.. todo::
Update sample problems. They are old and use some old versions of the
COUPLE/ORIGEN inputs. But we can wait for a system where we can import
test problems directly.
Create an example of properly referencing the perturbed library.
.. _sec-sampler:
Sampler: Statistical Uncertainty Analysis with SCALE Sequences
==============================================================
*U. Mertyurek, W. A. Wieselquist, F. Bostelmann, M. L. Williams, F. Havlůj* [#f1]_, *R. A. Lefebvre, W.
Zwermann* [#f2]_, *D. Wiarda, M. T. Pigni, I. C. Gauld*,
*M. A. Jessee, J. P. Lefebvre, K. J. Dugan* [#f3]_, *and B. T. Rearden*
ABSTRACT
Sampler is a "super-sequence" that performs general uncertainty analysis
for SCALE sequences by statistically sampling the input data and
analyzing the output distributions for specified responses. Among the
input parameters that can be sampled are multigroup nuclear data,
resonance self-shielding data (shielding factors and CENTRM pointwise
cross sections), depletion data such as fission product yields and decay
data, and model parameters such as nuclide concentrations, temperatures,
and simple dimension specifications. Random perturbation factors for
nuclear cross sections and depletion data are pre-computed with the
XSUSA module Medusa by sampling covariance information and are stored in
libraries read during the Sampler execution, while model parameters are
sampled "on the fly". A wide variety of output response types for
virtually all SCALE sequences can be specified for the uncertainty
analysis, and correlations in uncertain parameters between multiple
systems are also generated.
ACKNOWLEDGMENTS
Contributions from the Gesellschaft fur Anlagen- und Reaktorsicherheit
(GRS) in Germany are gratefully acknowledged. The development of the SCALE
Sampler module is based on GRS’s suggestion that their XSUSA code could be used
in conjunction with SCALE for stochastic uncertainty calculations. The original
Sampler sequence was developed based on the XSUSA sampling sequence as well as
collaboration and knowledge exchange with GRS staff members. The GRS module
Medusa is used to generate perturbations of the MG cross sections, fission
yields, and decay data.
The U.S. Nuclear Regulatory Commission Office of Nuclear Regulatory Research,
the U.S. DOE Nuclear Fuel Storage and Transportation Planning Project, and the
U.S. DOE Nuclear Criticality Safety Program supported the development of
Sampler.
Introduction
------------
The SCALE nuclear analysis code system provides a unified set of
computational tools and data libraries to address a wide range of
applications, including criticality safety, reactor physics, spent fuel
characterization, burnup credit, national security, and neutron/photon
radiation shielding :cite:`SAMPLER-rwjmw_2011`. In addition to determining the problem
solutions, SCALE also provides tools to compute uncertainties in the
results, arising from uncertainties in the data used for the
calculations. Due to the diverse types of computational methods in
SCALE, robust sensitivity/uncertainty (S/U) methods are necessary.
Sampler implements stochastic sampling of uncertain parameters that can
be applied to any type of SCALE calculation, propagating uncertainties
throughout a computational sequence. Sampler treats uncertainties from
two sources: 1) nuclear data and 2) input parameters. Sampler generates
the uncertainty in any result generated by the computational sequence
through stochastic means by repeating numerous passes through the
computational sequence, each with a randomly perturbed sample of the
requested uncertain quantities. The mean value and uncertainty in each
parameter is reported along with the correlation in uncertain parameters
where multiple systems are simultaneously sampled with correlated
uncertainties.
Used in conjunction with nuclear data covariances available in SCALE,
Sampler is a general, overarching sequence for obtaining uncertainties
for many types of applications. SCALE includes covariances for
multigroup neutron cross-section data, as well as for fission product
yields and radioactive decay data, which allows uncertainty calculations
to be performed for most multigroup (MG) computational sequences in
SCALE. At the present time, nuclear data sampling cannot be applied to
SCALE continuous energy (CE) Monte Carlo calculations (i.e., CE-KENO and
CE-Monaco), although the fundamental approach is still valid.
Used in conjunction with uncertainties in input data, Sampler can
determine the uncertainties and correlations in computed results due to
uncertainties in dimensions, densities, distributions of material
compositions, temperatures, or many other quantities that are defined in
the user input for any SCALE computational sequence. This methodology
was especially developed to produce uncertainties and correlations in
criticality safety benchmark experiments, but it has a wide range of
applications in numerous scenarios in nuclear safety analysis and
design. The input sampling capabilities of Sampler also include a
parametric capability to determine the response of a system to a
systematic variation of an arbitrary number of input parameters.
Uncertainty analysis with stochastic versus perturbation methods
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Two quite different approaches may be used for uncertainty analysis. One
method uses first order perturbation theory expressions to compute
sensitivity coefficients for a given response. This requires performing
a forward transport calculation for the specified system and (sometimes)
adjoint calculations for each response of interest. After the forward
and adjoint transport solutions are obtained, sensitivity coefficients
for all nuclear cross sections and material concentrations can be
computed very efficiently with perturbation theory :cite:`SAMPLER-rwjmw_2011`. The
sensitivities may be folded with covariance matrices to obtain response
uncertainties due to nuclear data. The TSUNAMI modules and sequences in
SCALE use perturbation theory for S/U analysis in this manner (see
TSUNAMI-1D and TSUNAMI-3D).
For some types of applications, the adjoint-based perturbation
methodology is not adequate or is inefficient. These include:
(a) Cases requiring codes with no adjoint functionality. SCALE has
capability for critical eigenvalue adjoint solutions and generalized
adjoint calculations using XSDRN, NEWT or KENO, but adjoint methods
are not currently available for coupled neutronics-depletion
calculations.
(b) Cases for which first order perturbation theory is not valid
(i.e., problems with significant second order effects).
The Sampler module described in this section provides an alternative
method for uncertainty analysis based on stochastic sampling (Monte
Carlo) and does not require adjoint calculations. This approach samples
joint probability density functions (PDFs) –-- such as given in the SCALE
nuclear data covariance library --- to produce a random sample for the
nuclear cross sections used a transport calculation. If PDFs are
available for other parameters such as depletion data or model
parameters, etc., then these too can be sampled and included in the
perturbed input vector. The perturbed data vector can be input to any
SCALE sequence or functional module to obtain a single forward solution
for all desired perturbed responses. The process is repeated for the
desired number of samples-typically a few hundred; and the output
distributions of results are analyzed to obtain standard deviations and
correlation coefficients for all responses. The stochastic sampling
method is not restricted to current SCALE modules; any new sequences or
codes can be used for the forward calculations, without having to
develop the capability for adjoint calculations.
Output distributions from the SCALE sampling also may be propagated to
downstream codes for follow-on uncertainty analysis. For example, input
for the TRITON lattice physics sequence can be sampled to produce a
random set of output assembly-averaged, two-group cross section
libraries. The two-group libraries can be input to a 3D core simulator
that performs steady-state or transient calculations, and statistical
analysis of the simulator output provides response uncertainties
(possibly time-dependent) due to the SCALE input data uncertainties.
Response uncertainties computed with this approach are not limited to
first order accuracy; i.e., they account for all non-linearities and
discontinuities with the same accuracy as the original codes.
Thus there are several advantages to the statistical sampling method
because it requires only forward calculations. The typical Sampler
computational procedure perturbs the entire input data vector
simultaneously, so that the total uncertainty in all responses, due to
all data uncertainties, is obtained. This standard approach does not
provide individual data sensitivity coefficients, unlike the
perturbation theory method. In this sense, the statistical sampling
method is complementary to the adjoint-based sensitivity method in the
TSUNAMI modules. Computation of sensitivities using only forward
calculations requires that each input parameter be varied individually,
rather than collectively; and this may require a large number of
simulations to obtain a full set of sensitivity coefficients.
Methodology
-----------
The main components of a Sampler calculation are the procedures for
perturbing input data, obtaining the desired responses, and performing
statistical analysis of the output distributions.
Definition of input data perturbations
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The input data for a SCALE computation will generally be one of three
types:
(a) *Nuclear data for transport calculations*. This includes multigroup
(MG) and continuous energy (CE) cross sections, multiplicities,
secondary particle distributions, and data used for resonance
self-shielding of MG cross sections.
(b) *Nuclide transmutation data for depletion and burnup calculations*.
This includes fission product yield data, decay constants, branching
ratios to excited states, decay energies and distributions.
(c) *Modeling parameters for the system*. This includes information for
defining nuclide number densities (e.g., density, weight fractions,
enrichment, void fraction, etc.), temperature, and dimensions.
In principle Sampler can perform uncertainty analysis for all the above
types of input data if uncertainties and correlations are known. The
main restriction at this time is that CE cross sections for Monte Carlo
calculations are not sampled (although the continuous data used for
self-shielding *are* treated), so data perturbation applications are
limited to MG calculations. Perturbations to input number densities and
model dimensions are not impacted by this data limitation.
Nuclear data perturbations for multigroup calculations
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Input MG nuclear data for SCALE sequences are obtained from an AMPX
Master formatted library, which contains infinitely-dilute
one-dimensional (1D) cross sections, two-dimensional (2D) scattering
distributions, and Bondarenko self-shielding factors for various types
of reactions. Only the 1D data and Bondarenko factors are varied in
Sampler because no covariance data are available for the 2D scattering
distributions; however, the 2D data are renormalized to be consistent
the perturbed 1D scattering cross sections.
The Medusa module of the XSUSA program :cite:`SAMPLER-khk1994` is used to generate
perturbation factors for the 1D cross sections on the MG library,
assuming that the probability density functions are multivariate normal
distributions with covariances given in the SCALE nuclear data
covariance library. The library covariance data are given as
infinitely-dilute, relative values; therefore a random sample for cross
section :math:`\sigma_{\mathrm{x}, \mathrm{g}}` corresponds to
:math:`\frac{\Delta \sigma_{\mathrm{x}, \mathrm{g}}}{\sigma_{\mathrm{x}, \mathrm{g}}}`,
where subscript x defines the nuclide/reaction
type and g is the group number. The relative variations are transformed
to multiplicative perturbation factors, defined by
.. math::
:label: eq6-7-1
\mathrm{Q}_{\mathrm{x}, \mathrm{g}}=1+\frac{\Delta \sigma_{\mathrm{x}, \mathrm{g}}}{\sigma_{\mathrm{x}, \mathrm{g}}}
that can be applied to the reference data to obtain the altered
infinitely-dilute values. A master sample file containing perturbation
factors for 1000 samples (see note below) of the infinitely-dilute 1D data has been
pre-computed and stored in the SCALE data directory. Each sample in the
file contains perturbation factors for all groups and reactions in all
materials. The master sample file is used for all cases, which avoids
having to perform the data sampling during SCALE execution.
Because the 1D data in the MG library are infinitely-dilute (i.e.,
problem-independent), SCALE sequences include modules that compute
resonance shielding corrections for the MG data. The self-shielding
calculations generally require two additional types of input data: (a)
Bondarenko self-shielding factors for the BONAMI module, which typically
performs self-shielding calculations outside of the resolved resonance
range; and (b) CE cross sections for the CENTRM/PMC modules, which
compute pointwise (PW) flux spectra and process self-shielded cross
sections for the resolved resonance range. Perturbations in the
Bondarenko factors and CE cross sections used in self-shielding
calculations must be consistent with perturbations made to the
infinitely dilute 1D cross sections since all these data are based on
the same fundamental ENDF/B information. It was shown in reference :cite:`SAMPLER-SCALE_XSUSA`
that consistent perturbations can be obtained by using the same
perturbation factors :math:`Q_{x, g}` in following expressions:
(a) infinitely-dilute MG cross sections :math:`\sigma_{\mathrm{x}, \mathrm{g}}`:
.. math::
:label: eq6-7-2
\sigma_{\mathrm{x}, \mathrm{g}}^{\prime}=\mathrm{Q}_{\mathrm{x},
\mathrm{g}} \sigma_{\mathrm{x}, \mathrm{g}}
(b) Bondarenko factors :math:`\mathrm{f}\left(\sigma_{0}, \mathrm{~T}\right)`,
at background cross section :math:`\sigma_{0}` and temperature T:
.. math::
:label: eq6-7-3
\mathrm{f}_{\mathrm{x}, \mathrm{g}}^{\prime}\left(\sigma_{0},
\mathrm{~T}\right)=\mathrm{f}_{\mathrm{x},
\mathrm{g}}\left(\sigma_{0}^{\prime}, \mathrm{T}\right) ; \quad \text
{ where } \sigma_{0}^{\prime}=\sigma_{0} / \mathrm{Q}_{\mathrm{x},
\mathrm{g}}
(c) CE data :math:`\sigma_{\mathrm{x}}(\mathrm{E})`:
.. math::
:label: eq6-7-4
\sigma_{\mathrm{x}}^{\prime}(\mathrm{E})=\mathrm{Q}_{\mathrm{x},
\mathrm{g}} \sigma_{\mathrm{x}}(\mathrm{E}), \text { for } \mathrm{E}
\in \mathrm{g}
In the above expressions, subscript x defines the nuclide/reaction type and g is the group number.
