Structured treatment of model uncertainty in complex thermal-hydraulics codes: Technical challenges, prospective and characterization

Uncertainty and sensitivity analyses for steady-state thermal–hydraulics of research reactors

Chapter Eighteen Uncertainty and Sensitivity Issues in Process-based Models of Carbon and Nitrogen Cycles in Terrestrial Ecosystems

Development of a Multi-Compartment Containment thermal hydraulic code: PARIRODHAN

Hydrologic and water quality models (HWQMs) are increasingly used to support decisions on various environmental issues and policy directions for present and future scenarios, at scales varying from watershed to continental levels. Uncertainty associated with such models may affect the ability of the models to accurately evaluate the response of complex systems, leading to misguided assessments and risk management decisions. Current well-known HWQMs contain numerous input parameters, many of which are not known with certainty, and in other cases model users can hardly recognize the genesis of uncertainty. Uncertainty in data, model structure, and model parameters can propagate throughout model runs, causing the model output to substantially deviate from the expected response of the natural system. Various uncertainty assessment methods have been used with different HWQMs, creating concerns about an adequate approach for handling uncertainty in these models and how such an approach can be implemented across various discretization complexities and scales. In this article, our primary intention is to review uncertainty in the currently used HWQMs and to provide guidance and useful information for researchers and investigators. In this regard, we explore the genesis of uncertainty in hydrologic and water quality modeling (i.e., spatiotemporal scales, model representation, model discretization, model parameterization) and provide strategies for assessing uncertainty in hydrologic and water quality modeling on local and global scales when interpreting the model output.

Analysis of loss of flow without scram test in the FFTF reactor – Part I: Preparation of neutronics data

A tightly coupled scheme for neutronics and thermal–hydraulics using open-source software

The complete failure of the reactor scram system upon request during an operational transient is called anticipated transient without scram (ATWS). According to the German regulatory guidelines, postulated ATWS events have to be analyzed with regard to their consequences on the safety of nuclear power plants. Since the course of ATWS transients is determined by a strong interaction of the neutron kinetics with the thermal hydraulics of the system, coupled 3D neutron kinetic/thermal hydraulic code systems are adequate tools for the analysis of such transients. The coupled code system DYN3D/ATHLET developed at FZD is applied to the analysis of an ATWS transient. The objective of the present work is to perform a best-estimate analysis with consequent use of a 3D neutron kinetic code (DYN3D) in combination with an advanced thermal hydraulic system code (ATHLET) together with a quantification of differences in the course and the results of transients, which arise from the uncertainties of thermal hydraulic and neutron-physical conditions. Typically, the complete failure of the main feed water supply is assumed to be the bounding ATWS event with regard to the maximum primary coolant pressure, which can be reached during the transient. The limitation of the coolant pressure is a precondition for the integrity of the primary circuit. The situation is aggravated if the main coolant pumps remain in operation. For this particular transient, the influence of different thermal hydraulic and neutron-physical conditions on the course of the transient was analyzed. In a number of code runs all systems which have an influence on the course of the transient were varied. These are the auxiliary boration system and the auxiliary feed water supply. Further, the influence of the modeling of the pressurizer safety and relief valves as well as the steam bypass system on the secondary side was assessed. The variation of the pressurizer relief and safety valve behavior has the biggest influence on the primary circuit coolant pressure. In the second part, two different core loading patterns were generated for the analyses by varying the number of MOX (mixed oxide) fuel assemblies (FA) in the core. The basic core loading contains 64 MOX FA. All these MOX FA were replaced by standard uranium oxide FA. The presence of MOX in the core has a remarkable influence on the reactivity coefficients of the fuel temperature and the moderator density. These two parameters mainly influence the behavior of the coolant pressure in the first part of the transient. It has been demonstrated that the pressure maximum decreases with growing MOX portion in the core. The maximum pressure determined in the calculations with variation of system and neutron-physical boundary conditions does not reach the allowed limit for the primary circuit.

