Artificial Neural Network Surrogate Model Research Articles

Multi-objective optimization of CO2 ejector by combined significant variables recognition, ANN surrogate model and multi-objective genetic algorithm

The ejectors are crucial in enhancing the efficiency of the CO2-based refrigeration cycle. Although the ejector can be optimized by experimental and computational fluid dynamic simulation to improve its performance, these methods are time-consuming and complicated. This research aims to present a fast and systematic approach for optimizing CO2 ejector by combining variance analysis, surrogate model, and non-dominated sorting genetic algorithm. Firstly, the key geometric structures affecting the performance of ejector were determined by variance analysis. Secondly, the influence of key geometric structures and boundary conditions on ejector efficiency and entrainment ratio was analyzed by using computational fluid dynamic simulation, and the database was generated. Next, the artificial neural network surrogate model was established to forecast the ejector performance. Finally, the non-dominated sorting genetic algorithm was involved to optimize the ejector for maximizing ejector efficiency and entrainment ratio. The results show that the efficiencies of the optimized ejectors are above 42%, and the entrainment ratios exceed 0.7. Compared with the basic model, the average efficiencies have increased about 13.20%. When the pressure lift is 0.7 MPa, the entrainment ratios of the optimized ejectors are 0.696 (−20 °C ≤ Te < −15 °C), 0.82(-15 °C ≤ Te < −5 °C), 0.60 (−5 °C ≤ Te < 5 °C) and 0.90 (5 °C ≤ Te < 15 °C), respectively. The above research demonstrates that the success of this approach in addressing time-consuming multi-optimization problems. It offers a fast and systematic approach for the multi-objective optimization of CO2 ejector as a valuable reference for engineering applications.

Multi-Objective Optimization of Air-Cooled Perforated Micro-Pin Fin Heat Sink Via an Artificial Neural Network Surrogate Model Coupled With NSGA-II

Abstract This research aims to create an artificial neural network (ANN) regression model for predicting the performance parameters of the perforated micro-pin fin (MPF) heat sinks for various geometric parameters and inflow conditions. A three-dimensional computational fluid dynamics (CFD) simulation system is developed to generate dataset samples under different operational conditions, which are specified using Latin hypercube sampling (LHS). An ANN model is first obtained by optimizing the model hyper-parameters, which are then deployed to learn from the input feature space that consists of perforation diameter, perforation location, and inflow velocity. For accurate training of the ANN, the model is trained over a range of uniformly distributed data points in the input feature space. The developed multi-layer model predicted Nusselt number and friction factor with the mean absolute percentage error of 4.45% and 1.80%, respectively. Subsequently, the developed surrogate model is used in the optimization study to demonstrate the application of the surrogate model. A multi-objective non-dominated sorting genetic algorithm (NSGA-II) is used to perform the optimization of the perforation location, diameter, and inflow conditions. Negative of the Nusselt number and friction factor are chosen as objectives to minimize. A Pareto front is obtained from the optimization study that shows a set of optimal solutions. Thermal performance of the perforated MPF is increased between 11.5% and 39.77%. The optimizer selected a significantly smaller hole diameter at a higher location and a faster speed to maximize the Nusselt number and minimize the friction factor.

An integrated modelling framework for multiple pollution source identification in surface water

Pollution source identification is vital in water safety management. An integrated simulation-optimization modelling framework comprising a process-based hydrodynamic water quality model, artificial neural network surrogate model and particle swarm optimization (PSO) was proposed to achieve rapid, accurate and reliable pollution source identification. In this study, the hydrodynamics and water quality processes in a straight lab-based flume were simulated to test pollution source identification under steady flow conditions. Additionally, the pollution source identification in the unsteady flow conditions was examined using a real-life estuary, specifically the Yangtze River estuary. First, we developed two process-based models to simulate hydrodynamics and water quality in the flume and estuary. Then, the data generated from the process-based models were used to develop surrogate models. Three typical artificial neural networks (ANNs) algorithms: backpropagation (BP), radial basis function (RBF) and general regression neural networks (GRNN) were selected to develop surrogates for process-based models (PBMs), and they were coupled with PSO algorithm to achieve the hybrid modelling framework for pollution source identification. Our results showed that hybrid PBM-ANNs-PSO models could be applied to identify the pollution source and quantify release intensity in spatial distribution when the discharge type was assumed as the point source with a continuous release. Multiple-performance criteria metrics, in terms of the coefficient of determination, root-mean-square error, mean absolute error, evaluated the model performance as “Excellent prediction”. The BP-PSO models consistently appear to be the top-performing source identification model within the developed models, with most cases of relative error (RE) values lower than 5%. The new insights from the hybrid modelling framework would provide useful information for the local government agency to make reasonable decisions regarding pollution source identification issues.