During Sampler execution the module ClarolPlus reads perturbation factors (:math:`Q_{x, g}`)
for a specified sample number from the master sample file, and evaluates
Equations :eq:`eq6-7-2` and :eq:`eq6-7-3`. ClarolPlus also writes a file containing
perturbation factors only for the particular sample number used by the
CrawdadPlus module, as described below.
.. note:: The tradeoff of size on disk of the pre-calculated samples
distributed with SCALE versus the maximum number of perturbations required in
practice has led to the current maximum of 1000 samples. Based on limited
experience, correlation coefficients of near zero require the most samples to
converge and typically about 1000 samples has been sufficient.
Depletion data perturbations
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Multiplicative perturbation factors for fission product yields have
been generated with XSUSA by sampling the covariances for the
independent yield uncertainties. The yield uncertainties are taken
from ENDF/B VII.1, which in general are given by fissionable nuclide and
for up to three energies: 0.025 eV, 0.5 MeV, and 14 MeV. The ENDF/B
yield uncertainties do not include correlations between fission
products, which may arise due to constraints such as (a) the sum of
all yields must always be two (i.e., the uncertainty in the yield sum
is zero), and (b) the uncertainties in independent yields should be
consistent with uncertainties given for cumulative yields. The
constraints generally introduce positive and negative correlations
into the yields covariance matrix. A method developed by Pigni :cite:`SAMPLER-pifrga2015`
was used to determine the correlations in :sup:`235`\ U yields.
Correlations in yields from other fissionable nuclides are not
available in SCALE at this time.
During Sampler execution the perturbation factors are read for a given
data sample, compute a complete set of perturbed independent yields for
all fissionable nuclides and energies, and renormalize the yields to
ensure that they sum to two. An output file containing the perturbed
yield data is written to an external file in the format read by ORIGEN.
The perturbation factors are read once each time a sequence executed
(i.e., for each data sample).
A set of 1,000 decay data perturbations has also been generated with
XSUSA and stored in decay-only ORIGEN library files. Sampler
automatically aliases the appropriate sample to the file "end7dec".
.. note:: In order for decay data perturbations to be performed, the
"end7dec" decay library must be used **directly**. Typical TRITON and
Polaris calculations **do not use "**\ end7dec" directly, due to using
the unperturbed decay data embedded in a special ORIGEN reaction library
aliased to "transition.def" as the basis for all coupled
transport/depletion calculations. Experience has been that decay data
contributes very little additional uncertainty compared to yield data
and cross section data.
Model data perturbations
~~~~~~~~~~~~~~~~~~~~~~~~
An approach presented by Areva NP GmbH utilizes statistical sampling on
uncertain parameters to assess the uncertainty in individual system as
well as correlations between multiple systems :cite:`SAMPLER-bhns2010`. In this approach,
values for individual parameters in the input model are randomly
modified within the reported uncertainty and distribution function and a
series of perturbed values are obtained. Where sufficient samples are
made, the distribution of the perturbed values is used to determine the
uncertainty in the computed quantity due to uncertainties in the input
parameters. In cases where the same uncertain parameters influence
multiple experiments the simultaneous perturbation of the parameter for
multiple cases will provide the correlation in uncertainties between the
different configurations.
To obtain the uncertainty and correlation due to all uncertain
parameters, all parameters are randomly perturbed for each calculation
and the uncertainties and correlations are determined. Mathematically,
the uncertainty in an individual output parameter *k* is determined as
shown in Eq. :eq:`eq6-7-5`.
.. math::
:label: eq6-7-5
\Delta k^{\exp }(i)=\hat{\mu}_{i}=\sqrt{\frac{1}{n-1}
\sum_{a=1}^{n}\left(\left(k_{c a l c}^{M
C}(i)\right)_{a}-\overline{k_{\text {calc}}^{M C}(i)}\right)^{2}} ,
where :math:`\Delta k^{\exp }(i)` is the uncertainty (in terms of standard deviation) in
system *i* due to uncertainties in the input parameters. :math:`\left(k_{c a l c}^{M C}(i)\right)_{a}` is
the *a*\ :sup:`th` Monte Carlo (MC) sample of system *i*, where all uncertain
input parameters have been randomly varied within the specified
distribution.
The covariance between two systems, *i* and *j*, is determined as shown
in Eq. :eq:`eq6-7-6`.
.. math::
:label: eq6-7-6
\hat{\Sigma}_{i j}=\sqrt{\frac{1}{n-1}
\sum_{a=1}^{n}\left(\left(k_{\text {calc}}^{M
C}(i)\right)_{a}-\overline{k_{\text {calc}}^{M
C}(i)}\right)\left(\left(k_{\text {calc}}^{M
C}(j)\right)_{a}-\overline{k_{\text {calc}}^{M C}(j)}\right)} .
The correlation coefficient between systems i and j can be determined from Eqs.
:eq:`eq6-7-5` and :eq:`eq6-7-6` as shown in Eq. :eq:`eq6-7-7`.
.. math::
:label: eq6-7-7
c_{i j}=\frac{\hat{\Sigma}_{i j}}{\hat{\mu}_{i} \hat{\mu}_{j}} .
The correlation coefficients determined with Eq. :eq:`eq6-7-7` are the values needed
to perform the Generalized Least Linear Square (GLLS) analysis using TSURFER,
which solves for a set of cross section data perturbations that would improve
agreement between the computational simulations and experimental benchmark
results. The correlation coefficients can be shown to be analogous to
sensitivity/sensitivity coefficients (i.e., c\:sub:`k`) calculated by
SAMS :cite:`SAMPLER-HMA-2020`.
.. _sec-sampler.r2:
Importance Ranking :math:`R^2` Methodology
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Sampler allows the analysis of the impact of cross section uncertainties
on any output quantity of a reactor physics calculation. However,
identification of top contributing nuclide reactions to this
uncertainty, requires a more detailed analysis. Such rankings can be
used for recommendations for additional measurements and evaluations of
nuclear data can be made.
A ranking of important nuclide reactions to the uncertainty of response
:math:`y` can be obtained by the determination of the squared multiple
correlation coefficient :math:`R^2` :cite:`SAMPLER-BWAW-2022`. All the
cross sections of all nuclides that are relevant for the model of
interest are divided into group A, the nuclide reaction of interest, and
group B, all other nuclide reactions. Then :math:`R^2` is calculated as
follows:
.. math:: :label: eq6-7-8
R^2_{y,A}=\bar{\rho}_{\bar{\sigma}_{A},y} \cdot
\bar{\bar{\rho}}_{\bar{\sigma}_{A},\bar{\sigma}_{A}} \cdot
\bar{\rho}^t_{\bar{\sigma}_{A},y}
:math:`\bar{\rho}_{\bar{\sigma}_{A},y}:` vector of correlation
coefficients between sampled input parameters of group A and response
:math:`y`
:math:`\bar{\bar{\rho}}_{\bar{\sigma}_{A},\bar{\sigma}_{A}}:` sample
correlation matrix between input parameters of group :math:`A`
:math:`R^2` values are between 0 and 1. It is important to note that
:math:`\bar{\bar{\rho}}` is a matrix consisting of correlation
coefficients between the input parameters. It is not to be confused with
a correlation matrix derived from the original covariance matrix used
for sampling the parameters. However, if the sample size approaches
infinity, then the sample correlation matrix converges toward the
correlation matrix that can be derived from the original covariance
matrix and that is used for sampling the cross sections.
:math:`R^2` can be interpreted as the expected amount by which the total
output variance would be reduced in case the true values of the input
parameter group A would become known. The sample size for the
determination of :math:`R^2` must be larger than the number of
independently sampled input cross sections in group A.
Since :math:`R^2` is determined based on a statistical approach, they
are provided with a statistical error estimate. Both values are
accompanied with a 95% confidence interval. The :math:`R^2` values are
additionally provided with a 95% significance level; only values above
this level are considered statistically significant.
Input Description
-----------------
This section describes the Sampler input file format.
Overall input structure
~~~~~~~~~~~~~~~~~~~~~~~
The order of the blocks is arbitrary, with the exception of dependent
variables (see :numref:`6-7-3-7-3`. Below is the layout of a typical
sampler input.
.. code-block:: scale
=sampler
read parameters
(control flags)
end parameters
read parametric
(parametric studies definitions)
end parametric
read case[casename]
sequence=(sequence name)
(sequence input)
end sequence
... (more sequences) ...
read variable[id1]
(variable definition)
end variable
... (more variables) ...
read response[name1]
(response definition)
end response
... (more responses) ...
end case
... (more cases) ...
read analysis[name1]
(analysis definition)
end analysis
... (more analysis) ...
read save
(file save definition)
end save
... (more saves) ...
end
Every Sampler input file has to contain the parameters block and at least one
case block. Other input blocks are optional.
.. _6-7-3-2:
Cases and sequences
^^^^^^^^^^^^^^^^^^^
Within Sampler, multiple independent SCALE calculations, or *cases*, can
be included. Since the same set of responses is extracted from each of
the cases, these should have the same structure (i.e. produce the same
kind of output files); the benefit of having multiple cases within one
Sampler input deck is that it is possible to generate cross-correlations
between cases as an output.
Every *case* contains one or more stacked *sequences*. The whole case is
always run together.
Each case has an unique *identifier*. The identifier is a single word
beginning with a letter followed by letters, numbers and underscores.
Note that the dash "-" cannot be used in a case identifier.
Within the case block, the user can enter any number of sequences, which
contain the actual user input. The format of each sequence block is:
::
sequence=(sequence name) (optional parm= setting)
(sequence data)
end sequence
The sequence data is a SCALE input that is not processed by Sampler,
except to substitute sampled values for variable placeholders (see :numref:`6-7-3-7-4`
for more information). For ``parm=`` settings, no limit on column
number is enforced.
Importing input data from external files
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Instead of directly specifying the SCALE sequence input within the Sampler input
file, the user can specify the path to a previously generated input file which
can be imported for use within Sampler as:
.. code-block:: scale
read case[c1]
import = "/home/usr/sampler_samples/sampler_1x_case.inp"
end case
In this case, absolute paths should be used (or a ``shell`` sequence before invoking
Sampler, to copy the appropriate files into the temporary directory). This
approach provides concise input files and is advantageous for quality assurance
controlled input data.
Configuration parameters
~~~~~~~~~~~~~~~~~~~~~~~~
In the parameters block the user can control the main workflow and
output parameters for sampler. Valid keywords are shown in :numref:`tab6-7-1`.
.. important:: Note that of the major perturbation modes, only "perturb_geometry=yes"
is on by default. (Bondarenko factor and pointwise data perturbation for
CENTRM controls how "perturb_xs=yes" is performed.)
.. tabularcolumns:: |p{5cm}|p{7cm}|p{3cm}|
.. table:: Parameter input for Sampler.
:name: tab6-7-1
:align: center
:class: longtable
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| KEYWORD | DESCRIPTION | DEFAULT |
+=================================+=======================================================================================================+==============+
| ``n_samples=N`` | Number of samples (1--1000 for nuclear data | none |
| | perturbations, unlimited for input file perturbations) | |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``first_sample=N`` | Number of the first sample | 1 |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``perturb_geometry=(yes/no)`` | Perform input file/model data/geometry perturbations | yes |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``perturb_xs=(yes/no)`` | Perform cross-section (XS) perturbation | no |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``perturb_yields=(yes/no)`` | Perform fission yield perturbation | no |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``perturb_decay=(yes/no)`` | Perform decay data perturbation | *no* |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``perturb_bondarenko=(yes/no)`` | When perturbing XS, perturb Bondarenko factors | yes |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``perturb_pointwise=(yes/no)`` | When perturbing XS, perturb pointwise data | yes |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``perturb_kinetics=(yes/no)`` | When perturbing XS, perturb decay constants of delayed neutron groups | no |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``library=â€..â€`` | Name of the master XS library (in quotes), it is | none |
| | possible to use the filename or an alias (e.g. “ v7.1-252nâ€) | |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``perturbed_library=â€..â€`` | Name of the perturbed library (in quotes); this is the perturbed XS library used by the actual | (same as |
| | computational sequences | ``library``) |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``mg_factors_library=â€..â€`` | Name of the multigroup XS perturbation factors | (blank) |
| | library (in quotes); if not given, built-in library is used | |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``coverx_library=".."`` | Name of the covariance library (in quotes); this is the covariance library, that was used to | 56groupcov7.1|
| | generate the samples, and required for :math:`R^2` analysis | |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``run_cases=(yes/no)`` | Actually run inputs through SCALERTE or just generates them. | yes |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``force_run=(yes/no)`` | Enforce running SCALE even when the output | no |
| | files are present | |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``plt=(yes/no)`` | Produce plot file histograms (PTP format) with response distributions that can be viewed with Fulcrum | yes |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``csv=(yes/no)`` | Produce CSV files with individual tables | yes |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``print_data=(yes/no)`` | Print per-sample values in the main output | no |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
| ``print_chi2=(yes/no)`` | Print chi-square normality test in the main output | no |
+---------------------------------+-------------------------------------------------------------------------------------------------------+--------------+
**Notes on sample numbers:**
The samples are selected from the perturbation factor libraries (except
for geometry perturbation); it is up to the user to fit inside the range
of samples available (i.e. n_samples+first_sample-1 must be less or
equal to the number of samples). The built-in perturbation libraries
based nuclear data covariances contain 1000 samples.
