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Spectral Proper Orthogonal Decomposition of uPSP Measurements in Recent NASA Ames Wind Tunnel Test

This paper discusses Spectral Proper Orthogonal Decomposition (SPOD) of the Unsteady Pressure-Sensitive Paint (uPSP) measurements in recent NASA Ames wind tunnel test. The uPSP measurements were collected using Innovative Scientific Solutions, Inc. (ISSI) porous, fast-response pressure-sensitive paint, 40 ISSI four-inch air-cooled Light-Emitting Diodes, and 8 Phantom v2512 high-speed cameras at 10,000 frames per second in the uPSP Launch Vehicle Demonstration Test (LVDT) of the Space Launch System (SLS) vehicle in the 11-by 11-foot transonic test section of the Unitary Plan Wind Tunnel at NASA Ames Research Center in April 2024. SPOD is derived from a space-time proper orthogonal decomposition problem for statistically stationary flows. SPOD modes are determined in the frequency domain. Each SPOD mode oscillates at a single frequency. SPOD can be viewed as an extension of the Discrete Fourier Transform composition and the Dynamic Mode Decomposition. In this paper, the outputs of SPOD of the uPSP measurements in the uPSP LVDT are presented and the effectiveness of SPOD in the identification, diagnosis and analysis of the aerodynamic and aeroacoustic phenomena is demonstrated. The unsteady and dynamic property of the pressure field on the surface of the SLS Block 1B crew vehicle is presented with the visualization of the SPOD modes of the uPSP measurements in the tests of a Mach sweep run of the uPSP LVDT. The SPOD outputs were generated with the execution in parallel of a code in Python, with the library of Message Passing Interface for parallel processing, on the NASA Pleiades supercomputer. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. Funding was provided by the NASA Aerosciences Evaluation and Test Capabilities Portfolio Office.

Aeroacoustics↗
DOE OSTI2021

Modeling and Simulation of Inrush Currents in Harmonic Domain

Modeling and simulation capabilities are critical to the stability analysis and evaluation of power distribution systems, with respect to the emphasis on resiliency, microgrids, and distributed energy resources. In this paper, a computational method in the harmonic domain is proposed for the periodic steady-state analysis of the nonlinear inrush current phenomenon. The efficient inrush calculation facilitates the predictions of current amplitudes for the power system operation and control. To demonstrate the accuracy and efficiency, simulation results in the harmonic domain are compared with results from PSCAD in an electromagnetic timescale, as well as the authors’ previous works in the frequency-domain. Impacts of the settings of both offset flux and interested harmonic order are discussed. In addition, within the proposed harmonic-domain method, a general approach that utilizes the discrete Fourier transform to obtain the response of a nonlinear device from a stimulus represented in the frequency-domain is utilized. This method can also be extended to perform the transient analysis in future, using trapezoidal rule for the integration.

Xie, Jing↗
NASA NTRS1984

Discrete orthogonal function expansions for non-uniform grids using the fast Fourier transform

A technique for applying discrete Fourier series to infinite domains is presented. The technique uses mappings designed to minimize truncation error and can be applied to solve mixed initial boundary value problems among others. The method is alias-free and yields consistent differentiation and integration operators. The mapping-induced truncation error is explicitly expressible and small in nearly all cases of interest. The method is illustrated for three problems involving convection, diffusion, and vortex interaction.

Cain, A. B.↗
DOE OSTI2023

Time-Frequency Warped Waveforms for Well-Contained Massive Machine Type Communications

Herein this paper proposes a novel time-frequency warped waveform for short symbols, massive machine-type communication (mMTC), and internet of things (IoT) applications. The waveform is composed of asymmetric raised cosine (RC) pulses to increase the signal containment in time and frequency domains. The waveform has low power tails in the time domain, hence better performance in the presence of delay spread and time offsets. The time-axis warping unitary transform is applied to control the waveform occupancy in time-frequency space and to compensate for the usage of high roll-off factor pulses at the symbol edges. The paper explains a step-by-step analysis for determining the roll-off factors profile and the warping functions. Gains are presented over the conventional Zero-tail Discrete Fourier Transform-spread-Orthogonal Frequency Division Multiplexing (ZT-DFT-s-OFDM), and Cyclic prefix (CP) DFT-s-OFDM schemes in the simulations section.

