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At least 829 records · Page 46

MPAS-Seaice (v1.0.0): sea-ice dynamics on unstructured Voronoi meshes

Abstract. We present MPAS-Seaice, a sea-ice model which uses the Model for Prediction Across Scales (MPAS) framework and spherical centroidal Voronoi tessellation (SCVT) unstructured meshes. As well as SCVT meshes, MPAS-Seaice can run on the traditional quadrilateral grids used by sea-ice models such as CICE. The MPAS-Seaice velocity solver uses the elastic–viscous–plastic (EVP) rheology and the variational discretization of the internal stress divergence operator used by CICE, but adapted for the polygonal cells of MPAS meshes, or alternatively an integral (“finite-volume”) formulation of the stress divergence operator. An incremental remapping advection scheme is used for mass and tracer transport. We validate these formulations with idealized test cases, both planar and on the sphere. The variational scheme displays lower errors than the finite-volume formulation for the strain rate operator but higher errors for the stress divergence operator. The variational stress divergence operator displays increased errors around the pentagonal cells of a quasi-uniform mesh, which is ameliorated with an alternate formulation for the operator. MPAS-Seaice shares the sophisticated column physics and biogeochemistry of CICE and when used with quadrilateral meshes can reproduce the results of CICE. We have used global simulations with realistic forcing to validate MPAS-Seaice against similar simulations with CICE and against observations. We find very similar results compared to CICE, with differences explained by minor differences in implementation such as with interpolation between the primary and dual meshes at coastlines. We have assessed the computational performance of the model, which, because it is unstructured, runs with 70 % of the throughput of CICE for a comparison quadrilateral simulation. The SCVT meshes used by MPAS-Seaice allow removal of equatorial model cells and flexibility in domain decomposition, improving model performance. MPAS-Seaice is the current sea-ice component of the Energy Exascale Earth System Model (E3SM).

58 GEOSCIENCES↗

Discrete model reference adaptive systems with measurement noise

A digital computer simulation study is presented for a class of discrete model reference adaptive systems designed using Liapunov's direct method. Plant output measurements are assumed to contain uniformly distributed additive noise. It is shown that the design works well even when such noise is relatively extreme. A new result is presented pertaining to improving the convergence properties of these systems. This result is obtained by modifying the dynamic characteristics of the augmented error equation.

Monopoli, R. V.↗

Interpolation of a surface from sets of discrete height data of different statistical characteristics

This paper presents and analyzes a method for the interpolation of a unique surface from two sets of independent digital height data of differing statistical characteristics. This method is based on linear prediction and thus relies on the concepts of auto- and cross-covariance functions. The linear prediction algorithm for two sets of digital height measurements is first derived and then evaluated using the method of moving averages and bilinear interpolation for comparison. It is found that the overall root mean square interpolation errors of linear prediction are similar to those from moving averages and bilinear interpolation. This accuracy performance, together with the well known potential for controlled filtering of measuring errors and good-behavior in areas of poor control, makes linear prediction a versatile and general method for interpolating a unique surface from two sets of digital height data, with applications in photogrammetric mapping, remote sensing, and other fields.

Leberl, F.↗

Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by incorporating physical principles into the model. Most PiDL approaches regularize training by embedding governing equations into the loss function, yet this depends heavily on extensive hyperparameter tuning to weigh each loss term. To this end, we propose to leverage physics prior knowledge by “baking” the discretized governing equations into the neural network architecture via the connection between the partial differential equations (PDE) operators and network structures, resulting in a PDE-preserved neural network (PPNN). This method, embedding discretized PDEs through convolutional residual networks in a multi-resolution setting, largely improves the generalizability and long-term prediction accuracy, outperforming conventional black-box models. The effectiveness and merit of the proposed methods have been demonstrated across various spatiotemporal dynamical systems governed by spatiotemporal PDEs, including reaction-diffusion, Burgers’, and Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗

Comparison of phase modulation systems

Comparison of the energy to noise ratio necessary to obtain a given modulation bit error probability has indicated that three-phase modulation is about 0.75 db superior to four-phase. It is shown that this apparent superiority results entirely from the greater bandwidth required by the three-phase system for the same bit transmission rate. Two further comparison criteria are proposed, which are based on the cut-off rate R sub 0 of the discrete channel created by the modulation system. For the criterion which constrains both the bandwidth and transmitted power, it is shown that four-phase modulation is always superior to three-phase modulation. The conclusion is that three-phase modulation offers no practical advantage over four-phase modulation.