**Note on perturbed library name:**
The default behavior for Sampler is to set ``perturbed_library`` to the same
name as ``library``. Since Sampler creates a local file in the temporary
directory, which is used by SCALE instead of the library in the lookup
table, it in general results in the desired behavior. SCALE sequences
only provide pre-defined resonance self-shielding options for known
libraries, so where ``perturbed_library`` differs from the name of a
standard SCALE library, the type of resonance self-shielding calculation
desired must be specified (via the *PARM=* setting). Please review the
documentation of the specified sequence for available options, such as
*PARM=CENTRM*.
.. warning:: The library name must result in a valid filename. In some
cases the use of "``xn252``" instead of "``v7.1-252``" is recommended
because the dash might result in improper links to the perturbed
library. This guidance applies only to the cases when ``perturb_xs=yes`` is
used; otherwise, Sampler does not generate a perturbed library.
Sampler responses
~~~~~~~~~~~~~~~~~
For every case run within Sampler any number of responses can be
extracted. A response can be a single number or a time-dependent series,
which is assigned a name and optionally several parameters. The
responses can be entered entered once and shared across all selected cases, i.e. every
selected case returns the same set of responses or can be entered inside a case block and only returned for that case.
Sampler recognizes these kinds of responses:
- ``opus_plt`` – data from an OPUS-generated PLT file
- ``triton`` - TRITON homogenized cross-sections (xfile016)
- ``stdcmp`` – standard composition files
- ``f71`` – concentrations from the F71 ORIGEN dump
- ``grep`` – general expression from the text output file
- ``variables`` – the geometry perturbation sampled values
The general format of the response block is:
::
read response[(response id)]
type = (response type)
(response parameters)
cases = (case list) end
end response
The *(response id)* is an arbitrary identifier (a single word) by which
the the response is denoted in the results. The *(response type)* is one
of the keywords ``opus_plt``, ``triton``, ``stdcmp``, ``f71``, variables and ``grep``.
Response parameters are different for each response type and are
explained in :numref:`6-7-3-4-1` through :numref:`6-7-3-4-6` . The ``cases=`` specification applies only to the response defined at the global scope.
The response block can be placed either:
a) inside a case block. This response is collected only to this particular case.
In the following example, response ``x`` is only collected for the case ``c1`` and the
response ``y`` is collected for the case ``c2``.
.. code-block:: scale
read case[c1]
sequence=...
...
end sequence
read response[x]
...
end response
end case
read case[c2]
sequence=...
...
end sequence
read response[y]
...
end response
end case
b) at the global scope. The ``cases=... end`` has to be used to specify the
cases for which this response is collected.
In this example, response ``x`` is collected for the both cases ``c1`` and ``c2`` and the response
``y`` is only collected the case ``c1``. Since no ``cases=`` entry is provided, the response ``z`` is collected for all cases.
.. code-block:: scale
read case[c1]
sequence=...
...
end sequence
end case
read case[c2]
sequence=...
...
end sequence
end case
read response[x]
...
cases = c1 c2 end
end response
read response[y]
...
cases = c1 end
end response
read response[z]
...
end response
.. _6-7-3-4-1:
OPUS PLT file responses
^^^^^^^^^^^^^^^^^^^^^^^
This response extracts any data from a PLT file generated by OPUS. The
user specifies which PLT file should be used and which elements/nuclides
should be used.
Parameter ``ndataset`` provides the number of the selected PLT file, i.e.
``ndataset=1`` will read data from the file ending with
.00000000000000001.plt (which is the second generated PLT file in the
given case).
Parameter ``nuclides=…end`` specifies the list of nuclides (or elements)
which are read from the PLT file; nuclides can be specified as
alphanumeric identifiers (U-235, ba137m) or six-digit ZAI identifiers
(922350). In addition to that, any other PLT file response identifiers
(i.e. the character strings in the first column of the plot table) may
be used, which allows for example the usage of ``total`` and ``subtotal``
keywords.
**Example**
::
read response[fisrates]
type = opus_plt
ndataset = 1
nuclides = u238 pu239 total end
end response
TRITON homogenized cross-section responses
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
This response extracts the homogenized cross-section data saved by
TRITON on the ``xfile016``.
Responses are retrieved for a selected homogenized mixture and all
branches (which are then denoted by response name suffixes).
Using a ``data= … end`` assignment specifies which data types are to be
saved.
The available options for data entries are:
.. code-block:: none
kinf sigma_total sigma_fission sigma_absorption
sigma_capture sigma_transport_out sigma_transport_in
sigma_transport sigma_elastic sigma_n2n nu_fission
kappa_fission nu chi flux diffusion
**Example**:
::
read response[xs]
type = triton
mixture = 1
data = kinf sigma_absorption end
end response
Standard composition file responses
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
This response retrieves isotopic concentrations (in atoms/barn-cm) from
the standard composition file. Parameter ``nuclides=…end`` specifies which
nuclides should be retrieved. The parameter mixture specifies the number
of the StdCmpMix file, so ``mixture=10`` would load concentrations from the
file ``StdCmpMix00010_*`` (for all time steps).
**Example:**
::
read response[mix10]
nuclides = u-235 pu-239 end
mixture = 10
end response
ORIGEN concentration (F71) responses
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
This response retrieves the isotopic concentrations (in gram-atoms) from
the ORIGEN concentration edit in the ``ft71f001`` file.
Parameter ``nuclides=…end`` specifies the list of nuclides (or elements)
which are read from the F71 file; nuclides can be specified as
alphanumeric identifiers (U-235, ba137m) or six-digit ZAI identifiers
(922350).
Two options are available to choose the positions on the file from which data
should be retrieved. Either ``step_from=start`` and ``step_to=end`` can be used to
select a range of positions, or ``mixture=N`` can be used to choose either an
ORIGEN case or a TRITON case mixture. This is convenient for TRITON cases where
step numbers are usually not known in advance.
**Example:**
::
read response[concentrations]
type=origen_nuclides
nuclides = u-235 pu-239 pu-240 pu-241 end
mixture = 10
end response
Generic regular expression (GREP) responses
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
In order to allow the user to collect other responses from the SCALE
output, a generic regular expression (regexp) mechanism is provided by
Sampler. For every response the user can enter one (or more) regular
expressions, which are applied (using the "grep" system tool) to the
main output file. "grep" is executed with the "-o" option, which returns
only the matched portion of the line (and not the whole line). Usually
it is necessary to use two expressions, one to find the line of interest
and another to extract only the desired value. The POSIX character
classes are supported in the grep used-the most commonly used are
"[[:digit:]]" to match a single digit 0-9 and [[:space:]] to match a
single space or tab. The "+" and "*" are used to match one or more and
zero or more repeats, respectively. Note that as per standard regexp
rules, "." matches any character and an escape is necessary, i.e. "\.",
in order to match a period.
Each regular expression is defined by the keyword ``regexp=``"…". The result
of the last regular expressions should be a single number (and is
treated as such by Sampler).
The following example defines regular expression for extraction of
k-effective from a CSAS5/6 output file:
::
read response[keff]
type = grep
regexp = "best estimate system k-eff[[:space:]]+[[:digit:]]+\.[[:digit:]]+"
regexp = "[[:digit:]]+\.[[:digit:]]+"
end response
With the first ``regexp`` statement, a line containing "best estimate system
k-eff" followed by a number is found, and then just the number part is
extracted with the second ``regexp`` statement.
For ease of use, Sampler provides several regular expression shortcuts
shown in :numref:`tab6-7-2`.
.. table:: Regular expression shortcuts for SCALE sequences.
:align: center
:name: tab6-7-2
+------------------------+---------------------------------------------------------+
| ``regexp`` | keff from KENO5 / CSAS5 sequence |
| = "``:kenova.keff:``" | |
+------------------------+---------------------------------------------------------+
| ``regexp`` | EALF from KENO5 / CSAS5 sequence |
| = "``:kenova.ealf:``" | |
+------------------------+---------------------------------------------------------+
| ``regexp`` | nu-bar from KENO5 / CSAS5 sequence |
| = "``:kenova.nubar:``" | |
+------------------------+---------------------------------------------------------+
| ``regexp`` | keff from KENO6 / CSAS6 sequence |
| = "``:kenovi.keff:``" | |
+------------------------+---------------------------------------------------------+
| ``regexp`` | lambda from XSDRN / CSAS1 sequence |
| = "``:xsdrn.lambda:``" | |
+------------------------+---------------------------------------------------------+
| ``regexp`` | matches any number (e.g. "1", "1.0", "1.23e-7", "-0.3") |
| = "``:scale.number:``" | |
+------------------------+---------------------------------------------------------+
Thus, the previous example may be alternately rephrased as such:
::
read response[keff]
type = grep
regexp = ":kenova.keff:"
end response
In addition to this, the ``grep`` response also supports extraction of data
with uncertainties. In order to get the response uncertainty, use the
``eregexp=`` keyword, which follows the same rules as ``regexp=``. The same
shortcuts as for ``regexp=`` may be used as well (for KENO V.a/VI
multiplication coefficient). Therefore, to get KENO multiplication
factor including the uncertainty, one might define the response like
this:
::
read response[keff]
type = grep
regexp = ":kenova.keff:"
eregexp = ":kenova.keff:"
end response
.. _6-7-3-4-6:
Sampled variable values
^^^^^^^^^^^^^^^^^^^^^^^
Using the ``variables`` response, the user can extract information from the
sampled values of the geometry/material perturbation variables. The
``data=`` key contains the list of variable identifiers of interest.
This option is useful to generate the correlations between
geometry/material perturbations and the responses of interest.
**Example:**
::
read variable[r1]
...
end variable
read response[r]
type=variables
data = r1 end
end response
Quick response definition overview
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
:numref:`tab6-7-3` summarizes the available options for the different response
types. The nuclides specification can either be in terms of the standard
alphanumeric identifier, e.g. "u235m" for :sup:`235m`\ U, or the IZZZAAA
integer identifier, e.g. "1092235" for :sup:`235m`\ U.
.. table:: Response definition overview.
:align: center
:name: tab6-7-3
+---------------+------------------------------------------------------------+
| **Key** | **Description** |
+===============+============================================================+
| response type ``opus_plt`` |
+---------------+------------------------------------------------------------+
| Ndataset | Number of the PTP file |
+---------------+------------------------------------------------------------+
| Nuclides | List of nuclides (alphanumeric/IZZZAAA, terminated by end) |
+---------------+------------------------------------------------------------+
| response type ``stdcmp`` |
+---------------+------------------------------------------------------------+
| ``Mixture`` | Number of the StdCmpMix file |
+---------------+------------------------------------------------------------+
| ``Nuclides`` | List of nuclides (alphanumeric/IZZZAAA, terminated by end) |
+---------------+------------------------------------------------------------+
| response type ``triton`` |
+---------------+------------------------------------------------------------+
| Mixture | Homogenized mixture index |
+---------------+------------------------------------------------------------+
| ``Nuclides`` | List of nuclides (alphanumeric/IZZZAAA, terminated by end) |
+---------------+------------------------------------------------------------+
| ``Data`` | List of homogenized data types (terminated by end) |
+---------------+------------------------------------------------------------+
| response type ``f71`` |
+---------------+------------------------------------------------------------+
| ``Nuclides`` | List of nuclides (alphanumeric/IZZZAAA, terminated by end) |
+---------------+------------------------------------------------------------+
| ``Mixture`` | ORIGEN case number / TRITON mixture number |
+---------------+------------------------------------------------------------+
| ``step_from`` | Lower bound of position range |
+---------------+------------------------------------------------------------+
| ``step_to`` | Upper bound |
+---------------+------------------------------------------------------------+
| response type ``grep`` |
+---------------+------------------------------------------------------------+
| ``regexp`` | Regular expression for the response value (quoted) |
+---------------+------------------------------------------------------------+
| ``eregexp`` | Regular expression for the response uncertainty (quoted) |
+---------------+------------------------------------------------------------+
| response type ``variables`` |
+---------------+------------------------------------------------------------+
| ``data`` | List of variable names (terminated by end) |
+---------------+------------------------------------------------------------+
Saving files
~~~~~~~~~~~~
By default, Sampler saves from each run the input, output, message and
terminal log files. In addition to that, if respective responses are
requested, it saves the ``ft71f001`` as basename\ ``.f71``, x``file016`` as
basename\ ``.x16`` and the ``StdCmpMix*`` files.
The user might specify additional files to be saved into the sample
subdirectory; this is achieved by defining one or more ``save`` blocks.
Each save block contains a ``file="…"`` parameter, which specifies the
filename in the sample run temporary directory. Optionally, the user can
specify ``name="…"`` to let Sampler rename the file to
*basename*.\ *extension*, where *extension* is the value of the ``name``
parameter. If ``name`` is not specified, the file is not renamed and is just
copied to the sample subdirectory. The ``name`` parameter cannot be used if
wildcards are used in the ``file`` parameter.
