Uncertainty Quantification for Nuclear Systems

Challenge

Uncertainty Quantification is an important process for understanding key drivers and variability in any process. For the development of fusion reactors, it is crucial for gaining a deeper understanding of their design and operation. There are large uncertainties in the design and operation of breeder blankets, which can make their performance deviate significantly from what was expected. Uncertainty quantification (UQ) methods such as sensitivity analysis aim to identify key drivers of uncertainty, allowing design engineers to create more robust and feasible designs.

The UK Atomic Energy Authority wanted to more easily and rapidly understand the effect of uncertainty on the performance of fusion reactors and the critical breeder blankets. Achieving this experimentally is prohibitively expensive and time consuming, requiring a different approach. UKAEA’s existing focus had been on developing appropriate physics models to predict performance, rather than using modelling to undertake engineering design. Our extensive cross-sector experience in of using Multiphysics simulations tools to solve conceptual design challenges and understand process variability, complemented their existing work and led to the project.

Solution

We worked with both a tritium transport and a neutronics model of the pin-cell, a conceptual design component of the breeder blanket. The goal was to apply sensitivity analysis to estimate the relative contribution of each of the inputs to the output of the system, allowing for key drivers of performance to be identified.

To achieve this, the inputs of the system must be identified and bounds defined for their uncertainty. Then a number of designs are generated with each input set to a pseudo-randomly generated value within the bounds. Each design is evaluated and the results extracted. Statistical methods can then be used to determine the contribution of each input to the variability in the output.

This type of analysis requires a large number (thousands to millions) of design evaluations to be robust, it was required to fully parameterise the models and build automated pipelines to define, run and analyse each design. The total runtime of the models was improved by tuning the mesh and solver options with nominal loss in accuracy. More designs were evaluated in the same amount of time, improving the quality of results.

Impact

Thousands of design points were evaluated over a weekend on a standard 24-core box with the ability to scale to HPC-level in future studies. Several investigations were made to explore areas that engineers at UKAEA were interested in.

Results from the sensitivity analysis showed that out of the hundreds of inputs in the breeder blanket models, only a handful were key drivers with a significant impact on the output. This helped to narrow down the focus of future experiments and investigations, ensuring their efforts are spent exploring areas that matter. For parameters that have little impact, UKAEA can loosen tolerances and potentially save time and costs, without impacting the overall performance of the breeder blanket.

One input had an unexpectedly large impact on the output. This allowed UKAEA to realise that one of their modelling assumptions was pushing the model into a regime that was not previously predicted and thus needed to be explored further. Additionally, a proof-of-concept was conducted, coupling the two models to fully understand the main difficulties in performing UQ at scale over the entire blanket. Key challenges in coupling the models were identified and a path forward created.