Source Term Estimation Research Articles

Bayesian Inverse Modelling for Probabilistic Multi-Nuclide Source Term Estimation Using Observations of Air Concentration and Gamma Dose Rate

In case of a release of hazardous radioactive matter to the atmosphere from e.g., a nuclear power plant accident, atmospheric dispersion models are used to predict the spatial distribution of radioactive particles and gasses. However, at the early stages of an accident, only limited information about the release may be available. Thus, there is a need for source term estimation methods suitable for operational use shortly after an accident. We have developed a Bayesian inverse method for estimating the multi-nuclide source term describing a radioactive release from a nuclear power plant. The method provides a probabilistic source term estimate based on the early available observations of air concentration and gamma dose rate by monitoring systems. The method is intended for operational use in case of a nuclear accident, where no reliable source term estimate exists. We demonstrate how the probabilistic formulation can be used to provide estimates of the released amounts of each radionuclide as well as estimates of future gamma dose rates. The method is applied to an artificial case of a radioactive release from the Loviisa nuclear power plant in southern Finland, considering the most important dose-contributing nuclides. The case demonstrates that only limited air concentration measurement data may be available shortly after the release, and that to a large degree one will have to rely on gamma dose rate observations from a frequently reporting denser monitoring network. Further, we demonstrate that information about the core inventory of the nuclear power plant can be used to constrain the release rates of certain radionuclides, thereby decreasing the number of free parameters of the source term.

LES study of turbulent ethanol spray flames using CSE coupled with non-adiabatic chemistry tables

Conditional Source-term Estimation (CSE) is applied to three turbulent ethanol spray flames (EtF3, EtF6, and EtF8) in Large Eddy Simulation (LES). The objectives of this paper are to include the heat losses due to spray evaporation and gas radiation in the chemistry tabulation, assess the impact of these changes on the temperature and droplet statistics, and evaluate the performance of LES-CSE for the selected flames. The profiles of gas temperature, spray velocity, velocity root mean square (rms) and droplet size distribution are well reproduced in the simulations compared to available experimental data. Temperature underpredictions near the centreline are observed, in particular, at locations closer to the jet exit for flames with lower jet velocity. A wider flame is predicted in EtF8 compared to the experiment and regions of local extinction are visible. The use of non-adiabatic chemistry library results in a noticeable improvement in the temperature predictions near the peak locations, especially for flames with higher velocity and closer to the jet exit. The heat losses due to evaporation are larger than those from radiation, confirming the importance of including the evaporation effects in the chemistry tables. The droplet velocity is well predicted, except for EtF8 where an underprediction is observed far downstream. The velocity rms is slightly underpredicted at some locations, probably due to the simple stochastic model used. Overall, LES-CSE with non-adiabatic chemistry tables successfully captures the gas-spray quantities in the selected flames.

Autonomous search of an airborne release in urban environments using informed tree planning

The use of autonomous vehicles for source localisation is a key enabling tool for disaster response teams to safely and efficiently deal with chemical emergencies. Whilst much work has been performed on source localisation using autonomous systems, most previous works have assumed an open environment or employed simplistic obstacle avoidance, separate from the estimation procedure. In this paper, we explore the coupling of the path planning task for both source term estimation and obstacle avoidance in an adaptive framework. The proposed system intelligently produces potential gas sampling locations that will reliably inform the estimation engine by not sampling in the wake of buildings as frequently. Then a tree search is performed to generate paths toward the estimated source location that traverse around any obstacles and still allow for exploration of potentially superior sampling locations.The proposed informed tree planning algorithm is then tested against the standard Entrotaxis and Entrotaxis-Jump techniques in a series of high fidelity simulations. The proposed system is found to reduce source estimation error far more efficiently than its competitors in a feature rich environment, whilst also exhibiting vastly more consistent and robust results.

