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At least 595 records · Page 33

Design of Neural Networks for Fast Convergence and Accuracy

A novel procedure for the design and training of artificial neural networks, used for rapid and efficient controls and dynamics design and analysis for flexible space systems, has been developed. Artificial neural networks are employed to provide a means of evaluating the impact of design changes rapidly. Specifically, two-layer feedforward neural networks are designed to approximate the functional relationship between the component spacecraft design changes and measures of its performance. A training algorithm, based on statistical sampling theory, is presented, which guarantees that the trained networks provide a designer-specified degree of accuracy in mapping the functional relationship. Within each iteration of this statistical-based algorithm, a sequential design algorithm is used for the design and training of the feedforward network to provide rapid convergence to the network goals. Here, at each sequence a new network is trained to minimize the error of previous network. The design algorithm attempts to avoid the local minima phenomenon that hampers the traditional network training. A numerical example is performed on a spacecraft application in order to demonstrate the feasibility of the proposed approach.

Maghami, Peiman G.↗

Evaluation of the Analysis Influence on Transport in Reanalysis Regional Water Cycles

Regional water cycles of reanalyses do not follow theoretical assumptions applicable to pure simulated budgets. The data analysis changes the wind, temperature and moisture, perturbing the theoretical balance. Of course, the analysis is correcting the model forecast error, so that the state fields should be more aligned with observations. Recently, it has been reported that the moisture convergence over continental regions, even those with significant quantities of radiosonde profiles present, can produce long term values not consistent with theoretical bounds. Specifically, long averages over continents produce some regions of moisture divergence. This implies that the observational analysis leads to a source of water in the region. One such region is the Unite States Great Plains, which many radiosonde and lidar wind observations are assimilated. We will utilize a new ancillary data set from the MERRA reanalysis called the Gridded Innovations and Observations (GIO) which provides the assimilated observations on MERRA's native grid allowing more thorough consideration of their impact on regional and global climatology. Included with the GIO data are the observation minus forecast (OmF) and observation minus analysis (OmA). Using OmF and OmA, we can identify the bias of the analysis against each observing system and gain a better understanding of the observations that are controlling the regional analysis. In this study we will focus on the wind and moisture assimilation.

Bosilovich, M. G.↗

Application of an improved Nelson-Nguyen analysis to eccentric, arbitrary profile liquid annular seals

An improved dynamic analysis for liquid annular seals with arbitrary profile based on a method, first proposed by Nelson and Nguyen, is presented. An improved first order solution that incorporates a continuous interpolation of perturbed quantities in the circumferential direction, is presented. The original method uses an approximation scheme for circumferential gradients, based on Fast Fourier Transforms (FFT). A simpler scheme based on cubic splines is found to be computationally more efficient with better convergence at higher eccentricities. A new approach of computing dynamic coefficients based on external specified load is introduced. This improved analysis is extended to account for arbitrarily varying seal profile in both axial and circumferential directions. An example case of an elliptical seal with varying degrees of axial curvature is analyzed. A case study based on actual operating clearances of an interstage seal of the Space Shuttle Main Engine High Pressure Oxygen Turbopump is presented.

Padavala, Satyasrinivas↗

Development of Global Operational Snow Analysis at the US Air Force 557th Weather Wing

The outdated SNODEP snow depth retrieval algorithm is replaced by the Foster et al. (1997; 2005) approach, which considers the effects of variations in forest cover. The simple blending algorithm (IDW) is replaced by the Bratseth scheme, a successive correction algorithm that converges to the solution provided by Optimal Interpolation (OI). Outdated quality control datasets are updated and quality control algorithms are reorganized to ensure the performance of the snow analysis. The spatial resolution of snow and ice estimates are increased from 25-km to 10-km.USAF-SI are fully integrated into the global operational land analysis configuration at the USAF 557th WW.

