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Sensitivity and Uncertainty Quantification of Transition Scenario Simulations

This report documents the first collective attempt at developing and applying capabilities to quantify uncertainties, assess parametric sensitivities, and optimize multiple parameters and metrics in fuel cycle simulations generated by the SA&I Campaign. To do this, external codes that were designed to perform sensitivity analysis and uncertainty quantification (SA&UQ) needed to be coupled to the SA&I Campaign’s nuclear fuel cycle simulators (NFCS). In FY20, two approaches were pursued: 1) coupling Cyclus to an ORNL-internal code called MOT (Metaheuristic Optimization Tool) and 2) coupling DYMOND to the opensource SA&UQ tool kit Dakota. The primary objective of having these NFCS/SA&UQ coupled capabilities is to better inform DOE-NE and other stakeholders on the results generated from the NFCS. For a given set of fuel cycle strategies, policies, and technology assumptions that make up a fuel cycle scenario, these NFCS have traditionally been used by the SA&I Campaign to provide quantitative answers in terms of year-by-year mass flows, infrastructure requirements, costs, etc. With these newly developed coupled capabilities, the SA&I Campaign can now efficiently simulate hundreds or thousands of these scenarios, sample large ranges of parameters and assumptions, and use the unique features of the SA&UQ tools to process the data. This enables providing answers with known and propagated uncertainties, determining the sensitivity of important metrics to different parameters and assumptions, quantifying how much fuel cycle and technology parameters impact each other, and producing optimized fuel cycle strategies for single and multiple variables. To demonstrate these new capabilities, the Cyclus/MOT was used to model several scenarios ranging from simple fleet retirements to transitions to advanced reactors. Specifically, for a transition scenario from LWRs to SFRs and advanced LWRs, uncertainty quantification, sensitivity analysis, and optimization studies were applied to cases involving single and multiple parameter (input) and single and multiple metric (output) variations. In addition, a similar transition scenario was modeled to demonstrate how to optimize the reprocessing capacity parameter to minimize two performance metrics while taking into account uncertainties from two other parameters. Lastly, a depletion module based on SCALE/ORIGEN was added in Cyclus to simulate the third scenario that was designed to quantify the impact of the modeling assumption that all LWR used nuclear fuel have the same burnup. The newly developed DYMOND/Dakota capability was also applied to a transition scenario from the existing fleet to small modular reactors and fast reactors. This particular scenario involves not only explicit isotopic depletion via ORIGEN-2, but also includes multirecycling and utilizing the criticality search feature to determine the fresh fuel composition of recycled fuel, a feature unique to the DYMOND NFCS. A large database of simulations were run with 4 main parameters that were sampled: start date of reprocessing, reprocessing capacity, energy demand growth rate, and advanced reactor share of the fleet. The 4 main metrics were uranium consumption, enrichment requirements, waste generation, and levelized cost of electricity using data from the Cost Basis Report. The demonstrated SA&UQ results include those that inform on how to choose parameters to avoid “failed” scenarios, Sobol’ indices that inform on the importance of various parameters individually and synergistically, and Analysis of Variance (ANOVA) studies that decompose parameter ranges into groups and informs on whether variations are statistically significant.

