Parameter Inference in CRUD Dynamics Models for Nuclear Reactor Systems

Sammanfattning

Accumulation of CRUD (Chalk-River Undentified Deposits) in reactor systems poses safety risks and can lead to operational degradation. However, measurements of the CRUD inventory are limited, creating a need for mathematical models to estimate the CRUD inventory. In this thesis, a simple ordinary differential equation (ODE) model is developed, and different parameter inference methods are investigated. The aim is to evaluate whether element-specific model parameters can be reliably estimated from sparse and uncertain data, and to identify the associated uncertainties and limitations. The model parameters are estimated using both deterministic optimization methods and Bayesian inference with the Metropolis-Hastings sampling algorithm. Synthetic data experiments are conducted to study how the methods are affected by measurement noise, data availability and the model structure. These experiments show that the methods successfully recover the true parameter values under ideal conditions but suffer from identifiablity issues in more realistic scenarios. The results show that uncertainty in the parameter estimates does not only originate from measurement noise, but also from model structure and parameter correlations. The use of more informative priors in the Bayesian inference did not resolve the identifiability issue. The inference methods are then applied to real operational data from a Swedish nuclear reactor, more specifically measurements of the radioactive iron isotope Fe-59. These results reveal additional challanges related to uncertain measurements and limited prior knowledge of the model parameters. Parameter correlations further indicate strucutral identifiability issues. The Bayesian method provided insight to the uncertainty quantification but remained sensitive to the selection of parameter priors and the data availability. In conclusion, this study shows that reliable parameter inference depends on model structure, data quality and data availablity. Although advanced inference methods can provide import insights into parameter uncertainty, the model structure and the available measurements impose fundamental limitations on the parameter inference. This work provides the foundation for future efforts to improve CRUD modeling, parameter estimation and uncertainty quantification.