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At least 91 records · Page 5

Robust wind farm layout optimization

Wake interactions in wind farms cause losses in annual energy production (AEP) on the order of 10%. Wind farm designers optimize the layout of the farm to mitigate wake losses, especially in the dominant site-specific wind directions. As wind turbines and wind farms grow in scale, optimization becomes more complex. Offshore wind farms regularly comprise more than 100 wind turbines and are characterized by complex boundaries due to shipping lanes, neighboring wind farms, and other constraints. Layout optimization methods are broadly split between gradient-based and gradient-free approaches. Gradient-based approaches can converge quickly and perform well for smaller, academic problems but are often sensitive to initial conditions and tuning parameters and require expert knowledge to use. On the other hand, gradient-free approaches can be more robust to problem complexities. We present a robust layout optimization approach based on a random search algorithm. The algorithm is intended for those who are not optimization experts and has few tuning parameters that need specification to achieve satisfactory results. Unlike off-the-shelf methods, which use generally available, non-domain-specific optimization routines that accept as inputs an optimization function and constraint definitions, this approach takes advantage of the relative computational costs of the different evaluations by evaluating cheaper computations first (boundary and minimum distance constraints) and running expensive AEP evaluations only if all other checks pass. Moreover, an outer genetic algorithm allows multiple solutions to evolve in parallel, enabling rapid solution development on high-performance computers. We discuss the relative ease of selecting necessary tuning parameters and demonstrate the efficacy of the genetic random search on a complex layout problem consisting of placing 70 turbines in a nonconvex and unconnected boundary region.

17 WIND ENERGY↗

Shedding light on shadow generalized parton distributions

The feasibility of extracting generalized parton distributions (GPDs) from deeply virtual Compton scattering (DVCS) data has recently been questioned because of the existence of an infinite set of so-called “shadow GPDs” (SGPDs). These SGPDs depend on the process and manifest as multiple solutions (at a fixed scale 𝑄 2 ) to the inverse problem that needs to be solved to infer GPDs from DVCS data. SGPDs therefore pose a significant challenge for extracting GPDs from DVCS data. With this motivation we study the extent to which QCD evolution can provide constraints on SGPDs. This is possible because the known classes of SGPDs begin to contribute to observables after evolution, and can then be constrained (at the input scale 𝑄$^{2}_{0}$) by data that has a finite 𝑄 2 range. The impact that SGPDs could have on determining the total angular momentum, pressure and sheer force distributions, and tomography is also discussed. We find that 𝑄 2 evolution, given empirical data over a wide range of skewness (𝜉 ) and 𝑄 2 scales, constrains the SGPDs studied at low 𝑥 and low 𝜉. If this finding generalizes to all SGPDs—and we have not been able to find any SGPDs with qualitatively different behavior—then this potentially makes extraction of GPDs from DVCS possible over a limited range of 𝑥 and 𝜉.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A Cross-Domain Optimization Framework of PMU and Communication Placement for Multidomain Resiliency and Cost Reduction

Phasor measurement units (PMUs) play a crucial role in real-time monitoring and control of power grids. They rely on a communication network to transfer measurement data to the phasor data concentrator (PDC) for further processing and analysis. In this paper, a resilient cross-domain PMU and communication link placement method for minimizing the overall installation cost of the wide-area measurement system (WAMS) is proposed. Here, the main idea is to break down the barrier between the power grid domain and the communication domain, and consider the impact of one when design the other. The PMU placement in the power grid domain takes into account the cost of communication links by generating multiple solutions with equally minimum PMU costs for communication link placement evaluation. On the other hand, the communication link placement problem reduces the cost by customizing the routing policies based on the different roles of PMUs in grid observability. The proposed WAMS design is capable of withstanding any single component failure in the power domain (PMU failure or power branch failure) or in the communication domain (communication link failure or PDC failure). Numerical study on the IEEE 57-bus system reveals that the developed cross-domain optimization framework can significantly reduce the overall installation cost of WAMS while attaining multi-domain resiliency.

24 POWER TRANSMISSION AND DISTRIBUTION↗

nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multifidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius δ goes to zero, and to the fractional Laplacian as δ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We provide theoretical convergence rates with respect to δ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, δ and α, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order α(γ), which is more suitable for modeling turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as δ. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On the Viability of Quantum Annealers to Solve Fluid Flows

This paper explores the suitability of upcoming novel computing technologies, particularly adiabatic annealing based quantum computers, to solve fluid dynamics problems that form a critical component of several science and engineering applications. For our experiments, we start with a well-studied one-dimensional simple flow problem, and provide a framework to convert such problems in continuum to a form amenable for deployment on such quantum annealers. Since the DWave annealer returns multiple states sampling the energy landscape of the problem, we explore multiple solution selection strategies to approximate the solution of the problem. We analyze the continuum solutions obtained both qualitatively and quantitatively as well as their sensitivities to the particular solution selection scheme.

