Uncertainty Propagation Research Articles

Uncertainty modeling and propagation for groundwater flow: a comparative study of surrogates

We compare sparse grid stochastic collocation and Gaussian process emulation as surrogates for the parameter-to-observation map of a groundwater flow problem related to the Waste Isolation Pilot Plant in Carlsbad, NM. The goal is the computation of the probability distribution of a contaminant particle travel time resulting from uncertain knowledge about the transmissivity field. The latter is modelled as a lognormal random field which is fitted by restricted maximum likelihood estimation and universal kriging to observational data as well as geological information including site-specific trend regression functions obtained from technical documentation. The resulting random transmissivity field leads to a random groundwater flow and particle transport problem which is solved realization-wise using a mixed finite element discretization. Computational surrogates, once constructed, allow sampling the quantities of interest in the uncertainty analysis at substantially reduced computational cost. Special emphasis is placed on explaining the differences between the two surrogates in terms of computational realization and interpretation of the results. Numerical experiments are given for illustration.

Uncertainty propagation for MAPoD in eddy current NDT by polynomial chaos–kriging

ABSTRACT In this article, the Polynomial Chaos–Kriging (PCK) metamodel is proposed to surrogate the physical model for model-assisted probability of detection (MAPoD) analysis in eddy current non-destructive testing (ECNDT). Two popular non-intrusive metamodels, the Polynomial Chaos Expansion (PCE) and Kriging, are combined properly to replace the time-consuming boundary element method-based ECNDT forward solver for accelerating the uncertainty propagation within MAPoD analysis in NDT. In PCK, the global behaviour of the model is estimated by the trend function of PCE, and the remaining local changes of it are captured by Kriging. Both the accuracy and efficiency of the proposed PCK metamodel are demonstrated on 3D ECNDT MAPoD cases involving surface flaws on the conducting thick plate using the detecting coil with rectangular cross section. Numerical results show improved performance of PCK metamodel over PCE and Kriging metamodels, respectively, while maintaining at least two digits of accuracy of the PoD metrics.

Natural ventilation cooling effectiveness classification for building design addressing climate characteristics

The evaluation of natural ventilation potential for effective sustainable options and innovative green building design strategies is of great interest to architects, researchers and governments. From a retrospective review, we found that the potential evaluation of natural ventilation (NV) cooling effectiveness in the same category based on similar meteorological uncertainty, research objectives and objects showed significant differences. Uncertainties added and uncertainty propagation (both model form uncertainties and parameter uncertainties) could result in large discrepancies between simulation outcomes and real scenarios, especially in the design performance modeling (DPM) phase. In this conceptual design stage, a few parameters are available and therefore decisive. It is necessary to review and identify the key performance indicators and explore the extent to which deviations are caused by inconsistencies or biases in model information. As a basis for more concrete research, we propose statistical tests based on quantitative evaluations to explore the rule of natural ventilation potential volatility and identify whether there is a significant potential improvement resulting from the critical parameter enhancement with the optimal relationship. The showcase is applied in China, where there has been a significant amount of criticism regarding the current building climate zoning due to the perceived coarseness of the system and where there has been an active exploration into the possibility of redefining building climate zoning with a view toward improving its accuracy and effectiveness.

Study on quantitative generation technology of bio-fluorescence calibration particles based on inkjet generator

Accurate measurements are critical for timely early warning and effective prevention of epidemics due to the continuing impact of bioaerosols on human health. In recent years, researchers have been focused on developing and calibrating online monitoring instruments. However, there is still a lack of laboratory-generated standard aerosol samples suitable for calibration. Therefore, in this study, we utilized a self-developed Ink Jet Aerosol Generator (H-IJAG) to achieve controllable generation of monodisperse aerosol standard particles. The Aerosol Particle Size Spectrometer (APSS, TOPAS 323) was employed as the particle detector. The diameter of the droplet was calculated by measuring the projected area of the droplet in the same image using Image-J software. Experimental results demonstrated that under standardized inkjet parameters, H-IJAG exhibited good reliability and reproducibility, and generated solid particles within (0.4–15) μm. To better simulate the laser-induced fluorescence emission properties of ambient bioaerosol, tryptophan (Trp) and 7-hydroxycoumarin-4-acetic acid (7-HCA) were selected as solutes of the laboratory-generated aerosol samples, which are known bio-fluorescent materials. According to the law of propagation of uncertainty, the relative uncertainty of the volume equivalent diameter of Trp and 7-HCA solid particles by H-IJAG were 0.42 %, while the relative uncertainty of the particle number concentrations of Trp and 7-HCA solid particles generated by H-IJAG were 1.4 %. This optimized IJAG technique provides a promising solution for the accurate calibration of bioaerosol monitors.