Simulations of complex scenarios in nuclear power plants have been improved by the utilization of coupled thermal hydraulic (TH) and neutron kinetics (NK) system codes with the development of computer technology and new calculation methodology which made it possible to perform transport calculation schemes with accurate solutions. This paper presents a model for the IPR-R1 TRIGA research reactor using the RELAP5-3D 3.0.0 code. By using this code, a multi-dimensional neutron kinetics model based on the NESTLE code can be implemented also. In this way, during a 3D TH/NK coupled simulation, RELAP5-3D calls the appropriate NESTLE subroutines to perform the calculations. The development and the assessment of the thermal hydraulic RELAP5 code model for the IPR-R1 TRIGA have been validated for steady state and transient situations and the results were published in preceding works. The model has been adapted to RELAP5-3D code and was verified to point kinetic calculations. After this, adequate cross sections to the NK code were supplied using the WIMSD5 code. The results of steady state and transient calculations using the 3D neutron modeling to the IPR-R1 are being presented in this paper.

The need for more accurate asteroid models is perhaps secondary to the need to measure their quality. The uncertainties of models' parameters propagate to quantities like volume or density -- the most important and informative properties of asteroids -- affecting conclusions about their physical nature. Our knowledge on shapes and spins of small solar system bodies comes mostly from visual, disk-integrated photometry. In this work we present a method for asteroid model uncertainty assessment based on visual photometry (lightcurves and sparse-in-time absolute measurements) allowing the determination of realistic volume uncertainty, as well as spin axis orientation, rotational period and local surface features. The sensitivity analysis is conducted by creating clones of the nominal model and accepting the ones that fit the observations within a confidence level. The uncertainties of model parameters are extracted from the extreme values found in the accepted clone population. Creation of such population of clones enables the conversion of a deterministic asteroid model into stochastic one, and can be utilized to create observation predictions with error bars. The method was used to assess the uncertainties of fictitious test models and real targets, i.e. (21) Lutetia, (89) Julia, (243) Ida, (433) Eros and (162173) Ryugu. We conclude that volumes, and subsequently, densities of asteroids derived from lightcurve-based models likely have vastly understated uncertainties, the biggest source of which is the inability to establish the extent of the model along its spin axis.

In this study, a factorial multimodel Bayesian copula (FMBC) method is proposed to investigate various uncertainties in the copula-based multivariate risk models and further track the major contributors to the imprecise predictions for different risk indices. In FMBC, the copula models with different marginals and dependence structures will be firstly established with the parameter uncertainties being quantified by the adaptive Metropolis algorithm. A multilevel factorial analysis approach is then adopted to characterize the individual and interactive effects of marginals, copula functions and the associated parameter uncertainties on different risk indices. Moreover, a copula-based dependent sampling algorithm is proposed in the factorial analysis process to generate parameter samples under consideration of their correlation. The applicability of the FMBC approach is demonstrated through the multivariate flood risk analysis at two gauging stations in Wei River basin. The results indicate that extensive fluctuation exists in the inferences of multivariate return periods resulting from different marginal and dependence structures as well as the associated parameter uncertainties. For risk indices of the failure probabilities in AND and Kendall, their predictive variability can be mainly attributed to the uncertainties in model parameters and copula structure, with their total contribution more than 75%. In comparison, the failure probability in OR would be mainly influenced by the parameter uncertainty and also marginal structures, with their total contribution more than 80%. The copula structure would not have a visible effect on the failure probability in OR, with its contribution less than 5% for most scenarios. The obtained results can provide scientific support for reliable hydrological risk inferences within a multivariate context.

