In nuclear reactor system design and safety analysis, the Best Estimate plus Uncertainty (BEPU) methodology requires that computer model output uncertainties must be quantified in order to prove that the investigated design stays within acceptance criteria. "Expert opinion" and "user self-evaluation" have been widely used to specify computer model input uncertainties in previous uncertainty, sensitivity and validation studies. Inverse Uncertainty Quantification (UQ) is the process to inversely quantify input uncertainties based on experimental data in order to more precisely quantify such ad-hoc specifications of the input uncertainty information.In this paper, we used Bayesian analysis to establish the inverse UQ formulation, with systematic and rigorously derived metamodels constructed by Gaussian Process (GP). Due to incomplete or inaccurate underlying physics, as well as numerical approximation errors, computer models always have discrepancy/bias in representing the realities, which can cause over-fitting if neglected in the inverse UQ process. The model discrepancy term is accounted for in our formulation through the "model updating equation". We provided a detailed introduction and comparison of the full and modular Bayesian approaches for inverse UQ, as well as pointed out their limitations when extrapolated to the validation/prediction domain. Finally, we proposed an improved modular Bayesian approach that can avoid extrapolating the model discrepancy that is learnt from the inverse UQ domain to the validation/prediction domain.

Inverse Uncertainty Quantification (UQ) is a process to quantify the uncertainties in random input parameters while achieving consistency between code simulations and physical observations. In this paper, we performed inverse UQ using an improved modular Bayesian approach based on Gaussian Process (GP) for TRACE physical model parameters using the BWR Full-size Fine-Mesh Bundle Tests (BFBT) benchmark steady-state void fraction data. The model discrepancy is described with a GP emulator. Numerical tests have demonstrated that such treatment of model discrepancy can avoid over-fitting. Furthermore, we constructed a fast-running and accurate GP emulator to replace TRACE full model during Markov Chain Monte Carlo (MCMC) sampling. The computational cost was demonstrated to be reduced by several orders of magnitude.A sequential approach was also developed for efficient test source allocation (TSA) for inverse UQ and validation. This sequential TSA methodology first selects experimental tests for validation that has a full coverage of the test domain to avoid extrapolation of model discrepancy term when evaluated at input setting of tests for inverse UQ. Then it selects tests that tend to reside in the unfilled zones of the test domain for inverse UQ, so that one can extract the most information for posterior probability distributions of calibration parameters using only a relatively small number of tests. This research addresses the "lack of input uncertainty information" issue for TRACE physical input parameters, which was usually ignored or described using expert opinion or user self-assessment in previous work. The resulting posterior probability distributions of TRACE parameters can be used in future uncertainty, sensitivity and validation studies of TRACE code for nuclear reactor system design and safety analysis.

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The critical heat flux (CHF) corresponding to the departure from nucleate boiling (DNB) crisis is essential to the design and safety of a two-phase flow boiling system. Despite the abundance of predictive tools available to the thermal engineering community, the path for an accurate, robust CHF model remains elusive due to lack of consensus on the DNB triggering mechanism. This work aims to apply a physics-informed, machine learning (ML)-aided hybrid framework to achieve superior predictive capabilities. Such a hybrid approach takes advantage of existing understanding in the field of interest (i.e., domain knowledge) and uses ML to capture undiscovered information from the mismatch between the actual and domain knowledge-predicted target. A detailed case study is carried out with an extensive DNB-specific CHF database to demonstrate (1) the improved performance of the hybrid approach as compared to traditional domain knowledge-based models, and (2) the hybrid model's superior generalization capabilities over standalone ML methods across a wide range of flow conditions. The hybrid framework could also readily extend its applicability domain and complexity on the fly, showing an elevated level of flexibility and robustness. Based on the case study conclusions, the window-type extrapolation mapping methodology is further proposed to better inform high-cost experimental work. Keywords: critical heat flux, departure from nucleate boiling, hybrid framework, machine learning, domain knowledge. API application programming interface CHF critical heat flux DK domain knowledge DNB departure from nucleate boiling EPRI Electric Power Research Institute LUT look-up table MAE mean absolute error ML machine learning MSE mean squared error NN (feed-forward) neural network PWR pressurized water reactor ReLU rectified linear unit RF random forest rRMSE relative root-mean-square error

The first-of-a-kind (FOAK) nuclear plants built in the last 20 years are 2X over budget and schedule in the US and some European countries. One of the nuclear industry's proposed remedies is the small modular reactor (SMR). SMR designs leverage five factors to be more economically competitive than large reactors: 1) multiple units; 2) increased factory production and learning; 3) reduced construction schedules; 4) plant design simplification and 5) unit timing. There are currently no studies that quantitatively account for these factors and compare different near term SMRs with Gen III+ large plants. This work presents a nuclear plant cost estimating methodology using a detailed bottom up approach for over 200 structures, systems, and components. The results compare relative cost for two large pressurized water reactors, one with active safety and one with passive safety, to two SMR designs, one with multiple reactor power modules and one with a single reactor module. Passive safety systems showed noticeable savings at both the large and small scale reactors. The power uprating of a SMR by 20% resulted in ~15% savings in the overnight unit capital cost. Overall, if built by an inexperience vendor and work force, the two SMRs' overnight cost were higher than large reactors since significant on-site labor still remains while losing economy of scale. However, the single-unit SMR had significantly less total person-hours of onsite labor, and if built by an experienced workforce, its overnight construction cost showed potential to be competitive and avoid cost-overrun risks associated with megaprojects. Highlights:• Bottom-up cost estimation of large and small nuclear plants are made.• Typical SMRs require at least similar unit on-site labor hours vs. large reactors.• Introduction of passive safety and power uprate are effective at reducing cost.• FOAK overnight unit cost of SMRs can be noticeably higher than large reactors.• Experienced vendor and work force could make SMRs competitive with large plants.