Search NASA⌕ Search

SEARCH · Search NASA

Results for “Quadrature error estimate”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

32 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Analysis and Compensation of Tx and Rx IQ Imbalances in Uplink IM-OFDMA Systems

Index modulation-based orthogonal division multiple access (IM-OFDMA) has recently been proposed as a potential technique for future wireless communication systems due to its superior spectral efficiency and error performance over conventional multiple access schemes. However, its performance is still under investigation by researchers in light of a variety of scenarios and assumptions. Following this direction, in this Article, the individual and joint effects of the transmitter (Tx) and receiver (Rx) in-phase and quadrature imbalances (IQI) on the bit-error-rate (BER) performance of the uplink IM-OFDMA scheme are investigated by considering whether each user's RF front-end is identical or not. Moreover, to reduce the detrimental effect of IQI, a preamble-based estimation and compensation method is proposed for IM-OFDMA. Closed-form expressions for the average BER of IM-OFDMA are obtained by considering the physical effect of the Tx and Rx IQI. Also, using Monte Carlo simulations, the derived expressions are verified under different system configurations. Furthermore, analytical and simulation results reveal that Tx and Rx IQI cause an error floor in the BER performance of IM-OFDMA schemes. However, the proposed estimation and compensation method not only reduces the impact of IQI but also leads to a better BER performance compared to the case of no IQI, which mainly refers to the frequency diversity caused by the IQI.

42 ENGINEERING↗
DOE OSTI2025

Optimized Auxiliary Functions for Robust Mitigation of Finite-Size Errors in Periodic Hybrid Density Functional Theory

When calculating properties of periodic systems at the thermodynamic limit (TDL), the dominant source of finite size error (FSE) arises from the long-range Coulomb interaction, and can manifest as a slowly converging quadrature error when approximating an integral in the reciprocal space by a finite sum. The singularity subtraction (SS) method offers a systematic approach for reducing this quadrature error and thus the FSE. Here, in this work, we first investigate the performance of the SS method in the simplest setting, aiming at reducing the FSE in exact exchange calculations by subtracting the Coulomb contribution with a single, adjustable Gaussian auxiliary function. We demonstrate that a simple fitting method can robustly estimate the optimal Gaussian width and leads to rapid convergence toward the TDL. Furthermore, we suggest new forms of the auxiliary function, whose optimal parameters could also be determined through least-squares fitting. For a range of semiconductors and insulators, the proposed auxiliary functions achieve robust, millihartree-level accuracy in hybrid density functional theory calculations, including cases with sparse k-meshes and large basis sets.

Quiton, Stephen Jon [University of California, Ber↗
DOE OSTI2024

Reconnaissance with JWST of the J-region Asymptotic Giant Branch in Distance Ladder Galaxies: From Irregular Luminosity Functions to Approximation of the Hubble Constant

Abstract We study stars in the J-regions of the asymptotic giant branch (JAGB) of near-infrared color–magnitude diagrams in the maser host NGC 4258 and four hosts of six Type Ia supernovae (SNe Ia): NGC 1448, NGC 1559, NGC 5584, and NGC 5643. These clumps of stars are readily apparent near 1.0 < F150W − F277W < 1.5 andm F150W = 22–25 mag with James Webb Space Telescope NIRCam photometry. Various methods have been proposed to assign an apparent reference magnitude to this recently proposed standard candle, including the mode, median, sigma-clipped mean, or a modeled luminosity function parameter. We test the consistency of these by measuring intrahost variations, finding differences of up to ∼0.2 mag that significantly exceed statistical uncertainties. Brightness differences appear intrinsic, and are further amplified by the nonuniform shape of the JAGB luminosity function, also apparent in the LMC and SMC. We follow a “many methods” approach to measure consistently JAGB magnitudes and distance moduli to the SN Ia host sample calibrated by NGC 4258. We find broad agreement with distance moduli measured from Cepheids, tip of the red giant branch, and Miras. However, the SN host mean distance modulus estimated via the JAGB method necessary to estimateH 0 differs by ∼0.19 mag among the above definitions, the result of different levels of luminosity function asymmetry. The methods yield a full range of 71−78 km s −1 Mpc −1 , i.e., a fiducial result ofH 0 = 74.7 ± 2.1(stat) ± 2.3(sys, ±3.1 if combined in quadrature) km s −1 Mpc −1 , with systematic errors limited by the differences in methods. Future work may seek to standardize and refine this promising tool further, making it more competitive with established distance indicators.

