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NASA NTRS2021

Weekly Mapping of Sea Ice Freeboard in the Ross Sea from ICESat-2

NASA’s ICESat-2 has been providing sea ice freeboard measurements across the polar regions since October 2018. In spite of the outstanding spatial resolution and precision of ICESat-2, the spatial sparsity of the data can be a critical issue for sea ice monitoring. This study employs a geostatistical approach (i.e., ordinary kriging) to characterize the spatial autocorrelation of the ICESat-2 freeboard measurements (ATL10) to estimate weekly freeboard variations in 2019 for the entire Ross Sea area, including where ICESat-2 tracks are not directly available. Three variogram models (exponential, Gaussian, and spherical) are compared in this study. According to the cross-validation results, the kriging-estimated freeboards show correlation coefficients of 0.56–0.57, root mean square error (RMSE) of ~0.12 m, and mean absolute error (MAE) of ~0.07 m with the actual ATL10 freeboard measurements. In addition, the estimated errors of the kriging interpolation are low in autumn and high in winter to spring, and low in southern regions and high in northern regions of the Ross Sea. The effective ranges of the variograms are 5–10 km and the results from the three variogram models do not show significant differences with each other. The southwest (SW) sector of the Ross Sea shows low and consistent freeboard over the entire year because of the frequent opening of wide polynya areas generating new ice in this sector. However, the southeast (SE) sector shows large variations in freeboard, which demonstrates the advection of thick multiyear ice from the Amundsen Sea into the Ross Sea. Thus, this kriging-based interpolation of ICESat-2 freeboard can be used in the future to estimate accurate sea ice production over the Ross Sea by incorporating other remote sensing data.

Satellite altimeter↗

NASA NTRSDate not supplied

Progress on Inverse Estimation Technique of Non-Linear Pitch Damping Coefficient Curves Using Free-Flight CFD Generated Trajectories

Characterization of entry vehicle pitch damping coefficient curves is crucial to ensure appropriate re-entry and overall mission success. The pitch damping coefficient (C_(m_q )+C_(m_α ̇ )) is used to encapsulate the oscillatory growth or decay of a body during a trajectory. The inverse estimation technique utilizes an existing Free-Flight CFD (FF-CFD) dataset and wraps a reconstruction algorithm in an optimizer. The reconstruction integrates the planar equations of motion derived by Schoenenberger, Queen [1] using Python’s scipy.integrate.solve_ivp. The optimizer’s objective function is the normalized 𝐿2 residual of the angle of attack peaks between the reconstructed trajectory and the original data produced with FF-CFD. Inclusion of the peak times in this residual calculation allows for simultaneous optimization of the pitch moment coefficient, C_(m_α ). This residual equation is shown below in Eq. 1. The optimizer scipy.optimize.minimize was used with the gradient-based Powell method for the analysis presented, however the differential evolution method was investigated as means of comparison, and was found to produce marginally lower residual values with prohibitively longer run times. Further, the pitch damping curve is found by fitting a cubic interpolation function to a set of (α, (C_(m_q )+C_(m_α ̇ ))) control points, where the α points are held constant and the (C_(m_q )+C_(m_α ̇ )) values are the optimized parameters. The pitch moment curve uses a linear interpolation between the minimum and maximum α in the dataset. FF-CFD generated trajectories using the Dragonfly capsule geometry with the Genesis ballistic range model parameters were simulated and used for this analysis. These FF-CFD trajectories simulate planar motion, as restricted by the reconstructing the equations of motion, of three different cases: 1-DoF (free-to-pitch), 2-DoF (free-to-pitch and heave), and 3-DoF (free-to-pitch, heave, and decelerate). Pitch damping coefficient curves generated using this inverse estimation curve technique with FF-CFD 1-DoF Dragonfly data are found in Fig. 1. Preliminary results reconstructing ballistic range shots using these FF-CFD derived predictions of the pitch damping curve (Fig. 1) are shown in Fig. 2. It should be noted that the ballistic range shot used a Genesis model whereas the FF-CFD data used a Dragonfly geometry, however these geometries are similar.

entry↗

NASA NTRS2023

Kamodo: Simplifying Model Data Access and Utilization

To address the lack of user-friendly software needed to simplify the utilization of model data across Heliophysics, the Community Coordinated Modeling Center (CCMC) at NASA’s Goddard Space Flight Center has developed a model-agnostic method via Kamodo for users to easily access and utilize model data in their workflows. By abstracting away the broad range of file formats and the intricacies of interpolation on specialized grids, this approach significantly lowers the barrier to model data access and utilization for the community while adding exciting new capabilities to their tool boxes. This paper describes the direct interfaces to the model data, called model readers, and a basic introduction on how to use them. Additionally, we detail the planned approach for including custom interpolation codes, and include current progress on specialized visualization developments. The CCMC is maintaining Kamodo as an official NASA open-sourced software to enable and encourage community collaboration.

