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NASA NTRS2019

Correlation of Full-Scale Isolated Proprotor Performance and Loads

A full-scale isolated proprotor test was recently conducted in the USAF National Full-Scale Aerodynamics Complex (NFAC) at NASA Ames Research Center. The test article was a 3-bladed research rotor derived from the right-hand rotor of the AW609. For this test, the NASA Tiltrotor Test Rig (TTR) and rotor were installed in the 40- by 80-foot test section. This paper presents correlations between data and predictions of rotor performance and blade moments using the newly acquired test data and the comprehensive analysis CAMRAD II. The operational conditions covered in this analytical study are: hover (actually, low speed vertical climb), cruise (airplane mode), conversion, and helicopter mode. Mean and 1/2 peak-to-peak quantities (hpp) are correlated; time-history correlation for the helicopter condition is also included. The correlation is reasonable to good. Also, the hover calculations turned out to be useful in providing reality checks on the test hardware such as: a) the functioning of the blade strain gages and b) calibration of the measurement of the collective pitch hardware. The time-history correlation shows that, compared to the rolled-up wake model, the multiple-trailer wake model improves the correlation slightly; the longitudinal cyclic correlation is reasonable but the lateral cyclic correlation is not good, and the collective is predicted well by the rolled-up wake model; the flap moment correlation is reasonable; the pitch link load and lag moment are underpredicted; and the torsion moment correlation is poor and needs further study.

Kottapalli, Sesi↗

NASA NTRS2016

An Integrated Circuit for Radio Astronomy Correlators Supporting Large Arrays of Antennas

Radio telescopes that employ arrays of many antennas are in operation, and ever larger ones are being designed and proposed. Signals from the antennas are combined by cross-correlation. While the cost of most components of the telescope is proportional to the number of antennas N, the cost and power consumption of cross-correlationare proportional to N2 and dominate at sufficiently large N. Here we report the design of an integrated circuit (IC) that performs digital cross-correlations for arbitrarily many antennas in a power-efficient way. It uses an intrinsically low-power architecture in which the movement of data between devices is minimized. In a large system, each IC performs correlations for all pairs of antennas but for a portion of the telescope's bandwidth (the so-called "FX" structure). In our design, the correlations are performed in an array of 4096 complex multiply-accumulate (CMAC) units. This is sufficient to perform all correlations in parallel for 64 signals (N=32 antennas with 2 opposite-polarization signals per antenna). When N is larger, the input data are buffered in an on-chipmemory and the CMACs are re-used as many times as needed to compute all correlations. The design has been synthesized and simulated so as to obtain accurate estimates of the IC's size and power consumption. It isintended for fabrication in a 32 nm silicon-on-insulator process, where it will require less than 12mm2 of silicon area and achieve an energy efficiency of 1.76 to 3.3 pJ per CMAC operation, depending on the number of antennas. Operation has been analyzed in detail up to N = 4096. The system-level energy efficiency, including board-levelI/O, power supplies, and controls, is expected to be 5 to 7 pJ per CMAC operation. Existing correlators for the JVLA (N = 32) and ALMA (N = 64) telescopes achieve about 5000 pJ and 1000 pJ respectively usingapplication-specific ICs in older technologies. To our knowledge, the largest-N existing correlator is LEDA atN = 256; it uses GPUs built in 28 nm technology and achieves about 1000 pJ. Correlators being designed for the SKA telescopes (N = 128 and N = 512) using FPGAs in 16nm technology are predicted to achieve about 100 pJ.

ASIC↗

DOE OSTI2021

Importance of charge self-consistency in first-principles description of strongly correlated systems