MOPSO-based structure optimization on RPV sealing performance with machine learning method

The structure integrity of reactor pressure vessels (RPV) plays an important role in the safety of nuclear power plants, which mainly concerns the risk of sealing failure. In the present work, a hybrid method consisting of an artificial neural network (ANN) and multi-objective particle swarm optimization (MOPSO) is proposed, aiming to find an optimized RPV structure with improved sealing performance. The ANN model provides a more accurate prediction of sealing performance than the radial basis function neural network (RBFNN) model. There is also a better generalization ability in the ANN model with R2 above 0.96 and RMSE below 0.06 in the test set. With ANN as a surrogate model, multi-objective optimization is applied in RPV structure design. Compared with that of the original RPV structure, the sealing performance can be improved by even over 25% in the optimized structure. The application of ANN surrogate models can save more than 99% computation cost, compared with optimization based on finite element analysis (FEA).

Performance improvement of CO2 two-phase ejector by combining CFD modeling, artificial neural network and genetic algorithm

The ejector, as one of the core components of the CO2 trans-critical ejection refrigeration system, plays an important role in improving refrigeration capacity and reducing compressor power consumption. Although the ejector can be optimized by experiment and Computational Fluid Dynamics (CFD) simulation to improve its performance, these methods are time-consuming and complicated. This study aims to propose a method to improve the performance of the CO2 trans-critical two-phase ejector assisted by using CFD, artificial neural network (ANN), and genetic algorithm (GA). Firstly, the influence of geometric parameters on ejector efficiency was analyzed by using CFD technology, and the database was generated. Next, the complex and time-consuming CFD model was replaced by the ANN surrogate model established to predict the ejector performance. Finally, the GA method was used to optimize the ejector to maximize the ejector efficiency. The results show that the efficiency of the optimized ejector is 35.39%. The optimized ejector increases the secondary flow velocity and eliminates the vortex in ejector, and the efficiency of the optimized ejector is raised by more than 8% on average than that of initial ejector under different primary and secondary flow conditions. The research shows that the combination of CFD, ANN, and GA has higher reliability and better performance in the optimization design of CO2 two-phase ejector.

Optimal redesign of coastal groundwater quality monitoring networks under uncertainty: application of the theory of belief functions.

This paper presents a new methodology for the optimal redesign of water quality monitoring networks in coastal aquifers. The GALDIT index is used to evaluate the extent and magnitude of seawater intrusion (SWI) in coastal aquifers. The weights of the GALDIT parameters are optimized using the genetic algorithm (GA). A SEAWAT-based simulation model, a spatiotemporal Kriging interpolation technique, and an artificial neural network surrogate model are then implemented to simulate total dissolved solids (TDS) concentration in coastal aquifers. To obtain more precise estimations, an ensemble meta-model is developed using the Dempster-Shafer's belief function theory (D-ST) to combine the results obtained from the three individual simulation models. The combined meta-model is then used for calculating more precise TDS concentration. Some plausible scenarios are defined for variation of water elevation and water salinity at the coastline to incorporate uncertainty through the concept of value of information (VOI). Finally, the potential wells with the highest values of information are taken into consideration to redesign coastal groundwater quality monitoring network under uncertainty. The performance of the proposed methodology is evaluated by applying it to the Qom-Kahak aquifer, north-central Iran, which is threatened by SWI. At first, the individual and ensemble simulation models are developed and validated. Then, several scenarios are defined regarding the plausible changes in TDS concentration and water level at the coastline. In the next step, the scenarios, the GALDIT-GA vulnerability map, and the VOI concept are used for redesigning the existing monitoring network. The results illustrate that the revised groundwater quality monitoring network containing 10 new sampling locations outperforms the existing one based on the VOI criterion.

