In the safety oriented nuclear engineering world, managing uncertainties on fundamental parameters is crucial. Large uncertainties in the neutron cross sections of materials used in these systems propagate through the modeling process and result in large uncertainties in the predicted behavior of the system. Without reducing the uncertainties on the input neutron cross sections by evaluating new experimental data, the only solution to the safety concern of the large uncertainties is to provide large safety margins. The practice of over designing is economically wasteful and adds to the already high cost of nuclear reactors. On the other hand, investing the funds in better nuclear data would result in less uncertainty in the predicted behavior of the system. The high cost of cross section experiments and evaluations requires a procedure to best allocate the funds by proposing experiments that can have the biggest impact on reducing the uncertainties that directly impact the operation and safety of nuclear systems.

This work develops a novel method based on first order sensitivity analysis that propagates the nuclear cross section uncertainty to uncertainties in calculated quantities, such as $k_{\mathrm{eff}}$, reactivity coefficients, multigroup cross sections, and reaction rate ratios. The method developed here improves on existing methods by fully accounting for temperature effects, and by providing a natural, physics-inspired strategy for binning the sensitivity coefficient which aids in the statistical convergence of the sensitivity tallies. These benefits are achieved by using the windowed multipole cross section representation.

As part of the development of the framework, several individual capabilities were developed. First, an algorithm for calculating the sensitivity coefficients to the windowed multipole parameters based on the CLUTCH-FM method is developed and implemented in OpenMC. Second, a process for converting the existing resonance parameter uncertainties to uncertainties in the windowed multipole parameters is introduced. Finally, an analytical benchmark is developed for the purposes of validating the framework, as well as the implementation. This analytical benchmark consists of a solution to the forward and adjoint neutron transport equations.

The windowed multipole covariance matrix is obtained for three nuclides; ²³Na, ¹⁵⁷Gd, and ²³⁸U. The framework is used to calculate the uncertainties for two criticality safety benchmarks, and a beginning-of-life PWR model. The uncertainty of several reaction rate ratios due to the uncertainty in the ¹⁵⁷Gd cross section is also calculated for the PWR model. The resonances of ²³⁸U and ¹⁵⁷Gd that have the largest contribution to the uncertainty are identified for the criticality safety benchmarks.

在面向安全的核工程世界中，管理基本参数的不确定性至关重要。这些系统中使用的材料的中子截面的较大不确定性会在建模过程中传播，并导致系统的预测行为具有较大的不确定性。在不通过评估新的实验数据而减少输入中子截面的不确定性的情况下，解决不确定性大的安全问题的唯一方法是提供较大的安全余量。过度设计的做法在经济上是浪费的，并增加了核反应堆本来已经很高的成本。另一方面，将资金投资于更好的核数据将减少系统预测行为的不确定性。

这项工作开发了一种基于一阶敏感性分析的新方法，该方法将核截面的不确定性传播到计算量的不确定性，例如 ${ķ}_{\mathrm{效}}$，反应系数，多组截面和反应速率比。这里开发的方法通过充分考虑温度影响，并提供一种自然的，受物理学启发的策略来对敏感度系数进行分箱，从而对现有方法进行了改进，从而有助于敏感度统计的统计收敛。通过使用开窗的多极截面表示法可以实现这些好处。

作为框架开发的一部分，开发了一些单独的功能。首先，在OpenMC中开发并实现了一种基于CLUTCH-FM方法计算对开窗多极参数敏感系数的算法。其次，介绍了将现有共振参数不确定性转换为加窗多极参数不确定性的过程。最后，为了验证框架和实现的目的，开发了一个分析基准。该分析基准包括正向和伴随中子输运方程的解。

对于三个核素，获得了窗口化多极协方差矩阵。²³ Na，¹⁵⁷ Gd和^238U。该框架用于计算两个临界安全性基准和寿命开始的PWR模型的不确定性。对于PWR模型，还计算了由于¹⁵⁷ Gd横截面的不确定性而导致的几个反应速率比的不确定性。对于临界安全性基准，确定了对不确定性影响最大的²³⁸ U和¹⁵⁷ Gd共振。