First-principles approaches have been successful in solving many-body Hamiltonians for real materials to an extent when correlations are weak or moderate. As the electronic correlations become stronger often embedding methods based on first-principles approaches are used to better treat the correlations by solving a suitably chosen many-body Hamiltonian with a higher level theory. The success of such embedding theories, often referred to as second-principles, is commonly measured by the quality of self-energy Σ which is either a function of energy or momentum or both. However, Σ should, in principle, also modify the electronic eigenfunctions and thus change the real space charge distribution. While such practices are not prevalent, some works that use embedding techniques do take into account these effects. In such cases, choice of partitioning, of the parameters defining the correlated Hamiltonian, of double-counting corrections, and the adequacy of low-level Hamiltonian hosting the correlated subspace hinder a systematic and unambiguous understanding of such effects. Further, for a large variety of correlated systems, strong correlations are largely confined to the charge sector. Then an adequate nonlocal low-order theory is important, and the high-order local correlations embedding contributes become redundant. Here we study the impact of charge self-consistency within two example cases, TiSe 2 and CrBr 3 , and show how real space charge re-distribution due to correlation effects taken into account within a first-principles Green’s function-based many-body perturbative approach is key in driving qualitative changes to the final electronic structure of these materials.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Geometrical picture of the electron–electron correlation at the large- D limit

In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schrödinger equation. Such an error in the different calculations is not directly observable as there is no simple quantum mechanical operator, apart from correlation functions, that correspond to such quantity. Here, we use the dimensional scaling approach, in which the electrons are localized at the large-dimensional scaled space, to describe a geometric picture of the electronic correlation. Both, the mean field, and the exact solutions at the large-D limit have distinct geometries. Thus, the difference might be used to describe the correlation effect. Moreover, correlations can be also described and quantified by the entanglement between the electrons, which is a strong correlation without a classical analog. Entanglement is directly observable and it is one of the most striking properties of quantum mechanics and bounded by the area law for local gapped Hamiltonians of interacting many-body systems. This study opens up the possibility of presenting a geometrical picture of the electron–electron correlations and might give a bound on the correlation energy. Furthermore, the results at the large-D limit and at D = 3 indicate the feasibility of using the geometrical picture to get a bound on the electron–electron correlations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Correlation between the gas-phase metallicity and ionization parameter in extragalactic H II regions

The variations of the metallicity and ionization parameter in H II regions are usually thought to be the dominant factors that produce the variations we see in the observed emission line spectra. There is an increasing amount of evidence that these two quantities are physically correlated, although the exact form of this correlation is debatable in the literature. Simulated emission line spectra from photoionized clouds provide important clues about the physical conditions of H II regions and are frequently used for deriving metallicities and ionization parameters. Through a systematic investigation on the assumptions and methodology used in applying photoionization models, we find that the derived correlation has a strong dependence on the choice of model parameters. On the one hand, models that give consistent predictions over multiple emission-line ratios yield a positive correlation between the metallicity and ionization parameter for the general population of H II regions or star-forming galaxies. On the other hand, models that are inconsistent with the data locus in high-dimensional line ratio space yield discrepant correlations when different subsets of line ratios are used in the derivation. The correlation between the metallicity and ionization parameter has a secondary dependence on the surface density of the star formation rate (SFR), with the higher SFR regions showing a higher ionization parameter but weaker correlations. The existence of the positive correlation contradicts the analytical wind-driven bubble model for H II regions. We explore assumptions in both dynamical models and photoionization models, and conclude that there is a potential bias associated with the geometry. However, this is still insufficient to explain the correlation. Mechanisms that suppress the dynamical influence of stellar winds in realistic H II regions might be the key to solving this puzzle, though more sophisticated combinations of dynamical models and photoionization models to test are required.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Projections of two-particle correlations onto transverse rapidity in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV at STAR

Two-particle correlation measurements projected onto two-dimensional, transverse rapidity coordinates (y T1 ,y T2 ), allow access to dynamical properties of the QCD medium produced in relativistic heavy-ion collisions that angular correlation measurements are not sensitive to. Here, we report non-identified charged-particle correlations for Au + Au minimum-bias collisions at $\sqrt{s_{NN}}$ = 200 GeV taken by the STAR experiment at the Relativistic Heavy-Ion Collider (RHIC). Correlations are presented as 2D functions of transverse rapidity for like-sign, unlike-sign and all charged-particle pairs, as well as for particle pairs whose relative azimuthal angles lie on the near-side, the away-side, or at all relative azimuth. The correlations are constructed using charged particles with transverse momentum p T ≥ 0.15 GeV/c, pseudorapidity from –1 to 1, and azimuthal angles from –π to π. The significant correlation structures that are observed evolve smoothly with collision centrality. The major correlation features include a saddle shape plus a broad peak with maximum near y T ≈ 3, corresponding to p T ≈ 1.5 GeV/c. The broad peak is observed in both like- and unlike-sign charge combinations and in near- and away-side relative azimuthal angles. The all-charge, all-azimuth correlation measurements are compared with the theoretical predictions of HIJING and EPOS. The results indicate that the correlations for peripheral to mid-central collisions can be approximately described as a superposition of nucleon + nucleon collisions with minimal effects from the QCD medium. Strong medium effects are indicated in mid- to most-central collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Correlations between maximum mass of neutron stars and the nuclear matter properties and the constraints from PSR J0740+6620 and GW190814