Massey, J. L.↗

Image-adapted visually weighted quantization matrices for digital image compression

A method for performing image compression that eliminates redundant and invisible image components is presented. The image compression uses a Discrete Cosine Transform (DCT) and each DCT coefficient yielded by the transform is quantized by an entry in a quantization matrix which determines the perceived image quality and the bit rate of the image being compressed. The present invention adapts or customizes the quantization matrix to the image being compressed. The quantization matrix comprises visual masking by luminance and contrast techniques and by an error pooling technique all resulting in a minimum perceptual error for any given bit rate, or minimum bit rate for a given perceptual error.

Watson, Andrew B.↗

Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method

Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes.

Nemec, Marian↗

Kepler Observations of Rapid Optical Variability in the BL Lac Object W2r192+42

We present the first Kepler monitoring of a strongly variable BL Lac, W2R1926+42. The light curve covers 181 days with approx. 0.2% errors, 30 minute sampling and >90% duty cycle, showing numerous delta-I/I > 25% flares over timescales as short as a day. The flux distribution is highly skewed and non-Gaussian. The variability shows a strong rms-flux correlation with the clearest evidence to date for non-linearity in this relation. We introduce a method to measure periodograms from the discrete autocorrelation function, an approach that may be well-suited to a wide range of Kepler data. The periodogram is not consistent with a simple power-law, but shows a flattening at frequencies below 7x10(exp -5) Hz. Simple models of the power spectrum, such as a broken power law, do not produce acceptable fits, indicating that the Kepler blazar light curve requires more sophisticated mathematical and physical descriptions than currently in use.

galaxies↗

Simulation of Mechanical Fractionation of Chopped Whole-Plant Corn (WPC) Using Discrete Element Method (DEM)

Fractionating whole-plant corn (WPC) in a single-pass harvesting system requires studies on the WPC-to-equipment interaction for improved property control, as well as mechanical and air-driven separation processes compared to the traditional multi-pass grain and stover harvesting system. The discrete element method (DEM) technique has the potential to simulate WPC mechanical fractionation and support simulation-based design of WPC separation processes. In this study, methods to develop DEM particle models of WPC (kernel, cob, stalk, and husk) and their material properties for simulating mass fractionation using the ASABE standard mechanical shaker were proposed. Measurement was done on the axial dimensions (major, intermediate, and minor) and mass of each WPC type (mean sample size is 56), sampled from single-pass harvesting. Applying gaussian multivariate regression and bootstrapping re-sampling techniques, a DEM particle approximate to each WPC was developed. Sensitivity analysis of the DEM Young‘s modulus, Poisson‘s ratio, and interaction parameters of coefficient of restitution, coefficient of rolling friction, and coefficient of static friction on mass fraction was performed after 156 ASABE sieve-shaking DEM simulation runs, generated using Latin Hypercube Design (LHD) design of experiment (DOE) from 19 DEM material parameters. DEM simulation using Hertz-Mindlin with flexible bond contact laws and DOE optimized material properties successfully reproduced the mass fractions retained in ASABE sieves at 9.8% mean relative error and a coefficient of determination of R2 = 0.87. Here, the DEM methodology developed for mechanical WPC mass fractionation could be deployed to perform virtual design of feedstock handling equipment and performance analysis of mechanical fraction systems.

09 BIOMASS FUELS↗

Risk-Averse Control of Fractional Diffusion with Uncertain Exponent

In this paper, we introduce and analyze a new class of optimal control problems constrained by elliptic equations with uncertain fractional exponents. We utilize risk measures to formulate the resulting optimization problem. We develop a functional analytic framework, study the existence of solution and rigorously derive the first-order optimality conditions. Additionally, we employ a sample-based approximation for the uncertain exponent and the finite element method to discretize in space. Further, we prove the rate of convergence for the optimal risk neutral controls when using quadrature approximation for the uncertain exponent and conclude with illustrative examples.

finite element method↗

Evaluation of the Global Multi-Resolution Terrain Elevation Data 2010 (GMTED2010) Using ICESat Geodetic Control