Astronomy & Astrophysics↗
NASA NTRS1985

Geologic analysis of averaged magnetic satellite anomalies

To investigate relative advantages and limitations for quantitative geologic analysis of magnetic satellite scalar anomalies derived from arithmetic averaging of orbital profiles within equal-angle or equal-area parallelograms, the anomaly averaging process was simulated by orbital profiles computed from spherical-earth crustal magnetic anomaly modeling experiments using Gauss-Legendre quadrature integration. The results indicate that averaging can provide reasonable values at satellite elevations, where contributing error factors within a given parallelogram include the elevation distribution of the data, and orbital noise and geomagnetic field attributes. Various inversion schemes including the use of equivalent point dipoles are also investigated as an alternative to arithmetic averaging. Although inversion can provide improved spherical grid anomaly estimates, these procedures are problematic in practice where computer scaling difficulties frequently arise due to a combination of factors including large source-to-observation distances ( 400 km), high geographic latitudes, and low geomagnetic field inclinations.

Goyal, H. K.↗
NASA NTRS1989

Problems in determining the surface density of the Galactic disk

A new method is presented for determining the local surface density of the Galactic disk from distance and velocity measurements of stars toward the Galactic poles. The procedure is fully three-dimensional, approximating the Galactic potential by a potential of Staeckel form and using the analytic third integral to treat the tilt and the change of shape of the velocity ellipsoid consistently. Applying the procedure to artificial data superficially resembling the K dwarf sample of Kuijken and Gilmore (1988, 1989), it is shown that the current best estimates of local disk surface density are uncertain by at least 30 percent. Of this, about 25 percent is due to the size of the velocity sample, about 15 percent comes from uncertainties in the rotation curve and the solar galactocentric distance, and about 10 percent from ignorance of the shape of the velocity distribution above z = 1 kpc, the errors adding in quadrature. Increasing the sample size by a factor of 3 will reduce the error to 20 percent. To achieve 10 percent accuracy, observations will be needed along other lines of sight to constrain the shape of the velocity ellipsoid.

Statler, Thomas S.↗
NASA NTRSDate not supplied

Uncertainty Estimates for Sonic-Boom Pressure Signatures and Loudness Carpets

A non-intrusive uncertainty quantification method is applied to computational analysis of supersonic, low-boom aircraft. The mean and standard deviation statistics of the pressure waveforms and loudness metrics are evaluated through use of numerical quadrature. The probability density function (p.d.f.) of these outputs is evaluated via kernel density estimation. The simulations use an inviscid, embedded-boundary Cartesian-mesh flow solver in the nearfield combined with an augmented Burgers’ equation solver for propagation in the farfield. The results show that the p.d.f. of the waveform is bimodal at shocks, which makes the mean and standard deviation statistics inappropriate. Despite this limitation, we show that the moment statistics can provide effective assessment of discrepancies when comparing with experimental data. This is demonstrated by presenting uncertainty analysis of a wind-tunnel test and showing that we significantly improve the predictions when we include the test uncertainties in the simulation. Normal distributions are obtained for the ground signature and loudness metrics, which is primarily due to the careful shaping of the low-boom waveform. Separation of variables and error control are used to reduce computational cost. We demonstrate that this is an efficient approach in the sense of balancing numerical errors in the statistics quadrature with discretization errors in the solvers.

ARMD↗
NASA NTRS2018

Combined Error and Uncertainty Estimates for CFD Problems

Given input sources of uncertainty, non-intrusive uncertainty propagation methods quantify the uncertainty in output quantities of interest (QoI) by performing a nite number of CFD (Computational Fluid Dynamics) instance realizations needed in the calculation of output statistics. It is well known that this introduces multiple sources of error. CFD codes often utilize finite-dimensional approximation (grids, basis functions, etc.) thus incurring CFD numerical errors often approximately reinterpreted as a statistical bias. Uncertainty propagation methods calculate uncertainty statistics for output quantities of interest using a numerical method (e.g. deterministic quadrature, sampling, etc.) thus incurring UQ (Uncertainty Quantification) numerical errors. Importance of quantifying these errors in large scale scientific computing: How accurate is an output statistic?; How should additional computational resources be invested to further reduce the error in a statistic?