The quotes for both ``name`` and ``file`` parameter values are mandatory.
**Example 1**:
.. code-block:: scale
read save
name = "ft2"
file = "ft71f002"
end save
**Example 2**:
.. code-block:: scale
read save
file = "StdCmpMix*"
end save
Parametric studies
~~~~~~~~~~~~~~~~~~
The Sampler infrastructure allows an efficient implementation of studies
of parameter variation effects on various responses. This mode is
activated by entering the ``read parametric … end parametric`` block.
This block contains two arrays: ``variables = … end`` and ``n_samples = … end``.
The variables array lists the variables of the parametric study. The
variables must have "``distribution=uniform``", and the minimum and maximum
becomes the range for that variable in the parametric study. For each
variable, the corresponding value in the ``n_samples`` = ``… end`` array
indicates the number of evenly spaced values to assume *in that
dimension.* The total number of calculations is therefore the
multiplication of all the ``n_samples`` values. Note that for a single
sample with ``n_samples=1``, only the minimum value is used. Below is as an
example of the parametric block.
.. code-block:: scale
read parametric
variables = density temperature end
n_samples = 10 6 end
end parametric
The two variables are ``density ``and ``temperature``, and there will be 10
evenly spaced density values (including the minimum and maximum) and 6
evenly spaced temperature values, for a total of
:math:`10 \times 6 = 60` calculations. To perform the same number of
samples in each dimension, the keyword ``n_samples`` in the parameters block
may also be used.
Sampler generates a summary table of the parametric study, including
values for which the minimum and maximum of each response occurs.
Sampler also generates PTP plot files showing the dependency of each
response on each variable.
Geometry and material perturbations
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In addition to data perturbations, Sampler also allows the user to
include geometry and material uncertainties in the calculation. This is
achieved by defining ``variable`` blocks. Each variable may be linked to a
particular value in the input and is associated either with a random
variable distribution or with an arithmetic expression. The expression
capability allows for dependent or derived parameters, such as
:sup:`238`\ U content depending on enrichment or outer clad radius
depending on the inner radius.
For each sample, Sampler creates a perturbed input by generating a set
of variable values and substituting them into the input. For every
variable, the user has to define the variable and specify its
distribution (using one of the predefined random variable distributions
described in :numref:`6-7-3-2`) or its dependence on other variables (using an
arithmetic expression). If desired, the user can also specify which part
of the input will be replaced by the variable. This can be achieved
either by specifying a SCALE Input Retrieval ENgine (SIREN) expression
or by putting placeholders directly inside the input deck (see Appendix
A for details on SIREN).
Variable definition
^^^^^^^^^^^^^^^^^^^
Variables are defined by a ``read variable..end variable`` block. The general format of the block is:
.. code-block:: scale
read variable[(variable id)]
distribution = (distribution type)
siren = "(siren expression)"
(distribution-specific parameters)
cases = (case list) end
end variable
The variable id is an arbitrary, single word consisting of letters,
numbers and underscores (with number not being the first character). The
variable id has to be unique and is case dependent. ``distribution`` is one
of the distribution-type keywords (see :numref:`6-7-3-7-2`) or ``expression`` for
the dependent variable definition. The ``cases=`` specification applies only
to the variables defined at the global scope (see below). The ``siren=``
specification is optional, see below.
The block can be placed either:
a) inside a case block. This variable applies only to this particular case.
In the following example, variable ``x`` applies to the case ``c1`` and the
variable ``y`` applies to the case ``c2``.
.. code-block:: scale
read case[c1]
sequence=...
...
end sequence
read variable[x]
...
end variable
end case
read case[c2]
sequence=...
...
end sequence
read variable[y]
...
end variable
end case
b) at the global scope. The ``cases=... end`` has to be used to specify the
cases to which this variable applies.
In this example, variable ``x`` applies to the both cases ``c1`` and ``c2`` and the variable
``y`` applies only to the case ``c1``.
.. code-block:: scale
read case[c1]
sequence=...
...
end sequence
end case
read case[c2]
sequence=...
...
end sequence
end case
read variable[x]
...
cases = c1 c2 end
end variable
read variable[y]
...
cases = c1 end
end variable
.. _6-7-3-7-2:
Distribution types
^^^^^^^^^^^^^^^^^^
Sampler supports three random ``distribution`` types, selected using the
distribution= keyword.
1) ``uniform``: uniform distribution over a (closed) interval.
Additional parameters for a uniform distribution are shown in :numref:`tab6-7-4`.
.. table:: Parameters for uniform distributions.
:align: center
:widths: auto
:name: tab6-7-4
+-------------+--------------------------+----------+
| **KEYWORD** | **DESCRIPTION** | **NOTE** |
+=============+==========================+==========+
| minimum= | Lower bound value | required |
+-------------+--------------------------+----------+
| maximum= | Upper bound value | required |
+-------------+--------------------------+----------+
**Example**:
.. code-block:: scale
read variable[rfuel]
distribution=uniform
minimum = 0.40
value = 0.41
maximum = 0.42
end variable
2) ``normal``: normal (optionally truncated) distribution.
Additional parameters for normal distribution are shown in :numref:`tab6-7-5`.
.. table:: Parameters for normal distributions.
:align: center
:name: tab6-7-5
+-------------+--------------------+----------+
| **KEYWORD** | **DESCRIPTION** | **NOTE** |
+=============+====================+==========+
| value= | Mean value | required |
+-------------+--------------------+----------+
| stddev= | Standard deviation | required |
+-------------+--------------------+----------+
| minimum= | Lower cutoff value | optional |
+-------------+--------------------+----------+
| maximum= | Upper cutoff value | optional |
+-------------+--------------------+----------+
The user can specify both ``minimum`` and ``maximum``, one of them, or neither. If a
cutoff is not specified, the distribution is not truncated on that side.
**Example**:
.. code-block:: scale
read variable[c1_u235]
distribution=normal
value=95.0
stddev=0.05
end variable
3) ``beta``: beta distribution.
Additional parameters for the beta distribution are shown in :numref:`tab6-7-6`.
.. table:: Parameters for beta distributions.
:align: center
:name: tab6-7-6
+-------------+-----------------------------------+----------+
| **KEYWORD** | **DESCRIPTION** | **NOTE** |
+=============+===================================+==========+
| minimum= | Lower cutoff value | required |
+-------------+-----------------------------------+----------+
| maximum= | Upper cutoff value | required |
+-------------+-----------------------------------+----------+
| beta_a= | First parameter for distribution | required |
+-------------+-----------------------------------+----------+
| beta_b= | Second parameter for distribution | required |
+-------------+-----------------------------------+----------+
The Beta distribution is defined in the standard way given by Eq.
:eq:`eq6-7-9`. The parameters for the distribution determine where the peak is
located in the interval [``minimum``, ``maximum``] and the variance of the
distribution; the parameters :math:`\alpha` and :math:`\beta` are required to be integer values.
.. math::
:label: eq6-7-9
f(x ; \alpha, \beta)=\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha) \Gamma(\beta)} x^{\alpha-1}(1-x)^{\beta-1} ,
**Example**:
.. code-block:: scale
read variable[rclad]
distribution=beta
value=0.47
minimum=0.45
maximum=0.50
beta_a=2
beta_b=6
end variable
.. _6-7-3-7-3:
Dependent variables (expressions)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Using ``distribution=expression`` allows the user to specify a variable
using the values of other variables. Setting ``expression=``\ "(expression)"
then specifies how to evaluate the variable. Sampler supports basic
arithmetic operators and other variables can be used as well. However,
Sampler currently provides no variable dependency resolution and
therefore only variables that were defined (using the variable block)
previously in the input deck can be referenced in an expression.
**Example**:
.. code-block:: scale
read variable[c1_u238]
distribution = expression
expression="100.0-c1_u235"
end variable
.. _6-7-3-7-4:
Using placeholders
^^^^^^^^^^^^^^^^^^
Inside the ``sequence=`` blocks, a #{*variable id*} placeholder can be used.
This will be replaced by a variable value when Sampler builds the
particular input deck. Only a simple variable reference can be used; no
expressions are allowed here.
**Example**:
.. code-block:: scale
sequence=csas5
...
uranium 1 den=18.76 1 300 92235 #{u235} 92238 #{u238} end
...
end sequence
read variable[u235]
...
end variable
read variable[u238]
...
end variable
In the input deck snippet the :sup:`235`\ U and :sup:`238`\ U content
are inserted directly to the respective places (defined by variables
u235 and u238).
Using placeholders is straightforward and simple; however, if for input
deck quality assurance or other reasons it is not desirable to modify
the input deck directly, SIREN expressions can be used.
Using SIREN expressions
^^^^^^^^^^^^^^^^^^^^^^^
SIREN is a package which provides an XPath-like interface to the SCALE
input deck represented by a Document Object Model (DOM). In Sampler, the
user can specify ``siren=``"*path*" to have the respective token(s) replaced
by a variable value.
Please refer to Appendix A for more details on specifying the SIREN path
expressions.
**Example:**
.. code-block:: scale
read variable[c1_u235]
distribution=normal
value=95.0
stddev=0.05
siren="/csas5/comps/stdcomp[decl=’uranium’]/wtpt_pair[id='92235']/wtpt"
end variable
The variable ``c1_u235`` value is inserted as the weight percent of
:sup:`235`\ U in the basic standard composition declared as "uranium" in
the CSAS5 sequence.
.. _sec-sampler.analysis:
Response analysis
~~~~~~~~~~~~~~~~~
Sampler provides several statistical post processing options to analyze
results of propagated uncertainties. Variations in a user selected response,
mutual variations between two different responses with respect to perturbed
data can provide insight to dependecy to input data or any correlation
between responses.
The general format of the analysis block is:
::
read analysis[(analysis id)]
type = (analysis type)
targets = (list of target responses) end
sources = (list of source responses or nuclides) end
end analysis
The analysis block mainly provides three input fields: target response,
source response, and analysis type. Both the target and source responses
can be a list of responses. The calculation of the selected analysis type
is performed between the source and target response lists.
Sampler reconizes the following analysis types:
- ``pearson_corr`` - pearson correlation coefficient (similarity index)
calculation between each response in the sources response list and the
target response list
- ``covariances`` - covariance calculation between each response in the
sources response list and the target response list
- ``correlation_matrix`` - pearson correlation coefficient calculation
between responses in the sources response list (target responses are
ignored for this type)
- ``covariance_matrix`` - covariance calculation between responses in
the sources response list (target responses are ignored for this type)
- ``r2`` - sensitivity indices :math:`R^2` are calculated for responses
in the target response list for the isotopes listed in the sources
response list
Responses in target and sources lists are specified using the CASE:RESPONSE.SUB(INSTANCE) notation
where
- ``CASE`` : User-selected Sampler case name in the case block from
which the response is collected.
- ``RESPONSE`` : Response name in the response block
- ``SUB`` : Sub-response listed in the specified response block, such as
isotope names in origen or opus response types. If the response type has
no sub-response (e.g., in the case of a grep response), then it is not
used.
- ``INSTANCE`` : Index of occurrence in the collected response, such as
the depletion step index for a burnup dependent response, or the line
number in which the selected response occurs in the case of grep type
responses. Note that the instance counting starts with 0 in case of grep
responses. A missing index field is interpreted as if the response is
requested for index=0. In addtion to integer indexes the following
special keywords are also accepted
- last : the last occurence
- all : all occurences. This keyword populates the requested sub
response for all occurence indices. For
example, case:response.sub(all) is the same as case:response.sub(0)
case:response.sub(1) ... case:response.sub(last)
The following input example calculates the similarity indices between
:sup:`235`\ U concentration at the 15th time step in the MOX depletion
model with :sup:`235`\ U, :sup:`239`\ Pu , :sup:`243`\ Am, and
:sup:`109`\ Ag concentrations at the 14th depletion step from the UO2
model:
Pearson Correlation Example
^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. code-block:: scale
read case[c1]
import = "/home/usr/samples/moxdepletion.inp"
end case
read case[c2]
import = "/home/usr/samples/uo2depletion.inp"
read response [experiments]
type = origen_nuclides
nuclides = u-235 pu-239 am-243 ag-109 end
mixture = 5
end response
end case
read response [application]
type = origen_nuclides
nuclides = u-235 end
mixture = 10
cases = c1 end
end response
read analysis [iso_ck]
type = pearson_corr
targets = c1:application.u-235(15) end
sources = c2:experiments.u-235(last) c2:experiments.pu-239(14) end
end analysis
Correlation Matrix Example
^^^^^^^^^^^^^^^^^^^^^^^^^^
Correlation and covariance matrices only require the sources card since they are symmetric
.. code-block:: scale
read analysis [corr-covmatrix]
type = correlation_matrix
sources = c2:experiments.u-235(all) end
end analysis
Squared Correlation Example
^^^^^^^^^^^^^^^^^^^^^^^^^^^
For the analysis of :math:`R^2`, isotopes need to be entered as sources:
.. code-block:: scale
read analysis [sensindex]
type = r2
targets = c1:application.u-235(15) end
sources = h-1 u-235 u-238 end
end analysis
Converting a standard SCALE input to a Sampler input
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In this section, a short walkthrough is provided on how to convert a
"normal" SCALE input into a Sampler input for cross section uncertainty
propagation.