Unsupervised stochastic learning and reduced order modeling for global sensitivity analysis in cardiac electrophysiology models

Background and Objective:Numerical simulations in electrocardiology are often affected by various uncertainties inherited from the lack of precise knowledge regarding input values including those related to the cardiac cell model, domain geometry, and boundary or initial conditions used in the mathematical modeling. Conventional techniques for uncertainty quantification in modeling electrical activities of the heart encounter significant challenges, primarily due to the high computational costs associated with fine temporal and spatial scales. Additionally, the need for numerous model evaluations to quantify ubiquitous uncertainties increases the computational challenges even further. Methods:In the present study, we propose a non-intrusive surrogate model to perform uncertainty quantification and global sensitivity analysis in cardiac electrophysiology models. The proposed method combines an unsupervised machine learning technique with the polynomial chaos expansion to reconstruct a surrogate model for the propagation and quantification of uncertainties in the electrical activity of the heart. The proposed methodology not only accurately quantifies uncertainties at a very low computational cost but more importantly, it captures the targeted quantity of interest as either the whole spatial field or the whole temporal period. In order to perform sensitivity analysis, aggregated Sobol indices are estimated directly from the spectral mode of the polynomial chaos expansion. Results:We conduct Uncertainty Quantification (UQ) and global Sensitivity Analysis (SA) considering both spatial and temporal variations, rather than limiting the analysis to specific Quantities of Interest (QoIs). To assess the comprehensive performance of our methodology in simulating cardiac electrical activity, we utilize the monodomain model. Additionally, sensitivity analysis is performed on the parameters of the Mitchell-Schaeffer cell model. Conclusions:Unlike conventional techniques for uncertainty quantification in modeling electrical activities, the proposed methodology performs at a low computational cost the sensitivity analysis on the cardiac electrical activity parameters. The results are fully reproducible and easily accessible, while the proposed reduced-order model represents a significant contribution to enhancing global sensitivity analysis in cardiac electrophysiology.

Parameter identification and uncertainty propagation of hydrogel coupled diffusion-deformation using POD-based reduced-order modeling

AbstractThis study explores reduced-order modeling for analyzing time-dependent diffusion-deformation of hydrogels. The full-order model describing hydrogel transient behavior consists of a coupled system of partial differential equations in which the chemical potential and displacements are coupled. This system is formulated in a monolithic fashion and solved using the finite element method. We employ proper orthogonal decomposition as a model order reduction approach. The reduced-order model performance is tested through a benchmark problem on hydrogel swelling and a case study simulating co-axial printing. Then, we embed the reduced-order model into an optimization loop to efficiently identify the coupled problem’s material parameters using full-field data. Finally, a study is conducted on the uncertainty propagation of the material parameter.

Propagation of Modelling Uncertainties for Seismic Risk Assessment: The Effect of Sampling Techniques on Low-Rise Non-Ductile RC Frames

ABSTRACT Quantifying the impact of modelling uncertainty on seismic performance assessment of existing buildings is non-trivial when considering the partial information available on material properties, construction details, and the uncertainty in the capacity models. This task is further complicated when uncertainty related to ground motion representation is considered. To address this issue, record-to-record variability, uncertainties in structural model parameters, and fragility model parameters due to limited sample size are propagated herein by employing a nonlinear dynamic analysis procedure based on recorded ground motions. A one-to-one sampling approach is adopted in which each recorded ground motion is paired up with a different structural model realization. Uncertainty propagation is explored by measuring the impact of different sampling techniques, such as Monte Carlo simulation with standard random sampling and Latin Hypercube sampling (with Simulated Annealing) in the presence of three alternative nonlinear dynamic analysis procedures: Incremental Dynamic Analysis (IDA), Modified Cloud Analysis (MCA), and Cloud to IDA (a highly efficient IDA-like procedure). This is all illustrated through application to an existing reinforced-concrete school building in southern Italy. It is shown that with a small subset of records, both MCA and Cloud to IDA can provide reliable structural fragility (and risk) estimates for three considered limit states, comparable to the results of more resource-intensive schemes.

