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3. The sensitivity analysis benchmark
Many PAMINA partners were interested in getting in depth knowledge and experience in the use of
SA techniques. This was the reason to set a benchmark on SA techniques that could help them getting
that objective. The SA benchmark has been designed as a two-step process. The first step is
dedicated to analyse a set of mathematical functions most of whose sensitivity indices are well
known. The second step consists in analysing a simplified, though representative, PA model. Finally,
though not included as a part of the benchmark but as other tasks committed within PA-
MINA, several partners will study their respective system models, or parts of them, using SA techniques.
The first part of the benchmark consists in studying twelve mathematical models (seven mandatory,
five voluntary) with different SA techniques (the techniques are chosen by each participant, attending
to their respective interests). The first target is to provide the right simple framework to test and
debug their respective SA tools. The second one is to start with rather simple models (three input
parameter linear model) and to continue analysing models with some added complexity: increase
the number of parameters, add nonlinearities, consider non-monotonic models, include periodicity,
consider continuous models whose derivative does not exist at some given points, consider models
with interactions, check the different capability to estimate accurately large and small sensitivity
indices, etc. An additional target is to see the importance of the sample size in the accuracy of the
sensitivity indices.
The model under study in the second step of the benchmark reproduces the behaviour of a radioactive
HLW repository and the contaminant disposed of. Only four radionuclides are considered in
this model, 129 I and the decay chain 237 Np, 233 U and 229 Th. The repository is considered without any
geometric complexity, just a point. Engineered barriers are modelled through a containment time
during which there is no release. After such containment period, the contaminant starts releasing at
a fractional constant rate (one rate for Iodine, a different one for the chain members). The contaminant
is carried by groundwater through two consecutive geosphere layers to the biosphere, where it
gets into a water stream from which exposed population take drinking water. This model has thirtythree
inputs, twelve of which are affected by uncertainty. These model inputs are the initial inventory
of each considered radionuclide, their decay rates (�), their dose conversion factors (�), and all
the other inputs that characterise the physical-chemical properties of the near field, both geosphere
layers and the biosphere. The complex input-output relation, characterised by strong interactions
among input parameters, makes it a challenging model to test SA techniques.
In this case, the target is twofold: firstly to compare different options within a given SA techniques
(to study the added value of using more complex versions of a given technique – classical FAST
versus extended FAST, first order regressions versus higher order regressions, the benefits of using
transformations of inputs and outputs in the SA, the added value of and the problems that arise
when estimating the effect of interactions and total sensitivity indices, etc.); secondly to crosscompare
the results obtained using different techniques. This cross-comparison may be studied
from two points of view: what differences arise when using techniques that target different objectives
and why; i.e.: PCC and FAST, what differences arise when using techniques that target equal
objectives; i.e.: FAST and Sobol’s indices. Additionally, the effect of the sample size is also in the
focus of the second step of the benchmark.
Many PAMINA partners are interested in bringing to their PA studies all the knowledge and experience
acquired during the benchmark. PAMINA RTDC2 and RTDC4 offer a very good opportunity
to test all those techniques in real PA models proposed by several participants. Table 1 shows a
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