The correlations between the maximum mass of neutron stars (NSs) with the properties of nuclear matter at saturation density ρ 0 , i.e., the incompressibility K 0 , the symmetry energy E sym (ρ 0 ), and its slope L(ρ 0 ), the isoscalar effective mass m$^{*}_{s0}$, and the parameter f I , have been investigated using several sets of Skyrme interactions based on the momentum-dependent (MD) Skyrme interactions SAMi-J27 (soft), SAMi-J31 (stiff), and SAMi-J35 (super-stiff), as well as the momentum-independent (MI) Skyrme interaction SkT5. Only one physical quantity is varied at a time for a given set of Skyrme interactions. It is found that the maximum mass of NSs has (1) a strong positive linear correlation with K 0 for stiff and super-stiff equation of state (EOS) and no correlation with K 0 for soft EOS; (2) a negative logarithm correlation with the symmetry energy E sym (ρ 0 ) for all the EOSs; (3) a positive logarithm correlation with the slope L(ρ 0 ) for all the EOSs; (4) a positive logarithm correlation with the parameter f I for MD EOS; (5) a negative power-law correlation with m$^{*}_{s0}$ for MD EOS. Based on these established correlations, the constraints to the nuclear matter properties from the mass of PSR J0740+6620 and GW190814 are investigated. Furthermore, we find that while rotation enhances the maximum mass of NSs, it does not effect the underlying correlations between the maximum mass and the aforementioned nuclear matter parameters.

Zhou, M. [Shaanxi Normal University, Xi’an (China)↗

DOE OSTI2020

Conservative Release Fraction Correlation for Spray Releases

Washington River Protection Solutions, LLC (WRPS) is planning to conduct repairs in the Liquid Effluent Retention Facility (LERF), and prior to conducting this work they will re-evaluate the hazard category designation for LERF. As part of this evaluation, WRPS needs estimates of the release fraction of potential accidental sprays, because a spray release is a potential bounding accident. Pacific Northwest National Laboratory previously developed a conservative correlation for the cumulative generation rate (volume per time) of aerosol droplets less than or equal to specific sizes from spray releases as a function of the spray pressure, orifice area, and droplet diameter. To obtain release fraction estimates from the conservative generation rate correlation, the correlation needs to be recast by dividing the aerosol generation rate by the flow rate of a spray. In the current study, a conservative release fraction correlation was developed from the conservative aerosol generation rate correlation developed previously by dividing the generation rate correlation by the flow rate of a spray using an orifice flow rate equation and then this correlation was adjusted to be conservative. Test data were also extrapolated to a lower pressure than the lowest pressure tested (100 psig) for the spray data used for developing the previous conservative generation rate correlation. The new conservative release fraction correlation was then used to predict release fractions of respirable droplets (droplets = 10 µm) for four specific pipes that are part of LERF.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Review and Analysis of Heat Transfer Correlations For Horizontal Pseudocritical CO 2 Heat Exchanger Applications