Beginning with a simple CSAS5 input deck:
.. code-block:: scale
=csas5
sample problem 1 case 2c8 bare
v7.1-252
read comp
uranium 1 den=18.76 1 300 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end
end comp
read geometry
unit 1
cylinder 1 1 5.748 5.3825 -5.3825
cuboid 0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
end geometry
read array
gbl=1 ara=1 nux=2 nuy=2 nuz=2 fill f1 end fill
end array
end data
end
First, wrap the given input in sequence and case blocks and assign the
case an arbitrary identifier (``c1``). It is also recommended to change the
library alias to the actual filename.
.. code-block:: scale
=sampler
read case[c1]
sequence=csas5
sample problem 1 case 2c8 bare
xn252
read comp
uranium 1 den=18.76 1 300 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end
end comp
read geometry
unit 1
cylinder 1 1 5.748 5.3825 -5.3825
cuboid 0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
end geometry
read array
gbl=1 ara=1 nux=2 nuy=2 nuz=2 fill f1 end fill
end array
end data
end sequence
end case
end
Second, add the parameters block to identify the base cross-section
library used for building the perturbed ones. Note that this is the only
SCALE module that uses the plural form of parameters and that the
reference to the library matches exactly the one inside the CSAS5 input.
.. code-block:: scale
=sampler
read parameters
library="xn252"
end parameters
read case[c1]
sequence=csas5
sample problem 1 case 2c8 bare
xn252
read comp
uranium 1 den=18.76 1 300 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end
end comp
read geometry
unit 1
cylinder 1 1 5.748 5.3825 -5.3825
cuboid 0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
end geometry
read array
gbl=1 ara=1 nux=2 nuy=2 nuz=2 fill f1 end fill
end array
end data
end sequence
end case
end
Finally, set up the perturbations (number of samples and what to perturb):
.. code-block:: scale
=sampler
read parameters
library="xn252"
n_samples = 40
perturb_xs = yes
end parameters
read case[c1]
sequence=csas5
sample problem 1 case 2c8 bare
xn252
read comp
uranium 1 den=18.76 1 300 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end
end comp
read geometry
unit 1
cylinder 1 1 5.748 5.3825 -5.3825
cuboid 0 1 6.87 -6.87 6.87 -6.87 6.505 -6.505
end geometry
read array
gbl=1 ara=1 nux=2 nuy=2 nuz=2 fill f1 end fill
end array
end data
end sequence
end case
end
Execution Details
-----------------
General workflow
~~~~~~~~~~~~~~~~
The overall workflow for Sampler is as follows:
- for each sample, pick the perturbation factors and generate geometry
perturbations
- for each case, build SCALE input decks, which include:
- calls to the perturbation modules, which generate the perturbed
data libraries (based on the perturbation factors for this
sample)
- user sequence inputs
- output data retrieval
- insert each of the constructed input decks into the processing
queue
- run all SCALE cases from the queue (serial or parallel, as available)
- perform data extraction (using the response mechanism) and
statistical analysis
- print output and generate data files
The advantage of this workflow is that the individual SCALE runs are
completely identified by the sample number (so they are reproducible)
and they are independent. Each of the runs is executed within its own
environment (with SCALE runtime as a subprocess), with its own decay
data, fission yield and cross section library. This arrangement is very
robust and, as there is no coupling between the runs, can be effectively
parallelized.
File management
~~~~~~~~~~~~~~~
For every SCALE run, Sampler creates a subdirectory within its own
temporary directory. Each subdirectory has a name in the form
*(casename)* ``_pert_`` *(sample number)*. Within this directory all the
useful data for the particular run are stored: the input file, the
output file, the message file, the terminal log file (which is a joint
capture of SCALE both standard output and standard error stream) along
with the saved data files (ft71, xfile016, PTP files etc.)
By retaining the temporary directory, the user can then examine and
possibly reuse saved files for the individual SCALE runs.
Parallel execution
~~~~~~~~~~~~~~~~~~
Since the Sampler calculations usually consist of several hundred
mutually completely independent calculations, it is desirable to run the
subcases in parallel.
In SCALE 6.3, Sampler only supports threading for parallel calculations.
In order to run Sampler in parallel simply specify the ``–I``
command line arguments to ScaleRTE. .
Behavior when encountering errors
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Any time a parameter within a SCALE input is perturbed, there is the
possibility that the perturbation will cause unrealistic behavior (fuel
pellet passing through cladding, etc.) that will cause SCALE to fail.
The default behavior of Sampler is to finish all perturbed cases and
check whether there are errors present for each case once all cases have
been run.
Example Problems and Output Description
---------------------------------------
This section describes output files created by Sampler and provides
several sample cases.
Output description
~~~~~~~~~~~~~~~~~~
This section describes the contents of the main Sampler output file, as
well as the other files generated by Sampler.
All of the CSV, PTP and SDF files are, for convenience, copied into a
separate directory called *${OUTBASENAME}*.\ ``samplerfiles``, where
*${OUTBASENAME}* is the base name of the main SCALE output file, e.g.
"my" in "my.out".
Main text output
^^^^^^^^^^^^^^^^
The main text output summarizes the Sampler run progress and presents
the most important results.
Sampler banner
''''''''''''''
The program verification information banner shows the program version and the
main execution information (date and time, user name, computer name).
.. raw:: latex
\begin{landscape}
.. code-block:: none
************************************************************************************************************************************
************************************************************************************************************************************
************************************************************************************************************************************
***** *****
***** program verification information *****
***** *****
***** code system: SCALE version: 6.2 *****
***** *****
************************************************************************************************************************************
************************************************************************************************************************************
***** *****
***** *****
***** program: sampler *****
***** *****
***** version: 6.2.0 *****
***** *****
***** username: usr *****
***** *****
***** hostname: node11.ornl.gov *****
***** *****
***** *****
***** date of execution: 2013-04-04 *****
***** *****
***** time of execution: 14:40:01 *****
***** *****
************************************************************************************************************************************
************************************************************************************************************************************
************************************************************************************************************************************
.. raw:: latex
\end{landscape}
Input parameters echo
'''''''''''''''''''''
Input echo table summarizes the user selected parameters and options.
.. code-block:: none
:class: long
------------------------------------------------------------------------------------------------------------------------------------
- Input parameters echo -
------------------------------------------------------------------------------------------------------------------------------------
Number of cases : 1
Number of samples : 500
First sample index : 1
Number of MAT-MT pairs : 0
Perturb cross-sections : yes
Perturb decay data : no
Perturb fission yields : no
Perturb pointwise XS : yes
Perturb Bondarenko factors : yes
Master XS library : xn252
Perturbed XS library : xn252
Multigroup factors library :
Sensitivity factors library : sensitivity_factors
Covariance library : 44groupcov
Print CSV tables : yes
Print PTP histograms/histories : yes
Print per-sample data : no
Print covariances : no
Print correlations : no
Print chi-square test : no
SCALE run overview
''''''''''''''''''
The run overview table displays the list of SCALE calculations processed by
Sampler, i.e. for each case the baseline calculation (sample 0) and the
requested number of samples.
.. raw:: latex
\begin{landscape}
.. code-block:: none
************************************************************************************************************************************
* Sampling *
************************************************************************************************************************************
case | run sample running? sample directory
-----------+----------------------------------------------------------------------------------------------------------------
case00001 | sample #1 / 41 #00000 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00000
case00001 | sample #2 / 41 #00001 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00001
case00001 | sample #3 / 41 #00002 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00002
case00001 | sample #4 / 41 #00003 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00003
case00001 | sample #5 / 41 #00004 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00004
case00001 | sample #6 / 41 #00005 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00005
case00001 | sample #7 / 41 #00006 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00006
case00001 | sample #8 / 41 #00007 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00007
case00001 | sample #9 / 41 #00008 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00008
case00001 | sample #10 / 41 #00009 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00009
case00001 | sample #11 / 41 #00010 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00010
case00001 | sample #12 / 41 #00011 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00011
case00001 | sample #13 / 41 #00012 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00012
case00001 | sample #14 / 41 #00013 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00013
case00001 | sample #15 / 41 #00014 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00014
case00001 | sample #16 / 41 #00015 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00015
case00001 | sample #17 / 41 #00016 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00016
case00001 | sample #18 / 41 #00017 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00017
case00001 | sample #19 / 41 #00018 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00018
case00001 | sample #20 / 41 #00019 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00019
case00001 | sample #21 / 41 #00020 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00020
case00001 | sample #22 / 41 #00021 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00021
case00001 | sample #23 / 41 #00022 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00022
case00001 | sample #24 / 41 #00023 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00023
case00001 | sample #25 / 41 #00024 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00024
case00001 | sample #26 / 41 #00025 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00025
case00001 | sample #27 / 41 #00026 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00026
case00001 | sample #28 / 41 #00027 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00027
case00001 | sample #29 / 41 #00028 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00028
case00001 | sample #30 / 41 #00029 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00029
case00001 | sample #31 / 41 #00030 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00030
case00001 | sample #32 / 41 #00031 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00031
case00001 | sample #33 / 41 #00032 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00032
case00001 | sample #34 / 41 #00033 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00033
case00001 | sample #35 / 41 #00034 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00034
case00001 | sample #36 / 41 #00035 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00035
case00001 | sample #37 / 41 #00036 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00036
case00001 | sample #38 / 41 #00037 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00037
case00001 | sample #39 / 41 #00038 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00038
case00001 | sample #40 / 41 #00039 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00039
case00001 | sample #41 / 41 #00040 yes /home/usr/sampler_samples/sampler_3_tmp/case00001_pert_00040
--- Master process needs to run 41 SCALE runs.
.. raw:: latex
\end{landscape}
The table shows case name, sample index, sample number (i.e. the number in the
perturbation factor library), whether the case has to be executed (if not it
means that the results were already available in the samplerfiles directory) and
the full path to the run subdirectory.
Response tables
'''''''''''''''
According to the print flags set by the user in the parameters block,
Sampler prints the following tables:
- values of all responses for all samples (printed if ``print_data=yes``)
- average values and standard deviation over the samples population
(always printed)
- comparison of average and baseline value (always printed)
- chi-square normality test (printed if ``print_chi2=yes``)
- covariance matrices (printed if ``print_cov=yes``)
- correlation matrices (printed if ``print_corr=yes``)
- case- and response- specific tables
The case-specific tables contain only responses for a given case (so it
is possible to explore correlations only within a given case). The
response-specific tables are, on the other hand, contain responses
across all cases, so they are useful for case cross-correlation
analysis.
All of the tables are, regardless of the print flags, saved in the CSV
files (see the following section).
CSV tables
^^^^^^^^^^
Every table produced by Sampler is (regardless of whether it has been
selected for the main text output) saved also in the CSV (comma
separated values) format, which makes it convenient to process Sampler
results with a spreadsheet program, plotting package, or any scripting
workflow.
These types of tables are created:
- values for every sample for time-independent responses
..
(``response_table.static.val.all.csv``)
- values for every sample for time-independent responses for each case
..
(``response_table.static.val.case-*.csv``)
- values for every sample for time-independent responses for each
response
..
(``response_table.static.val.response-*.csv``)
- values for every sample for time-dependent responses
..
(``response_table.*.csv``)
- average values for time-dependent responses
..
(``response_table.*.avg.csv``)
- standard deviations for time-dependent responses
..
(``response_table.*.stddev.csv``)
- analysis results for the analysis named myAnalysis
..
(``response_table.analysis.myAnalysis.csv``)
Sampling histograms and running averages
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
In order to provide information on sampling convergence, Sampler
provides two plots for each response at every time step:
- histogram plot – distribution of the response values in directory
*${OUTBASENAME}*.samplerfiles/histogram
- running average plot – average and standard deviation for first N
samples of the population in directory
*${OUTBASENAME}*.samplerfiles/running_averages
Both plots are in the PTP format and can be plotted by Fulcrum, as shown
in :numref:`fig6-7-1` and :numref:`fig6-7-2`.
.. figure:: figs/Sampler/fig1.png
:align: center
:width: 600
:name: fig6-7-1
Example histogram viewed in Fulcrum.
.. figure:: figs/Sampler/fig2.png
:align: center
:width: 600
:name: fig6-7-2
Example running average viewed in Fulcrum.
Response histories
^^^^^^^^^^^^^^^^^^
For time-dependent responses, Sampler produces two plots with
time-dependent summary data.
- standard deviation plot – time-dependent average response with
1-sigma uncertainty bars in directory
*${OUTBASENAME}*.samplerfiles/histories/history.avg.\*
- min/max plot – time-dependent average response with min/max error
bars in directory *${OUTBASENAME}*.samplerfiles/
histories/history.min_max.\*
An example of the standard deviation plot is shown :numref:`fig6-7-3` and the
min/max plot in :numref:`fig6-7-4`.