Feng, B.↗

FORCE-DISPATCHES Integration - Initial Demonstration

Integrated energy systems (IES) combine, in mutually beneficial ways, power from variable renewable energy sources and nuclear power plants (NPP) to improve economic viability under uncertain market and weather conditions. The open-source Framework for Optimization of Resources and Economics (FORCE) tool suite, developed at Idaho National Laboratory (INL), has enabled comprehensive modeling and simulation of IES. The capabilities within FORCE include grid portfolio optimization through the Holistic Energy Resource Optimization Network (HERON) and the transient process model analysis library HYBRID, among others. Continuous efforts and investments from the IES programs have been made to expand and improve the versatility of the FORCE toolset in fiscal year 2022. Code-coupling and cross-tool communication have been important methods for improving this versatility. This report focuses on an additional workflow in the HERON tool for capacity and dispatch stochastic optimization through integration with the external tool Design Integration and Synthesis Platform to Advance Tightly Coupled Hybrid Energy Systems (DISPATCHES). DISPATCHES was primarily developed by the National Energy Technology Laboratory, in collaboration with other national laboratories, which included INL, universities, and industry partners. It is coupled to a library of algebraic models for specific plant components, and to a framework for stochastic optimization different from that provided in the current Risk Analysis Virtual Environment (RAVEN)-running-RAVEN algorithm in HERON. HERON currently conducts stochastic optimization via an outer-inner loop: it optimizes over variable capacity on the outer loop, and at each step within the capacity parameter space, conducts an inner optimization over scenarios (of market signals, demand, and/or weather patterns) and hourly dispatch throughout a user-specified number of years. On the other hand, DISPATCHES conducts stochastic optimization via an “all-at-once” strategy in which capacity variables are optimized at the same level as dispatch variables, as all scenarios are considered at once. The latter method works especially well for projects of limited size and project length, as the necessary computational power and memory increases with the number of variables and scenarios. The new capability to use the DISPATCHES workflow in HERON enhances standalone simulations by leveraging FORCE tools—namely, the economic metrics from the Tool for Economic Analysis (TEAL) and reduced-order model (ROM) sampling from RAVEN. The initial demonstration of the DISPATCHES workflow simulates an existing nuclear-case flowsheet within the DISPATCHES repository—this models a NPP with a secondary revenue stream for hydrogen production. Electrical output from the plant is converted to hydrogen via a proton-exchange membrane (PEM) electrolyzer, hydrogen tanks are used for storage, and an additional turbine is added for hydrogen combustion. Continued work regarding this FORCE-DISPATCHES integration will include automatic generation of DISPATCHES models from HERON inputs, offering analysts the option of using either the RAVEN-runsRAVEN or DISPATCHES workflow to solve technoeconomic optimization problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A stable and accurate partitioned algorithm for conjugate heat transfer

We describe a new partitioned approach for solving conjugate heat transfer (CHT) problems where the governing temperature equations in different material domains are time-stepped in a implicit manner, but where the interface coupling is explicit. The new approach, called the CHAMP scheme (Conjugate Heat transfer Advanced Multi-domain Partitioned), is based on a discretization of the interface coupling conditions using a generalized Robin (mixed) condition. The weights in the Robin condition are determined from the optimization of a condition derived from a local stability analysis of the coupling scheme. The interface treatment combines ideas from optimized-Schwarz methods for domain-decomposition problems together with the interface jump conditions and additional compatibility jump conditions derived from the governing equations. For many problems (i.e. for a wide range of material properties, grid-spacings and time-steps) the CHAMP algorithm is stable and second-order accurate using no sub-time-step iterations (i.e. a single implicit solve of the temperature equation in each domain). In extreme cases (e.g. very fine grids with very large time-steps) it may be necessary to perform one or more sub-iterations. Each sub-iteration generally increases the range of stability substantially and thus one sub-iteration is likely sufficient for the vast majority of practical problems. The CHAMP algorithm is developed first for a model problem and analyzed using normal-mode the- ory. The theory provides a mechanism for choosing optimal parameters in the mixed interface condition. A comparison is made to the classical Dirichlet-Neumann (DN) method and, where applicable, to the optimized- Schwarz (OS) domain-decomposition method. For problems with different thermal conductivities and dif- fusivities, the CHAMP algorithm outperforms the DN scheme. For domain-decomposition problems with uniform conductivities and diffusivities, the CHAMP algorithm performs better than the typical OS scheme with one grid-cell overlap. Lastly, the CHAMP scheme is also developed for general curvilinear grids and CHT ex- amples are presented using composite overset grids that confirm the theory and demonstrate the effectiveness of the approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Characteristics of miniature electronic brachytherapy x-ray sources based on TG-43U1 formalism using Monte Carlo simulation techniques