There is significant interest in the development of supercritical carbon dioxide (sCO 2 ) power cycles because of the potential for smaller and more energy efficient systems than a steam Rankine cycle. Heat exchanger designs typically use empirical correlations, but the applicability of these correlations near the CO 2 critical point is a potential issue. Though numerous correlations have been proposed in the literature, there are some disagreements when it comes to the accuracy. The current work recognizes the role of thermophysical properties, and its impacts on the heat transfer correlations and cycle efficiency. Heat transfer correlations proposed for horizontal flow inside circular pipes were analyzed with the help of numerical simulations. Steady state RANS simulations were performed using SST k-w turbulence model to evaluate the Nusselt number empirical correlations. It was found that the most of correlations (except Yoon) produced a Nusselt number that differed significantly with the one predicted numerically. Some of the correlations were developed for pure forced convection regime and as mentioned in Lin et al. do not account for mixed convection or free convection effects. Based on the limited observation, it appears that Yoon et al. predictions match well with the numerically predicted Nusselt Numbers. However, further analysis is required understand the applicability of various correlations and is contingent on accurate measurements or predictions of wall temperature profiles in the axial and the circumferential directions.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS1995

Pressure correlations at a fluid/structure interface

The structure of pressure-pressure correlations at the interface of an incompressible steady-state turbulent flow with a rigid boundary was investigated. For the sake of completeness, the absolute value of the correlation between two random varying functions is herein defined as a number greater than or equal to zero and less than or equal to unity which is a measure of that fraction of one of the functions that 'follows' the second function (or vice versa). It was found that the soughtafter correlations can be determined by consideration of the high Re Navier-Stokes equation, but that the complexity of boundary layer turbulence, in particular the inhomogeneity perpendicular to the boundary and the anisotropy due to convective flow gradients, makes the structure of said correlations extremely difficult to assess. One of the earlier researchers in this field described the quantity under present consideration as 'a quantity which is beyond assessment.' Nonetheless, it was found that under some rather simplifying assumptions the determination of the required structure necessitates the formulation of the related structure of second order two-point correlations of turbulent velocity gradients, as well as third order two-point correlations of velocity gradients. The presence of these latter gradients is due to the nonlinearity in the turbulence ('turbulence self-interaction'). Both of these correlations are scaled, although not similarly, by factors dependent upon the magnitude of the convective flow, which can be modeled using a log law approximation. Fourth order correlations, although present, can be ignored, since they constitute 'higher order terms.' In a slightly more complex situation, it was found that convective flow gradients also have to be incorporated. At the moment, no definitive algebraic information peculiar to pressure-pressure correlations is available in the most highly idealized cases.

Trevino, George↗

NASA NTRS1999

The Impact of Anisotropic Error Correlation Modelling

Most data assimilation systems assume isotropic forecast error correlations, but results from two dimensional Kalman Filter experiments indicate that the correlations can be far from isotropic. In this paper we use a simple two-dimensional data assimilation system, which analyses trace chemical species such as ozone, to assess different approaches to modelling the error correlations. We compare assimilation results using isotropic correlations with results obtained using different approaches to modelling anisotropic correlations: first, using correlations based on the concentrations of the trace chemicals, and secondly using an advective correlation model. We show that these relatively cheap ways of modelling anisotropic correlations give objectively better results than using isotropic correlations. We discuss the possible extension of these approaches to a full 3-D meteorological data assimilation system.

Swinbank, R.↗

NASA NTRS1996

Quantifying the Correlation Between Eye-Movement and Perceptual Responses to Moving Plaids

To determine the extent to which the pursuit eye-movement and perceptual systems share a common neural motion-processing pathway, we simultaneously measure the psychophysical and eye-movement responses to drifting plaids in a direction-discrimination task. Correlation between the noise in the eye movements and percepts would suggest a shared neural substrate. Three observers were asked to track a plaid (Type I 90 deg; TF = 4 Hz, SF = 0.6 c/d; direction = -2, 0, or 2 deg), and to respond whether the motion was to the right or left of vertical. The eye-movement direction is computed from the initial 300 ms of saccade-free tracking (near open-loop). On each trial, we use the eye-movement direction to predict the perceptual response. We then compute the probability of successfully predicting the observer's response. We also use SOC analysis as an alternate measure of the correlation. We compare the data from both these analyses to the predictions of two models in which the eye movements and the percept are driven by either a common noisy signal (correlated model) or by two separate noisy signals (uncorrelated model). We also allow for the fact that our measured eye movements are degraded by eye-tracker noise. This noise causes our measured correlation to be lower than the actual biological correlation. The correlations in our data are higher than those predicted by the uncorrelated model, and are similar to the predictions of the correlated model. The proportion of perceptual responses correctly predicted by the eye movements were 0.66, 0.60, 0.73 for the -2, 0, 2 deg stimuli respectively (correlated model 0.65, 0.60, 0.70; uncorrelated model 0.58, 0.51, 0.60).The SOC proportions were 0.71, 0.64, 0.72 (correlated model 0.66, 0.64, 0.69; uncorrelated model 0.5, 0.5, 0.5). These results show that the oculomotor and perceptual system share a performance-limiting noise source and provide strong evidence that a common neural mechanism (perhaps MT or MST) drives both perception and smooth eye movements.