A Preconditioner-Based Data-Driven Polynomial Expansion Method: Application to Compressor Blade With Leading Edge Uncertainty

Abstract In engineering practice, the amount of measured data is often scarce and limited, posing a challenge in uncertainty quantification (UQ) and propagation. Data-driven polynomial chaos (DDPC) is an effective way to tackle this challenge. However, the DDPC method faces problems from the lack of robustness and convergence difficulty. In this paper, a preconditioner-based data-driven polynomial chaos (PDDPC) method is developed to deal with UQ problems with scarce measured data. Two numerical experiments are used to validate the computational robustness, convergence property, and application potential in case of scarce data. Then, the PDDPC is first applied to evaluate the uncertain impacts of real leading edge (LE) errors on the aerodynamic performance of a two-dimensional compressor blade. Results show that the overall performance of compressor blade is degraded and there is a large performance dispersion at off-design incidence conditions. The actual blade performance has a high probability of deviating from the nominal performance. Under the influence of uncertain LE geometry, the probability distributions of the total pressure loss coefficient and static pressure ratio have obvious skewness characteristics. Compared with the PDDPC method, the UQ results obtained by the fitted Gaussian and Beta probability distributions seriously underestimate the performance dispersion of compressor blade. The mechanism analysis illustrates that the large flow variation around the leading edge is the main reason for the overall performance degradation and the fluctuations of the entire flow field.

Robust Trajectory Planning of Gliding-Guided Projectiles with Weak Maneuverability

Due to constraints in launch platforms and cost, the maneuverability of gliding-guided projectiles is limited, necessitating a rational design of their trajectory schemes. To reduce the sensitivity of trajectory schemes to uncertainties while ensuring compatibility between flight schemes and guidance control systems and fully exploiting the control capability of the projectile, a closed-loop robust trajectory planning method is proposed. Models of major uncertain factors and state deviation at the control start point are established. Based on the NIPCE method, the stochastic dynamic model is transformed into a high-dimensional deterministic model with PCE coefficients as state variables, and the uncertainty propagation law is obtained. A PID algorithm is employed to design a tracking guidance law based on position error feedback, and open-loop and closed-loop robust trajectory planning models are established accordingly. The optimal control problem is solved by transforming it into a nonlinear programming problem using the direct shooting method. Our simulation results indicate that the NIPCE method can significantly improve the computational efficiency of uncertainty propagation while ensuring accuracy; compared with parallel MCS, the computation time is reduced by 96.8%. Open-loop robust planning can effectively mitigate the sensitivity of gliding trajectories to uncertainties (the standard deviations of terminal altitude and lateral deviations are reduced by 23.6% and 35.3%, respectively, compared to deterministic planning) but cannot completely eliminate terminal dispersion. Closed-loop robust planning effectively improves control effort consumption on the basis of open-loop planning.

Uncertainty Quantification in Radial Anisotropy Models Based on Transdimensional Bayesian Inversion of Receiver Functions and Surface-Wave Dispersion: Case Study Sri Lanka

ABSTRACT In geophysical inference problems, quantification of data uncertainties is required to balance the data-fitting ability of the model and its complexity. The transdimensional hierarchical Bayesian approach is a powerful tool to evaluate the level of uncertainty and determine the complexity of the model by treating data errors and model dimensions as unknown. In this article, we take account of the uncertainty through the whole procedure, thus developing a two-step fully Bayesian approach with coupled uncertainty propagation to estimate the crustal isotropic and radial anisotropy (RA) model based on Rayleigh and Love dispersion as well as receiver functions (RFs). First, 2D surface-wave tomography is applied to determine period-wise ambient noise phase velocity maps and their uncertainty for Rayleigh and Love waves. Probabilistic profiles of the isotropic average VS and RA as a function of depth are then derived at station sites by inverting the local surface-wave dispersion and model errors and RFs jointly. The workflow is applied to a temporary seismic broadband array covering all of Sri Lanka. The probabilistic results enable us to effectively quantify the uncertainty of the final RA model and provide robust inferences. The shear-wave velocity results show that the range of Moho depths is between 30 and 40 km, with the thickest crust (38–40 km) beneath the central Highland Complex. Positive RA (VSH>VSV) observed in the upper crust is attributed to subhorizontal alignment of metamorphic foliation and stretched layers resulting from deformation. Negative RA (VSV>VSH) in the midcrust of central Sri Lanka may indicate the existence of melt inclusions and could result from the uplift and folding process. The positive RA in the lower crust could be caused by crustal channel flow in a collision orogeny.