42 ENGINEERING↗
DOE OSTI2025

Physics-Informed Gaussian Process Inference of Liquid Structure from Scattering Data

We present a nonparametric Bayesian framework to infer radial distribution functions from experimental scattering measurements with uncertainty quantification using nonstationary Gaussian processes. The Gaussian process prior mean and kernel functions are designed to mitigate well-known numerical challenges with the Fourier transform, including discrete measurement binning and detector windowing, while encoding fundamental yet minimal physical knowledge of the liquid structure. We demonstrate uncertainty propagation of the Gaussian process posterior to unmeasured quantities of interest. Experimental radial distribution functions of liquid argon and water with uncertainty quantification are provided as both a proof of principle for the method and a benchmark for molecular models.

Chemical structure↗
DOE OSTI2023

Warping Functions Design for Long Warped ZT-DFT-s-OFDM

Time-frequency warped waveform is a novel type of well-contained waveform composed of raised cosine (RC) pulses with roll-off factors profile customized for spectrally efficient signal containment. The waveform is suited for massive machine-type communication (mMTC), and Internet-of-Things (IoT) applications. The paper is a follow-up to the original work of time-frequency warped waveforms; here, we are proposing a warping function suited for length-independent symbols, which is missing from the previous work. The paper proposes the design steps starting from a piecewise warping function with parts of straight segments and other curved parts. A maximum Out-of-band leakage is used as a criterion to determine the warping function parameters. The roll-off factors profile determined in the previous study is used as a minimum bound for the leakage limits. Gains are presented over Windowed Zero-tail Discrete Fourier Transform-spread-Orthogonal Frequency Division Multiplexing (ZT-DFT-s-OFDM) in the simulations section.

Ibrahim, Mostafa↗
NASA NTRS1985

A numerical method for approximating antenna surfaces defined by discrete surface points

A simple numerical method for the quadratic approximation of a discretely defined reflector surface is described. The numerical method was applied to interpolate the surface normal of a parabolic reflector surface from a grid of nine closest surface points to the point of incidence. After computing the surface normals, the geometrical optics and the aperture integration method using the discrete Fast Fourier Transform (FFT) were applied to compute the radiaton patterns for a symmetric and an offset antenna configurations. The computed patterns are compared to that of the analytic case and to the patterns generated from another numerical technique using the spline function approximation. In the paper, examples of computations are given. The accuracy of the numerical method is discussed.

Lee, R. Q.↗
DOE OSTI2026

Enhancing photoionization rate calculations in low-temperature plasmas using spectral methods

Photoionization plays a central role in the development of streamer discharges and other non-equilibrium plasma phenomena. It creates seed electrons, which are essential for positive streamer propagation, allowing the ionization front to move forward. Because of this, accurate modeling of photoionization is very important for predicting streamer behavior and plasma evolution. The photoionization process in air (N 2 – O 2 mixture) is often described by the Zheleznyak model (1982). This model is usually solved through Helmholtz-type equations that approximate the Zheleznyak photoionization model (Zheleznyak et al. 1982) as Partial Differential Equations (PDEs). Conventional numerical methods, such as the Finite Difference Method (FDM) or Finite Volume Method (FVM), are widely used to solve these equations. Although they are prevalent, the computational cost of these methods due to their need for matrix operations and iterative solver is demanding. To address this challenge, this work develops a spectral solver based on the Fast Fourier Transform (FFT) combined with Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) to calculate the photoionization rate efficiently in an axisymmetric cylindrical domain. This method naturally satisfies the boundary conditions used in the model and converts the PDE into algebraic ones in spectral space. Thus, avoids the need for iterative matrix solvers. When compared with FDM results, it is demonstrated that the new solver not only maintains accuracy, but also reduces the computational cost, showing a performance increase of approximately 100 compared to FDM over a wide range of problem sizes. The method is parallelized using Message Passing Interface (MPI) and has been integrated into a fluid plasma model for streamer simulation. Here, this FFT-based approach provides a fast and reliable alternative for calculating photoionization in fluid models, helping large-scale plasma simulations run faster and efficiently, and allows higher-resolution simulation without extra computational cost.

