesian nuclear data uncertainty quantification from auto-generated experimental covariances
Open this publication in new window or tab >>Combining Total Monte Carlo and Unified Monte Carlo: Bayesian nuclear data uncertainty quantification from auto-generated experimental covariances
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2017 (English)In: Progress in nuclear energy (New series), ISSN 0149-1970, E-ISSN 1878-4224, Vol. 96, p. 76-96Article in journal (Refereed) Published
Abstract [en]

The Total Monte Carlo methodology (TMC) for nuclear data (ND) uncertainty propagation has been subject to some critique because the nuclear reaction parameters are sampled from distributions which have not been rigorously determined from experimental data. In this study, it is thoroughly explained how TMC and Unified Monte Carlo-B (UMC-B) are combined to include experimental data in TMC. Random ND files are weighted with likelihood function values computed by comparing the ND files to experimental data, using experimental covariance matrices generated from information in the experimental database EXFOR and a set of simple rules. A proof that such weights give a consistent implementation of Bayes' theorem is provided. The impact of the weights is mainly studied for a set of integral systems/applications, e.g., a set of shielding fuel assemblies which shall prevent aging of the pressure vessels of the Swedish nuclear reactors Ringhals 3 and 4.

In this implementation, the impact from the weighting is small for many of the applications. In some cases, this can be explained by the fact that the distributions used as priors are too narrow to be valid as such. Another possible explanation is that the integral systems are highly sensitive to resonance parameters, which effectively are not treated in this work. In other cases, only a very small number of files get significantly large weights, i.e., the region of interest is poorly resolved. This convergence issue can be due to the parameter distributions used as priors or model defects, for example.

Further, some parameters used in the rules for the EXFOR interpretation have been varied. The observed impact from varying one parameter at a time is not very strong. This can partially be due to the general insensitivity to the weights seen for many applications, and there can be strong interaction effects. The automatic treatment of outliers has a quite large impact, however.

To approach more justified ND uncertainties, the rules for the EXFOR interpretation shall be further discussed and developed, in particular the rules for rejecting outliers, and random ND files that are intended to describe prior distributions shall be generated. Further, model defects need to be treated.

Place, publisher, year, edition, pages
Elsevier, 2017
Keywords
Nuclear data, Uncertainty propagation, Total Monte Carlo, Experimental correlations, Unified Monte Carlo
National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-313644 (URN)10.1016/j.pnucene.2016.11.006 (DOI)000392676800007 ()
Available from: 2017-01-23 Created: 2017-01-23 Last updated: 2018-04-16Bibliographically approved
3. Sampling of systematic errors to estimate likelihood weights in nuclear data uncertainty propagation
Open this publication in new window or tab >>Sampling of systematic errors to estimate likelihood weights in nuclear data uncertainty propagation
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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
Keywords
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:nbn:se:uu:diva-265321 (URN)10.1016/j.nima.2015.10.024 (DOI)000365596200019 ()
Available from: 2015-10-27 Created: 2015-10-27 Last updated: 2018-04-16
4. Uncertainty driven nuclear data evaluation including thermal (n,alpha) applied to Ni-59
Open this publication in new window or tab >>Uncertainty driven nuclear data evaluation including thermal (n,alpha) applied to Ni-59
2017 (English)In: Nuclear Data Sheets, ISSN 0090-3752, E-ISSN 1095-9904, Vol. 145, p. 1-24Article in journal (Refereed) Published
Abstract [en]

This paper presents a novel approach to the evaluation of nuclear data (ND), combining experimental data for thermalcross sections with resonance parameters and nuclear reaction modeling. The method involves sampling of variousuncertain parameters, in particular uncertain components in experimental setups, and provides extensive covarianceinformation, including consistent cross-channel correlations over the whole energy spectrum. The method is developed for, and applied to, Ni-59, but may be used as a whole, or in part, for other nuclides. Ni-59 is particularly interesting since a substantial amount of Ni-59 is produced in thermal nuclear reactors by neutron capture in Ni-58 and since it has a non-threshold (n,α) cross section. Therefore, Ni-59 gives a very important contribution to the helium production in stainless steel in a thermal reactor. However, current evaluated ND libraries contain old information for Ni-59, without any uncertainty information. The work includes a study of thermal cross section experiments and a novel combination of this experimental information, giving the full multivariate distribution of the thermal cross sections. In particular, the thermal (n,α) cross section is found to be (12.7 ± .7) b. This is consistent with, but yet different from, current established values. Further, the distribution of thermal cross sections is combined with reported resonance parameters, and with TENDL-2015 data, to provide full random ENDF files; all this is done in a novel way, keeping uncertainties and correlations in mind. The random files are also condensed into one single ENDF file with covariance information, which is now part ofa beta version of JEFF 3.3.Finally, the random ENDF files have been processed and used in an MCNP model to study the helium productionin stainless steel. The increase in the (n,α) rate due to Ni-59 compared to fresh stainless steel is found to be a factor of 5.2 at a certain time in the reactor vessel, with a relative uncertainty due to the Ni-59 data of 5.4 %.