This report presents guidelines for evaluating uncertainty in mathematical equations and computer models applied to assess human health and environmental risk. Uncertainty analyses involve the propagation of uncertainty in model parameters and model structure to obtain confidence statements for the estimate of risk and identify the model components of dominant importance. Uncertainty analyses are required when there is no a priori knowledge about uncertainty in the risk estimate and when there is a chance that the failure to assess uncertainty may affect the selection of wrong options for risk reduction. Uncertainty analyses are effective when they are conducted in an iterative mode. When the uncertainty in the risk estimate is intolerable for decision-making, additional data are acquired for the dominant model components that contribute most to uncertainty. This process is repeated until the level of residual uncertainty can be tolerated. A analytical and numerical methods for error propagation are presented along with methods for identifying the most important contributors to uncertainty. Monte Carlo simulation with either Simple Random Sampling (SRS) or Latin Hypercube Sampling (LHS) is proposed as the most robust method for propagating uncertainty through either simple or complex models. A distinction is made between simulating a stochastically varying assessment endpoint (i.e., the distribution of individual risks in an exposed population) and quantifying uncertainty due to lack of knowledge about a fixed but unknown quantity (e.g., a specific individual, the maximally exposed individual, or the mean, median, or 95%-tile of the distribution of exposed individuals). Emphasis is placed on the need for subjective judgement to quantify uncertainty when relevant data are absent or incomplete.

Molten salt reactor (MSR) using liquid fuel is one of the Generation-IV candidate reactors. Its liquid fuel characteristics are fundamentally different from those of the conventional solid-fuel reactors, especially the much stronger neutronics and thermal hydraulics coupling is drawing significant attention. In this study, the fundamental thermal hydraulic model, neutronic model, and some auxiliary models were established for the liquid-fuel reactors, and a time-dependent coupled neutronics and thermal hydraulics code named COUPLE was developed to solve the mathematic models by the numerical method. After the code was verified, it was applied to the molten salt fast reactor (MSFR) to perform the steady state calculation. The distributions of the neutron fluxes, delayed neutron precursors, velocity, and temperature were obtained and presented. The results show that the liquid fuel flow affects the delayed neutron precursors significantly, while slightly influences the neutron fluxes. The flow in the MSFR core generates a vortex near the fertile tank, which leads to the maximal temperature about 1100 K at the centre of the vortex. The results can provide some useful information for the reactor optimization.

Reliable analyses of thermal–hydraulic (TH) transients are becoming fundamental to supporting the design of magnets for fusion applications based on high temperature superconducting (HTS) cable-in-conduit-conductors (CICCs). However, currently available TH codes were developed and validated only for the analysis of magnets wound with low temperature superconductor (LTS) CICCs. In order to confirm the applicability of such tools to HTS CICCs, a two-step strategy is presented in this paper. First, a qualitative assessment of the characteristic time and spatial scales in HTS CICCs, based on the twisted-stacked-tape cable (TSTC) concept, has been performed. It shows that the different geometry and materials of TSTC strands lead to heat transfer time scales on the conductor cross-section, which are comparable to those of fast transients, ranging from milliseconds to few seconds, e.g. quench initiation and propagation as well as AC losses. Therefore, the assumptions of temperature uniformity on the cross-section, typical of the well-established 1D codes developed for LTS magnets, become questionable. A second, quantitative assessment, based on detailed electro-thermal models of the conductor and of the single TSTC strand cross-section, provides guidelines for the development of more reliable 1D models for the analysis of TH transients in HTS fusion magnets.

Obesity poses significant health and economic burdens globally, with interventions requiring robust cost-effectiveness evaluations. Markov models are widely utilized in economic evaluation of obesity interventions, their structure, assumptions, and related uncertainties have not yet been thoroughly evaluated. This study aimed to systematically review the Markov models used for the economic evaluation of anti-obesity interventions, describe their structural characteristics, identify key uncertainties, and provide insights for future research. The review was conducted across three databases (PubMed, Embase, the Cochrane Library) and health technology assessment agency websites to identify published Markov model-based full economic evaluations in adults with obesity from their inception to 2 June 2024. Model structure, model uncertainty, and validation were extracted from the included studies. Philips checklist for the methodology quality of modeling studies was performed. The review included 21 primary publications with 21 unique Markov models. Two modeling approaches regarding the progression of obesity and its impact were identified: direct BMI to cost and utility; and BMI-linked complications, with diabetes and cardiovascular diseases most frequently modeled. Validation practices were inconsistently reported (43% of models), and structural uncertainty (eg, BMI trajectory assumptions) was rarely addressed. Quality assessment revealed moderate rigor (a mean compliance rate of 78% across all criteria), with gaps in transparency and generalizability, particularly for non-Western populations. Probabilistic sensitivity analysis was universal, yet scenario analyses highlighted outcome sensitivity to complication inclusion and time horizons. While Markov models are commonly utilized in obesity intervention evaluations, methodological heterogeneity and insufficient validation limit comparability and reliability. Future models should prioritize standardized validation (eg, ISPOR guidelines), broader complication spectrum, and diverse population data. Enhancing transparency in structural assumptions and uncertainty analysis is critical for robust policy recommendations.