A Multisurrogate-Assisted Optimization Framework for SSPP-Based mmWave Array Antenna

Spoof surface plasmon polariton (SSPP) transmission lines are frequently used to excite millimeter-wave (mmWave) antenna arrays due to high field confinement and easy integration with planar structures. However, the design of the SSPP-based array antennas requires significant efforts because of multiple specifications, the high cost of electromagnetic (EM) evaluations, and a large number of design parameters. This article proposes a multisurrogate-assisted optimization framework for the efficient design of SSPP-based mmWave array antennas. The framework has three stages. In each stage, a surrogate is proposed to solve a specific task. The first stage is to find the initial values of four key design parameters using artificial neural network (ANN)-based surrogate model optimization. The second stage focuses on the optimization of sidelobe level based on another ANN surrogate model. The third stage is a beamforming-focused optimization procedure using the space mapping technique with an improved array factor formula as a surrogate. An mmWave SSPP-based array antenna with 16 circular patches at a central frequency of 28 GHz is successfully designed using the proposed framework. The antenna is also redesigned for five sets of main lobe directions and null locations at 24 GHz. All antennas are verified using full-wave EM simulations.

Fast and robust parameter estimation with uncertainty quantification for the cardiac function

Background and objectivesParameter estimation and uncertainty quantification are crucial in computational cardiology, as they enable the construction of digital twins that faithfully replicate the behavior of physical patients. Many model parameters regarding cardiac electromechanics and cardiovascular hemodynamics need to be robustly fitted by starting from a few, possibly non-invasive, noisy observations. Moreover, short execution times and a small amount of computational resources are required for the effective clinical translation. MethodsIn the framework of Bayesian statistics, we combine Maximum a Posteriori estimation and Hamiltonian Monte Carlo to find an approximation of model parameters and their posterior distributions. Fast simulations and minimal memory requirements are achieved by using an accurate and geometry-specific Artificial Neural Network surrogate model for the cardiac function, matrix–free methods, automatic differentiation and automatic vectorization. Furthermore, we account for the surrogate modeling error and measurement error. ResultsWe perform three different in silico test cases, ranging from the ventricular function to the entire cardiocirculatory system, involving whole-heart mechanics, arterial and venous hemodynamics. By employing a single central processing unit on a standard laptop, we attain highly accurate estimations for all model parameters in short computational times. Furthermore, we obtain posterior distributions that contain the true values inside the 90% credibility regions. ConclusionsMany model parameters regarding the entire cardiovascular system can be fastly and robustly identified with minimal hardware requirements. This can be achieved when a small amount of non-invasive data is available and when high levels of signal-to-noise ratio are present in the quantities of interest. With these features, our approach meets the requirements for clinical exploitation, while being compliant with Green Computing practices.

An efficient synthesis method for large unequally spaced sparse linear arrays based on surrogate models of subarrays

The synthesis of large arrays with optimization of element locations including mutual coupling effects is always known as a computationally cost task. In this article, an efficient synthesis method for large unequally spaced sparse linear arrays in the presence of coupling effects based on artificial neural network (ANN) surrogate models of subarrays is presented. High-quality ANN surrogate models of arbitrary large linear arrays are built by grouping the surrogate models of subarrays together to tackle the “curse of dimensionality” of ANNs caused by the large number of array elements. The surrogate models of a complete group of subarrays with the given physical structures are built by several independent ANNs which are used to characterize the effects of mutual coupling on the active element patterns (AEPs) with variable element location distributions. After training, the surrogate models of subarrays can be called by an alternating convex optimization (ACO) method, so that arbitrary large arrays can be quickly synthesized including mutual coupling effects. Numerical experiments are conducted to determine the suitable parameters of subarray partition and build surrogate models of subarrays. The results of four examples for synthesizing unequally spaced linear arrays are demonstrated to validate the effectiveness of the proposed method.