42 ENGINEERING↗

Stability of absorption phenomena in laser-thermal propulsion

The mean flow and stability characteristics of laser absorption phenomena in a choked converging-diverging nozzle are considered. Calculations are presented for a given nozzle geometry and a series of laser intensities. Gas absorptivities corresponding to a hydrogen-cesium mixture are used with different initial temperatures being selected to investigate the effects of changes in the shape of the k-T curve. Both stability and mean flow calculations are limited to the one-dimensional case. The mean flow results show a decrease in mass flow as laser power is increased, along with increasingly steep temperature profiles. Calculations span regions of partial and complete absorption. One region is found where multiple solutions exist. Local stability results indicate the u-c characteristic is the only unstable mode in the unheated case. Laser heat addition makes this mode more unstable and also destabilizes the u-characteristic. Numerical calculations of disturbance propagation show that the instability of the u-c disturbances is counteracted by their reflection to u + c disturbances at the upstream end. The growth of the u-disturbances is localized in regions where the temperature profile is steep and they are damped in other regions. The increasing destabilization that is observed with increased laser power is probably the reason for difficulty in obtaining converged mean flow solutions at high laser intensities.

Merkle, C. L.↗

Squeeze-film dampers for turbomachinery stabilization

A technique for investigating the stability and damping present in centrally preloaded radially symmetric multi-mass flexible rotor bearing systems is presented. In general, one needs to find the eigenvalues of the linearized perturbation equations, though zero frequency stability maps may be found by solving as many simultaneous non-linear equations as there are dampers; and in the case of a single damper, such maps may be found directly, regardless of the number of degrees of freedom. The technique is illustrated for a simple symmetric four degree of freedom flexible rotor with an unpressurized damper. This example shows that whereas zero frequency stability maps are likely to prove to be a simple way to delineate multiple solution possibilities, they do not provide full stability information. Further, particularly for low bearing parameters, the introduction of an unpressurized squeeze film damper may promote instability in an otherwise stable system.

Mclean, L. J.↗

Breakdown of the conservative potential equation

The conservative full-potential equation is used to study transonic flow over five airfoil sections. The results of the study indicate that once shock waves are present in the flow, the qualitative approximation is different from that observed with the Euler equations. The difference in behavior of the potential eventually leads to multiple solutions.

Salas, M. D.↗

Breakdown of the conservative potential equation

The conservative full-potential equation is used to study transonic flow over five airfoil sections. The results of the study indicate that once shock are present in the flow, the qualitative approximation is different from that observed with the Euler equations. The difference in behavior of the potential eventually leads to multiple solutions.

Salas, M. D.↗

Calculation of symmetric and asymmetric vortex seperation on cones and tangent ogives based on discrete vortex models

An inviscid discrete vortex model, with newly derived expressions for the tangential velocity imposed at the separation points, is used to investigate the symmetric and asymmetric vortex separation on cones and tangent ogives. The circumferential locations of separation are taken from experimental data. Based on a slender body theory, the resulting simultaneous nonlinear algebraic equations in a cross-flow plane are solved with Broyden's modified Newton-Raphson method. Total force coefficients are obtained through momentum principle with new expressions for nonconical flow. It is shown through the method of function deflation that multiple solutions exist at large enough angles of attack, even with symmetric separation points. These additional solutions are asymmetric in vortex separation and produce side force coefficients which agree well with data for cones and tangent ogives.

Chin, S.↗

Effect of joint damping and joint nonlinearity on the dynamics of space structures

Analyses of the effect of linear joint characteristics on the vibrations of a free-free, three-joint beam model show that increasing joint damping increases resonant frequencies and increases modal damping but only to the point where the joint gets 'locked up' by damping. This behavior is different from that predicted by modeling joint damping as proportional damping. Nonlinear analyses of the three-joint model with cubic springs at the joints show all the classical single DOF nonlinear response behavior at each resonance of the multiple DOF system: nondoubling of response for a doubling of forcing amplitude, multiple solutions, jump behavior, and resonant frequency shifts. These properties can be concisely quantified by characteristic backbone curves, which show the locus of resonant peaks for increasing forcing amplitude.