Oscillation-free source term inversion of atmospheric radionuclide releases with joint model bias corrections and non-smooth competing priors

The source term of atmospheric radionuclide releases is essential for the hazardous consequence assessment and emergency response. However, the artificial release oscillations in the source term estimate remain a fundamental challenge and may deliver misleading information, because of the unavoidable model biases and observation uncertainties. We propose a new method that removes oscillations while recovering the release details. This method explicitly corrects the model biases using the joint correction model and compensates the observation uncertainties through non-smooth competing priors that involve two rival functions. The new priors better model the unsteady feature of the radionuclide releases and distinguish the true releases from oscillations, enabling release-preserving oscillation removal. We extend the projected alternating minimization algorithm for an efficient solution. The method achieves oscillation-free and nearly perfect profiles for real releases of the Perfluoro-Methyl-Cyclo-Hexane on continental and regional scales, and the radionuclide 41Ar on a local scale, outperforming state-of-the-art and very recent methods. The sensitivities to model inputs and key parameters are also investigated. Robust performance is exhibited under emissions of both radioactive and non-radioactive substances, different meteorological inputs and numbers of observations, paving the way for identifying dynamic atmospheric radionuclide releases at multiple scales, especially when the release status is unknown.

A Novel Multi-Sensor Data-Driven Approach to Source Term Estimation of Hazardous Gas Leakages in the Chemical Industry

Source term estimation (STE) is crucial for understanding and addressing hazardous gas leakages in the chemical industry. Most existing methods basically use an atmospheric transport and dispersion (ATD) model to predict the concentrations of hazardous gas leakages from different possible sources, compare the predicted results with multi-sensor data, and use the deviations to search and derive information on the real sources of leakages. Although performing well in principle, complicated computations and the associated computer time often make these methods difficult to apply in real time. Recently, many machine learning methods have also been proposed for the purpose of STE. The idea is to build offline a machine-learning-based STE model using data generated with a high-fidelity ATD model and then apply the machine learning model to multi-sensor data to perform STE in real time. The key to the success of a machine-learning-based STE is that the machine-learning-based STE model has to cover all possible scenarios of concern, which is often difficult in practice because of unpredictable environmental conditions and the inherent robust problems with many supervised machine learning methods. In order to address challenges with the existing STE methods, in the present study, a novel multi-sensor data-driven approach to STE of hazardous gas leakages is proposed. The basic idea is to establish a multi-sensor data-driven STE model from historical multi-sensor observations that cover the situations known as the independent hazardous-gas-leakage scenarios (IHGLSs) in a chemical industry park of concern. Then the established STE model is applied to online process multi-sensor data and perform STE for the chemical industry park in real time. The new approach is based on a rigorous analysis of the relationship between multi-sensor data and sources of hazardous gas leakages and derived using advanced data science, including unsupervised multi-sensor data clustering and analysis. As an example of demonstration, the proposed approach is applied to perform STE for hazardous gas-leakage scenarios wherein a Gaussian plume model can be used to describe the atmospheric transport and dispersion. Because of no need of ATD-model-based online optimization and supervised machine learning, the new approach can potentially overcome many problems with existing methods and enable STE to be literally applied in engineering practice.

A spent nuclear fuel source term calculation code BESNA with a new modified predictor-corrector scheme

This paper introduces a new point depletion-based source term calculation code named BESNA (Bateman Equation Solver for Nuclear Applications), which is aimed to estimate nuclide inventories and source terms from spent nuclear fuels. The BESNA code employs a new modified CE/CM (Constant Extrapolation – Constant Midpoint) predictor-corrector scheme in depletion calculations for improving computational efficiency. In this modified CE/CM scheme, the decay components leading to the large norm of the depletion matrix are excluded in the corrector, and hence the corrector calculation involves only the reaction components, which can be efficiently solved with the Talyor Expansion Method (TEM). The numerical test shows that the new scheme substantially reduces computing time without loss of accuracy in comparison with the conventional scheme using CRAM (Chebyshev Rational Approximation Method), especially when the substep calculations are applied. The depletion calculation and source term estimation capability of BESNA are verified and validated through several problems, where results from BESNA are compared with those calculated by other codes as well as measured data. The analysis results show the computational efficiency of the new modified scheme and the reliability of BESNA in both isotopic predictions and source term estimations.

Source Term Estimation Using Deep Reinforcement Learning With Gaussian Mixture Model Feature Extraction for Mobile Sensors

This paper proposes a deep reinforcement learning method for mobile sensors to estimate the properties of the source of the hazardous gas release. The problem of estimating the properties of the released gas is generally termed as the source term estimation (STE) problem. Since the sensor measurements from atmospheric gas dispersion are sparse, intermittent, and time-varying due to the turbulence and the sensor noise, STE is considered to be a challenging problem. The particle filter is adopted to estimate the source term under such stochastic noise conditions. The deep deterministic policy gradient (DDPG) is also employed to find the best source search policy in terms of successful estimation and traveled distance. Through ablation studies, we demonstrate that the use of the Gaussian mixture model, which clusters the potential source positions from the particle filter, as an input to the DDPG and the gated recurrent unit functioning as a memory in DDPG help to improve the STE performance. Besides, simulation results in randomized source term conditions and previously-unseen environments show the superior STE performance of the proposed algorithm compared with the existing information-theoretic STE algorithm.