Yoon, Yeosang↗

Error Estimate of the Ares I Vehicle Longitudinal Aerodynamic Characteristics Based on Turbulent Navier-Stokes Analysis

Numerical predictions of the longitudinal aerodynamic characteristics for the Ares I class of vehicles, along with the associated error estimate derived from an iterative convergence grid refinement, are presented. Computational results are based on the unstructured grid, Reynolds-averaged Navier-Stokes flow solver USM3D, with an assumption that the flow is fully turbulent over the entire vehicle. This effort was designed to complement the prior computational activities conducted over the past five years in support of the Ares I Project with the emphasis on the vehicle s last design cycle designated as the A106 configuration. Due to a lack of flight data for this particular design s outer mold line, the initial vehicle s aerodynamic predictions and the associated error estimates were first assessed and validated against the available experimental data at representative wind tunnel flow conditions pertinent to the ascent phase of the trajectory without including any propulsion effects. Subsequently, the established procedures were then applied to obtain the longitudinal aerodynamic predictions at the selected flight flow conditions. Sample computed results and the correlations with the experimental measurements are presented. In addition, the present analysis includes the relevant data to highlight the balance between the prediction accuracy against the grid size and, thus, the corresponding computer resource requirements for the computations at both wind tunnel and flight flow conditions. NOTE: Some details have been removed from selected plots and figures in compliance with the sensitive but unclassified (SBU) restrictions. However, the content still conveys the merits of the technical approach and the relevant results.

Aerodynamic characteristics↗

Time-Frequency Analysis of Rocket Nozzle Wall Pressures During Start-up Transients

Surveys of the fluctuating wall pressure were conducted on a sub-scale, thrust- optimized parabolic nozzle in order to develop a physical intuition for its Fourier-azimuthal mode behavior during fixed and transient start-up conditions. These unsteady signatures are driven by shock wave turbulent boundary layer interactions which depend on the nozzle pressure ratio and nozzle geometry. The focus however, is on the degree of similarity between the spectral footprints of these modes obtained from transient start-ups as opposed to a sequence of fixed nozzle pressure ratio conditions. For the latter, statistically converged spectra are computed using conventional Fourier analyses techniques, whereas the former are investigated by way of time-frequency analysis. The findings suggest that at low nozzle pressure ratios -- where the flow resides in a Free Shock Separation state -- strong spectral similarities occur between fixed and transient conditions. Conversely, at higher nozzle pressure ratios -- where the flow resides in Restricted Shock Separation -- stark differences are observed between the fixed and transient conditions and depends greatly on the ramping rate of the transient period. And so, it appears that an understanding of the dynamics during transient start-up conditions cannot be furnished by a way of fixed flow analysis.

Baars, Woutijn J.↗

Aeroelastic stability analyses of two counter rotating propfan designs for a cruise missile model

A modal aeroelastic analysis combining structural and aerodynamic models is applied to counterrotating propfans to evaluate their structural integrity for wind-tunnel testing. The aeroelastic analysis code is an extension of the 2D analysis code called the Aeroelastic Stability and Response of Propulsion Systems. Rotational speed and freestream Mach number are the parameters for calculating the stability of the two blade designs with a modal method combining a finite-element structural model with 2D steady and unsteady cascade aerodynamic models. The model demonstrates convergence to the least stable aeroelastic mode, describes the effects of a nonuniform inflow, and permits the modification of geometry and rotation. The analysis shows that the propfan designs are suitable for the wind-tunnel test and confirms that the propfans should be flutter-free under the range of conditions of the testing.

Mahajan, Aparajit J.↗

High-Accuracy Mesh-Free Quadrature for Trimmed Parametric Surfaces and Volumes

This work presents a high-accuracy, mesh-free, generalized Stokes theorem-based numerical quadrature scheme for integrating functions over trimmed parametric surfaces and volumes. The algorithm relies on two fundamental steps: (1) We iteratively reduce the dimensionality of integration using the generalized Stokes theorem to line integrals over trimming curves, and (2) we employ numerical antidifferentiation in the generalized Stokes theorem using high-order quadrature rules. Additionally, the scheme achieves exponential convergence up to trimming curve approximation error and has applications to computation of geometric moments, immersogeometric analysis, conservative field transfer between high-order curvilinear meshes, and initialization of multi-material simulations. We compare the quadrature scheme to commonly-used quadrature schemes in the literature and show that our scheme is much more efficient in terms of number of quadrature points used. We provide an open-source implementation of the scheme in MATLAB as part of QuaHOG, a software package for Quadrature of High-Order Geometries.