Bowden, Mary↗

Warm O(+) polar wind and the DE-1 polar cap electron density profile

Theoretical steady state semikinetic polar wind density profiles, based on DE1/RIMS polar wind data (up to 3700 km), were obtained which agree very well with the power law electron density profile measured by the DE1/PWI for high altitudes. The polar wind is found to be O(+) dominated for the full altitude range considered (up to 8 R(E)). Multiple solutions are obtained for various combinations of base altitude ion temperatures and electron temperatures, such that the densities fit the Persoon et al. (1983) profile. For example, good fits to measured density profile are found for low base ion temperatures (5000 K) and high electron temperatures (9000 K), and also for unheated H(+) and O(+)(3000 K) with electron temperatures of 11,000 K. Below 2.8 R(E) the theoretical polar wind density deviates somewhat from the r exp -3.85 power law. It is concluded that this theoretical polar wind density profile, with a sum of base electron and ion temperatures of 14,000 K, yields a close match with the measured DE-1 electron density profile.

Ho, C. W.↗

Measuring attitude with a gradiometer

This paper explores using a gravity gradiometer to measure the attitude of a satellite, given that the gravity field is accurately known. Since gradiometers actually measure a combination of the gradient and attitude rate and acceleration terms, the answer is far from obvious. The paper demonstrates that it can be done and at microradian accuracy. The technique employed is dynamic estimation, based on the momentum biased Euler equations. The satellite is assumed nominally planet pointed, and subject to control, gravity gradient, and partly radom drag torques. The attitude estimator is unusual. While the standard method of feeding back measurement residuals is used, the feedback gain matrix isn't derived from Kalman theory. instead, it's chosen to minimize a measure of the terminal covariance of the error in the estimate. This depends on the gain matrix and the power spectra of all the process and measurement noises. An integration is required over multiple solutions of Lyapunov equations.

Sonnabend, David↗

Optimal Estimation of Rain-Rate Profiles from Single-Frequency Radar Echoes

The significant ambiguities inherent in the determination of a particular vertical rain intensity profile from a given time profile of radar echo powers measured by a downward-looking (spaceborne or airborne) radar at a single attenuating frequency are well documented. Indeed, one already knows that by appropriately varying the parameters of the reflectivity-rain rate (Z-R) and/or attenuation-rain rate (k- R) relationships one can produce several substantially different rain-rate profiles that would produce the same radar power profile. Imposing the additional constraint that the path-averaged rain rate be a given fixed number does reduce the ambiguities but falls far short of eliminating them. While formulas to generate all mutually ambiguous rain-rate profiles from a given profile of received radar reflectivities have already been derived, there remains to be produced a quantitative measure to assess how likely each of these profiles is, what the appropriate "average" profile should be, and what the "variance" of these multiple solutions is. To do this, one needs to spell out the stochastic constraints that can allow us to make sense of the words "average" and "variance" in a mathematically rigorous way. Such a quantitative approach would be particularly well suited for such systems as the planned precipitation radar of the Tropical Rainfall Measuring Mission (TRMM). Indeed, one would then be able to use the radar reflectivities measured by the TRMM radar to estimate the rain-rate profile that would most likely have produced the measurements, as well as the uncertainty in the estimated rain rates as a function of range. Such an optimal approach is described in this paper.

Haddad, Ziad S.↗

A Possible Bifurcation in Atmospheres of Strongly Irradiated Stars and Planets

We show that under certain circumstances the differences between the absorption mean and Planck mean opacities can lead to multiple solutions for an LTE atmospheric structure. Since the absorption and Planck mean opacities are not expected to differ significantly in the usual case of radiative equilibrium, nonirradiated atmospheres, the most interesting situations in which the effect may play a role are strongly irradiated stars and planets, and also possibly structures in which there is a significant deposition of mechanical energy, such as stellar chromospheres and accretion disks. We have presented an illustrative example of a strongly irradiated giant planet in which the bifurcation effect is predicted to occur for a certain range of distances from the star.

Hubeny, Ivan↗

Post-Stall Aerodynamic Modeling and Gain-Scheduled Control Design

A multidisciplinary research e.ort that combines aerodynamic modeling and gain-scheduled control design for aircraft flight at post-stall conditions is described. The aerodynamic modeling uses a decambering approach for rapid prediction of post-stall aerodynamic characteristics of multiple-wing con.gurations using known section data. The approach is successful in bringing to light multiple solutions at post-stall angles of attack right during the iteration process. The predictions agree fairly well with experimental results from wind tunnel tests. The control research was focused on actuator saturation and .ight transition between low and high angles of attack regions for near- and post-stall aircraft using advanced LPV control techniques. The new control approaches maintain adequate control capability to handle high angle of attack aircraft control with stability and performance guarantee.