Combined Grey Wolf Optimizer Algorithm and Corrected Gaussian Diffusion Model in Source Term Estimation

It is extremely critical for an emergency response to quickly and accurately use source term estimation (STE) in the event of hazardous gas leakage. To determine the appropriate algorithm, four swarm intelligence optimization (SIO) algorithms including Gray Wolf optimizer (GWO), particle swarm optimization (PSO), genetic algorithm (GA) and ant colony optimization (ACO) are selected to be applied in STE. After calculation, all four algorithms can obtain leak source parameters. Among them, GWO and GA have similar computational efficiency, while ACO is computationally inefficient. Compared with GWO, GA and PSO, ACO requires larger population and more iterations to ensure accuracy of source parameters. Most notably, the convergence factor of GWO is self-adaptive, which is in favor of obtaining accurate results with lower population and iterations. On this basis, combination of GWO and a modified Gaussian diffusion model with surface correction factor is used to estimate the emission source term in this work. The calculation results demonstrate that the corrected Gaussian plume model can improve the accuracy of STE, which is promising for application in emergency warning and safety monitoring.

Geometrical aspects of alpha dose rates from UO2 based fuels

Models for calculating dose rates of spherical particles as well as in fuel cracks are important for radionuclide source term estimations. Dose rates from UO2 based fuels were calculated for planar, spherical, and crack geometries. The escape probability for α-particles in spherical UO2 particles was derived as a continuous equation. The dose rate increased with increasing spherical radius due to the decreasing relative volume of the surrounding water layer. The model produced escape probabilities that were closely predicted by the theoretical derivation. It was shown that the dose rate in water filled fuel cracks with width smaller than the range of an α-particle led to dissolution rates that were lower per unit surface area.

Organic Telluride Formation from Paint Solvents Under Gamma Irradiation

The interactions between tellurium and organic material during a nuclear reactor accident are critical to source term estimations because of the possible formation of volatile species. Reactions taking place in the containment sump are of interest since these can lead to re-volatilization and increase the fission product source term. This paper presents results from experiments investigating the interaction of tellurium dioxide with three paint solvents—texanol ester, methyl isobutyl ketone, and toluene—under containment sump conditions. The experiments were performed by irradiating a mixed solution of tellurium dioxide and paint solvents at a dose rate of 4 kGy/h up to 300 kGy. The resulting samples were analyzed for tellurium concentration and speciation. Tellurium(IV) was found to reduce to metallic tellurium under irradiation when paint solvents were present. More importantly, several volatile organic tellurides were identified in the irradiated samples, which suggests that tellurium can form volatile species in sump conditions when in contact with dissolved paint solvents. This paper provides novel evidence of organic telluride formation in the sump and raises further interest in tellurium chemistry during a severe nuclear reactor accident.

Sensor layout strategy for source term estimation of external pollution sources in urban neighbourhoods

The estimation of source parameters is essential when hazardous substances are leaked or released around urban neighbourhoods, and the layout of the sensor plays an important role in source term estimation (STE). Currently, few sensor layout strategies exist for external pollution sources in urban neighbourhoods. In this study, the STE performance of 10 strategies for arranging sensors around urban neighbourhoods was analyzed, and the impact of each factor in the layout strategy on the STE performance was discussed. The results show that the number of sensors has a considerable influence on the STE performance, and better STE performance can be achieved by adding a large number of sensors. However, the STE performance could no longer be noticeably improved when the number of sensors increased to a certain extent. With the same number of sensors, a better STE performance can be obtained by arranging sensors around buildings rather than at the crossing of city streets. An optimal sensor layout strategy is proposed for the STE of external pollution sources, which uses fewer sensors while considering a good STE performance. Finally, the full posterior distributions of the source parameters with different sensor numbers were compared to understand the impact of the sensor amount on the estimation of the source location and strength.