Performance limits of neural networks for optimizing an adsorption process for hydrogen purification and CO2 capture

In this work, we use surrogate models to accelerate the optimization of an adsorption process for H2 purification and CO2 capture within the context of fossil-based low-carbon H2 production. A one dimensional column model was used to generate a training set for different feed compositions with up to four impurities and for varying process conditions. Subsequently, an artificial neural network (ANN) surrogate model was trained for six key performance indicators, achieving adjusted R2 values over 0.999 for all indicators. Finally, the ANN was used for the constrained optimization of the H2 separation performance and of the process performance (energy consumption and productivity), and the results were compared to full model optimization results. The agreement is very good for the H2 separation performance, and in the case of low H2 purity targets (99%) also for the process performance. For higher H2 purities, however, the energy-productivity Pareto front features a very high sensitivity toward the H2 purity constraint, and even small deviations in H2 purity between full model and ANN surrogate model can translate to big deviations in the energy-productivity Pareto front. This is particularly pronounced for poorly sampled input regions at the edge of the sampling domain, for example for a binary H2-CO2 feed. If the ANN surrogate model is used at such edges of the sampling domain, additional sampling is required in this region to increase its accuracy. For all other cases, the deviations between the full model and the ANN surrogate model regarding the minimum energy consumption (or the maximum productivity) were well below 5%, showing that the ANN can be used with good accuracy instead of the full model.

Transient Modeling of Induction Machine Using Artificial Neural Network Surrogate Models

A transient model of an induction machine (IM) is developed in this work using an artificial neural network (ANN) surrogate model. The model is suitable to be used for direct-on-line IMs. The finite-element (FE)-based model of IM is used to generate the training, validation, and testing datasets. Different inputs and model configurations are investigated to find an optimal solution in developing the transient model. The proposed transient model is suitable to be used in digital twin services since it can estimate the current and torque accurately in real time based on only voltage and measured shaft speed.

Improvement of the three-dimensional fine-mesh flow field of proton exchange membrane fuel cell (PEMFC) using CFD modeling, artificial neural network and genetic algorithm

This study proposes a systematic methodology for improving PEMFC's performance combining computational fluid dynamic (CFD), artificial neural network (ANN), and intelligent optimization algorithms. Firstly, a three-dimensional (3-D) multiphase PEMFC CFD model with 3-D fine-mesh flow field is developed. Then the key structural features of the fine-mesh flow field are extracted as optimization decision variables, and the sampling points are selected by using the Latin hypercube sampling (LHS) experimental method. The power density and oxygen uniformity index of sampling points are calculated by CFD modeling to form the database, which is used to train the artificial neural network (ANN) surrogate model. Finally, the single-objective optimization (SOO) and multi-objective optimization (MOO) are implemented by using genetic algorithm (GA) and non-dominated sorting genetic algorithm (NSGA-II), respectively. It was found that using trained ANN surrogate models can get a high prediction precision. The maximum power density of SOO is increased by 7.546% than that of base case and is 0.562% larger than that of MOO case. However, the overall pressure drop in cathode flow field of SOO case is greater than that of MOO case and the base case. Furthermore, the oxygen concentration, the oxygen uniformity index and the water removal capacity of MOO case are better than that of SOO case. It is recommended that the improved flow field structure optimized by MOO is more beneficial to improve the overall performance of PEMFC.

ANNEXE: An open-source building energy design optimisation framework using artificial neural networks and genetic algorithms

It is expected that the building sector will be a major contributor to greenhouse gas emissions by 2050, as end-use services such as cooling demand is expected to rise significantly. Building energy design optimisation, applied either for new buildings or refurbishments, is a critical approach to achieve sustainable and adaptable cities, reducing sectoral emissions and increasing occupant's life quality. However, the design optimisation process has been characterised by following outdated approaches, mostly using physics-based thermal models and stochastic optimisation tools with large computational requirements. In addition, physics-based simulation tools still lack appropriate thermodynamic analysis which limits the potential to reduce actual energy inefficiencies in building energy systems. This paper introduces the ANNEXE (Artificial Neural Network (ANN) and EXErgy-based surrogate modelling) building design optimisation framework. Presented as an open-source tool, the framework proposes the integration of exergy analysis to improve building energy efficiency, combined with an efficient two-stage optimisation process allowing to initially optimise hyperparameters from data-driven ANN surrogate models using an Auto Machine Learning (AutoML) approach. Later, the near optimal building design parameters can be found in the second optimisation stage. A house building case study is presented to illustrate the applicability and validity of the proposed framework. The application of the framework and the obtained results have been compared to outputs from a typical optimisation approach based on physics-based energy simulations. It was found that the proposed approach was able to find similar Pareto solutions while reducing computational times by 98%. Compared to the baseline, the optimal design resulted in an increase of 27% in life cycle cost (50 years) but improving thermodynamic efficiency by reducing 26% of exergy destructions while decreasing annual thermal discomfort from 17% to about 5% annually. The results reveal that the proposed method provides a robust surrogate-based optimisation framework for designers and decision makers that could be applied to other energy research areas.