Supported by NASA's Earth Surface and Interior (ESI) Program, we are producing a global set of Ground Control Points (GCPs) derived from the Ice, Cloud and land Elevation Satellite (ICESat) altimetry data. From February of 2003, to October of 2009, ICESat obtained nearly global measurements of land topography (+/- 86deg latitudes) with unprecedented accuracy, sampling the Earth's surface at discrete approx.50 m diameter laser footprints spaced 170 m along the altimetry profiles. We apply stringent editing to select the highest quality elevations, and use these GCPs to characterize and quantify spatially varying elevation biases in Digital Elevation Models (DEMs). In this paper, we present an evaluation of the soon to be released Global Multi-resolution Terrain Elevation Data 2010 (GMTED2010). Elevation biases and error statistics have been analyzed as a function of land cover and relief. The GMTED2010 products are a large improvement over previous sources of elevation data at comparable resolutions. RMSEs for all products and terrain conditions are below 7 m and typically are about 4 m. The GMTED2010 products are biased upward with respect to the ICESat GCPs on average by approximately 3 m.

Carabajal, Claudia C.↗

A Nonlinear Adaptive Filter for Gyro Thermal Bias Error Cancellation

Deterministic errors in angular rate gyros, such as thermal biases, can have a significant impact on spacecraft attitude knowledge. In particular, thermal biases are often the dominant error source in MEMS gyros after calibration. Filters, such as J\,fEKFs, are commonly used to mitigate the impact of gyro errors and gyro noise on spacecraft closed loop pointing accuracy, but often have difficulty in rapidly changing thermal environments and can be computationally expensive. In this report an existing nonlinear adaptive filter is used as the basis for a new nonlinear adaptive filter designed to estimate and cancel thermal bias effects. A description of the filter is presented along with an implementation suitable for discrete-time applications. A simulation analysis demonstrates the performance of the filter in the presence of noisy measurements and provides a comparison with existing techniques.

Galante, Joseph M.↗

Accelerated Aging in Electrolytic Capacitors for Prognostics

The focus of this work is the analysis of different degradation phenomena based on thermal overstress and electrical overstress accelerated aging systems and the use of accelerated aging techniques for prognostics algorithm development. Results on thermal overstress and electrical overstress experiments are presented. In addition, preliminary results toward the development of physics-based degradation models are presented focusing on the electrolyte evaporation failure mechanism. An empirical degradation model based on percentage capacitance loss under electrical overstress is presented and used in: (i) a Bayesian-based implementation of model-based prognostics using a discrete Kalman filter for health state estimation, and (ii) a dynamic system representation of the degradation model for forecasting and remaining useful life (RUL) estimation. A leave-one-out validation methodology is used to assess the validity of the methodology under the small sample size constrain. The results observed on the RUL estimation are consistent through the validation tests comparing relative accuracy and prediction error. It has been observed that the inaccuracy of the model to represent the change in degradation behavior observed at the end of the test data is consistent throughout the validation tests, indicating the need of a more detailed degradation model or the use of an algorithm that could estimate model parameters on-line. Based on the observed degradation process under different stress intensity with rest periods, the need for more sophisticated degradation models is further supported. The current degradation model does not represent the capacitance recovery over rest periods following an accelerated aging stress period.

Celaya, Jose R.↗

Projection-Based Reduced Order Modeling for Spacecraft Thermal Analysis

This paper presents a mathematically rigorous, subspace projection-based reduced order modeling (ROM) methodology and an integrated framework to automatically generate reduced order models for spacecraft thermal analysis. Two key steps in the reduced order modeling procedure are described: (1) the acquisition of a full-scale spacecraft model in the ordinary differential equation (ODE) and differential algebraic equation (DAE) form to resolve its dynamic thermal behavior; and (2) the ROM to markedly reduce the dimension of the full-scale model. Specifically, proper orthogonal decomposition (POD) in conjunction with discrete empirical interpolation method (DEIM) and trajectory piece-wise linear (TPWL) methods are developed to address the strong nonlinear thermal effects due to coupled conductive and radiative heat transfer in the spacecraft environment. Case studies using NASA-relevant satellite models are undertaken to verify the capability and to assess the computational performance of the ROM technique in terms of speed-up and error relative to the full-scale model. ROM exhibits excellent agreement in spatiotemporal thermal profiles (<0.5% relative error in pertinent time scales) along with salient computational acceleration (up to two orders of magnitude speed-up) over the full-scale analysis. These findings establish the feasibility of ROM to perform rational and computationally affordable thermal analysis, develop reliable thermal control strategies for spacecraft, and greatly reduce the development cycle times and costs.