.. figure:: figs/Sampler/fig3.png
:align: center
:width: 600
:name: fig6-7-3
Time-dependent average plus standard deviation plot.
.. figure:: figs/Sampler/fig4.png
:align: center
:width: 600
:name: fig6-7-4
Time-dependent average plus min/max plot.
Sample problems
~~~~~~~~~~~~~~~
The following sample problems demonstrate various computational and
output capabilities of Sampler in various situations, for both
uncertainty and parametric calculations.
Input files for those sample problems can be found in the ``samples/input``
directory of the SCALE installation. The naming convention for the
inputs is sampler\_\ *N*.inp, where *N* is the sample problem number.
The number of samples (n_samples) shown here may vary from the number
included in the sample inputs.
Sample problem 1
^^^^^^^^^^^^^^^^
This simple, single-case problem, evaluates uncertainty in eigenvalue
for a T-XSDRN calculation of a MOX pincell. Only the cross-sections are
perturbed.
.. code-block:: scale
:class: long
=sampler
read parameters
n_samples=250
library="xn252"
perturb_xs = yes
end parameters
read case[c1]
sequence=t-xsdrn parm=2region
pin-cell model with MOX
xn252
read comp
uo2 1 0.95 900 92235 4.5 92238 95.5 end
zirc2 2 1 600 end
h2o 3 den=0.75 0.9991 540 end
end comp
read cell
latticecell squarepitch pitch=1.3127 3 fuelr=0.42 1 cladd=0.9500 2 end
end cell
read model
pin-cell model with MOX
read parm
sn=16
end parm
read materials
mix=1 com='fuel' end
mix=2 com='clad' end
mix=3 com='moderator' end
end materials
read geom
geom=cylinder
rightBC=white
zoneIDs 1 2 3 end zoneids
zoneDimensions 0.42 0.475 0.7406117 end zoneDimensions
zoneIntervals 3r10 end zoneIntervals
end geom
end model
end sequence
end case
read response[lambda]
type = grep
regexp = ":xsdrn.lambda:"
end response
end
The distribution of lambda (k-eff) from sample problem 1 is shown in :numref:`fig6-7-5`.
.. figure:: figs/Sampler/fig5.png
:align: center
:width: 600
:name: fig6-7-5
Distribution of lambda (k-eff) obtained from sample problem 1.
Sample problem 2
^^^^^^^^^^^^^^^^
This problem demonstrates a two-dimensional parametric study (using
inline placeholders) for two pincell systems.
.. code-block:: scale
:class: long
=sampler
read parametric
variables = temp rho end
n_samples = 3 5 end
end parametric
read case[c1]
sequence=t-xsdrn parm=2region
pin-cell model with MOX
xn252
read comp
uo2 1 0.95 #{temp} 92235 4.5 92238 95.5 end
zirc2 2 1 600 end
h2o 3 den=#{rho} 0.9991 540 end
end comp
read cell
latticecell squarepitch pitch=1.8127 3 fuelr=0.45 1 cladd=0.9500 2 end
end cell
read model
pin-cell model with MOX
read parm
sn=16
end parm
read materials
mix=1 com='fuel' end
mix=2 com='clad' end
mix=3 com='moderator' end
end materials
read geom
geom=cylinder
rightBC=white
zoneIDs 1 2 3 end zoneids
zoneDimensions 0.45 0.475 1.0006117 end zoneDimensions
zoneIntervals 3r10 end zoneIntervals
end geom
end model
end sequence
end case
read case[c2]
sequence=t-xsdrn parm=2region
pin-cell model with MOX
xn252
read comp
uo2 1 0.95 #{temp} 92235 4.5 92238 95.5 end
zirc2 2 1 600 end
h2o 3 den=#{rho} 0.9991 540 end
end comp
read cell
latticecell squarepitch pitch=1.9127 3 fuelr=0.45 1 cladd=0.9500 2 end
end cell
read model
pin-cell model with MOX
read parm
sn=16
end parm
read materials
mix=1 com='fuel' end
mix=2 com='clad' end
mix=3 com='moderator' end
end materials
read geom
geom=cylinder
rightBC=white
zoneIDs 1 2 3 end zoneids
zoneDimensions 0.45 0.475 1.0406117 end zoneDimensions
zoneIntervals 3r10 end zoneIntervals
end geom
end model
end sequence
end case
read variable[rho]
distribution=uniform
minimum = 0.5
value = 0.65
maximum = 0.8
cases = c1 c2 end
end variable
read variable[temp]
distribution=uniform
minimum = 700
value = 900
maximum = 1100
cases = c1 c2 end
end variable
read response[lambda]
type = grep
regexp = ":xsdrn.lambda:"
end response
end
The dependency of eigenvalue on coolant density for the two systems is
printed to the output file, as shown in :numref:`fig6-7-6`, where the first
table shows the temperature and density combinations in the first two
columns and the corresponding eigenvalue from case 1 and case 2 in the
next two columns. Two summary tables are printed, identifying the
conditions of the maximum and minimum for each response, in each case.
.. figure:: figs/Sampler/fig6.png
:align: center
:width: 600
:name: fig6-7-6
Dependency of lambda (k-eff) on coolant density and fuel
temperature for sample problem 2.
Sample problem 3
^^^^^^^^^^^^^^^^
This sample problem demonstrates enrichment variation using SIREN
expressions and dependent variables.
.. code-block:: scale
:class: long
=sampler
read parameters
n_samples=50
perturb_geometry=yes
end parameters
read case[sphere]
sequence=csas5 parm=bonami
sample problem 14 u metal cylinder in an annulus
xn252
read comp
uranium 1 den=18.69 1 300 92235 94.4 92238 5.6 end
end comp
read geom
global unit 1
cylinder 1 1 8.89 10.109 0.0 orig 5.0799 0.0
cylinder 0 1 13.97 10.109 0.0
cylinder 1 1 19.05 10.109 0.0
end geom
end data
end sequence
read variable[u235]
distribution=uniform
minimum=91.0
value=94.4
maximum=95.0
siren="/csas5/comps/stdcomp/wtpt_pair[id='92235']/wtpt"
end variable
read variable[u238]
distribution=expression
expression="100.0-u235"
siren="/csas5/comps/stdcomp/wtpt_pair[id='92238']/wtpt"
end variable
end case
read response[keff]
type=grep
regexp=":kenovi.keff:"
end response
The distribution of the multiplication factor with the specified
enrichment distribution is shown in :numref:`fig6-7-7`.
.. figure:: figs/Sampler/fig7.png
:align: center
:width: 600
:name: fig6-7-7
Distribution of multiplication factor with sampled enrichment distribution
for sample problem 3.
Sample problem 4
''''''''''''''''
Sample problem 4 demonstrates sampling with covariance data for neutron
cross sections and fission product yields. Note that decay sampling does
not work with TRITON at this time due to not using the perturbed ORIGEN
decay libraries *directly*. Additionally, it demonstrates how to extract
reaction rates from a TRITON case, combining an additional OPUS run with
the ``opus_plt`` response.
.. code-block:: scale
:class: long
=sampler
read parameters
n_samples=100
library="xn252"
perturb_xs = yes
perturb_decay = no
perturb_yields = yes
end parameters
read case[c1]
sequence=t-depl parm=(bonami,addnux=0)
pincell model
xn252
read composition
uo2 10 0.95 900 92235 3.6 92238 96.4 end
zirc2 20 1 600 end
h2o 30 den=0.75 0.9991 540 end
end composition
read celldata
latticecell squarepitch pitch=1.2600 30 fuelr=0.4095 10 cladr=0.4750 20 end
end celldata
read depletion
10
end depletion
read burndata
power=25 burn=1200 nlib=30 end
end burndata
read model
read materials
mix=10 com="4.5 enriched fuel" end
mix=20 com="cladding" end
mix=30 com="water" end
end materials
read geom
global unit 1
cylinder 10 0.4095
cylinder 20 0.4750
cuboid 30 4p0.63
media 10 1 10
media 20 1 20 -10
media 30 1 30 -20
boundary 30 3 3
end geom
read collapse
150r1 88r2
end collapse
read homog
500 mini 10 20 30 end
end homog
read bounds
all=refl
end bounds
end model
end sequence
sequence=opus
typarams=nuclides
units=fissions
symnuc=u238 pu239 end
library="ft33f001.cmbined"
case = 10
end sequence
sequence=opus
typarams=nuclides
units=captures
symnuc=u238 pu239 end
library="ft33f001.cmbined"
case = 10
end sequence
end case
read response[hmgxs]
type = triton
mixture = 1
data = kinf end
end response
read response[concentrations]
type=origen_nuclides
nuclides = u-235 pu-239 pu-240 pu-241 nd-148 sm-149 sm-150 sm-151 cs-133 cs-134 cs-137 end
mixture = 10
end response
read response[fisrates]
type = opus_plt
ndataset = 1
nuclides = u238 pu239 end
end response
read response[caprates]
type = opus_plt
ndataset = 2
nuclides = u238 pu239 end
end response
end
Plots of various isotopic uncertainties as a function of time are shown
in :numref:`fig6-7-8` for :sup:`235`\ U, :numref:`fig6-7-9` for :sup:`239`\ Pu,
:numref:`fig6-7-10` for :sup:`240`\ Pu, :numref:`fig6-7-11` for :sup:`241`\ Pu,
:numref:`fig6-7-12` for :sup:`148`\ Nd, :numref:`fig6-7-13` for :sup:`150`\ Sm, and
:numref:`fig6-7-14` for :sup:`151`\ Sm in terms of the unperturbed with error
bars for the *minimum* and *maximum*, that is over the 100 samples
performed, the minimum value at that time and the maximum value at that
time. Note that most isotopes accumulate uncertainty over time, but this
is not always the case, e.g. for :sup:`151`\ Sm. Two common burnup
indicators (measured in spent fuel to infer/confirm burnup)
:sup:`148`\ Nd and :sup:`150`\ Sm show linear increase with time (as
expected for a burnup indicator).
.. figure:: figs/Sampler/fig8.png
:align: center
:width: 600
:name: fig6-7-8
Uncertainty in :sup:`235`\ U concentration for problem 4.
.. figure:: figs/Sampler/fig9.png
:align: center
:width: 600
:name: fig6-7-9
Uncertainty in :sup:`239`\ Pu concentration for problem 4.
.. figure:: figs/Sampler/fig10.png
:align: center
:width: 600
:name: fig6-7-10
Uncertainty in :sup:`240`\ Pu concentration for problem 4.
.. figure:: figs/Sampler/fig11.png
:align: center
:width: 600
:name: fig6-7-11
Uncertainty in :sup:`241`\ Pu concentration for problem 4.
.. figure:: figs/Sampler/fig12.png
:align: center
:width: 600
:name: fig6-7-12
Uncertainty in :sup:`148`\ Nd concentration for problem 4.
.. figure:: figs/Sampler/fig13.png
:align: center
:width: 600
:name: fig6-7-13
Uncertainty in :sup:`150`\ Sm concentration for problem 4.
.. figure:: figs/Sampler/fig14.png
:align: center
:width: 600
:name: fig6-7-14
Uncertainty in :sup:`151`\ Sm concentration for problem 4.
Sample problem 5
^^^^^^^^^^^^^^^^
This problem provides an example of two correlated depletion cases. The second
"c2" case has a larger pitch and lower enrichment fuel. All data libraries are
perturbed.
.. code-block:: scale
:class: long
=sampler
read parameters
n_samples = 100
library = "xn252"
perturb_xs = yes
perturb_yields = yes
perturb_decay = yes
end parameters
read case[c1]
sequence=t-depl parm=(bonami,addnux=0)
pincell model
xn252
read composition
uo2 10 0.95 900 92235 3.6 92238 96.4 end
zirc2 20 1 600 end
h2o 30 den=0.75 0.9991 540 end
end composition
read celldata
latticecell squarepitch pitch=1.2600 30 fuelr=0.4095 10 cladr=0.4750 20 end
end celldata
read depletion
10
end depletion
read burndata
power=25 burn=1200 nlib=30 end
end burndata
read model
read materials
mix=10 com="4.5 enriched fuel" end
mix=20 com="cladding" end
mix=30 com="water" end
end materials
read geom
global unit 1
cylinder 10 0.4095
cylinder 20 0.4750
cuboid 30 4p0.63
media 10 1 10
media 20 1 20 -10
media 30 1 30 -20
boundary 30 3 3
end geom
read collapse
150r1 88r2
end collapse
read homog
500 mini 10 20 30 end
end homog
read bounds
all=refl
end bounds
end model
end sequence
end case
read case[c2]
sequence=t-depl parm=(bonami,addnux=0)
pincell model
xn252
read composition
uo2 10 0.95 900 92235 3.6 92238 96.4 end
zirc2 20 1 600 end
h2o 30 den=0.75 0.9991 540 end
end composition
read celldata
latticecell squarepitch pitch=1.6600 30 fuelr=0.4095 10 cladr=0.4750 20 end
end celldata
read depletion
10
end depletion
read burndata
power=25 burn=1200 nlib=30 end
end burndata
read model
read materials
mix=10 com="3.6 enriched fuel" end
mix=20 com="cladding" end
mix=30 com="water" end
end materials
read geom
global unit 1
cylinder 10 0.4095
cylinder 20 0.4750
cuboid 30 4p0.83
media 10 1 10
media 20 1 20 -10
media 30 1 30 -20
boundary 30 3 3
end geom
read collapse
150r1 88r2
end collapse
read homog
500 mini 10 20 30 end
end homog
read bounds
all=refl
end bounds
end model
end sequence
end case
read response[concentrations]
type=origen_nuclides
nuclides = u-235 pu-239 pu-240 pu-241 nd-148 sm-149 sm-150 sm-151 cs-133 cs-134 cs-137 end
mixture = 10
end response
end
The correlation matrix for concentrations at 1200 days of irradiation is
shown in :numref:`fig6-7-15`, post-processed with Excel to show high and low
correlation coefficients. The bold and underline entries indicate that
the each extracted isotope shows a correlation coefficient of 1.0
between the two cases. This means that the two cases are the same in
terms of their isotopic response to data perturbations.