Axisymmetric system↗
DOE OSTI2022

Kinetic theory of particle-in-cell simulation plasma and the ensemble averaging technique

Abstract We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlation at the start of the simulation between the statistical fluctuations of the weighted densities of macroparticle centers in the plasma particle phase-space. The fluctuations are associated with different initial conditions, typically due to the random initial conditions (in velocity space) of the macroparticles/simulation plasma, assigned according to their initial distribution of probability. The single-time correlations at all time steps and in each spatial grid cell are then determined from the Laplace–Fourier transforms of the discretized Klimontovich-like equation for the macroparticles and Maxwell’s equations for the fields, as computed by modern PIC codes. We recover the expressions for the electrostatic field and the plasma particle density fluctuation autocorrelation spectra as well as the kinetic equations describing the average evolution of PIC-simulated plasma particles, first derived by Langdon (1970b Proc. 4th Conf. Numerical Simulation of Plasmas ) using a test macroparticle approach perturbing a discretized Vlasovian plasma and then averaging the obtained physical quantity over the initial macroparticle velocity distribution. We generalize and extend these results to the modern algorithms in PIC codes using arbitrary macroparticle weights. Analytical estimates of statistical fluctuation amplitudes are derived as a function of the plasma simulation parameters, using the central limit theorem in the limit of a large number of macroparticles per cell. The theory is then used to analyze the ensemble averaging technique of PIC simulations where statistical averages are performed over ensembles of PIC simulations, modeling the same plasma physics problem but using different statistical realizations of the initial distribution functions of the macroparticles. This method is illustrated by linear Landau damping uncovering (from noise, which is usually considered numerical) the physical fluctuations driven by a single small amplitude electrostatic wave perturbing a PIC simulation plasma in equilibrium.

fluctuations correlations↗
NASA NTRS1972

Evidence for the 300-second oscillation from OSO-7 extreme-ultraviolet observations.

The detection and significance of 300-second oscillations in extreme-ultraviolet lines formed in the solar transition region are discussed. Detection was accomplished with the Goddard extreme-ultraviolet spectroheliograph and the Wolter type II grazing-incidence telescope. The Cooley-Tukey algorithm was used to compute the required Fourier transform of the discrete data. Presence of significant power in the observed lines around 262 sec seems to be the first observational evidence that periodic waves in this frequency range persist at heights where local kinetic temperatures are close to one million degrees K. The observed horizontal extent of the wave fronts appears to be much greater than the extent of coherent oscillating elements at chromospheric heights. Several implications are stated for the problem of heating of the transition region and low corona.

Chapman, R. D.↗
NASA NTRS2006

Estimation of Stability and Control Derivatives of an F-15

A technique for real-time estimation of stability and control derivatives (derivatives of moment coefficients with respect to control-surface deflection angles) was used to support a flight demonstration of a concept of an indirect-adaptive intelligent flight control system (IFCS). Traditionally, parameter identification, including estimation of stability and control derivatives, is done post-flight. However, for the indirect-adaptive IFCS concept, parameter identification is required during flight so that the system can modify control laws for a damaged aircraft. The flight demonstration was carried out on a highly modified F-15 airplane (see Figure 1). The main objective was to estimate the stability and control derivatives of the airplane in nearly real time. A secondary goal was to develop a system to automatically assess the quality of the results, so as to be able to tell a learning neural network which data to use. Parameter estimation was performed by use of Fourier-transform regression (FTR) a technique developed at NASA Langley Research Center. FTR is an equation- error technique that operates in the frequency domain. Data are put into the frequency domain by use of a recursive Fourier transform for a discrete frequency set. This calculation simplifies many subsequent calculations, removes biases, and automatically filters out data beyond the chosen frequency range. FTR as applied here was tailored to work with pilot inputs, which produce correlated surface positions that prevent accurate parameter estimates, by replacing half the derivatives with predicted values. FTR was also set up to work only on a recent window of data, to accommodate changes in flight condition. A system of confidence measures was developed to identify quality-parameter estimates that a learning neural network could use. This system judged the estimates primarily on the basis of their estimated variances and of the level of aircraft response. The resulting FTR system was implemented in the Simulink software system and auto-coded in the C programming language for use on the Airborne Research Test System (ARTS II) computer installed in the F-15 airplane. The Simulink model was also used in a control room that utilizes the Ring Buffered Network Bus hardware and software, making it possible to evaluate test points during flights. In-flight parameter estimation was done for piloted and automated maneuvers, primarily at three test conditions. Figure 2 shows results for pitching moment due to symmetric stabilator actuations for a series of three pitch doublet maneuvers (in a doublet maneuver, a command to change attitude in a given direction by a given amount is followed immediately by a command to change attitude in the opposite direction by the same amount). A time window of 5 seconds was used. The portions of the curves shown in red are those that passed the confidence tests. The technique showed good convergence for most derivatives for both kinds of maneuvers - typically within a few seconds. The confidence tests were marginally successful, and it would be necessary to refine them for use in an IFCS.