Heliophysics↗

NASA NTRSDate not supplied

Assessing the Uncertainty Impact of CERES Fast Longwave and SHortwave Radiative Flux (FLASHFlux) Level 3 Product With and Without Terra Observations

The Clouds and Earth’s Radiant Energy System (CERES) project provides satellite-based observations of how Earth’s energy flows are varying in time and space and how clouds and aerosols are affecting the Earth’s radiation budget. Nominally, CERES data products require months of validation and calibration before releasing a climate quality data. The Fast Longwave And SHortwave radiative Flux (FLASHFlux) data product was developed to provide data for applied science research involving the renewable energy and agricultural sectors within a week of observation. FLASHFlux achieves this by using simplified calibration, an operational meteorological product from Global Monitoring and Assimilation Office (GMAO), and a surface parameterizations model. The CERES FLASHFlux provides two data products: 1) an hourly Level 2 Single Scanner Footprint (SSF) data separately for Terra and NOAA-20 observations. 2) a daily Level 3 Time Interpolated and Spatially Averaged (TISA) gridded data that combines NOAA-20 and Terra observations on a one-degree equal angle grid. FLASHFlux TISA data product interpolate on a diurnal model that assumes a satellite equilateral crossing time of 10:30 AM and 1:30 PM from Terra and Aqua, respectively. Aqua was replaced by NOAA-20 starting on September 2022. Terra is planned to be replace by the Satellite ClOud and Radiation Property retrieval System (SatCORPS) soon. We are currently using the Terra observations as it continues to drift. We assess the impact of FLASHFlux TISA data when Terra is removed. An uncertainty estimate of the Top-Of-Atmosphere (TOA) fluxes are given of FLASHFlux Version4A (before Terra drift) and Version4B (current), and Version4B (no Terra) in comparison to the CERES EBAF and SYN1deg. In addition, we compare FLASHFlux Version4B and Version4B (no Terra) surface radiative fluxes to ground base measurements to determine the impact of running without Terra data.

PC Sawaengphokhai↗

NASA NTRS2024

Validation and Application of Satellite-Derived Sea Surface Temperature Gradients in the Bering Strait and Bering Sea

The Arctic is one of the most important regions in the world’s oceans for understanding the impacts of a changing climate. Yet, it is also difficult to measure because of extreme weather and ice conditions. In this work, we directly compare four datasets from the Group for High-Resolution Sea Surface Temperature (GHRSST) with a NASA Saildrone deployment along the Alaskan Coast and the Bering Sea and Bering Strait. The four datasets used are the Remote Sensing Systems Microwave Infrared Optimally Interpolated (MWIR) product, the Canadian Meteorological Center (CMC) product, the Daily Optimally Interpolated Product (DOISST), and the Operational Sea Surface Temperature and Ice Analysis (OSTIA) product. Spatial sea surface temperature (SST) gradients were derived for both the Saildrone deployment and GHRSST products, with the GHRSST products collocated with the Saildrone deployment. Overall, statistics indicate that the OSTIA product had a correlation of 0.79 and a root mean square difference of 0.11 °C/km when compared with Saildrone. CMC had the highest correlation of 0.81. Scatter plots indicate that OSTIA had the slope closest to one, thus best reproducing the magnitudes of the Saildrone gradients. Differences increased at latitudes > 65°N where sea ice would have a greater impact. A trend analysis was then performed on the gradient fields. Overall, positive trends in gradients occurred in areas along the coastal regions. A negative trend occurred at approximately 60°N. A major finding of this study is that future work needs to revolve around the impact of changing ice conditions on SST gradients. Another major finding is that a northward shift in the southern ice edge occurred after 2010 with a maxima at approximately 2019. This indicates that the shift of the southern ice edge is not gradual but has dramatically increased over the last decade. Future work needs to revolve around examining the possible causes for this northward shift.