Integrated management of safety and security barriers in chemical plants to cope with emerging cyber-physical attack risks under uncertainties

Chemical facilities face threats from accidental and intentional events, including the rising concern of cyber-physical (C2P) attacks in the digitized industrial control system era. Addressing major accident risks from safety hazards and C2P attacks requires an immediate unified framework for safety and security barrier management. This study presents a systematic risk-based approach to integrate conventional safety risks with emerging C2P attack risks. Adverse scenarios are identified, integrated into an attack-tree-bow-tie diagram, and modelled using a Bayesian network (BN). A vulnerability assessment model is developed to quantify industrial control system vulnerability to C2P attacks, considering uncertainties in attackers' knowledge levels. Monte Carlo simulations are used to handle uncertainty propagation in risk assessment, allowing the use of probability distributions for BN root nodes. Sensitivity analysis identifies critical factors/events, guiding the proposal of candidate strategies for barrier improvements. Combining cost-effectiveness analysis with a risk matrix yields the optimal strategy for safety and security barrier enhancements based on risk estimations. A hypothetical case study demonstrates the proposed approach's effectiveness in integrated safety and security barrier management, considering security vulnerability patching and safety barrier maintenance scheduling from a cost-effective perspective.

Novel gradient-enhanced Bayesian neural networks for uncertainty propagation

Uncertainty propagation (UP) is crucial for assessing the impact of input uncertainty on structural responses, holding significant importance in engineering applications. However, achieving accurate and efficient UP remains challenging, especially for highly nonlinear structures. Bayesian neural networks (BNN) have gained attention for addressing UP issues, yet current BNN models only utilize input samples and corresponding structural responses for training. However, incorporating gradients of structural responses with respect to input samples provides valuable information. This study proposes a novel approach called gradient-enhanced Bayesian neural networks (GEBNN) to tackle UP tasks. In the GEBNN, a modified evidence lower bound (MELBO) loss is developed to consider both structural responses and gradient information simultaneously. This includes disparities between actual and predicted responses, as well as disparities between actual and predicted derivatives. Additionally, a gradient screening strategy based on the marginal probability density functions (PDFs) of input samples is established to identify significant derivative data for GEBNN training. Once the GEBNN is configured, it is utilized to replace the computationally intensive finite element model to efficiently provide UP results. Various applications, including nonlinear numerical examples, and mechanical, civil, and aeronautical structures, are presented to demonstrate the effectiveness of the GEBNN. The results show that the GEBNN significantly enhances the computational accuracy of the BNN in solving UP tasks.

Bayesian Parameter Estimation of Vibrating Systems via Physics-Based Biases from Neural Networks

Often, Structural Health Monitoring (SHM) campaigns draw damage-identifiers from vibration-based monitoring data. One of the downstream tasks of vibration-based SHM is that of system identification, i.e., inference of a model which is able to describe the system. For vibration-based monitoring, such models often rely on partial-differential equation formulations, where the identification task may be tied to inference of the parameters of such models. The probabilistic nature of SHM incentivises the extraction of stochastic estimates of these parameters, allowing for propagation of uncertainties associated to measurement noise or model imprecision. Common approaches to generating such stochastic estimates require an assumption on the shape and independence of the posterior distributions. To circumvent these assumptions, the Hamiltonian Monte-Carlo (HMC) sampling approach simulates the posterior distribution, allowing for freedom in the posterior. However, this requires intensive computational effort, especially when the governing equations have increased complexities, such as nonlinearities. Physics-informed neural networks (PINNs) utilise physics-based objective functions in the form of known PDEs, exploiting the automatic differentiation of NN architectures. This implies that additional terms in the PDE, such as nonlinearities, or boundary conditions can be accounted for. When the domain of observations encapsulates the collocation domain of the PINN, they can be exploited for parameter identification, by optimising over these parameters in addition to the network weights. However, classic objective functions in the form of mean-squared-norms underperform on noisy data, as a consequence of their deterministic nature. In this work, PINNs are combined with a HMC sampler to estimate the posterior distribution of the parameters of dynamic systems with noisy measurements. Multiple types of dynamic systems are simulated, varying the system complexity in terms of type and strength, and with different levels of noise. The results are assessed against the known values, and the codependent posterior distributions of each system are discussed.

