VI. Conclusions
6.1. Future Work
The fission pulse decay heat is not considered in this work. In consequence, subsequent validation work should include STREAM decay heat at very short decay times using pulse fission irradiation experiments. These are important for applications in the analysis of loss of coolant accident and emergency core cooling system performance [93,94]. Future benchmarking work should also include validation of STREAM neutron and gamma source intensities using measured SNF assembly neutron and gamma emission rates. These are important in nuclear safeguard and non-proliferation. Neutron source intensity validation should account for subcritical neutron multiplication in spent fuel to improve agreement with measurements.
On the propagation of modeling parameter uncertainties, the correlations between the input parameters should be explored so as to sample correlated input parameters from a joint PDF.
Although a neutronics only simulation is sufficient for source term calculations, a neutronics- thermal hydraulic coupled simulation may be needed to consider correlations such as those between power and fuel or moderator temperature. On the propagation of neutron and gamma source uncertainties in SNF cask shielding, further verification or validation should be conducted to determine the importance and reliability of the calculations and justify the results and conclusions. Other uncertainties such as Cobalt content of the hardware region, axial burnup profile, cask geometry, and material densities should be considered. The effect of uncertainties from assemblies in the periphery versus center locations, on the dose rate, should be examined. An SNF cask with optimized loading pattern of assemblies with different enrichments, burnups and cooling times should be analyzed in the UQ process.
The Bayesian work will need to consider incorporating the model bias term in the likelihood function of the inverse solution. In addition, how the correlations in the measurements could affect the posterior distributions should be investigated. The Bayesian concept could be explored in the validation of computer codes used in predicting SNF isotopic inventories. Such
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validation exercises are conducted against post irradiation examination (PIE) data. The Bayesian calibration approach can be employed to improve the agreement when calculated isotopic inventories are compared to measured isotopic assay of SNF. This would involve calibrating the model parameters of measured SNF samples. Besides, optimization of SNF in storage facilities e.g., cask can explore the Bayesian method coupled with MCMC, using the regulatory limits of keff and decay heat of the cask loaded with SNF as the objective functions. This application can include the use of a surrogate model to speed up the optimization process because a large number of loading pattern samples might be required from the MCMC. Cask loading optimization is essential to ensure the chosen loading pattern satisfies the requisite safety criteria. For instance, a loading pattern with higher burnup FAs at the cask periphery ensures a richer cooling conditions inside the cask. However, this will result in increased dose outside the cask in radiation shielding studies. Regulatory requirements impose a limit on the dose at the cask surface and at some distance away from the surface. The optimization work should consider the out-of-core SNF management. Several approaches have been investigated to optimize the loading pattern of spent fuel in storage facilities. The storage facilities mostly considered in the previously published works are for final disposal and few studies dealt with interim storage facilities such as dry casks.
Although the Bayesian method and MCMC concepts have been used to optimize the loading pattern of a PWR in-core fuel management [179], the techniques should be explored in out-of-core management of SNFs, especially in storage facilities, to demonstrate their applicability.
The ML work should expand the range of inputs considered to higher enrichments, burnups, and cooling times, by generating more training data with a computer code. Furthermore, one of the methodologies introduced in this research i.e., application of synthetic data, has great potential for RP M&S and other research areas employing computationally expensive codes. Data-driven and learning methods are currently not used extensively for most RP M&S applications such as UQ, SA and design optimization due to the huge computational cost of generating data for learning.
The computationally expensive tools can be employed to generate small dataset of solutions for training ML models or to be used as snapshots for developing reduced order or surrogate models.
One only needs to ensure that the range of input parameters of interest are covered in the small dataset generated. Afterwards, large size synthetic data can be generated to have similar statistical properties from the small dataset. This will not only save computation time; it will also remove the bottleneck caused by small datasets. Moreover, the ML models developed could be considered
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as a computationally efficient tool for both forward and inverse UQ. The ML input features could be calibrated in an IUQ exercise for further improvement of accuracy and reduction of input features induced uncertainties.
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