Arctic↗

NASA NTRSDate not supplied

Derivation of Integrated Load Distributions from Resampled Computational Data

Principal component analysis (PCA) has been the center of many surrogate models used to characterize fluid flows in recent years. However, little work has been done to character- ize the uncertainty in the PCA transform itself and its effect on derived surrogate models. To explore the uncertainty, a typical interpolated surrogate model is constructed for a represen- tative aerodynamic body from computational data. The computational data is then resampled to explore the robustness of the PCA transformation. The variations of the model predictions during this resampling are analyzed to get a measure of confidence in the PCA transformation, which is then applied to the interpolated surrogate model to get uncertainty on integrated force predictions. An initial test case has been explored with promising results.

Principal Component Analysis↗

NASA NTRSDate not supplied

A Queuing Theory Approach to Pilot-Controller Coordination for m:N Operations

In recent years, attention and interest by industry and researchers has grown in a control paradigm for remotely piloted aircraft termed “m:N operations.” In an m:N operation, a team of m remote pilots in command (RIPCs) collaboratively manage the flights of N aircraft. A consequence of an m:N concept of operations is that the RPICs will have to switch attention from one aircraft to another and from one task to another. Previous research in m:N operations has focused on the workload experienced by an RPIC and their level of situation awareness on their flights. Researchers have found that RPIC workload and situation awareness are generally sensitive to increasing N, although NASA’s Multi-Vehicle (m:N) Working Group has suggested that the driver of workload/situation awareness is the number of exceptions requiring human intervention as opposed to the value of N itself. In any case, a natural antecedent of workload is task load. In this paper, queueing theory is applied to a 1:N Urban Air Mobility (UAM) air taxi operation in order to estimate pilot task load for managing radio communications with air traffic controllers (ATCs) under increasing N. An M/M/1 queueing system is used to model the RIPC’s servicing of calls and clearance requests (e.g., departure, arrival, or airspace transition) to ATC for the N aircraft. Important parameters for the queueing model are the task arrival rate and the average service time for task completion. Radio communication times from past human-in-the-loop simulation studies are used to measure service times for a 1:4 and 1:12 UAM operation and to interpolate service times for 4 < N < 12. A Monte Carlo method is then employed, using the measured and interpolated service times, to estimate arrival rate and related queueing statistics. The paper concludes by considering the estimated queuing statistics, particularly the RPIC’s utilization (i.e., proportion of time actively servicing tasks), the length of the task queue over time, and the implications for task-balanced system design.

task load↗

NASA NTRSDate not supplied

Derivation of Integrated Load Distributions from Resampled Computational Data

Computational Fluid Dynamics↗

DOE OSTI2016

Optimal Temperature Grid for Accurate Doppler Kernel Reconstruction

For computational efficiency, both Monte Carlo and deterministic neutron transport codes often rely on pre-tabulated cross section sets and simple interpolation schemes to represent the Doppler broadening of the cross sections at a needed temperature. Accurate accounting of Doppler effects is of paramount importance for reactor analysis since it impacts the power distribution and the reactor response during transients. Temperature interpolation methods for Doppler broadening have traditionally been physically motivated engineering curve-fits, selected upon best-performance criteria on important nuclides.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2015

Guaranteed Quality Conformal Mesh Decomposition.

Interface-conforming elements generated by the conformal decomposition finite element method can have arbitrarily poor quality due to the arbitrary intersection of the base triangular or tetrahedral mesh with material interfaces. This can have severe consequences for both the solvability of linear systems and for the interpolation error of fields represented on these meshes. The present work demonstrates that snapping the base mesh nodes to the interface whenever the interface cuts close to a node results in conforming meshes of good quality. Theoretical limits on the snapping tolerance are derived, and even conservative tolerance choices result in limiting the stiffness matrix condition number to within a small multiple of that of the base mesh. Interpolation errors are also well controlled in the norms of interest. In 3D, use of node-to-interface snapping also permits a simpler and more robust vertex ID-based element decomposition algorithm to be used with no serious detriment to mesh quality.

42 ENGINEERING↗

DOE OSTI2023

Dynamic Model Agnostic Reliability Evaluation of Machine-Learning Models Integrated in Instrumentation & Control Systems