97 MATHEMATICS AND COMPUTING↗

Online Adaptive Algorithm for Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method

Here in this research, we propose an online basis enrichment strategy within the framework of a recently developed constraint energy minimizing generalized multiscale discontinuous Galerkin method. Combining the technique of oversampling, one makes use of the information of the current residuals to adaptively construct basis functions in the online stage to reduce the error of multiscale approximation. A complete analysis of the method is presented, which shows the proposed online enrichment leads to a fast convergence from multiscale approximation to the fine-scale solution. The error reduction can be made sufficiently large by suitably selecting oversampling regions and the number of oversampling layers. Further, the convergence rate of the enrichment algorithm depends on a factor of exponential decay regarding the number of oversampling layers and a user-defined parameter. Numerical results are provided to demonstrate the effectiveness and efficiency of the proposed online adaptive algorithm.

97 MATHEMATICS AND COMPUTING↗

A Class of Sparse Johnson–Lindenstrauss Transforms and Analysis of their Extreme Singular Values

The Johnson–Lindenstrauss (JL) lemma is a powerful tool for dimensionality reduction in modern algorithm design. The lemma states that any set of high-dimensional points in a Euclidean space can be projected into lower dimensions while approximately preserving pairwise Euclidean distances. Random matrices satisfying this lemma are called JL transforms (JLTs). Inspired by existing $s$-hashing JLTs with exactly $s$ nonzero elements on each column, the present work introduces an ensemble of sparse matrices encompassing so-called $s$-hashing-like matrices whose expected number of nonzero elements on each column is $s$. The independence of the sub-Gaussian entries of these matrices and the knowledge of their exact distribution play an important role in their analyses. Using properties of independent sub-Gaussian random variables, these matrices are demonstrated to be JLTs, and their smallest nontrivial singular values and largest singular values are estimated nonasymptotically using a technique from geometric functional analysis. As the dimensions of the matrix grow to infinity, these singular values are proved to converge almost surely to fixed quantities (by using the universal Bai–Yin law) and in distribution to the Gaussian orthogonal ensemble Tracy–Widom law after proper rescalings. Understanding the behaviors of extreme singular values is important in general because they are often used to define a measure of stability of matrix algorithms. For example, JLTs were recently used in derivative-free optimization algorithmic frameworks to select random subspaces in which are constructed random models or poll directions to achieve scalability, and hence estimating their smallest singular value in particular helps determine the dimension of these subspaces.

97 MATHEMATICS AND COMPUTING↗

Microstructure Scale Lithium-Ion Battery Modeling, Part IV: The Representativity of Microstructure Parameters and Electrochemical Response

Lithium-ion battery electrochemical models require an accurate description of the electrodes microstructures to be predictive, that can be achieved through nanoscale imaging. Such observations are however limited by their field of view (FOV), as they provide only a subset of the whole electrode volume that does not necessarily represent the whole electrode microstructure heterogeneity, and therefore can bias the analysis. A representativity analysis has been performed on the microstructure parameters and, in a novel way, on the full cell electrochemical response to evaluate the predictions representativeness, and thus relevance, of a microstructure scale electrochemical model. The microstructure parameter deviation propagations to the electrochemical response have been quantified for different charge rates. This defines a threshold for the microstructure parameters FOV for a desired maximum deviation of the electrochemical response. Electrochemical model shows cell representative section areas are increasing with C-rate, due to higher in-plane heterogeneities, indicating larger FOVs are required specifically for fast charge modeling. Representativity analysis determines a cell FOV of 144.4 × 154.4 μm 2 is large enough to establish a convergence on the representative section areas for low-intermediate C-rate (≤2.5 C), therefore positively concludes on the model representativeness for these rates, but is not large enough to conclude for higher rates.

25 ENERGY STORAGE↗

Tokamak disruption simulation

UT contribution in this Tokamak Disruption Simulation (TDS) is to develop a parallel high‐order hybridized Discontinuous Galerkin (HDG) methods for large‐s cale MHD simulations. The following are the major goals: 1) Construction of HDG methods for linearized MHD, 2) Rigorous analysis for the HDG formulations for linearized MHD, 3) 2D and 3D simulations to verify the convergent of the HDG methods for linearized MHD, 4) multigrid solvers/preconditioners for HDG formulations, 5) HDG for reconnection problems, 6) Divergence cleaning with HDG, 7) HDG formulations for nonlinear MHD, 8) Picard fixed point HDG approach, 9) IMEX HDG‐DG for nonlinear HDG; 10) parallel large‐scale HDG for linear and nonlinear MHD simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Hydro-particle-mesh Code for Efficient and Rapid Simulations of the Intracluster Medium