Uncertainty propagation of relevant soil and masonry parameters to design a SHM for the Baptistery of Pisa

Historic constructions are affected by several uncertainties, among which those on mechanical parameters of masonry, because of reduced knowledge given by the limitation imposed on performing extensive destructive tests not to jeopardize the structural integrity. Besides, uncertainties on soil characterization can play a significant role in the evaluation of structural response, however is often neglected. Finite Element Models (FEM) often represent a good compromise given the possibility of reproducing the complex geometry of historical structures while requiring relatively limited material parameters from experimental tests (to feed models). However, the computational burden can become prohibitive when the evaluation of the effects of the variation of input mechanical properties for the assessment of the current behavior of the structure and potential design of adequate interventions and definition of monitoring systems requires running several analyses. In this work, modal analyses of a monumental Medieval construction such as the Baptistery of Pisa are carried out within a probabilistic framework including material uncertainties on both mechanical parameters of soil and masonry, which are assigned suitable probability distributions based on the limited data from in-situ campaigns combined with engineering judgment. A gPCE-based surrogate model is employed to transform the onerous numerical runs into speeded-up analytical evaluations for the computation of Sobol’ indices to assess the influence of input variability on the first ten natural frequencies of the monument at issue. The method leads to the identification of the most relevant soil and masonry parameters and highlights which frequencies are primarily controlled by either the stiffness of the soil or that of the aboveground historical structure. In this sense, this work provides a first clue for designing a SHM of the Baptistery of Pisa with a view to assessing minimum detectable parameter change while monitoring natural frequencies.

Optimized Parameter Estimation and Integrating Neural Network Forecasting of Dynamic Plant-Livestock Model for Early Warning in Agro-Environment Control Systems

The research utilizes the Lotka-Volterra prey-predator model to study Plant-Herbivore dynamics, focusing on the relationship between traditional livestock farming and vegetation conditions. Advanced methods are developed to improve the precision and efficiency of parameter estimation in these models. Neural networks are incorporated to enhance forecasting abilities, and an extension of the Plant-Herbivore models includes Botswana's climate and livestock variables. Efficient parameter space exploration is achieved using the Runge-Kutta method along with Multistart and the local solver $fmincon$ in MATLAB. This method improves parameter estimation accuracy. To address the impact of homogeneity assumptions in the data, estimate aggregation through weighting and time conversion is applied. Furthermore, the study investigates the use of nonlinear least squares to further refine the process, allowing for the identification of parameters that best fit observed livestock data, even with non-linearity. By using optimized parameter estimation techniques along with normalized nonlinear least squares, the cumulative error was reduced from an initial 1563.4521 to a final value of 0.0038, well within the specified thresholds (1.0, 0.1, and 0.01). Comparisons between Autoregressive Integrated Moving Average (ARIMA) and Neural Network Auto-Regressive (NNAR) models showed that NNAR models outperformed ARIMA models, with lower variance estimates (0.000004 - 0.000562) compared to ARIMA (0.103 - 0.155). NNAR models displayed Mean Error (ME) values ranging from -0.0012 to 0.0140, indicating a close match between forecasts and actual values with minor deviations. As a result, NNAR forecasting was used for predicting soil moisture, death, and harvest rates, which were integrated into the extended Plant-Herbivore model. This integration enabled the estimation of livestock production trajectories for 2021-2022, along with corresponding interpretations. The study also assessed the uncertainty propagation from NNAR forecasts onto the Plant-Herbivore dynamic model, revealing an increase in uncertainty with longer lead times.

Nonlinear Curve Fitting to Measurement Points with WTLS Method Using Approximation of Linear Model

The paper presents an approximate method of fitting measurement points to parameterized arbitrary nonlinear curves described by complex equations, even implicit ones, the most commonly used method of least squares in general WTLS. An approximation of a linear model is used here, in which the laws of propagation of error and propagation of uncertainty are true, so that only the first derivative of the transforming function is relevant. The effectiveness of the method has been demonstrated in several numerical examples. The method was verified on several nonlinear functions using the iterative algorithm by Monte Carlo propagation of distribution and the classical method based on the Levenberg-Marquardt algorithm for nonlinear optimization.

A reduced-order model approach for fuzzy fields analysis

Characterization of the response of systems with governing parameters that exhibit both uncertainties and spatial dependencies can become quite challenging. In these cases, the accuracy of conventional probabilistic methods to quantify the uncertainty may be strongly affected by the availability of data. In such a scenario, fuzzy fields become an efficient tool for solving problems that exhibit uncertainty with a spatial component. Nevertheless, the propagation of the uncertainty associated with input parameters characterized as fuzzy fields towards the output response of a model can be quite demanding from a numerical point of view. Therefore, this paper proposes an efficient numerical strategy for forward uncertainty quantification under fuzzy fields. This strategy is geared towards the analysis of steady-state, linear systems. To reduce the numerical cost associated with uncertainty propagation, full system analyses are replaced by a reduced-order model. This reduced-order model projects the equilibrium equations into a small-dimensional space constructed from a single analysis of the system plus sensitivity analysis. The associated basis is enriched to ensure the quality of the approximate response and numerical cost reduction. Case studies of heat transfer and seepage analysis show that with the presented strategy, it is possible to accurately estimate the fuzzy responses with reduced numerical effort.