Purpose: The goal of this study is to determine a method for Monte Carlo (MC) characterization of the miniature electronic brachytherapy x-ray sources (MEBXS) and to set dosimetric parameters according to TG-43U1 formalism. TG-43U1 parameters were used to get optimal designs of MEBXS. Parameters that affect the dose distribution such as anode shapes, target thickness, target angles, and electron beam source characteristics were evaluated. Optimized MEBXS designs were obtained and used to determine radial dose functions and 2D anisotropy functions in the electron energy range of 25-80 keV. Methods: Tungsten anode material was considered in two different geometries, hemispherical and conical-hemisphere. These configurations were analyzed by the 4C MC code with several different optimization techniques. The first optimization compared target thickness layers versus electron energy. These optimized thicknesses were compared with published results by Ihsan et al.[Nucl. Instrum. Methods Phys. Res. B 264, 371-377 (2007)]. The second optimization evaluated electron source characteristics by changing the cathode shapes and electron energies. Electron sources studied included; (1) point sources, (2) uniform cylinders, and (3) nonuniform cylindrical shell geometries. The third optimization was used to assess the apex angle of the conical-hemisphere target. The goal of these optimizations was to produce 2D-dose anisotropy functions closer to unity. An overall optimized MEBXS was developed from this analysis. The results obtained from this model were compared to known characteristics of HDR {sup 125}I, LDR {sup 103}Pd, and Xoft Axxent electronic brachytherapy source (XAEBS) [Med. Phys. 33, 4020-4032 (2006)]. Results: The optimized anode thicknesses as a function of electron energy is fitted by the linear equation Y ({mu}m) = 0.0459X (keV)-0.7342. The optimized electron source geometry is obtained for a disk-shaped parallel beam (uniform cylinder) with 0.9 mm radius. The TG-43 distribution is less sensitive to the shape of the conical-hemisphere anode than the hemispherical anode. However, the optimized apex angle of conical-hemisphere anode was determined to be 60 deg. For the hemispherical targets, calculated radial dose function values at a distance of 5 cm were 0.137, 0.191, 0.247, and 0.331 for 40, 50, 60, and 80 keV electrons, respectively. These values for the conical-hemisphere targets are 0.165, 0.239, 0.305, and 0.412, respectively. Calculated 2D anisotropy functions values for the hemispherical target shape were F(1 cm, 0 deg.) = 1.438 and F(1 cm, 0 deg.) = 1.465 for 30 and 80 keV electrons, respectively. The corresponding values for conical-hemisphere targets are 1.091 and 1.241, respectively. Conclusions: A method for the characterizations of MEBXS using TG-43U1 dosimetric data using the MC MCNP4C has been presented. The effects of target geometry, thicknesses, and electron source geometry have been investigated. The final choices of MEBXS design are conical-hemisphere target shapes having an apex angle of 60 deg. Tungsten material having an optimized thickness versus electron energy and a 0.9 mm radius of uniform cylinder as a cathode produces optimal electron source characteristics.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

SU-E-J-89: Motion Effects On Organ Dose in Respiratory Gated Stereotactic Body Radiation Therapy