Beutter, Brent R.↗

NASA NTRS2003

On the Computation of Space-Time Correlations by Large-Eddy Simulation

Numerical comparisons in decaying isotropic turbulence suggest that there exist discrepancies in time correlations evaluated by DNS and LES using eddy-viscosity-type SGS models. This is consistent with the previous observations in forced isotropic turbulence. Therefore, forcing is not the main cause of the discrepancies. Comparisons among different SGS models in the LES also indicate that the model choice affects the time correlations in the LES. The multi-scale LES method using the dynamic Smagorinsky model on the small scale equation is the most accurate of the all models, the classic Smagorinsky model is the least accurate and the dynamic Smagorinsky model and spectral eddy viscosity model give intermediate results with small differences. The generalized sweeping hypothesis implies that time correlations in decaying isotropic turbulence are mainly determined by the instantaneous energy spectra and sweeping velocities. The analysis based on the sweeping hypothesis explains the discrepancies in our numerical simulations: the LES overpredicts the decorrelation time scales because the sweeping velocities are smaller than the DNS values, and underpredicts the magnitudes of time correlations because the energy spectrum levels are lower than the DNS ones. Since the sweeping velocity is determined by the energy spectra, one concludes that an accurate prediction of the instantaneous energy spectra guarantees the accuracy of time correlations. An analytical expression of sound power spectra based on Lighthill's theory and the quasi-normal closure assumption suggests that the sound power spectra are sensitive to errors in time correlations. Small errors in time correlations can cause significant errors in the sound power spectra, which exhibit a sizable drop at moderate to high frequencies accompanied by a shift of the peaks to lower frequencies. Based on the above analysis, two possible ways to improve the acoustic power spectrum predictions can be considered. The first is to construct better SGS models to improve the LES accuracy for time correlations. The second is to remedy the temporal statistics of the Lighthill stress tensor in order to "recover" the contribution from the unresolved scales in LES to time correlations.

He, Guo-Wei↗

NASA NTRS2007

Determination of Black Hole Mass in Cyg X-1 by Scaling of Spectral Index-QPO Frequency Correlation

It is well established that timing and spectral properties of Galactic Black Hole (BH) X-ray binaries (XRB) are strongly correlated. In particular, it has been shown that low frequency Quasi-Periodic Oscillation (QPO) nu(sub low) - photon index GAMMA correlation curves have a specific pattern. In a number of the sources studied the shape of the index-low frequency QPO correlations are self-similar with a position offset in the nu(sub low) - GAMMA plane determined by a BH mass M(sub BH). Specifically, Titarchuk & Fiorito (2004) gave strong theoretical and observational arguments that the QPO frequency values in this nu(sub low) - GAMMA correlation should be inversely proportional to M(sub BH). A simple translation of the correlation for a given source along frequency axis leads to the observed correlation for another source. As a result of this translation one can obtain a scaling factor which is simply a BH mass ratio for these particular sources. This property of the correlations offers a fundamentally new method for BH mass determination in XRBs. Here we use the observed QPO-index correlations observed in three BH sources: GRO J1655-40, GRS 1915+105 and Cyg X-1. The BH mass of (6.3 plus or minus 0.5) solar mass in GRO J1655-40 is obtained using optical observations. RXTE observations during the recent 2005 outburst yielded sufficient data to establish the correlation pattern during both rise and decay of the event. We use GRO J1655-40 as a standard reference source to measure the BH mass in Cyg X-1. We also revisit the GRS 1915+105 data as a further test of our scaling method. We obtain the BH mass in Cyg X-1 in the range 7.6-9.9.