.. figure:: figs/Sampler/fig15.png
:align: center
:width: 600
:name: fig6-7-15
Correlation matrix for concentrations in sample problem 5.
Sample problem 6
^^^^^^^^^^^^^^^^
Sample problem 6 provides an example of fission yield and decay data
sampling. First, COUPLE is run to assemble an ORIGEN library (on file
ft33f001) from the perturbed yields and decay data libraries. Burst
fission with long decay is then performed by ORIGEN and OPUS is used to
extract the fission product decay heat.
.. code-block:: scale
:class: long
=sampler
read parameters
n_samples = 500
perturb_yields = yes
perturb_decay = yes
end parameters
read case[heat]
sequence=couple
0$$ a3 80 21 0 33 e
1$$ a4 1 a18 238 e 1t
9**
13z 1.25 0.3 223z
2t
done
end sequence
sequence=origens
3$$ 1 1 e t
ft33f001
56$$ 40 1 1 0 -1 a9 0 1 2 1 1 e
t
u235 thermal fission energy release
59** 3.08617e12 f0 e
60** 1e-10 1 1.5 2 4 6 8 10 15 20 40 60 80 100
150 200 400 600 800 1000 1500 2000 4000 6000 8000 1e4
1.5e4 2e4 4e4 6e4 8e4 1e5
1e6 1e7 1e8 1e9 1e10 1e11 1e12 1e13
61** f1e-14
67$$ a47 1 0 1 e
68$$ a2 1 e
73$$ 922350
74** 1
75$$ 2
80$$ 0 f1
t
ft71f001
end sequence
sequence=opus
library="ft33f001"
units=watts
libtype=fiss
minposition=2
end sequence
end case
read response[heat]
type=opus_plt
ndataset=0
nuclides=total end
end response
end
The total decay heat with the uncertainty is shown in :numref:`tab6-7-7` and :numref:`fig6-7-16`.
.. list-table:: Decay heat and uncertainties from sample problem 6.
:align: center
:name: tab6-7-7
* - .. image:: figs/Sampler/tab7.svg
:width: 1000
.. figure:: figs/Sampler/fig16.png
:align: center
:width: 600
:name: fig6-7-16
Decay heat and uncertainties from sample problem 6.
Sample problem 7
^^^^^^^^^^^^^^^^
Sample problem 7 illustrates an example of a shielding parametric study
with MAVRIC. It also demonstrates usage of the grep response for both
response value and uncertainty.
.. code-block:: scale
:class: long
=sampler
read parameters
n_samples = 50
end parameters
read parametric
variables = thick end
end parametric
read case[graphite]
sequence=mavric
Monaco/MAVRIC Training - Exercise 3. Graphite Shielding Measurements Revisited
v7-27n19g
'-------------------------------------------------------------------------------
' Composition Block - standard SCALE input
'-------------------------------------------------------------------------------
read composition
para(h2o) 3 1.0 293.0 end
carbon 4 den=1.7 1.0 300.0 end
end composition
'-------------------------------------------------------------------------------
' Geometry Block - SCALE standard geometry package (SGGP)
'-------------------------------------------------------------------------------
read geometry
global unit 1
cuboid 1 25.0 -25.0 25.0 -25.0 25.0 -25.0
cone 2 10.35948 25.01 0.0 0.0 rotate a1=-90 a2=-90 a3=0
cuboid 3 #{x90} 70.0 40.0 -40.0 40.0 -40.0
cuboid 99 120.0 -30.0 50.0 -50.0 50.0 -50.0
media 3 1 1 -2
media 0 1 2
media 4 1 3
media 0 1 99 -1 -2 -3
boundary 99
end geometry
'-------------------------------------------------------------------------------
' Definitions Block
'-------------------------------------------------------------------------------
read definitions
location 1
position 110 0 0
end location
response 5
title="ANSI standard (1977) neutron flux-to-dose-rate factors"
specialDose=9029
end response
distribution 1
title="Cf-252 neutrons, Watt spectrum a=1.025 MeV and b=2.926/MeV"
special="wattSpectrum"
parameters 1.025 2.926 end
end distribution
gridGeometry 7
title="large meshes in paraffin, 5 cm mesh for shield thicknesses"
xLinear 5 -25 25
xLinear 12 30 #{x90}
xplanes 100 110 120 -30 end
yplanes -50 -40 40 50 end
yLinear 7 -35 35
zplanes -50 -40 40 50 end
zLinear 7 -35 35
end gridGeometry
end definitions
'-------------------------------------------------------------------------------
' Sources Block
' Cf-252 neutrons, Watt fission spectrum model
' with a=1.025 MeV and b=2.926/MeV
'-------------------------------------------------------------------------------
read sources
src 1
title="Cf-252 neutrons, Watt fission spectrum model"
strength=4.05E+07
cuboid 0.01 0.01 0 0 0 0
neutrons
eDistributionID=1
end src
end sources
'-------------------------------------------------------------------------------
' Tallies Block
'-------------------------------------------------------------------------------
read tallies
pointDetector 1
title="center of detector"
neutron
locationID=1
responseID=5
end pointDetector
meshTally 1
title="example mesh tally"
neutron
gridGeometryID=7
responseID=5
noGroupFluxes
end meshTally
end tallies
'-------------------------------------------------------------------------------
' Parameters Block
'-------------------------------------------------------------------------------
read parameters
randomSeed=00003ecd7b4e3e8b
library="v7-200n47g"
perBatch=10000 batches=10
fissionMult=0 noPhotons
end parameters
'-------------------------------------------------------------------------------
' Importance Map Block
'-------------------------------------------------------------------------------
read importanceMap
adjointSource 1
locationID=1
responseID=5
end adjointSource
gridGeometryID=7
mmTolerance=0.01
end importanceMap
end data
end sequence
read variable[thick]
value = 20
minimum = 10
maximum = 30
distribution = uniform
end variable
read variable[x90]
distribution = expression
expression = "thick+70"
end variable
end case
read response[flux]
type = grep
regexp = "total flux[[:space:]]+:scale.number:"
regexp = ":scale.number:"
end response
end
Flux dependence on the shielding thickness is shown in :numref:`fig6-7-17`.
.. figure:: figs/Sampler/fig17.png
:align: center
:width: 600
:name: fig6-7-17
Flux as a function of shielding thickness for sample problem 7.
SCALE Input Retrieval ENgine (SIREN)
------------------------------------
SIREN (SCALE Input Retrieval ENgine) provides a hierarchical representation of SCALE
input and enables access to individual input components or sets of related input
parameters. SIREN sorts the contents of supported SCALE input sequences into a
tree structure so that every component in a SCALE input can be accessed using an
XPath designation. The SIREN package is used by the SCALE super-sequence Sampler
to select individual components within an input file, perturb the parameter in
memory, and write the perturbed input to a new file. In this way, components
within an input file can be perturbed without modification to the original input
file, which can be maintained as a read-only file under configuration control
for quality assurance purposes.
To explore the use of SIREN expressions, two utilities are available in the
SCALE bin directory. The utilities are the executables "InputViewer" and
"InputSelector." The InputViewer utility accepts a SCALE input file and outputs
the XPath designation for each component of that input file. The InputSelector
utility accepts a SCALE input file and a SIREN select statement and then outputs
the part of the input file specified by the SIREN select statement. The
remainder of this section provides practical examples in the use of SIREN select
statements to designate specific components of a SCALE input.
A simple CSAS6 input file, which models a sphere of HEU, is used to show how to
use SIREN select statements to access specific portions of a SCALE input. The
contents of the example CSAS6 input file are shown below.
::
=csas6
sample problem 6 bare 93.2% U sphere, eighth sphere w/ mirror albedo
v7-238
read comp
uranium 1 den=18.76 1 293 92235 93.2 92238 5.6 92234 1.0 92236 0.2 end
end comp
read geometry
global unit 1
sphere 10 8.741 chord +x=0.0 chord +y=0.0 chord +z=0.0
cuboid 20 8.741 0.0 8.741 0.0 8.741 0.0
media 1 1 10 vol=2797.5121
media 0 1 20 -10 vol=2545.3424
boundary 20
end geometry
read bounds
-fc=mirror
end bounds
end data
end
The InputViewer utility is used to view the contents of the example input file
with their respective XPath designations. The utility accepts the path to the
input file as an argument so that the usage is:
.. highlight:: none
::
$ InputViewer inputfile
A portion of the output from InputViewer is shown below; this portion
corresponds to the material definition in the example input file. Notice that
each component of the composition has a specific XPath designation. For
instance, the "wtptPair" has several pieces of information (ids for each
component and the weight percent for that component). To gain access to a
specific component, the InputSelector utility is introduced below.
::
/csas6/comps
/csas6/comps/decl(read comp)
/csas6/comps/stdcomp
/csas6/comps/stdcomp/name(uranium)
/csas6/comps/stdcomp/mixture(1)
/csas6/comps/stdcomp/roth
/csas6/comps/stdcomp/roth/decl(den)
/csas6/comps/stdcomp/roth/assign(=)
/csas6/comps/stdcomp/roth/value(18.76)
/csas6/comps/stdcomp/vf(1)
/csas6/comps/stdcomp/temp(293)
/csas6/comps/stdcomp/wtpt_pair
/csas6/comps/stdcomp/wtpt_pair/id(92235)
/csas6/comps/stdcomp/wtpt_pair/wtpt(93.2)
/csas6/comps/stdcomp/wtpt_pair
/csas6/comps/stdcomp/wtpt_pair/id(92238)
/csas6/comps/stdcomp/wtpt_pair/wtpt(5.6)
/csas6/comps/stdcomp/wtpt_pair
/csas6/comps/stdcomp/wtpt_pair/id(92234)
/csas6/comps/stdcomp/wtpt_pair/wtpt(1.0)
/csas6/comps/stdcomp/wtpt_pair
/csas6/comps/stdcomp/wtpt_pair/id(92236)
/csas6/comps/stdcomp/wtpt_pair/wtpt(0.2)
/csas6/comps/stdcomp/term(end)
/csas6/comps/term(end comp)
To explore how SIREN select statements are used, the InputSelector
utility is used for a few cases with the example CSAS6 input file.
Suppose the :sup:`235`\ \ U weight percent needed to be accessed for
perturbation; the SIREN expression to access the :sup:`235`\ \ U
weight percent is as follows:
Long form:
::
'/csas6/comps/stdcomp/wtpt_pair[id="92235"]/wtpt'
Short form:
::
'///wtpt_pair[id="92235"]/wtpt'
This statement tells SIREN to look for the weight percent with an ID of 92235 in
the weight percent pair. A short form of the select statement (designated by the
triple slash) can be used when there are unique qualities about a component; for
instance, there is only a single material with an ID of 92235, so the weight
percent pair must belong to that material. There are many combinations of select
statements that can point to a specific input component, and the developers
suggest using the InputSelector utility to familiarize oneself with this
capability. The usage of InputSelector is:
::
$ InputSelector inputfile quoted_Select_Statement
Below is the screen output from the InputSelector with the example
CSAS6 input file and the select statement for the :sup:`235`\ \ U
weight percent.
::
---- 1 nodes selected with statement '///wtpt_pair[id='92235']/wtpt' ----
1) /csas6/comps/stdcomp/wtpt_pair/wtpt
93.2
The output from InputSelector shows that the select statement points
to a single component in the SCALE input, which is indeed the value for the
:sup:`235`\ \ U weight percent. There are cases where a select statement
points to a portion of the input that has multiple components and the
select statement may need to be refined to point to a specific component.
For instance, the cuboid defined in the geometry section of the input has
multiple dimensions (+x, -x, +y, -y, etc.). By using the select statement
below, the dimensions of the cuboid are shown
::
'//cuboid/[id="20"]/dimensions'
The output from using InputSelector with this select statement is shown below.