Purpose: Existing reports on gated radiation therapy focus mainly on optimizing dose delivery to the target structure. This work investigates the motion effects on radiation dose delivered to organs at risk (OAR) in respiratory gated stereotactic body radiation therapy (SBRT). A new algorithmic tool of dose analysis is developed to evaluate the optimality of gating phase for dose sparing on OARs while ensuring adequate target coverage. Methods: Eight patients with pancreatic cancer were treated on a phase I prospective study employing 4DCT-based SBRT. For each patient, 4DCT scans are acquired and sorted into 10 respiratory phases (inhale-exhale- inhale). Treatment planning is performed on the average CT image. The average CT is spatially registered to other phases. The resultant displacement field is then applied on the plan dose map to estimate the actual dose map for each phase. Dose values of each voxel are fitted to a sinusoidal function. Fitting parameters of dose variation, mean delivered dose and optimal gating phase for each voxel over respiration cycle are mapped on the dose volume. Results: The sinusoidal function accurately models the dose change during respiratory motion (mean fitting error 4.6%). In the eight patients, mean dose variation is 3.3 Gy on OARs with maximum of 13.7 Gy. Two patients have about 100cm{sup 3} volumes covered by more than 5 Gy deviation. The mean delivered dose maps are similar to plan dose with slight deformation. The optimal gating phase highly varies across the patient, with phase 5 or 6 on about 60% of the volume, and phase 0 on most of the rest. Conclusion: A new algorithmic tool is developed to conveniently quantify dose deviation on OARs from plan dose during the respiratory cycle. The proposed software facilitates the treatment planning process by providing the optimal respiratory gating phase for dose sparing on each OAR.

60 APPLIED LIFE SCIENCES↗

PANORAMA: An approach to performance modeling and diagnosis of extreme-scale workflows

Here we report that computational science is well established as the third pillar of scientific discovery and is on par with experimentation and theory. However, as we move closer toward the ability to execute exascale calculations and process the ensuing extreme-scale amounts of data produced by both experiments and computations alike, the complexity of managing the compute and data analysis tasks has grown beyond the capabilities of domain scientists. Therefore, workflow management systems are absolutely necessary to ensure current and future scientific discoveries. A key research question for these workflow management systems concerns the performance optimization of complex calculation and data analysis tasks. The central contribution of this article is a description of the PANORAMA approach for modeling and diagnosing the run-time performance of complex scientific workflows. This approach integrates extreme-scale systems testbed experimentation, structured analytical modeling, and parallel systems simulation into a comprehensive workflow framework called Pegasus for understanding and improving the overall performance of complex scientific workflows.

97 MATHEMATICS AND COMPUTING↗

Development of Multiresolution Capabilities for the Holistic Energy Resource Optimization Network (HERON) tool A progress update

INL researchers work on technoeconomic analyses for integrated energy systems (IES) using the Framework for Optimization of ResourCes and Economics (FORCE). Within FORCE, researchers use the Holistic Energy Resource Optimization Network (HERON) tool to conduct optimization of grid portfolios under uncertain market conditions. These optimizations determine optimal capacities for all IES components and strategies for resource dispatch which maximize some economic metric (e.g., net present value). Resource dispatch occurs on finer timescales (typically hours) and thus are asked to respond to a given time series (e.g. hourly load demand profiles for a grid, or pre-determined electricity prices). Volatile and complex bidding dynamics as well as poorly forecasted weather events within deregulated markets add uncertainty to the time series; FORCE can address this uncertainty by training a reduced order model on historical time series and generate unique synthetic time series which represent individual scenarios or realizations of the market. The IES configuration can be simulated under these different sampled realizations and a stochastic optimization is conducted which optimizes the expected value of the desired economic metric. The training of a synthetic time series generator is limited by the chosen time resolution; dynamics can occur on different time scales. Seasonal demand trends can dominate faster dynamical events (such as power outages from certain sectors or severe weather events) which might not get captured correctly by the trained model. In this report, we investigate different ways of addressing the training and generation of time series on multiple time scales using three main algorithms: wavelet decomposition, dynamic mode decomposition, and generative adversarial networks for time series. We demonstrate a time series analysis that yields information on not just the frequency space but also temporal space: where a fast Fourier transform can provide what frequencies dominate, the new algorithms can provide when the frequencies dominate as well. These analyses can help improve IES optimization by allowing researchers to couple simulations at different timescales when it is most needed - seasonal, day-ahead, and real time optimization - with greater computational efficiency. Future work will include implementation of a subset of the proposed algorithms into the FORCE toolset and application of these analyses into multiple timescale optimization.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Simulation and research of few-mode optical fiber DMD degradation due to geometry deviation from optimized form