We introduce the cosmological HYPER code based on an innovative hydro-particle-mesh (HPM) algorithm for efficient and rapid simulations of gas and dark matter. For the HPM algorithm, we update the approach of Gnedin & Hui to expand the scope of its application from the lower-density intergalactic medium (IGM) to the higher-density intracluster medium (ICM). While the original algorithm tracks only one effective particle species, the updated version separately tracks the gas and dark matter particles, as they do not exactly trace each other on small scales. For the approximate hydrodynamics solver, the pressure term in the gas equations of motion is calculated using robust physical models. In particular, we use a dark matter halo model, ICM pressure profile, and IGM temperature–density relation, all of which can be systematically varied for parameter-space studies. We show that the HYPER simulation results are in good agreement with the halo model expectations for the density, temperature, and pressure radial profiles. Simulated galaxy cluster scaling relations for Sunyaev–Zel’dovich (SZ) and X-ray observables are also in good agreement with mean predictions, with scatter comparable to that found in hydrodynamic simulations. HYPER also produces lightcone catalogs of dark matter halos and full-sky tomographic maps of the lensing convergence, SZ effect, and X-ray emission. These simulation products are useful for testing data analysis pipelines, generating training data for machine learning, understanding selection and systematic effects, and for interpreting astrophysical and cosmological constraints.

79 ASTRONOMY AND ASTROPHYSICS↗

Design and evaluation of a state-feedback vibration controller

The effectiveness and practicality of the state-feedback vibration controller is demonstrated by computer simulations. It is shown that: (1) the required measurements can be reduced to fuselage accelerations; (2) the system is stable over a wide range of flight conditions; (3) a discrete design for the controller provides effective digital implementation at 80-Hz sampling; (4) attenuation produced by the actuators does not create a problem, and a simple lead compensator provides vibration reduction; and (5) a design based on a hover model worked well at five knots. At 40 and 120 knots, vibrations in all but the vertical acceleration were effectively suppressed. The state-feedback vibration controller has a rapid convergence time and implementation is easier than with multicyclic control since no on-line harmonic analysis or identification algorithms are required.

Du Val, R. W.↗

Natural convection in steady solidification - Finite element analysis of a two-phase Rayleigh-Benard problem

Galerkin finite-element approximations and Newton's method for solving free boundary problems are combined with computer-implemented techniques from nonlinear perturbation analysis to study solidification problems with natural convection in the melt. The Newton method gives rapid convergence to steady state velocity, temperature and pressure fields and melt-solid interface shapes, and forms the basis for algebraic methods for detecting multiple steady flows and assessing their stability. The power of this combination is demonstrated for a two-phase Rayleigh-Benard problem composed of melt and solid in a veritical cylinder with the thermal boundary conditions arranged so that a static melt with a flat melt-solid interface is always a solution. Multiple cellular flows bifurcating from the static state are detected and followed as Rayleigh number is varied. Changing the boundary conditions to approach those appropriate for the vertical Bridgman solidification system causes imperfections that eliminate the static state. The flow structure in the Bridgman system is related to those for the Rayleigh-Benard system by a continuous evolution of the boundary conditions.

Chang, C. J.↗

An efficient cell-vertex multigrid scheme for the three-dimensional Navier-Stokes equations

A cell-vertex scheme for the three-dimensional Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing with locally varying coefficients, a multigrid method and carefully controlled dissipative terms, very good convergence rates are obtained for two- and three-dimensional flows. Details of the acceleration techniques, which are important for convergence on meshes with high aspect-ratio cells, are discussed. Emphasis is put on the analysis of the stability properties of the implicit smoothing of the explicit residuals with coefficients, which depend on cell aspect ratios.

Radespiel, R.↗

Diurnal variability of the hydrologic cycle in a general circulation model

In the present Colorado State University GCM simulation-based analysis of the diurnal and semidiurnal variability of precipitation, precipitable water, evaporation, cloudiness, horizontal moisture flux convergence, and cloud radiative forcing, a realistic afternoon precipitation maximum is obtained over land in warm rainy regions, as well as an early morning maximum over the oceans. The model has been further used to investigate the bases for the oceanic diurnal-precipitation cycle; the results thus obtained indicate that such an oceanic cycle occurs even in the absence of neighboring continents, and tends to have a morning maximum, although the observed phenomenon is generally stronger than the results indicate.

Randall, David A.↗