Shaposhnikov, Nickolai↗

NASA NTRS2004

Ultralow-Power Digital Correlator for Microwave Polarimetry

A recently developed high-speed digital correlator is especially well suited for processing readings of a passive microwave polarimeter. This circuit computes the autocorrelations of, and the cross-correlations among, data in four digital input streams representing samples of in-phase (I) and quadrature (Q) components of two intermediate-frequency (IF) signals, denoted A and B, that are generated in heterodyne reception of two microwave signals. The IF signals arriving at the correlator input terminals have been digitized to three levels (-1,0,1) at a sampling rate up to 500 MHz. Two bits (representing sign and magnitude) are needed to represent the instantaneous datum in each input channel; hence, eight bits are needed to represent the four input signals during any given cycle of the sampling clock. The accumulation (integration) time for the correlation is programmable in increments of 2(exp 8) cycles of the sampling clock, up to a maximum of 2(exp 24) cycles. The basic functionality of the correlator is embodied in 16 correlation slices, each of which contains identical logic circuits and counters (see figure). The first stage of each correlation slice is a logic gate that computes one of the desired correlations (for example, the autocorrelation of the I component of A or the negative of the cross-correlation of the I component of A and the Q component of B). The sampling of the output of the logic gate output is controlled by the sampling-clock signal, and an 8-bit counter increments in every clock cycle when the logic gate generates output. The most significant bit of the 8-bit counter is sampled by a 16-bit counter with a clock signal at 2(exp 8) the frequency of the sampling clock. The 16-bit counter is incremented every time the 8-bit counter rolls over.

Piepmeier, Jeffrey R.↗

NASA NTRS2003

Using Correlated Photons to Suppress Background Noise

A proposed method of suppressing the effect of background noise in an optical communication system would exploit the transmission and reception of correlated photons at the receiver. The method would not afford any advantage in a system in which performance is limited by shot noise. However, if the performance of the system is limited by background noise (e.g., sunlight in the case of a free-space optical communication system or incoherently scattered in-band photons in the case of a fiber-optic communication system), then the proposed method could offer an advantage: the proposed method would make it possible to achieve a signal-to-noise ratio (S/N) significantly greater than that of an otherwise equivalent background- noise-limited optical communication system based on the classical transmission and reception of uncorrelated photons. The figure schematically depicts a classical optical-communication system and a system according to the proposed method. In the classical system, a modulated laser beam is transmitted along an optical path to a receiver, the optics of which include a narrow-band-pass filter that suppresses some of the background noise. A photodetector in the receiver detects the laser-beam and background photons, most or all of which are uncorrelated. In the proposed system, correlated photons would be generated at the transmitter by making a modulated laser beam pass through a nonlinear parametric down-conversion crystal. The sum of frequencies of the correlated photons in each pair would equal the frequency of the incident photon from which they were generated. As in the classical system, the correlated photons would travel along an optical path to a receiver, where they would be band-pass filtered and detected. Unlike in the classical system, the photodetector in the receiver in this system would be one that intrinsically favors the detection of pairs of correlated photons over the detection of uncorrelated photons. Even though there would be no way of knowing the precise location and time of creation of a given pair of correlated signal photons in the nonlinear down-conversion crystal, the fact that the photons are necessarily created at the same time and place makes it possible to utilize conventional geometrical imaging optics to reunite the photons in coincidence in the receiving photodetector. Because most or all of the signal photons would be correlated while most or all of the noise photons would be uncorrelated, the S/N would be correspondingly enhanced in the photodetector output. An additional advantage to be gained by use of a correlated-photon detector is that it could be capable of recovering the signal even in the presence of background light so bright that a classical uncorrelated-photon detector would be saturated. A blocked-impurity-band (BIB) photodetector that preferentially detects pairs of correlated photons over uncorrelated ones and that operates at a quantum efficiency of 88 percent is commercially available. This detector must be cooled to the temperature of liquid helium to obtain the desired low-noise performance. It is planned to use this detector in a proof-of-principle demonstration. In addition, it may be possible to develop GaN-based photodetectors that could offer the desired low-noise performance at room temperature.