In recent years, the field of machine learning (ML), specifically neural networks, has grown significantly and has spurred research in its applicability to digital instrumentation and control systems (DI&C). While ML models have shown promise in operational contexts, the trustworthiness of using such algorithms has not been adequately assessed. Failures of ML integrated systems are not well understood, and the lack of comprehensive risk modeling can degrade the trustworthiness in these systems. In recent reports by the National Institute for Standards and Technology (NIST) [1] and the Nuclear Regulatory Commission (NRC) [2], they indicate that trustworthiness in ML is a critical barrier and will play a vital role in the safe, accountable, and secure operation of intelligent systems. Thus, in this work, we demonstrate a dynamic model-agnostic method to quantify the relative reliability of AI/ML predictions by incorporating out-of-distribution (OOD) detection on the training dataset. It is well documented that most ML algorithms excel at interpolation (or near-interpolation) tasks but experience significant performance degradation at extrapolation. The method, referenced as the Laplacian distributed decay for reliability (LADDR), determines the difference between the operational and training datasets which can used to the relative reliability of AI/ML predictions. LADDR is then demonstrated on a feedforward neural network based digital twin used for the prediction of safety significant factors during a loss-of-flow transient. LADDR is used to demonstrate how training data can be used as evidence to support the relative reliability of ML/AI predictions enhancing the overall trustworthiness of the system.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Phonon-informed Neural Thermal Scattering (NeTS) Optimization for Crystalline Graphite and Beryllium Metal

Fast neutrons born from fission lose energy through scattering interactions in the process of slowing-down. As neutrons thermalize to the order of $k$ $b$ $T$ (where $k$ $b$ is the Boltzmann constant, and $T$ is the temperature of the medium), their de Broglie wavelength and energy approaches the order of inter-atomic spacing and quantized lattice vibrations, i.e., phonons. At thermal energies, the thermal scattering law (TSL), i.e., $S$($α, β$), captures crystal binding contributions to the total reaction rate, or cross section. This dimensionless material property describes the energy ($β$) and momentum ($α$) exchanges available in a medium. Currently, $S$($α, β$) is evaluated in the Full Law Analysis Scattering System Hub (FLASSH) code for discrete inputs and stored as ENDF/B File 7 for 0-phonon elastic (MT 2) and n-phonon inelastic (MT 4) processes. Further processing recasts $S$($α, β$) into cumulative distribution functions for sampling post-collision scattering kinematics. In practice, interpolation schemes are employed to access data between tabulated values. An improvement to this juncture of the nuclear data pipeline is supplying cross sections on-the-fly (OTF), as has been developed for the un-resolved resonance region to minimize non-physical interpolation errors. This capability may improve simulation accuracy for accident and transient analyses, where rapidly varying changes in temperature and pressure are difficult to predict beforehand. To do so, deep artificial neural networks (ANNs) can be employed which collapse non-linear, complex data into a lightweight dictionary of neural weights and biases. This has been successfully demonstrated for the hydrogen in light water $S$($α, β$) dataset in the form of a Neural Thermal Scattering (NeTS) module. In this work, the NeTS framework is extended to consider the impact of material-dependent dynamical features on optimal neural pre-processing and architecture design decisions, such as number of neurons per hidden layer, residual skip connections and neural depth. New NeTS modules for crystalline graphite and beryllium metal illuminate a novel correlation between dynamical nonlinearity and optimal neural parametrization when deploying $S$($α, β$) on-the-fly.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Gated truncated readout system

A gated truncated readout system for position sensitive or imaging detectors that improves resolution over traditional readout systems. The readout system includes two or more amplifiers that receive a multichannel output analog data from the detector. Analog gates control circuitry, included in the readout circuit, receives the signals from the amplifiers, determines a fractional value of the sum-integral of the signals, and enables analog gates operation around an area of interest, disabling all other channels where noise dominates the signal value and thereby improving interpolation accuracy of the signals centroid position and the detector resolution. Filtered signals are transmitted to a centroid interpolation signal processing device for computation of the centroid position. As a result disabling all channels where noise dominates the signal value, the gated truncated readout system provides better accuracy improved detector resolution.

Popov, Vladimir↗

DOE OSTI2015

Innovative use of Cr(VI) plume depictions and pump-and-treat capture analysis to estimate risks of contaminant discharge to surface water at Hanford reactor areas - 15315