::
---- 1 nodes selected with statement '//cuboid/[id="20"]/dimensions' ----
1) /csas6/geometry/global_unit/cuboid/dimensions
8.741 0.0 8.741 0.0 8.741 0.0
The output from InputSelector shows six values, which correspond to the
dimensions of the cuboid (+x, x, +y, -y, +z, -z faces). To select a single
dimension, the select statement should include which component is desired. For
instance, to select the height of the cuboid the select statement becomes:
::
'//cuboid/[id="20"]/dimensions/plus_z'
In the same way, the radius of the sphere can be selected using the SIREN
expression that identifies the radius of a sphere with an ID of 10:
::
'//sphere/[id="10"]/dimensions/r'
The output from InputSelector is shown below.
::
---- 1 nodes selected with statement '//sphere/[id="10"]/dimensions/r' ----
1) /csas6/geometry/global_unit/sphere/dimensions/r
8.741
There are scenarios where there is no unique or obvious identifier for a
component. As an example, the media volume can utilize an array index to
retrieve the volume value.
::
'//media/volume/value'
The output from InputSelector illustrates both media’s volume value are selected below.
::
---- 2 nodes selected with statement '//media/volume/value' ----
1) /csas6/geometry/global_unit/media/volume/value
2797.5121
2) /csas6/geometry/global_unit/media/volume/value
2545.3424
The printed index (1) can be utilized to narrow the selection.
::
‘//media[1]/volume/value’
Here the first media is selected and subsequently, the media’s volume value,
removing the selection of the second media entirely. The output from
InputSelector is shown below.
::
---- 1 nodes selected with statement '//media[1]/volume/value' ----
1) /csas6/geometry/global_unit/media/volume/value
2797.5121
For the sake of completeness, the following example illustrates selection of
the media’s volume value via the mixture’s value comparator.
::
'//media[mixture="1"]/volume/value'
This illustrates the first media’s unique mixture component can be used to select the volume for the first media. The output from InputSelector is shown below.
::
---- 1 nodes selected with statement '//media[mixture="1"]/volume/value' ----
1) /csas6/geometry/global_unit/media/volume/value
2797.5121
The above examples were intended to provide users with an idea of how to use SIREN
select statements to access specific components within a SCALE input. The select
statements are primarily used in cases where the input is to be perturbed by the
Sampler super-sequence, but modification to the original input is not desirable.
The recommended way to ensure that the select statements are correct is to use
the InputSelector utility to check that a select statement points to the correct
input component.
For viewing the input paths, an alternative to the InputViewer command line
utility is available within the Fulcrum graphical user interface (GUI). By
clicking on the Run Button drop-down and selecting "Input Listing" as shown in
:numref:`fig6-7-18`, the full listing of the current input file is displayed in the
"Messages" box. Also, notice the path is displayed in the bottom left corner for
the input component located at the cursor.
.. figure:: figs/Sampler/fig18.png
:align: center
:width: 600
:name: fig6-7-18
Input Listing in Fulcrum.
A table of SIREN expressions is as follows.
.. raw:: latex
\clearpage
.. tabularcolumns:: |p{2.5cm}|p{6cm}|p{8cm}|
.. table:: Expressions for SIREN.
:name: tab6-7a-1
:class: longtable
+------------------------+-------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------+
| **Expressions** | **Description** | **Examples** |
+========================+=====================================================================================================================================+=================================================+
| component | Component match. | csas6 |
+------------------------+-------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------+
| / | Component separator. | csas6/xslib |
| | When the expression begins | / |
| | with this, it selects the root of the document. | |
+------------------------+-------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------+
| // | This expression is the 'Any Child' select. | csas6//uranium |
| | | // |
+------------------------+-------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------+
| [index] | Array index selector. When an array of objects has been selected, this expression | csas6/ geometry/global_unit/media**[1]** |
| | selects the object at the given index. | |
+------------------------+-------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------+
| [sindex:eindex] | Subarray index selector. When an array of objects has been selected, this expression | csas6/ comps/stdcomp/uranium/wtpt_pair**[2:3]** |
| | selects a subarray. | |
+------------------------+-------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------+
| [sindex:eindex:stride] | Subarray index selector. When an array of objects has been selected, this expression selects a subarray and subsequently components | csas6/comps/stdcomp/uranium/wtptPair**[1:4:2]** |
| | stride apart. | |
+------------------------+-------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------+
| \* | Component wild card. This can only be used in place of a component or to wild card the | csas6/read comp/\* csas6/read comp/ur\* |
| | remainder of a component. | |
+------------------------+-------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------+
Expression Operators and Functions for Sampler
----------------------------------------------
The expression engine utilized by Sampler supports all basic mathematical and
logical operators, as well as a number of functions. Logical expressions and
functions evaluate to the number 1 for true, and the number 0 for false.
.. tabularcolumns:: |m{3cm}|m{6cm}|m{7cm}|
.. table:: Expression operators and functions for Sampler.
:align: center
:class: longtable
:name: tab6-7b-1
+-----------------------+-----------------------+-----------------------+
| **Operator** | **Description** | **Example** |
+=======================+=======================+=======================+
| \+ | Addition | 3+3, x+y |
+-----------------------+-----------------------+-----------------------+
| \+ | Unary Plus | +3, +(-3), +x |
+-----------------------+-----------------------+-----------------------+
| \- | Subtraction | 3-3, x-y |
+-----------------------+-----------------------+-----------------------+
| \- | Unary Minus | -3, -(3+3), -x |
+-----------------------+-----------------------+-----------------------+
| \* | Multiplication | 3*3, x*y |
+-----------------------+-----------------------+-----------------------+
| / | Division | 3/3, x/y |
+-----------------------+-----------------------+-----------------------+
| % | Modulo | 3%3, x%y |
+-----------------------+-----------------------+-----------------------+
| ^ | Power | 3^3, x^y |
+-----------------------+-----------------------+-----------------------+
| == | Equal to | 3==3, x==y |
+-----------------------+-----------------------+-----------------------+
| != | Not equal to | 3!=3, x!=y |
+-----------------------+-----------------------+-----------------------+
| < | Less than | 3<3, x<y |
+-----------------------+-----------------------+-----------------------+
| > | Greater than | 3>3, x>y |
+-----------------------+-----------------------+-----------------------+
| <= | Less than or equal to | 3<=3, x<=y |
+-----------------------+-----------------------+-----------------------+
| >= | Greater than or equal | 3>=3, x>=y |
| | to | |
+-----------------------+-----------------------+-----------------------+
| and | Left is true and | 1 and 1 , x==y and |
| | right is true | y==z |
+-----------------------+-----------------------+-----------------------+
| or | Left is true or right | 1 or 1, x==y or y==z |
| | is true | |
+-----------------------+-----------------------+-----------------------+
| nand | Not and | 1 nand 1, 1 nand 0, x |
| | | nand y |
+-----------------------+-----------------------+-----------------------+
| xor | Exclusive or | 1 xor 1, 1 xor 0, x |
| | | xor y |
+-----------------------+-----------------------+-----------------------+
| nor | Not or | 1 nor 1, 1 nor 0, x |
| | | nor y |
+-----------------------+-----------------------+-----------------------+
| abs(x) | Absolute value | abs(1),abs(-1),abs(x) |
| | | ,abs(y) |
+-----------------------+-----------------------+-----------------------+
| min(x,…n) | Minimum of values | min(1),min(1,2,3,4,5, |
| | | x,y),etc |
+-----------------------+-----------------------+-----------------------+
| max(x,…n) | Maximum of values | max(1),max(1,2,3,4,5, |
| | | x,y),etc |
+-----------------------+-----------------------+-----------------------+
| avg(x,…n) | Average of values | avg(1),avg(1,2,3,4,5, |
| | | x,y),etc |
+-----------------------+-----------------------+-----------------------+
| Sum(x,…n) | Summation of values | sum(1),sum(1,2,3,4,5, |
| | | x,y),etc |
+-----------------------+-----------------------+-----------------------+
| mul(x,…n) | Multiply values | mul(1),mul(1,2,3,4,5, |
| | | x,y),etc |
+-----------------------+-----------------------+-----------------------+
| floor(x) | Floor of the value | floor(1)=1, |
| | | floor(-1.0)=-1.0, |
| | | floor(-1.1)=-2.0 |
+-----------------------+-----------------------+-----------------------+
| ceil(x) | Ceiling of the value | ceil(1)=1,ceil(-1.1)= |
| | | -1 |
+-----------------------+-----------------------+-----------------------+
| round(x) | Round the value to | round(1.1)=1,round(1.\|
| | nearest integer | 5)=2,round(1.9)=2 |
+-----------------------+-----------------------+-----------------------+
| roundn(x,n) | Round the value to | roundn(1.15,1)= 1.2, |
| | the nth decimal | roundn(1.519,2)= 1.52 |
| | position | |
+-----------------------+-----------------------+-----------------------+
| cos(x) | Cosine of the value | cos(0.0)=1 |
+-----------------------+-----------------------+-----------------------+
| sin(x) | Sine of the value | sin(0.0)=0 |
+-----------------------+-----------------------+-----------------------+
| tan(x) | Tangent of the value | tan(0.0)=0 |
+-----------------------+-----------------------+-----------------------+
| sec(x) | Secant of the value | sec(0.0)=1 |
+-----------------------+-----------------------+-----------------------+
| csc(x) | Cosecant of the value | csc(1.0)= 1.1884 |
+-----------------------+-----------------------+-----------------------+
| cot(x) | Cotangent of the | cot(1.0)= 0.642093 |
| | value | |
+-----------------------+-----------------------+-----------------------+
| sinh(x) | Hyperbolic sine of | sinh(1.0)= 1.1752 |
| | the value | |
+-----------------------+-----------------------+-----------------------+
| cosh(x) | Hyperbolic cosine of | cosh(1.0)= 1.54308 |
| | the value | |
+-----------------------+-----------------------+-----------------------+
| tanh(x) | Hyperbolic tangent of | tanh(1.0)= 0.761594 |
| | the value | |
+-----------------------+-----------------------+-----------------------+
| log(x) | Natural log of the | log(2.7182818)=1 |
| | value | |
+-----------------------+-----------------------+-----------------------+
| log10(x) | Common log of the | log10(10.0)=1 |
| | value | |
+-----------------------+-----------------------+-----------------------+
| exp(x) | Exponential of the | exp(1)=2.7182818 |
| | value | |
+-----------------------+-----------------------+-----------------------+
| clamp(l,x,u) | Clamp the value x | clamp(-1,1,+1)=1,clam\|
| | between lowerbound l | p(-1,-5,+1)=-1 |
| | and upperbound u | |
+-----------------------+-----------------------+-----------------------+
| inrange(l,x,u) | Determine if value x | inrange(-1,1,+1)=1,in\|
| | is greater than or | range(-1,-5,+1)=0 |
| | equal to lowerbound | |
| | l, and less than or | |
| | equal to upperbound u | |
+-----------------------+-----------------------+-----------------------+
| sgn(x) | Determine the sign of | sgn(+1)=1,sgn(-1)=-1, |
| | x. | sgn(0)=0,sgn(5)=1 |
+-----------------------+-----------------------+-----------------------+
| sqrt(x) | Square Root of the | sqrt(1)=1,sqrt(4)=2 |
| | value | |
+-----------------------+-----------------------+-----------------------+
| root(x,y) | Root of x given y | root(4,2)=2,root(8,3)\|
| | | =2 |
+-----------------------+-----------------------+-----------------------+
| true | Constant true value | true |
+-----------------------+-----------------------+-----------------------+
| false | Constant false value | False |
+-----------------------+-----------------------+-----------------------+
| if(condition,true,fal\| If function that | if( x > y, x, y) = x |
| se) | evaluates the | |
| | condition. If true, | |
| | the true value is | |
| | substituted, else the | |
| | false value is | |
| | substituted | |
+-----------------------+-----------------------+-----------------------+
Guidelines for Running Sampler in Parallel
------------------------------------------
Sampler calculations consist of three basic steps:
1. generate N perturbed input files and libraries,
2. run N independent SCALE jobs, and
3. analyze N results sets.
At this time, the preferred way of performing Sampler calculations is
to use *run_cases=no* (in the *parameters* block) and perform step 2
above outside of Sampler, i.e. using scripting or your system's
queuing system to launch the *N* SCALE jobs. The
"${OUTBASENAME}.samplerfiles" directory that Sampler creates in step
1 will contain all the perturbed input files. Each of these input
files should be run as a separate SCALE job. When all jobs are
complete, Sampler should be run again (still with *run_cases=no*).
Sampler will see that all jobs have completed, and perform the
analysis in step 3. The Sampler sample problem 8 is a quick-running
calculation that can be used to test and, if necessary adjust, the
manual 3-step scheme described above on your system.
However, for small jobs that fit on a single node, threading can be used.
To launch a Sampler calculation with 5 parallel threads, one would issue
the following from the command line:
::
scalerte –r –I 5 –m sample_8.inp
This will perform all 3 steps of the Sampler process.
.. [#f1]
ÚJV Řež, a. s., Czech Republic
.. [#f2]
Gesellschaft fur Anlagen- und Reaktorsicherheit (GRS)
.. [#f3]
Texas A&M University
.. only:: html
.. rubric:: References
.. bibliography:: zSCALE.bib
:cited:
:labelprefix: SAMPLER-
:keyprefix: SAMPLER-