This work presents an alternative fast and simple method for the design of a graded refractive index profile of silica few-mode optical fibers (FMFs) with enlarged core diameter that extremely improves mode effective area, and low differential mode delay (DMD). We demonstrate some results of refractive index profile optimization for 16-LP-mode FMF with enlarged core diameter up to 42 μm and mode effective area more 130 μm{sup 2} under DMD reduction less 120 ps/km all over “C”-band and less 40 ps/km at λ = 1550 nm region. We also propose approach for simulation of the deviation of “real” optical fiber geometry from the optimized form and rigorous method for analysis of large core complicated optical fiber. Here, FMF core asymmetrical ellipticity together with the refractive index profile distortions were considered. They were set and simulated by data from reports of the real commercially available laser-optimized multimode optical fibers of TIA/ISO Cat. OM2+/OM3 refractive index profile measurements, performed by lab optical fiber analyzer kit. We present results of researches of considered FMF DMD spectral curve degradation due to described core geometry deviation from the optimized form. It was noticed, that unlike to only refractive index local fluctuations, FMF core non-circularity strongly distorts higher-order mode field distribution that affects to spectral mode delay curves and may lead to critical total DMD increasing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An Online Prototype Toolset for Predicting and Optimizing P&T Performance (FY23 Status Report)

A new web-based toolset is being developed to support ongoing remediation optimization efforts and implementation of an adaptive site management strategy for the 200 West Area Pump-and-Treat (P&T) system at the Hanford Site. This toolset, comprising the well performance index tool and the well optimization pre-screening tool, will offer a user-friendly interface to predict and optimize the P&T well network’s performance at a preliminary level. Efforts in fiscal year (FY) 2023 focused on three main components: updating the existing deep learning model for predicting P&T performance, designing and developing a prototype of a web-based performance index tool, and initiating the conceptual design of the well optimization pre-screening tool. The well performance index tool is based on a pre-trained deep learning model that allows users to select a target contaminant and well screen length, then visualize the predicted performance of potential new wells across the site. The well optimization pre-screening tool includes two separate modules: the pre-computed scenario viewer, which organizes and visualizes offline optimization simulation results, and the quick analysis module, which provides real-time model prediction using user-specified well locations. In FY24, the plan is to add web-based applications to SOCRATES for both the well performance prediction tool and the optimization prescreening tool, with accompanying user and theory guides. These tools are intended to enable an accessible, easily applied, and transparent approach to remedy planning and decision-making.

97 MATHEMATICS AND COMPUTING↗

Optimal Control of Markov Processes with Age-Dependent Transition Rates

We study optimal control of Markov processes with age-dependent transition rates. The control policy is chosen continuously over time based on the state of the process and its age. We study infinite horizon discounted cost and infinite horizon average cost problems. Our approach is via the construction of an equivalent semi-Markov decision process. We characterise the value function and optimal controls for both discounted and average cost cases.

24 POWER TRANSMISSION AND DISTRIBUTION↗

An optimization method for flexural bearing design for high-stroke high-frequency applications