Posteriori↗
NASA NTRS1990

Numerical experiments in geomagnetic modeling

Numerical tests were made, using least squares fitting of a spherical harmonic model, to a selection of Magsat data to determine the practical limits of this technique with modern computers. The resulting (M102189) model, whose coefficients were adjusted up to n = 50, was compared with M07AV6, a previous model which used least squares (on vector data) for coefficients up to n = 29, and Gauss-Legendre quadrature (on Z residuals) to adjust the coefficients up to n = 63. For the new least squares adjustment to n = 50 a condition number of 115 was obtained for the solution matrix, with a resulting precision of 11 significant figures. The M102189 model shows a lower and more Gaussian residual distribution than did M07AV6, though the Gaussian envelope fits to the residual distributions, even for the scalar field, gives "standard deviations' never lower than 6 nT, a factor of three higher than the estimated Magsat observational errors. Ionospheric currents are noted to have a significant effect on the coefficients of the internal potential functions.

Cain, Joseph C.↗
NASA NTRS1979

A semi-analytic theory for the motion of a close-earth artificial satellite with drag

A semi-analytic method is used to estimate the decay history/lifetime and to generate orbital ephemeris for close-earth satellites perturbed by the atmospheric drag and earth oblateness due to the spherical harmonics J2, J3, and J4. The theory maintains efficiency through the application of the theory of a method of averaging and employs sufficient numerical emphasis to include a rather sophisticated atmospheric density model. The averaged drag effects with respect to mean anomaly are evaluated by a Gauss-Legendre quadrature while the averaged variational equations of motion are integrated numerically with automatic step size and error control.

Liu, J. J. F.↗
DOE OSTI2024

Tackling the curse of dimensionality in fractional and tempered fractional PDEs with physics-informed neural networks

Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems are mesh-based, thus struggling with the curse of dimensionality (CoD). Physics-informed neural networks (PINNs) offer a promising solution due to their universal approximation, generalization ability, and mesh-free training. In principle, Monte Carlo fractional PINN (MC-fPINN) estimates fractional derivatives using Monte Carlo methods and thus could lift CoD. However, this may cause significant variance and errors, hence affecting convergence; in addition, MC-fPINN is sensitive to hyperparameters. In general, numerical methods and specifically PINNs for tempered fractional PDEs are under-developed. Herein, we extend MC-fPINN to tempered fractional PDEs to address these issues, resulting in the Monte Carlo tempered fractional PINN (MC-tfPINN). To reduce possible high variance and errors from Monte Carlo sampling, we replace the one-dimensional (1D) Monte Carlo with 1D Gaussian quadrature, applicable to both MC-fPINN and MC-tfPINN. We validate our methods on various forward and inverse problems of fractional and tempered fractional PDEs, scaling up to 100,000 dimensions. Our improved MC-fPINN/MC-tfPINN using quadrature consistently outperforms the original versions in accuracy and convergence speed in very high dimensions.

42 ENGINEERING↗
DOE OSTI2020

Distributed quantum sensing enhanced by continuous-variable error correction

Abstract A distributed sensing protocol uses a network of local sensing nodes to estimate a global feature of the network, such as a weighted average of locally detectable parameters. In the noiseless case, continuous-variable (CV) multipartite entanglement shared by the nodes can improve the precision of parameter estimation relative to the precision attainable by a network without shared entanglement; for an entangled protocol, the root mean square estimation error scales like 1/ M with the number M of sensing nodes, the so-called Heisenberg scaling, while for protocols without entanglement, the error scales like 1 / M . However, in the presence of loss and other noise sources, although multipartite entanglement still has some advantages for sensing displacements and phases, the scaling of the precision with M is less favorable. In this paper, we show that using CV error correction codes can enhance the robustness of sensing protocols against imperfections and reinstate Heisenberg scaling up to moderate values of M . Furthermore, while previous distributed sensing protocols could measure only a single quadrature, we construct a protocol in which both quadratures can be sensed simultaneously. Our work demonstrates the value of CV error correction codes in realistic sensing scenarios.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1999

Mantle Q at Period 12.4 Hours: New Estimates from Satellite Tracking and Altimetry