Source term inversion of nuclear accident based on deep feedforward neural network

Source term estimation based on environmental monitoring data is a key method for obtaining source information, which is required by the emergency response system. This study investigates the applicability of deep feedforward neural network (DFNN) for source inversion. Twenty thousand sets of simulated data containing I-131 release rate, meteorological information, and simulated radioactive concentration are generated based on radionuclide atmospheric dispersion codes RADC. These are used to train and test a DFNN. The influence of key network hyperparameters is studied. The results show that the average prediction error of DFNN is 2.24%, and that over 80% of prediction errors are less than 2.0%. The Bayesian MCMC algorithm is used to analyze the prediction uncertainty of DFNN when there are uncertainties in the input parameters. The confidence interval and risk curve are likely to provide more reliable source-term information for nuclear accident emergency response and decision-making.

Radiological source terms estimation for the Divertor Tokamak Test (DTT) facility

The Divertor Tokamak Test (DTT) facility will start its operations in 2026. DTT will operate with D-D fuel only, for an expected operational period of 25 years. Nevertheless, tritium will be produced by the D(d,p)T reaction. A mandatory step in the safety assessment of the machine is the estimation of the different source terms. Major contributions to the source terms are due to tritium and to activated dust. The amount of tritium in the vacuum chamber, in co-deposited tungsten layers and implanted in the bulk of the first wall is computed in this work. Also, a preliminary estimation of dust production due to inter and intra ELMs sputtering is carried out. Results report small amount of source terms related to tritium, below 1 mg after one year of full power operations, and less than 300 g of activated dust at the end of life.

Investigation of conditional source-term estimation coupled with a semi-empirical model for soot predictions in two turbulent flames

The modelling of soot formation is investigated for two turbulent flames, at atmospheric and 3 atm pressure conditions. For the first time, a semi-empirical soot formulation that accounts for soot inception, coagulation, surface growth, and oxidation processes is coupled with the turbulent combustion model, Conditional Source-term Estimation (CSE) using Reynolds-Averaged Navier–Stokes equations. Detailed chemistry is included and an optically thin radiation model is considered. Non-adiabatic chemistry tabulations are created. Good agreement with the experiments is found for turbulent mixing and temperature fields in both flames, with some discrepancies believed to be due to the turbulence modelling approach. At 1 atm, the soot volume fractions are in reasonable agreement with the experiments, but typically smaller than the measurements with the centerline peak locating closer to the fuel exit. At 3 atm, good agreement between the numerical predictions and experimental data is achieved for the soot volume fraction within the experimental error. The centerline peak location is observed slightly farther downstream. Possible sources of discrepancies are examined and comparison with previously published numerical results is also undertaken. Differential diffusion and modified soot chemistry constants may bring further improvement. Without any particular tuning of soot chemistry, soot modelling within CSE is shown to be a promising approach.

Prediction of gas leakage and dispersion in utility tunnels based on CFD-EnKF coupling model: A 3D full-scale application

Natural gas compartment accommodated in utility tunnels is beneficial in meeting the pressing demand of energy supply and sustainable urban environment. However, the leaking gas characterized by flammable and explosive can pose a huge threat to the safe operation of the utility tunnel. When an unexpected gas leakage accident happens in the actual situation, the prior information associated with the leakage source is commonly unclear or unknown. Therefore, the absence of an available tool for reasonable leakage and dispersion prediction in the above scenario precludes the timely and appropriate emergency response treatment. In this study, a three-dimensional source term estimation (3D-STE) model with the combination of the computational fluid dynamics (CFD) and ensemble Kalman filter (EnKF) algorithm is proposed to achieve spatiotemporal gas concentration prediction and gas emission source estimation. In the proposed approach, the observation data can be incorporated into the gas dispersion simulations continuously, thus the simulation results can be revised by the observation data and the source term estimation of gas leakage can be achieved by employing the EnKF algorithm. A twin experiment is employed to validate the effectiveness and practicability of the proposed model. The results show that the proposed model can revise the prior errors in the gas leakage rate significantly and obtain an accurate prediction of gas concentration distribution as well as gas leakage rate. A feasible framework is also proposed serving as a good paradigm for the 3D-STE model application. This study helps for consequence assessment and emergency response of gas leakage accidents in utility tunnels.