0000↗

Optimizing multigrid reduction-in-time and Parareal coarse-grid operators for linear advection

Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent partial differential equations (PDEs) in modern high-performance computing environments. While these techniques have been very successful for parabolic equations, it has often been observed that their performance suffers dramatically when applied to advection-dominated problems or purely hyperbolic PDEs using standard rediscretization approaches on coarse grids. In this paper, we apply MGRIT or Parareal to the constant-coefficient linear advection equation, appealing to existing convergence theory to provide insight into the typically nonscalable or even divergent behavior of these solvers for this problem. To overcome these failings, we replace rediscretization on coarse grids with improved coarse-grid operators that are computed by applying optimization techniques to approximately minimize error estimates from the convergence theory. Therefore, one of our main findings is that, in order to obtain fast convergence as for parabolic problems, coarse-grid operators should take into account the behavior of the hyperbolic problem by tracking the characteristic curves. Our approach is tested for schemes of various orders using explicit or implicit Runge–Kutta methods combined with upwind-finite-difference spatial discretizations. In all cases, we obtain scalable convergence in just a handful of iterations, with parallel tests also showing significant speed-ups over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗

The delta-four-stream approximation for radiative flux transfer

An approximate technique for solving the radiative transfer problem for fluxes reflected, transmitted, and absorbed by a homogeneous scattering layer is presented. The technique is a straightforward delta-function modification of a solution to the transfer equation in closed form via the discrete-ordinates method with four streams. By the use of four streams, significant improvement in accuracy is obtained for anisotropic phase functions over that obtained by similarly employed two-stream approximations with delta-functions. However, the computational effort is increased only slightly. Equations are developed for the general case of a layer underlaid by a reflecting Lambert surface. Graphical comparisons are given of fractional error resulting from the use of this method with that resulting from the use of typical four-stream and delta-two-stream techniques.

Cuzzi, J. N.↗

Psychophysical rating of image compression techniques

Image compression schemes abound with little work which compares their bit-rate performance based on subjective fidelity measures. Statistical measures of image fidelity, such as squared error measures, do not necessarily correspond to subjective measures of image fidelity. Most previous comparisons of compression techniques have been based on these statistical measures. A psychophysical method has been used to estimate, for a number of compression techniques, a threshold bit-rate yielding a criterion level of performance in discriminating original and compressed images. The compression techniques studied include block truncation, Laplacian pyramid, block discrete cosine transform, with and without a human visual system scaling, and cortex transform coders.

Stein, Charles S.↗

Leveraging Machine Learning Capabilities for the Characterization of Irradiated Uranium: A Case Study of Analysis Methods for Nuclear Safeguards and Nuclear Forensics

Nondestructively determining the initial enrichment of irradiated uranium is a complex and laborious multivariable problem due to the presence of fission products. This work demonstrates the capabilities of machine learning to analyze gamma-ray spectral data to determine initial enrichment without knowledge of the decay time of the sample. The approach developed is agnostic to the particular scenario and is applicable to a wide variety of applications in nuclear forensics and nuclear safeguards. We irradiated 5 mg uranium standard reference materials at discrete enrichment values ranging from 0.02% to 97% 235 U (weight percent) in UT Austin’s Nuclear Engineering Teaching Laboratory TRIGA Mark II 1.1 MW research reactor, allowed each to decay for 8 hours, and then measured each sample via gamma-ray spectrometry for 50 hours post-irradiation yielding 1,400 individual gamma-ray spectra discretized into 8,192 energy bins. We then trained decision trees models to analyze individual gamma-ray spectra and estimate the associated initial enrichment without knowledge of the time since end of irradiation. We evaluated the performance of the models with a reserved test set not used for training or calibrating the model. A decision tree model constructed with this procedure achieved a mean absolute error in initial enrichment determination of 2.3% (weight percent 235 U). Next, we implemented a principal component analysis pre-processing routine of the gamma-ray spectrometry data to reduce the dimensionality of the dataset from 8,192 channels in the spectrum to 10 principal components while retaining over 99% of the inherent variance in the data. Decision tree models constructed with these data demonstrated decreased mean absolute error in enrichment determination, reduced computational time, and decreased complexity. A single decision tree model constructed with this procedure achieved a mean absolute error in initial enrichment determination of 0.05% (weight percent 235 U). Furthermore, we analyzed these models with learning curves to ensure that overfitting did not occur. The capabilities provided by these models can be naturally extended to other application-focused measurements in the fields of nuclear safeguards, nuclear forensics, and nuclear non-proliferation.

Drescher, Adam↗