Uncertainty Propagation in Fusion Neutronics using Imprecise Probabilities
Lead Research Organisation:
University of Liverpool
Department Name: Engineering (Level 1)
Abstract
Neutronics is the study of how neutrons propagate through matter: how they interact, what with, and their manipulation; and is of central importance to the operation of a nuclear reactor, fission or fusion. Monte Carlo has for a long time been the high fidelity method of choice for Neutronics, due to its simplicity and its ability to handle complicated geometries. Recently there has been a growing interest in the quantification and propagation of uncertainty in these types of calculation. This has yielded many methods which are effective for fission but have not been successful for fusion applications, due to the severity of the uncertainty and high number of variables that must be considered.
The current most rigorous method for propagation in Fusion Neutronics is Monte Carlo, however this is usually intractable even with modern high performance computing standards due to the computational cost of performing model evaluations (a full reactor simulation would require the simulation of - 1012 particles). In this project we explore alternatives to Monte Carlo for uncertainty propagation in neutron transport, which can yield a robust measure of uncertainty at a reduced computational cost.
Probabilistic Arithmetic (PA) promises the near automatic propagation of uncertainties in computational models. It achieves this by replacing standard floating point numbers with uncertain numbers, in the form of probability distributions, intervals (ranges) and probability boxes (sets of distributions); and replaces floating point arithmetic with an arithmetic defined over such uncertain numbers. This allows uncertainty to be propagated through every step of the computational model, given only a partial definition of its input uncertainty; as apposed to Monte Carlo which requires a complete description. In this project we extend PA for stochastic models such as those used in Neutronics.
The current most rigorous method for propagation in Fusion Neutronics is Monte Carlo, however this is usually intractable even with modern high performance computing standards due to the computational cost of performing model evaluations (a full reactor simulation would require the simulation of - 1012 particles). In this project we explore alternatives to Monte Carlo for uncertainty propagation in neutron transport, which can yield a robust measure of uncertainty at a reduced computational cost.
Probabilistic Arithmetic (PA) promises the near automatic propagation of uncertainties in computational models. It achieves this by replacing standard floating point numbers with uncertain numbers, in the form of probability distributions, intervals (ranges) and probability boxes (sets of distributions); and replaces floating point arithmetic with an arithmetic defined over such uncertain numbers. This allows uncertainty to be propagated through every step of the computational model, given only a partial definition of its input uncertainty; as apposed to Monte Carlo which requires a complete description. In this project we extend PA for stochastic models such as those used in Neutronics.
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509267/1 | 01/10/2015 | 30/03/2021 | |||
| 1966981 | Studentship | EP/N509267/1 | 01/10/2017 | 31/03/2021 | Ander Gray |
| Description | There were no Key Findings originally associated to this award, instead the general direction of the project was left to the student and their supervisors. I would like to use this section to discuss that direction and the findings thus far. The topic of this project is in Uncertainty Quantification for Fusion Neutronics, that is the propagation of uncertainty in neutron simulations of nuclear fusion reactors. The problem can be stated quite simply as: given an input distribution (describing the uncertainty in the input to the simulation) calculate the output uncertainty from the simulation. This is usually an incredibly computationally expensive task, usually requiring tens of thousands of simulations (sampling). The task of this project is therefore to find a computationally cheap method of doing so. The main direction that was taken is to develop a method known as "Probabilistic arithmetic" (PA) to work with neutronics simulations. In probabilistic arithmetic, standard floating point numbers that a computer uses are replaces by uncertain numbers, in the form of distributions, intervals (ranges) or p-boxes (sets of distributions); and the standard floating point arithmetic is replaced with an arithmetic that works over these mathematical structures. Once replaced, only a single simulation is required for the complete calculation of the output distribution. This method allows for the propagation of uncertainty that sampling alone cannot do, namely uncertainty in dependency, the exact bounding of distributional ranges, and uncertainty in input distribution: i.e. sampling requires the exact input distribution to be specified, and can only approximately calculate the output distribution. Apart from exploring this completely new direction for neutronics, we have two main long term goals: 1. Develop probabilistic arithmetic to work in stochastic models. Neutronics simulations are generally performing using Monte Carlo methods, a stochastic method. PA has only so far been developed for deterministic models, and so we extend this method to work for models which have stochasticity in the physic calculation. 2. Repeated variables. One of the main drawbacks from using PA is that it cannot handle "Repeated Variables", that is, variables which appear a multiple amount of times in an expression. We are extending PA so as to remove this problem, by calculating the dependency of repeated variables in the form of Copulas (a general model for probabilistic dependency). This allows us to calculate and incorporate the dependency of repeated variables in our calculations, resulting in much tighter output distributions. This development is vital for the first contribution. This has been a problem since the beginning of PA. We have also made developments in model calibration (uncertainty characterisation) and model validation. |
| Exploitation Route | Probabilistic arithmetic is very general, and allows for the near automatic propagation of uncertainties. Uncertainty is an important part of the scientific method, and must be performed in all of the scientific disciplines. It is often not performed correctly or in a non rigorous manner. This leads to overconfidence, and at best to the misinterpretation of results, and at worst to serious accidents. Uncertainty usually requires a high level of expertise to be done correctly. PA is a route that would make rigorous uncertainty propagation available to the wider scientific and engineering community. Particle transport Monte Carlo is one of the most widely used methods for radiation transport. Used for example in neutronics simulations of nuclear reactors (both fusion and fusion), the calculation of trajectories on particles born in accelerators, or in medical radiation calculations. These are often expensive computational models, and so often uncertainty propagation is usually inaccessible. If PA could be developed to work for such stochastic models, the application domain would extend to all of these fields. |
| Sectors | Digital/Communication/Information Technologies (including Software),Energy,Other |