The Hanford Site nuclear reactor operations required large quantities of high-quality cooling water, which was treated with chemicals including sodium dichromate dihydrate for corrosion control. Cooling water leakage, as well as intentional discharge of cooling water to ground during upset conditions, produced extensive groundwater recharge mounds consisting largely of contaminated cooling water and resulted in wide distribution of hexavalent chromium (Cr[VI]) contamination in the unconfined aquifer. The 2013 Cr(VI) groundwater plumes in the 100 Areas cover approximately 6 km{sup 2} (1500 acres), primarily in the 100-HR-3 and 100-KR-4 groundwater operable units (OUs). The Columbia River is a groundwater discharge boundary; where the plumes are adjacent to the Columbia River there remains a potential to discharge Cr(VI) to the river at concentrations above water quality criteria. The pump-and-treat systems along the River Corridor are operating with two main goals: 1) protection of the Columbia River, and 2) recovery of contaminant mass. An evaluation of the effectiveness of the pump-and-treat systems was needed to determine if the Columbia River was protected from contamination, and also to determine where additional system modifications may be needed. In response to this need, a technique for assessing the river protection was developed which takes into consideration seasonal migration of the plume and hydraulic performance of the operating well fields. Groundwater contaminant plume maps are generated across the Hanford Site on an annual basis. The assessment technique overlays the annual plume and the capture efficiency maps for the various pump and treat systems. The river protection analysis technique was prepared for use at the Hanford site and is described in detail in M.J. Tonkin, 2013. Interpolated capture frequency maps, based on mapping dynamic water level observed in observation wells and derived water levels in the vicinity of extraction and injection wells, are developed initially. Second, simulated capture frequency maps are developed, based on transport modelling results. Both interpolated and simulated capture frequency maps are based on operation of the systems over a full year. These two capture maps are then overlaid on the plume distribution maps for inspection of the relative orientation of the contaminant plumes with the capture frequency. To quantify the relative degree of protection of the river from discharges of Cr(VI) (and conversely, the degree of threat) at any particular location, a systematic method of evaluating and mapping the plume/capture relationship was developed. By comparing the spatial relationship between contaminant plumes and hydraulic capture frequency, an index of relative protectiveness is developed and the results posted on the combined plume/capture plan view map. Areas exhibiting lesser degrees of river protection are identified for remedial process optimization actions to control plumes and prevent continuing discharge of Cr(VI) to the river. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2019

Probability of Pinching Failure in PWR SNF after Long-Term Storage

A probabilistic assessment was performed on pinching failure of PWR SNF rod cladding under accidental SNF cask transport conditions. a set of 3,000 rod pinching scenarios was analyzed, with different geometrical, material, and loading parameters, using a Latin Hypercube Sampling (LHS). The investigated accidents include train derailments leading to cask collisions or cask drops. Pinching failure was related to cladding offset strain, defined as the plastic deformation interval in radial cladding direction normalized with respect to the outer cladding diameter. Finite element (FE) models were used to compute SNF rod deformations and the offset strain demand OSD in each of the assessed pinching scenarios. The numerical models account for the contribution of the degraded fuel pellets to rod pinching stiffness. The offset strain capacity OSC was computed using regression and interpolation models based on ring compression (RCT) test results, and account for hydride-related effects on cladding ductility. The results show a low probability of pinching failure. Hydride-related cladding embrittlement affects the structural integrity of PWR SNF rods after long-term dry storage of up to 300 years. Radial hydride patterns or large amounts of circumferentially oriented hydrides reduce the cladding ductile deformation capability when pinched at low material temperatures. The probability of hydride-related pinching failure of PWR cladding is estimated after long-term dry storage to address: How do PWR SNF rod conditions like hydrogen content, vacuum drying peak cladding hoop stress σ{sub θ}, and cladding material temperature affect cladding ductility? Is hydride-related cladding embrittlement a material degradation mechanism that affects the structural integrity of PWR SNF rods under pinching loading? What are the controlling parameters for deformation demands in PWR SNF rods under pinching loading? Is the pinching load amplitude an important parameter that controls the probability of pinching failure? How do parameters like pellet-cladding gap or fuel pellet degradation affect the pinching loading capacity of PWR SNF rods? Statistical modelling of PWR SNF rod conditions in U.S. inventory: A pseudo rod database was generated based on EIA database. Analysis of train accident scenarios: a probability density function (pdf) of a pinching load distribution P{sub 9m} of a 9-m cask drop is linearly scaled to generate a more representative: distribution P{sub AS}. The new distribution considers train collision velocities, cask drops for on- and off-bridge accidents, and cask impact orientation. LHS generates 3,000 rod pinching scenarios based on nine independent geometrical, material, and loading parameters. Probabilistic FE Analysis: The LHS realizations are used to generate 3,000 FE models. The FE analysis is conducted for P{sub 9m}, and P{sub AS}. The workflow is automatized. The OSC is computed with regression and interpolation models, as a function of the hydrogen content C{sub H}, vacuum drying peak σ{sub θ}, and SNF temperature T{sub FR}: The regression data was obtained in RCTs on PWR cladding. The OSD is derived from the cladding deformations in the FE models. Cladding failure was identified via a comparison of OSC and OSD. A 300 and a 30 years-of-dry-storage duration is investigated: The dry-storage period affects the expected SNF temperature and consequently, the OSC and the OSD. The material temperature LHS population is adapted to account for a SNF temperature variation. The probability of hydride-related, ductile cladding failure during a severe transportation accident is not significantly affected by the pinching load amplitude: The probability is slightly reduced from a range of less than 0.0333% to 0.1667% for P{sub 9m}, to a range of less than 0.0333% to 0.1333% for P{sub AS}, depending on the vacuum drying peak cladding hoop stress modelling assumptions. Further, the SNF dry-storage duration does not significantly affect the probability of ductile pinching failure. Based on available train accidents data, the pinching failure probability for a 5,000 km long transportation route ranges from less than 1.62 E-7 to a value of 6.47 E-7, depending on the vacuum drying peak cladding hoop stress modelling assumptions. The pinching load amplitude is not a controlling parameter for the probability of ductile cladding pinching failure, and does not control the cladding deformations once pellet-cladding contact is established, The pellet-cladding gap width, however, plays a key role. Fuel pellet degradation only affects the deformation capacity, if the pellet stiffness is significantly reduced (more than 90%). Only highly embrittled cladding is likely to fail. The deformation demands on the cladding under pinching loading are small.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2026