Experimental estimates of hygroscopic growth of particulate fission product species (mixed CsI–CsOH) with implications in reactor accident safety research

Studies on severe nuclear reactor accidents consider CsI and CsOH as the two predominant forms of cesium expected to be released following a reactor accident; 137Cs, 134Cs and 131I being their dominant radioactive forms. Recent studies have measured the hygroscopic growth factors (HGF) and activation fractions for laboratory generated CsI and CsOH particles in sub-saturation and super-saturation relative humidity environments. This work measures and compares the HGF of mixed CsI–CsOH particles with those of individual components. The experiments have been performed with hygroscopic tandem differential mobility analyser for varying mass ratios (w/w) of CsI: CsOH and the results have been compared with the theoretical estimates made using Brechtel and Kredneweis (2000) theory in conjugation of ZSR (Zdanovskii–Stokes–Robinson) mixing rule. The study shows different behavioural pattern of hygroscopic growth of mixed particles in comparison to individual components. A clear transitional change in the growth factor patterns was observed for the ratio below 1:1. Additionally, the experiments to study the effect of different dry diameters (50, 100, 150 and 200 nm) for 1:1 ratio revealed that hygroscopic growth was independent of initial dry diameter. Effect of dehydration for 3 mixing ratios viz., 1:02, 1:1 and 1:10 showed continuous pattern indicating the dominance of CsOH. Terminal settling velocities for the mixed and individual particles are compared for highlighting the probable impact on surface deposition flux calculations. The aerosol hygroscopic growth of mixed CsI–CsOH particles has direct implications in improving source term estimates for a severe reactor accident safety analysis.

Sensor configuration optimization based on the entropy of adjoint concentration distribution for stochastic source term estimation in urban environment

Sensor monitoring is foundational to source term estimation (STE). Recently, stochastic STE methods based mainly on Bayesian inference have been attracting attention. However, few studies have developed sensor configuration optimization (SCO) methods aiming to ensure good STE performance in the monitoring area, such that the posterior probability could aggregate around the truths while addressing most sources. This research proposes a deployment method by designing an objective function and applying a simulated annealing (SA) algorithm. The objective function is set as the information joint entropy of the adjoint concentration. The performance of the proposed method was assessed by Bayesian inference STE for 25 unknown sources based on the obtained optimal configuration in a regular block-arrayed building group model. The STE results were compared with those of uniform and random configurations. According to the results, because the optimal configuration can provide the most informative measurements, it yields the best estimations. If we quantize the STE errors and take the average for all unknown sources, the location and strength estimation errors of the optimal configuration significantly decrease by approximately 45% and 99%, respectively, when compared with the random configuration and 39% and 96%, respectively, when compared with the uniform configuration.

Autonomous Source Term Estimation in Unknown Environments: From a Dual Control Concept to UAV Deployment

In the gas source search and localisation problem, the use of autonomous robots is of increasing interest due to their deployment speed and lack of human interaction with hazardous materials. This letter presents an aerial robotic platform for performing source term estimation of an unknown chemical release in a challenging a-priori unknown and GPS-denied environment. The proposed system forms the search strategy using the state-of-the-art control concept, dual control for exploitation and exploration, and realises such a function in the aforementioned challenging scenario using an RRT* based path planner. A novel downsampling process on the RRT* is also proposed that addresses the computational infeasibility of calculating the utility of a large number of sample states, whilst still maintaining sample state diversity. The proposed algorithm is tested in a high fidelity simulation environment under a number of configurations, and compared against competing algorithms. The system architecture is also brought forward into a bespoke UAV platform and experimentally tested in real-world conditions. The proposed system is shown to be capable of performing source term estimation robustly and efficiently, which provides a step forward in showing the real world application of previously academic functions.

Statistical inverse estimation of source terms in the Helmholtz equation

In this paper, we study source identification for Helmholtz equation by using statistical inversion method. The approximate solutions are obtained from samples measured on the random boundary of the radiated electric field. Error estimates of exact solutions and their approximations are proven, and the validity of the methods is verified by numerical experiments.

The impact of sensor layout on Source Term Estimation in urban neighborhood

The layout of sensors in urban neighborhood has a great impact on the Source Term Estimation (STE) of dangerous or polluting gas leak sources. In this study, the effect of sensor layout on STE performance is analyzed using Computational Fluid Dynamics (CFD) approaches, and the best layout of sensors in the urban neighborhood is determined. The influence of source location and the border effect of measuring points on the performance of STE are analyzed. Results show that placing average two sensors around each building is the best sensor configuration for identifying source location parameters. Regarding the source intensity, no sensor configuration with obvious advantages has been observed. As the distance between pollutants and the city increases, the difficulty of STE increases. The result of STE is slightly more accurate and the posterior distribution is more concentrated after considering the border effect of measuring point.