Performance improvement of solid oxide fuel cells by combining three-dimensional CFD modeling, artificial neural network and genetic algorithm

Solid oxide fuel cell (SOFC) is the electrochemical device that directly convert the chemical energy of fuels into electrical energy, which are considered one of the promising methods for achieving high power generation efficiency. However, the commercialization of SOFC encounters the challenge due to its high manufacturing and operating cost. This study aims to present a framework and methodology for improving SOFC’ performance assisted by computational fluid dynamic (CFD) modeling, artificial neural network (ANN), and genetic algorithm (GA). Firstly, a three-dimensional computational fluid dynamic (CFD) model, referring to three types of parameters, e.g. geometry parameters, microscopic parameters and operating conditions, was developed and then the databases were obtained. Then 19 widely used intelligence algorithms, e.g. Artificial Neural Network (ANN), Boltzmann Machines (BMs), Support Vector Machines (SVMs), etc., were employed to train the databases. Next, the developed ANN surrogate model was used to replace the complicated and time-consuming CFD model and to predict SOFC’s performance and optimize the power density output of SOFC. Finally, the system optimization was performed by using genetic algorithm (GA) to maximize the power density. The results showed that artificial neural network (ANN) achieved the best accuracy (R2 = 0.99889) in terms of predictions of SOFC performance. Besides, it was found that the optimal SOFC had a better gas concentration distribution which can enhance the mass transfer in the electrode, and thus the SOFC performance was improved. The combination of CFD modeling, ANN and GA can provide a promising solution for the performance prediction, improvement and optimization of SOFC accurately and rapidly.

Multi-objective optimization of an explosive waste incineration process considering nitrogen oxides emission and process cost by using artificial neural network surrogate models

Fluidized bed incinerators are more efficient and safe for treating explosive waste than previous methods because they can emit nitrogen oxide (NOx) concentrations below the standard value (90 ppm). However, a limitation is that they have only focused on optimizing the operating conditions to minimize NOx emission concentrations till now. In this situation, it is crucial to balance NOx and process costs. Therefore, this study designed an explosive waste incineration process and performed multi-objective optimization. An artificial neural network surrogate modeling method is vital to reduce optimization time. Therefore, surrogate models with 95% and 99% accuracies were obtained, reducing the calculation time by 90%. Furthermore, an index combining NOx emission concentrations and process costs was proposed to obtain an optimal balanced operating condition of the process. By optimizing the process index, a new operating condition was obtained that could reduce 20% of the process costs while maintaining NOx emission concentrations within the standard limit. The proposed operating condition and data, such as from sensitivity analysis, would provide a valuable guideline for operating the abovementioned process associated with NOx emission standards.

Research on infilling strategy in surrogate-aided optimization for axial compressor blades

The hybrid Voronoi-Latin Hypercube Sampling (Voronoi-LHS) method is proposed for the surrogate-aided optimization of the axial compressor blades. The hybrid method is first applied to the fundamental test cases. The analytical results show that, compared with the Voronoi and LHS strategies, the hybrid method generally improves the robustness and convergency. Then the multi-objective genetic algorithm (MOGA) in conjunction with the artificial neural network (ANN) is applied to optimize the aerodynamic performance of an axial compressor rotor. Before the optimization process, the hybrid Voronoi-LHS sample infilling method is employed to refine the ANN surrogate model. Considering the typical intake distortion, the sweep and lean distributions of this rotor are optimized to pursue the maximum total pressure ratio and adiabatic efficiency. The results show that the optimization significantly improves the pressure ratio, efficiency and surge margin of the compressor with low computing cost.