National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-315678 (URN)10.1016/j.nds.2017.09.001 (DOI)000413732700001 ()
Note

Uncertainty-driven nuclear data evaluation including thermal (n,α) applied to 59Ni

Available from: 2017-02-17 Created: 2017-02-17 Last updated: 2018-04-16Bibliographically approved
5. Assessment of Novel Techniques for Nuclear Data Evaluation
Open this publication in new window or tab >>Assessment of Novel Techniques for Nuclear Data Evaluation
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2018 (English)In: Reactor Dosimetry: 16th International Symposium, ASTM International, 2018, p. 105-116Conference paper, Published paper (Refereed)
Abstract [en]

The quality of evaluated nuclear data can be impacted by, e.g., the choice of the evaluation algorithm. The objective of this work is to compare the performance of the evaluation techniques GLS, GLS-P, UMC-G, and, UMC-B, by using synthetic data. In particular, the effects of model defects are investigated. For small model defects, UMC-B and GLS-P are found to perform best, while these techniques yield the worst results for a significantly defective model; in particular, they seriously underestimate the uncertainties. If UMC-B is augmented with Gaussian processes,it performs distinctly better for a defective model but is more susceptible to an inadequate experimental covariance estimate.

Place, publisher, year, edition, pages
ASTM International, 2018
Series
American Society for Testing and Materials Selected Technical Papers, ISSN 0066-0558
National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-322558 (URN)10.1520/STP160820170087 (DOI)000474939900010 ()978-0-8031-7661-4 (ISBN)
Conference
16th International Symposium on Reactor Dosimetry, MAY 07-12, 2017, Santa Fe, NM
Available from: 2017-05-25 Created: 2017-05-25 Last updated: 2019-08-07Bibliographically approved
6. Fitting a defect non-linear model with or without prior, distinguishing nuclear reaction products as an example
Open this publication in new window or tab >>Fitting a defect non-linear model with or without prior, distinguishing nuclear reaction products as an example
2017 (English)In: Review of Scientific Instruments, ISSN 0034-6748, E-ISSN 1089-7623, Vol. 88, article id 115114Article in journal (Refereed) Published
Abstract [en]

Fitting parametrized functions to data is important for many researchers and scientists. If the model is non-linear and/or defect, it is not trivial to do correctly and to include an adequate uncertainty analysis. This work presents how the Levenberg-Marquardt algorithm for non-linear generalized least squares fitting can be used with a prior distribution for the parameters, and how it can be combined with Gaussian processes to treat model defects. An example, where three peaks in a histogram are to be distinguished, is carefully studied. In particular, the probability r1 for a nuclear reaction to end up in one out of two overlapping peaks is studied. Synthetic data is used to investigate effects of linearizations and other assumptions. For perfect Gaussian peaks, it is seen that the estimated parameters are distributed close to the truth with good covariance estimates. This assumes that the method is applied correctly; for example, prior knowledge should be implemented using a prior distribution, and not by assuming that some parameters are perfectly known (if they are not). It is also important to update the data covariance matrix using the fit if the uncertainties depend on the expected value of the data (e.g., for Poisson counting statistics or relative uncertainties). If a model defect is added to the peaks, such that their shape is unknown, a fit which assumes perfect Gaussian peaks becomes unable to reproduce the data, and the results for r1 become biased. It is, however, seen that it is possible to treat the model defect with a Gaussian process with a covariance function tailored for the situation, with hyper-parameters determined by leave-one-out cross validation. The resulting estimates for r1 are virtually unbiased, and the uncertainty estimates agree very well with the underlying uncertainty.

Keywords
Non-linear fitting, Model defects, Gaussian processes, Uncertainty analysis
National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-326313 (URN)10.1063/1.4993697 (DOI)000416780600071 ()
Available from: 2017-07-05 Created: 2017-07-05 Last updated: 2018-04-16Bibliographically approved
7. Treating model defects by fitting smoothly varying model parameters: Energy dependence in nuclear data evaluation
Open this publication in new window or tab >>Treating model defects by fitting smoothly varying model parameters: Energy dependence in nuclear data evaluation
2018 (English)In: Annals of Nuclear Energy, ISSN 0306-4549, E-ISSN 1873-2100, Vol. 120, p. 35-47Article in journal (Refereed) Published
Abstract [en]

The fitting of models to data is essential in nuclear data evaluation, as in many other fields of science. The models maybe necessary for interpolation or extrapolation, but they are seldom perfect; there are model defects present which can result in severe biases and underestimated uncertainties. This work presents and investigates the idea to treat this problem by letting the model parameters vary smoothly with an input parameter. To be specific, the model parameters for neutron cross sections are allowed to vary with neutron energy. The parameter variation is limited by Gaussian processes, but the method should not be confused with adding a Gaussian process to the model. The performance of the method is studied using a large number of synthetic data sets, such that it is possible to quantitatively study the distribution of results compared to the underlying truth. There are imperfections in the results, but the method is seen to readily outperform fits without the energy dependent parameters. In particular, the estimates of uncertainty and correlations are much better. Hence, the method seems to offer a promising route for future treatment of model defects, both for nuclear data and elsewhere.

National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-348552 (URN)10.1016/j.anucene.2018.05.026 (DOI)000441485700004 ()
Available from: 2018-04-16 Created: 2018-04-16 Last updated: 2018-10-03Bibliographically approved

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