Hybrid uncertainty propagation analysis of nonlinear systems in the frequency domain based on multi-scale random interval moment method

To quantify the impact of hybrid uncertainty (random and interval parameters) on the frequency-domain nonlinear dynamic response, the multi-scale method (MSM) and the random interval moment method (RIMM) are combined to establish a new uncertainty propagation analysis method, called the multi-scale random interval moment method (MS-RIMM). RIMM is used to describe the hybrid uncertainty, while MSM is used to determine the frequency-domain nonlinear dynamic response. The statistical characteristics (i.e., the expectation value and variance) of the amplitude-frequency response of the nonlinear system with hybrid uncertainties are derived. Furthermore, the accuracy and effectiveness of the proposed method are verified by comparing the results with those obtained using the multi-scale Monte Carlo simulation method (MS-MCSM). Overall, the results of this study can serve as a useful reference for the hybrid uncertainty propagation analysis of nonlinear systems and for predicting the frequency-domain nonlinear dynamic response.

Simplified and Detailed Evaluations of the Uncertainty of the Measurement of Microbiological Contamination of Pharmaceutical Products.

The control of the microbial contamination of pharmaceutical products (PP) is crucial to ensure their safety and efficacy. The validity of the monitoring of such contamination depends on the uncertainty of this quantification. Highly uncertain quantifications due to the variability of determinations or the magnitude of systematic effects affecting microbial growth or other analytical operations make analysis unfit for the intended use. The quantification of the measurement uncertainty expressing the combined effects of all random and systematic effects affecting the analysis allows for a sound decision about quantification adequacy for their intended use. The complexity of the quantification of microbial analysis uncertainty led to the development of simplified ways of performing this evaluation. This work assesses the adequacy of the simplified quantification of the uncertainty of the determination of the microbial contamination of PP by log transforming microbial count and dilution factor of the test sample whose uncertainty is combined in a log scale using the uncertainty propagation law. This assessment is performed by a parallel novel bottom-up and accurate evaluation of microbial analysis uncertainty involving the Monte Carlo method simulation of the Poisson log-normal distribution of counts and of the normally distributed measured volumes involved in the analysis. Systematic effects are assessed and corrected on results to compensate for their impact on the determinations. Poisson regression is used to predict precision affecting determinations on unknown test samples. Simplified and detailed models of the uncertainty of the measurement of the microbial contamination of PP are provided, allowing objective comparisons of several determinations and those with a maximum contamination level. This work concludes that triplicate determinations are required to produce results with adequately low uncertainty and that simplified uncertainty quantification underevaluates or overevaluates the uncertainty from determinations based on low or high colony numbers, respectively. Therefore, detailed uncertainty evaluations are advised for determinations between 50 and 200% of PP's maximum admissible contamination value. User-friendly tools for detailed and simplified evaluations of the uncertainty of the measurement of microbial contamination of PP are provided together with the understanding of when simplifications are adequate.

Tool Developments in the OpenMC Code: Correlated Sampling and Transient Fission Matrix Approach Coupled to OpenFOAM

This article outlines the advancements made in broadening the application scope of the OpenMC neutron transport code to include thermohydraulic coupling and nuclear data uncertainty propagation. These developments primarily involve the incorporation of the correlated sampling (CS) technique, facilitating the propagation of thermal feedback or cross-section sampling on neutronic calculations through neutron weight adjustments. The CS technique is integrated with computer-aided-design (CAD)–based meshing and the Transient Fission Matrix (TFM) approach. Together, these components enable comprehensive handling of neutronics-thermohydraulic coupling: The TFM approach addresses neutron kinetics via precalculated neutron transport matrices, the CS technique accounts for thermal feedback impacts on the matrices, and CAD meshing defines volumes corresponding to each matrix bin to align results with computational fluid dynamics codes, specifically OpenFOAM. Implementation details and verification procedures are elaborated, alongside an analysis on existing limitations and possible perspectives.