Scientists and decision-makers globally confront systemic challenges posed by the intertwining issues of water scarcity and climate change. These challenges give rise to cascading impacts across ecological and socioeconomic systems, often exacerbated by feedback loops and unforeseeable consequences (UNDRR, 2021). As non-linear changes loom, the reliance on consolidative modeling becomes dangerous, risking the activation of disastrous tipping points with severe implications for both nature and humans (Kreibich et al., 2022). The costs associated with neglecting uncertainties in modeling and policy spans diverse domains, including ecosystems, income, employment, capital value, insurance, etc. (UNDRR, 2022; Parrado et al., 2019; Adamson and Loch, 2021). This aligns with the concept of Knightian or deep uncertainty, where the external context, system dynamics, and conflicting outcomes are not fully known or agreed upon (Knight, 1921; Marchau et al., 2019; Lempert et al., 2006). A growing scientific and policy consensus emphasizes the need to move beyond traditional notions of optimality and deterministic prediction in conditions of deep uncertainty. Resilience and robustness emerge as crucial concepts, requiring the development of socio-ecological system (SES) models that explicitly quantify uncertainties (Adamson and Loch, 2021; Di Baldassarre et al., 2016; IPCC, 2021; UNDRR, 2021).Recent research in SES, including coupled human and natural systems and socio-hydrology science, offers innovative modeling techniques integrating human and natural components. These techniques account for feedbacks and heterogeneity between systems, improving insight and the ability to predict tipping points (Gain et al., 2021). Recent studies demonstrate the potential of linking coupled models of human-water systems with sensitivity analysis and multi-system ensembles for robust water management policies (Basheer et al., 2023; Smith et al., 2021).This review initially identified 2160 papers, filtering them to 198 studies that account quantitatively modelling in, both human and water systems. The geographical focus spans the USA, Europe, Australia, the Middle East, South America, China, and East Africa. The models range from piecewise equations to full-fledged representations. However, structural uncertainties are seldom explored, with only 3.5% of studies conducting multi-model ensemble experiments. This highlights a significant oversight in recognizing biases from simplifications. Conversely, parameter uncertainties are more frequently addressed (20.2%), focusing on hydrology, groundwater, behavioral, infrastructure, climatic, economic, and agronomic variables. Input uncertainties, notably contemporary (discharge data) and future (climate change) inputs, are extensively studied (148 out of 198), employing methods like expert judgment and Monte Carlo simulations. Despite this, the review highlights a limited exploration of structural uncertainties and the potential inadequacy of linear piecewise equations, emphasizing the need for more nuanced and robust approaches to enhance the accuracy and reliability of socio-environmental systems modeling.Based on this study, we make the following recommendations to mainstream uncertainty quantification into SES modeling: (i) Quantify parameter and structural uncertainties within systems, (ii) Quantify structural uncertainties between models, (iii) Input uncertainties must be more thoroughly assessed and model assumptions systematically revised, (iv) Deliver actionable science that mainstreams uncertainty quantification into decision making, (v) Establish balanced stakeholder engagement and clear and transparent science-policy engagement rules, (vi) Balance complexity and usefulness to keep the model relevant.