Smith, Mark↗
NASA NTRS1987

Relaxation schemes for spectral multigrid methods

The effectiveness of relaxation schemes for solving the systems of algebraic equations which arise from spectral discretizations of elliptic equations is examined. Iterative methods are an attractive alternative to direct methods because Fourier transform techniques enable the discrete matrix-vector products to be computed almost as efficiently as for corresponding but sparse finite difference discretizations. Preconditioning is found to be essential for acceptable rates of convergence. Preconditioners based on second-order finite difference methods are used. A comparison is made of the performance of different relaxation methods on model problems with a variety of conditions specified around the boundary. The investigations show that iterations based on incomplete LU decompositions provide the most efficient methods for solving these algebraic systems.

Phillips, Timothy N.↗
NASA NTRS1983

Preconditioners for the spectral multigrid method

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problems preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.

Phillips, T. N.↗
NASA NTRS1986

Preconditioners for the spectral multigrid method

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problem preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.

Phillips, T. N.↗
NASA NTRS1971

A comparison of orthogonal transformations for digital speech processing.

Discrete forms of the Fourier, Hadamard, and Karhunen-Loeve transforms are examined for their capacity to reduce the bit rate necessary to transmit speech signals. To rate their effectiveness in accomplishing this goal the quantizing error (or noise) resulting for each transformation method at various bit rates is computed and compared with that for conventional companded PCM processing. Based on this comparison, it is found that Karhunen-Loeve provides a reduction in bit rate of 13.5 kbits/s, Fourier 10 kbits/s, and Hadamard 7.5 kbits/s as compared with the bit rate required for companded PCM. These bit-rate reductions are shown to be somewhat independent of the transmission bit rate.

Campanella, S. J.↗
DOE OSTI2021

Spatiotemporal mapping of mesoscopic liquid dynamics

The study of liquid dynamics at mesoscopic scales is still strewn with difficulty due to limitations in theory and experiment. Historically, significant attention has been given to the analysis of space-time correlation functions and their frequency-Fourier transforms at a few discrete wave numbers. The massive computing power afforded by modern high performance computing clusters and the advent of a wide-angle neutron spin-echo spectrometer, however, have unlocked a more intuitive and fruitful approach to this problem. Using molecular dynamics simulations, here we demonstrate the benefits of spatiotemporally mapping intermediate scattering functions on a dense grid of correlation times and wave numbers. Four model systems are investigated: a Lennard-Jones liquid, a coarse-grained bead-spring polymer, a molten sodium chloride, and a poly(ethylene oxide) melt. We show that the spatiotemporal mapping approach is particularly useful for elucidating the mesoscopic dynamics in these liquids, where several underlying mechanisms, such as molecular relaxations, hydrodynamic modes, and nonhydrodynamic excitations, are potentially at play. Therefore, compared to the traditional method, direct visualization of density space-time correlation functions on two-dimensional color maps permits appraisals of complicated dynamical behavior at mesoscales in a global manner. For example, the scaling relations between space and time for different types of molecular motions can be straightforwardly identified on these plots, without any model-dependent analysis. Additionally, we show how theoretical ideas regarding collective mesoscopic dynamics, such as the classical hydrodynamic theory, the convolution approximation, and a recently proposed phenomenological model, can be discussed in terms of the global features of spatiotemporal maps of intermediate scattering functions. The new perspective offered by the spatiotemporal mapping method should prove useful for the study of liquid dynamics in general.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