Jackson, Deborah↗

DOE OSTI2020

How Wrong Can the Operational AEP Uncertainty Estimate Be When We Ignore the Correlations Between the Uncertainty Components?

Calculations of wind farm annual energy production (AEP) on operational data are essential for a variety of financial transactions during the life of wind plants. The AEP estimate is associated with an uncertainty value, which is calculated by combining contributions connected to on-site measurements, long-term reference measurements, losses, regression, windiness adjustment, and wind resource interannual variability. Although very limited documentation on the topic exists, the conventional approach currently used by the wind energy community to assess the uncertainty connected to the operational AEP estimate assume that the different uncertainty components are uncorrelated and therefore calculates the overall uncertainty with a sum of squares approach. In this analysis, we contrast the traditional technique to estimate the overall AEP uncertainty by ignoring the correlation between its different components with a novel Monte Carlo based approach, which can instead take into account the correlation between different uncertainty categories. We consider monthly operational data from 472 wind farms from the Energy Information Administration (EIA) 923 database to assess the difference between the two approaches. Long-term wind speed data needed for the AEP assessment are taken from three reanalysis products: the Modern-Era Retrospective analysis for Research and Applications v2 (MERRA-2), the European Reanalysis Interim (ERA-interim), and the National Centers for Environmental Prediction v2 (NCEP-2). The results of the Monte Carlo approach show that three pairs of AEP uncertainty components do show a statistically significant correlation: the uncertainty connected with wind resource inter-annual variability is positively correlated with the one related to the windiness correction and negatively correlated with the one due to the regression, and the wind measurement uncertainty is positively correlated with the regression uncertainty. All these correlations, which are found between uncertainty components which are not only part of an operational analysis, but also of a wind resource assessment, are currently ignored in the conventional techniques used as industry standard. We further investigate the causes of these correlations, in terms of common dependencies of different uncertainty components on wind resource variability, number of data points, and quality of the regression between wind speed and energy production data. Next, we quantify the error in the current industry standard technique, in terms of the percentage difference in total uncertainty calculated with the two considered approaches, for all the analyzed wind farms. We find a mean absolute percentage difference of about 6%, with the largest differences being greater than 20%. The data clearly confirm that ignoring the actual correlation between the uncertainty components can lead to large errors in the assessment of the operational AEP uncertainty, and the proposed Monte Carlo approach should be preferred.

Monte Carlo↗

DOE OSTI2026

Tomography of the gamma-ray sky from cross-correlation with DESI DR2 and unWISE galaxies

We study the origin of extragalactic gamma-ray emission observed by Fermi-LAT, using the cross-correlation of the gamma-ray sky with maps of large-scale structure provided by the DESI and unWISE surveys. Tomographic cross-correlation reveals the bias-weighted redshift distributions of gamma-ray sources. We first illustrate this method by cross-correlating detected gamma-ray point sources with large-scale structure. We find a significant cross-correlation and infer a point source redshift distribution broadly consistent with the distribution of identified optical counterparts previously reported in the literature, as well as a similar linear bias ($b \approx 2$) to massive galaxies that host bright active galactic nuclei. We then study the clustering of the Fermi unresolved gamma-ray background (UGRB), both in auto-correlation and in cross-correlation with large-scale structure. We detect the cross-correlation of the UGRB and LSS at $\sim 10σ$ in total, with highly significant detections from both DESI and unWISE. Our measurements suggest that the redshift distribution of the UGRB is broadly consistent with the redshift distribution of detected point sources. Additionally, we find a relatively weak amplitude for the cross-correlation with large-scale structure at z < 2, suggesting a significant fraction of the UGRB does not come from z < 2 large-scale structure. A natural candidate is contamination of from residual Galactic emission, and our best estimate of the contamination level derived from the UGRB auto-spectrum suggests that the mean bias of UGRB sources is indeed quite similar to the bias of detected Fermi point sources. However, we cannot exclude additional emission from gamma-ray sources at high redshift, z > 2, and we suggest that cross-correlation with tracers at z > 2, including CMB lensing, would be the ideal way to determine the fraction of z > 2 emission.

Krolewski, Alex [Waterloo U., Math. Dept.; Waterlo↗