Computing the Critical Temperature of the Affine-Transformed $D=3$ Ising Model Using Masked Autoregressive Flow

The simple Ising model provides a rich environment to build and study lattice field theories. As part of an ongoing project to construct a conformal field theory (CFT) on an arbitrarily curved manifold, in this work we develop methods to measure the critical temperature $β_c$ of the affine-transformed Ising model on the face-centered cubic (FCC) lattice. The main challenge in this endeavor is finding a computationally efficient and accurate method of interpolating and extrapolating Monte Carlo observables with respect to coupling coefficients and temperature. Herein, we compare two such methods. A traditional statistical approach uses the multiple histogram (MH) method, while a newer machine learning approach uses a masked autoregressive flow (MAF) to estimate the underlying probability density function of a set of observables. While the MH method is specifically designed to interpolate and extrapolate Monte Carlo observables, we find that MAF is a viable alternative for measuring $β_c$ with a computational cost that scales more favorably. Furthermore, we comment on additional advantages of MAF relevant to our work, such as extrapolating in system volume.

Svenson, Kai [Texas U.]↗

DOE OSTI2018

Detection of Lung Contour with Closed Principal Curve and Machine Learning

Radiation therapy plays an essential role in the treatment of cancer. In radiation therapy, the ideal radiation doses are delivered to the observed tumor while not affecting neighboring normal tissues. In three-dimensional computed tomography (3D-CT) scans, the contours of tumors and organs-at-risk (OARs) are often manually delineated by radiologists. The task is complicated and time-consuming, and the manually delineated results will be variable from different radiologists. We propose a semi-supervised contour detection algorithm, which firstly uses a few points of region of interest (ROI) as an approximate initialization. Then the data sequences are achieved by the closed polygonal line (CPL) algorithm, where the data sequences consist of the ordered projection indexes and the corresponding initial points. Finally, the smooth lung contour can be obtained, when the data sequences are trained by the backpropagation neural network model (BNNM). We use the private clinical dataset and the public Lung Image Database Consortium and Image Database Resource Initiative (LIDC-IDRI) dataset to measure the accuracy of the presented method, respectively. To the private dataset, experimental results on the initial points which are as low as 15% of the manually delineated points show that the Dice coefficient reaches up to 0.95 and the global error is as low as 1.47 × 10{sup −2}. The performance of the proposed algorithm is also better than the cubic spline interpolation (CSI) algorithm. While on the public LIDC-IDRI dataset, our method achieves superior segmentation performance with average Dice of 0.83.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2018

Numerical Method for Fractional Advection-Diffusion Equation with Heredity

We propose a method of construction of difference schemes for fractional partial differential equations with delay in time. For the fractional equation with two-sided diffusion, fractional transfer in time, and a functional aftereffect, we construct an implicit difference scheme. We use the shifted Grünwald–Letnikov formulas for the approximation of fractional derivatives with respect to spatial variables and the L1-algorithm for the approximation of fractional derivatives in time. Also we use piecewise constant interpolation and extrapolation by extending the discrete prehistory of the model in time. The algorithm is a fractional analog of a purely implicit method; on each time step, it is reduced to the solution of linear algebraic systems. We prove the stability of the method and find its order of convergence.

97 MATHEMATICS AND COMPUTING↗