Wu, Fen↗

To What Extent Can Raindrop Size Be Determined by a Multiple-Frequency Radar?

In this paper, an analytical treatment of the atmospheric remote sensing problem of determining the raindrop size distribution (DSD) with a spaceborne multifrequency microwave nadir-looking radar system is presented. It is typically assumed that with two radar measurements at different frequencies one ought to be able to calculate two state variables of the DSD: a bulk quantity, such as the rain rate, and a distribution shape parameter. To determine if this nonlinear problem can indeed be solved, the DSD is modeled as a Gamma distribution and quadratic approximations to the corresponding radar-rain relations are used to examine the invertibility of the resulting system of equations in the case of two as well as three radar frequencies. From the investigation, it is found that for regions of DSD state space multiple solutions exist for two or even three different frequency radar measurements. This should not be surprising given the nonlinear coupled nature of the problem.

rain characteristics↗

Design Evolution and Verification of the A-3 Chemical Steam Generator

Following is an overview of the Chemical Steam Generator system selected to provide vacuum conditions for a new altitude test facility, the A-3 Test Stand at Stennis Space Center (SSC) in Bay St. Louis, MS. A-3 will serve as NASA s primary facility for altitude testing of the J-2X rocket engine, to be used as the primary propulsion device for the upper stages of the Ares launch vehicles. The Chemical Steam Generators (CSGs) will produce vacuum conditions in the test cell through the production and subsequent supersonic ejection of steam into a diffuser downstream of the J-2X engine nozzle exit. The Chemical Steam Generators chosen have a rich heritage of operation at rocket engine altitude test facilities since the days of the Apollo program and are still in use at NASA White Sands Test Facility (WSTF) in New Mexico. The generators at WSTF have been modified to a degree, but are still very close to the heritage design. The intent for the A-3 implementation is to maintain this heritage design as much as possible, making minimal updates only where necessary to substitute for obsolete parts and to increase reliability. Reliability improvements are especially desired because the proposed system will require 27 generators, which is nine times the largest system installed in the 1960s. Improvements were suggested by the original design firm, Reaction Motors, by NASA SSC and NASA WSTF engineers, and by the A-3 test stand design contractor, Jacobs Technology, Inc. (JTI). This paper describes the range of improvements made to the design to date, starting with the heritage generator and the minor modifications made over time at WSTF, to the modernized configuration which will be used at A-3. The paper will discuss NASA s investment in modifications to SSC s E-2 test facility fire a full-scale Chemical Steam Generator in advance of the larger steam system installation at A-3. Risk mitigation testing will be performed in early 2009 at this test facility to verify that the CSGs operate as expected. The generator which will undergo this testing is of the most recent A-3 configuration, and will be instrumented far in excess of what is normally required for operation. The extra data will allow for easier troubleshooting and more complete knowledge of expected generator performance. In addition, the early testing will give SSC personnel experience in operating the CSG systems, which will expedite the process of installation and activation at A-3. Each Chemical Steam Generator is supported by a complement of valves, instruments, and flow control devices, with the entire assembly called a "module." The generators will be installed in groups of three, historically called "units". A module is so called because of its modular ability to be replaced or serviced without disturbing the other two modules installed on the same unit. A module is pictured in Figure 1, shown with its generator secured by white bands in its shipping (vs. installed) configuration. The heritage system at WSTF is composed of a single unit (three generator modules), pictured in Figure 2 as it was installed in 1965. In contrast, A-3 will have nine units operating in parallel to achieve vacuum conditions appropriate for testing the J-2X engine. Each of the combustors operates in two modes and achieves the so-called "full-steam" mode after all three of its stages ignite. Ignition of the first stage is achieved by exciting a spark plug; the second stage and main stage are lit by the flame front of the previous stage. The main stage burns approximately 97% of the total propellant flow and uses the heat energy to vaporize water into superheated steam. While the main stage remains unlit, the combustor is in so-called "idle" mode. In the WSTF system, this idle mode is not optimized for water usage, and does not need to be, as the water is pumped from a large reservoir. The water supply at A-3 will be contained in tanks with finite volume, so water optimization is preferred for the modnized configuration. Multiple solutions for this issue have been proposed, with the leading concept being a change to the operational definition of "idle mode," with the generator running in a lower heat flux condition.

Kirchner, Casey K.↗