A method for optimization of a high-stroke, high-frequency flexural bearing was completed. The main goal was to design a flexural bearing system as the energy restoration component of a one kW free piston linear engine alternator (LEA) operating at 90 Hz and maximum targeted displacement of 22 mm. Defined electricity output of 1 kW, with more than 30% efficiency, required engine operation under high speed and high stroke conditions. Under such challenging stroke and frequency requirements, a method of design was required to select between a wide range of parameters in flexural bearing design. A parametric CAD model was prepared and used in the optimization package of a finite element analysis (FEA) software. Four main parameters of flexural bearing geometry were identified and included the outer diameter, thickness, number of arms, and sweep angle of spiral cuts. Other design parameters including spiral gap width, shape factor and spiral start points angle were shown to be less important compared to these four main parameters in primary design and were examined separately. A neural network algorithm was used to investigate the interactions and effects of design parameters. The sensitivity of each parameter on output criteria such as maximum stress and natural frequency was examined and design charts developed. Methods for further modification of the spiral curve at end points were introduced to reduce the maximum stress level by up to 20%. Several steel alloys and a titanium-based alloy were identified as proper material candidates for high cycle applications and the final designed spring was manufactured and tested to validate the FEA results of axial stiffness and strain level throughout the flexure arms. The percent of the flexure’s moving mass was estimated to be 29% with FEA analysis and compared well with the experimental value of 31%. The stress/strain results of the FEA analysis matched with the experimental results – within ±5%.

42 ENGINEERING↗

Depth of manual dismantling analysis: A cost–benefit approach

Highlights: ► A mathematical modeling tool for OEMs. ► The tool can be used by OEMs, recyclers of electr(on)ic equipment or WEEE management systems’ regulators. ► The tool makes use of cost–benefit analysis in order to determine the optimal depth of product disassembly. ► The reusable materials and the quantity of metals and plastics recycled can be quantified in an easy-to-comprehend manner. - Abstract: This paper presents a decision support tool for manufacturers and recyclers towards end-of-life strategies for waste electrical and electronic equipment. A mathematical formulation based on the cost benefit analysis concept is herein analytically described in order to determine the parts and/or components of an obsolete product that should be either non-destructively recovered for reuse or be recycled. The framework optimally determines the depth of disassembly for a given product, taking into account economic considerations. On this basis, it embeds all relevant cost elements to be included in the decision-making process, such as recovered materials and (depreciated) parts/components, labor costs, energy consumption, equipment depreciation, quality control and warehousing. This tool can be part of the strategic decision-making process in order to maximize profitability or minimize end-of-life management costs. A case study to demonstrate the models’ applicability is presented for a typical electronic product in terms of structure and material composition. Taking into account the market values of the pilot product’s components, the manual disassembly is proven profitable with the marginal revenues from recovered reusable materials to be estimated at 2.93–23.06 €, depending on the level of disassembly.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

A retrospective analysis for patient-specific quality assurance of volumetric-modulated arc therapy plans

Volumetric-modulated arc therapy (VMAT) is now widely used clinically, as it is capable of delivering a highly conformal dose distribution in a short time interval. We retrospectively analyzed patient-specific quality assurance (QA) of VMAT and examined the relationships between the planning parameters and the QA results. A total of 118 clinical VMAT cases underwent pretreatment QA. All plans had 3-dimensional diode array measurements, and 69 also had ion chamber measurements. Dose distribution and isocenter point dose were evaluated by comparing the measurements and the treatment planning system (TPS) calculations. In addition, the relationship between QA results and several planning parameters, such as dose level, control points (CPs), monitor units (MUs), average field width, and average leaf travel, were also analyzed. For delivered dose distribution, a gamma analysis passing rate greater than 90% was obtained for all plans and greater than 95% for 100 of 118 plans with the 3%/3-mm criteria. The difference (mean ± standard deviation) between the point doses measured by the ion chamber and those calculated by TPS was 0.9% ± 2.0% for all plans. For all cancer sites, nasopharyngeal carcinoma and gastric cancer have the lowest and highest average passing rates, respectively. From multivariate linear regression analysis, the dose level (p = 0.001) and the average leaf travel (p < 0.001) showed negative correlations with the passing rate, and the average field width (p = 0.003) showed a positive correlation with the passing rate, all indicating a correlation between the passing rate and the plan complexity. No statistically significant correlation was found between MU or CP and the passing rate. Analysis of the results of dosimetric pretreatment measurements as a function of VMAT plan parameters can provide important information to guide the plan parameter setting and optimization in TPS.

61 RADIATION PROTECTION AND DOSIMETRY↗