Optimizing passive design strategies for energy efficient buildings using hybrid artificial neural network (ANN) and multi-objective evolutionary algorithm through a case study approach

Building energy reduction opportunities and thermal comfort of occupants are two major aspects that could be enhanced through passive design solutions. In tropical weather conditions such as in India, there have been very minimal efforts in developing simulation-based approaches to understand the impacts of common passive design solutions on energy needs and thermal comfort. Therefore, this study focuses on developing an Artificial Neural Network (ANN) and Building Energy Simulation and Optimization (BESO) based framework to improve building energy performance and thermal comfort using passive design solutions in Indian climate condition with mixed-mode operation strategy. The initial part of the study performs building energy simulation through a coupled approach of DesignBuilder and jEPlus to develop a valid ANN surrogate model. Eventually, ANN outputs are integrated with multi-objective evolutionary algorithm (Non-dominated Sorting Genetic Algorithm-II) to find the optimal solutions of predefined passive decision variables of the building for minimizing building energy consumption and maximizing thermal comfort. The optimized results in the study show decrease of 46% of building energy consumption and 7.58% of discomfort hours when the set of passive design solutions are opted. The findings of optimal passive design solutions could be helpful for designers and practitioners in developing energy-efficient buildings.

Neural Network Meta-Models for FPSO Motion Prediction From Environmental Data With Different Platform Loads

The current design process of mooring systems for Floating Production, Storage, and Offloading units (FPSOs) depends on the availability of the platform’s mathematical model and the accuracy of dynamic simulations. These simulations then provide the FPSO’s time series motion which is evaluated according to design constraints. This process can be time-consuming and present inaccurate results due to the mathematical model’s limitations and the overall complexity of the vessel’s dynamics. We propose a Neural Simulator, called NeuroSim, a set of data-based surrogate models with environmental data as input, each model specialized in predicting different motion statistics relevant to mooring system design: Maximum Roll, Platform Offset, and Fairlead Displacements. The surrogate models are trained by current, wind, and wave data given in 3 hours periods at a Brazilian Offshore Basin from 2003 to 2010, and the associated dynamic response of a spread-moored FPSO is obtained through time-domain simulations using the Dynasim software. Hyperparameter Optimization techniques are performed to obtain optimal Artificial Neural Network (ANN) models specialized in different platform drafts. Finally, the proposed models are shown to correctly capture platform dynamics, providing good results when compared to motion statistics obtained from Dynasim. We conclude that an ANN surrogate model can be trained directly on actual measured metocean conditions and corresponding FPSO motion statistics to provide increased accuracy and reduced computational time over traditional methods based on dynamic simulation. Moreover, the proposed architecture can be integrated into an automated learning framework: The data-based surrogate models can be continuously fine-tuned and updated with newly measured data, improving accuracy over time.

Stochastic natural frequency analysis of varying diameter functionally graded material pipe conveying fluid

This paper investigates the uncertainty of the structure and material parameters on the natural frequency of the varying diameter functionally graded material (FGM) pipe conveying fluid. Firstly, concentrating on the spatially dependent uncertainty of geometry varying in axial direction as well as the material varying in radial direction, the random field is employed to describe the uncertainty parameters. Then, a generalized eigenvalue equation of the varying diameter FGM pipe is derived by the dynamic stiffness method while introducing the random field and variables into the deterministic governing equation. Due to the input uncertainty, the natural frequencies of the varying diameter FGM pipe change to random variables. In this respect, the stochastic characteristics of natural frequencies can be approximated by the Monte Carlo simulation. However, the enormous computational cost is unbearable. The efficient artificial neural network surrogate model is introduced and incorporated for the natural frequency uncertainty quantification. Consequently, a stochastic natural frequency analysis approach based on the neural network is proposed for the varying diameter FGM pipe conveying fluid. Some examples are investigated to illustrate the effectiveness of the proposed method and the influence of input uncertainty on the probabilistic characterization of the natural frequencies.

Artificial Neural Network based Particle Swarm Optimization solution approach for the inverse depletion of used nuclear fuel

This work builds upon previous efforts to apply inverse analysis in the determination of the initial conditions and burnup history of used nuclear fuel for forensic purposes. In this work, the inverse depletion problem is defined and solved using a surrogate-based approach equipped with the Particle Swarm Optimization algorithm and an Artificial Neural Network surrogate model. The proposed approach is outlined and verified via a series of mockup forensic case studies based upon a VVER-1000 assembly model depleted via SCALE6.1 KENO VI module.The case studies considered retrieving the fuel initial enrichment and burnup using the final used nuclear fuel isotopic content. Results indicate that the proposed approach can estimate the initial fuel enrichment and maximum burnup with reasonable computational cost and acceptable accuracy. The relative error in estimating the fuel initial enrichment was <6% while that of the actual fuel burnup was <3% for all mockup case studies.