The most convincing estimates of mantle Q at periods of many hours have historically come from extrapolating seismic and free-oscillation estimates via some assumed frequency dependence, sometimes contrained by estimates from the Chandler Wobble. At the semidiurnal tidal period, direct estimates of Q have been difficult to obtain because of the dominating signals of the ocean tides, which account for more than 95!k of the tidal energy dissipation. But knowledge of the ocean tides has been rapidly improving, primarily owing to satellite altimetry, and in 1996 we reported (NATURE, 381, 595-7) an estimate of solid-earth tidal energy dissipation and mantle Q based on combining satellite altimeter measurements with tracking observations of tidally induced satellite orbit perturbations. Tidal estimates from both reveal a small systematic difference in the quadrature component of the degree-2, order-2 spherical harmonic coefficients, which we attribute to a small lag in the earth's body tide. The formalism accounts for this lag in both the altimeter and tracking solutions and also accounts for a very small contribution from the lunar atmospheric tide. Since this original report, both altimeter and tracking estimates have improved. Recent solutions for the body-tide lag at the M2 period are 0.20 +/- 0.09 degrees, implying an energy dissipation of 100 +/- 50 gigawatts and a solid-earth Q of 300. Further new solutions will be discussed, as will the prospects for significantly reducing error bars and for obtaining estimates from other tides in the diurnal band.

Ray, Richard D.↗
DOE OSTI2024

FLOWERS AEP: An Analytical Model for Wind Farm Layout Optimization

Annual energy production (AEP) is commonly used in objective functions for wind farm layout optimization. AEP is proportional to wind farm power production integrated over an annual distribution of free-stream wind conditions. Physics-based estimates of wind farm power production typically rely on low-fidelity engineering wake models that approximate the steady-state wind farm flow field. AEP estimates are then obtained by performing independent simulations for discrete wind conditions and using rectangular quadrature to account for each condition's expected frequency of occurrence. Depending on the number of simulated discrete wind conditions, this numerical integral could be hampered by poor accuracy or high computational costs. The FLOWERS AEP model instead poses an analytical integral of the engineering wake model over the variable wind conditions, yielding a closed-form, analytical function for wind farm AEP. This paper derives the analytical functions for FLOWERS AEP and its derivatives with respect to turbine position, which are useful for gradient-based wind farm layout optimization, in nondimensional form. We then analyze the benefits of the FLOWERS AEP model over conventional reference models, focusing on its low cost, adequate wake loss predictions, and smooth design space. Although the FLOWERS approach is found to predict the exact value of AEP with some error relative to the reference model (within 14% on average), it dramatically reduces computation time by an order of magnitude, produces a qualitatively similar design space at relatively low resolution, and yields comparable optimal layouts. This significant speed improvement is critical in layout optimization applications, where determining an optimal layout in an efficient manner is more important than precise AEP prediction.

17 WIND ENERGY↗
NASA NTRS2016

The Radial Speed-Expansion Speed Relation for Earth-Directed CMEs

Earth-directed coronal mass ejections (CMEs) are the main drivers of major geomagnetic storms. Therefore, a good estimate of the disturbance arrival time at Earth is required for space weather predictions. The STEREO and SOHO spacecraft were viewing the Sun in near quadrature during January 2010 to September 2012, providing a unique opportunity to study the radial speed (V (sub rad)) to expansion speed(V (sub exp)) relationship of Earth-directed CMEs. This relationship is useful in estimating the V (sub rad) of Earth-directed CMEs, when they are observed from Earth view only. We selected 19 Earth-directed CMEs observed by the Large Angle and Spectrometric Coronagraph (LASCO)/C3 coronagraph on SOHO and the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI)/COR2 coronagraph on STEREO during January 2010 to September 2012. We found that of the three tested geometric CME models the full ice-cream cone model of the CME describes best the V (sub rad) to V (sub exp) relationship, as suggested by earlier investigations. We also tested the prediction accuracy of the empirical shock arrival (ESA) model proposed by Gopalswamy et al.(2005a), while estimating the CME propagation speeds from the CME expansion speeds. If we use STEREO observations to estimate the CME width required to calculate the V (sub rad) from the V (sub exp) measurements, the mean absolute error (MAE) of the shock arrival times of the ESA model is 8.4 hours. If the LASCO measurements are used to estimate the CME width, the MAE still remains below 17 hours. Therefore, by using the simple V (sub rad) to V (sub exp) relationship to estimate the V (sub rad) of the Earth-directed CMEs, the ESA model is able to predict the shock arrival times with accuracy comparable to most other more complex models.

Makela, P.↗