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At least 1,171 records · Page 65

Quaternion Averaging

Many applications require an algorithm that averages quaternions in an optimal manner. For example, when combining the quaternion outputs of multiple star trackers having this output capability, it is desirable to properly average the quaternions without recomputing the attitude from the the raw star tracker data. Other applications requiring some sort of optimal quaternion averaging include particle filtering and multiple-model adaptive estimation, where weighted quaternions are used to determine the quaternion estimate. For spacecraft attitude estimation applications, derives an optimal averaging scheme to compute the average of a set of weighted attitude matrices using the singular value decomposition method. Focusing on a 4-dimensional quaternion Gaussian distribution on the unit hypersphere, provides an approach to computing the average quaternion by minimizing a quaternion cost function that is equivalent to the attitude matrix cost function Motivated by and extending its results, this Note derives an algorithm that deterniines an optimal average quaternion from a set of scalar- or matrix-weighted quaternions. Rirthermore, a sufficient condition for the uniqueness of the average quaternion, and the equivalence of the mininiization problem, stated herein, to maximum likelihood estimation, are shown.

Markley, F. Landis↗

Spatiotemporal Interpolation of Elevation Changes Derived from Satellite Altimetry for Jakobshavn Isbrae, Greenland

Estimation of ice sheet mass balance from satellite altimetry requires interpolation of point-scale elevation change (dHdt) data over the area of interest. The largest dHdt values occur over narrow, fast-flowing outlet glaciers, where data coverage of current satellite altimetry is poorest. In those areas, straightforward interpolation of data is unlikely to reflect the true patterns of dHdt. Here, four interpolation methods are compared and evaluated over Jakobshavn Isbr, an outlet glacier for which widespread airborne validation data are available from NASAs Airborne Topographic Mapper (ATM). The four methods are ordinary kriging (OK), kriging with external drift (KED), where the spatial pattern of surface velocity is used as a proxy for that of dHdt, and their spatiotemporal equivalents (ST-OK and ST-KED).

Jakobshavn Isbrae↗

Estimating Evaporative Fraction From Readily Obtainable Variables in Mangrove Forests of the Everglades, U.S.A.

A remote-sensing-based model to estimate evaporative fraction (EF) the ratio of latent heat (LE; energy equivalent of evapotranspiration -ET-) to total available energy from easily obtainable remotely-sensed and meteorological parameters is presented. This research specifically addresses the shortcomings of existing ET retrieval methods such as calibration requirements of extensive accurate in situ micro-meteorological and flux tower observations, or of a large set of coarse-resolution or model-derived input datasets. The trapezoid model is capable of generating spatially varying EF maps from standard products such as land surface temperature [T(sub s)] normalized difference vegetation index (NDVI)and daily maximum air temperature [T(sub a)]. The 2009 model results were validated at an eddy-covariance tower (Fluxnet ID: US-Skr) in the Everglades using T(sub s) and NDVI products from Landsat as well as the Moderate Resolution Imaging Spectroradiometer (MODIS) sensors. Results indicate that the model accuracy is within the range of instrument uncertainty, and is dependent on the spatial resolution and selection of end-members (i.e. wet/dry edge). The most accurate results were achieved with the T(sub s) from Landsat relative to the T(sub s) from the MODIS flown on the Terra and Aqua platforms due to the fine spatial resolution of Landsat (30 m). The bias, mean absolute percentage error and root mean square percentage error were as low as 2.9% (3.0%), 9.8% (13.3%), and 12.1% (16.1%) for Landsat-based (MODIS-based) EF estimates, respectively. Overall, this methodology shows promise for bridging the gap between temporally limited ET estimates at Landsat scales and more complex and difficult to constrain global ET remote-sensing models.

trapezoid↗

Pterodactyl: Thermal Protection System for Integrated Control Design of a Mechanically Deployed Entry Vehicle

The need for precision landing of high mass payloads on Mars and the return of sensitive samples from other planetary bodies to specific locations on Earth is driving the development of an innovative NASA technology referred to as the Deployable Entry Vehicle (DEV). A DEV has the potential to deliver an equivalent science payload with a stowed diameter 3 to 4 times smaller than a traditional rigid capsule configuration. However, the DEV design does not easily lend itself to traditional methods of directional control. The NASA Space Technology Mission Directorate (STMD)’s Pterodactyl project is currently investigating the effectiveness of three different Guidance and Control (G&C) systems – actuated flaps, Center of Gravity (CG) or mass movement, and Reaction Control System (RCS) – for use with a DEV using the Adaptable, Deployable, Entry, and Placement Technology (ADEPT) design. This paper details the Thermal Protection System (TPS) design and associated mass estimation efforts for each of the G&C systems. TPS is needed for the nose cap of the DEV and the flaps of the actuated flap control system. The development of a TPS selection, sizing, and mass estimation method designed to deal with the varying requirements for the G&C options throughout the trajectory is presented. The paper discusses the methods used to i) obtain heating environments throughout the trajectory with respect to the chosen control system and resulting geometry; ii) determine a suitable TPS material; iii) produce TPS thickness estimations; and, iv) determine the final TPS mass estimation based on TPS thickness, vehicle control system, vehicle structure, and vehicle payload.

Hays, Zane B.↗

Development Towards Stable Chlorine Isotope Measurements of Astromaterials Using the Modified Middleton Source of an Accelerator Mass Spectrometer

The volatile element Cl can be lost during the formation and evolution of planetary bodies, leading to fractionation of its two stable isotopes 35Cl and 37Cl. Chlorine isotope variations (reported as δ37Cl in parts per thousand (‰) relative to Standard Mean Ocean Chloride, SMOC) are documented to exceed 80‰ between different lunar rock samples and have been variably interpreted as the fingerprint of degassing during accretion, magma ocean, or volcanic portions of lunar history. The large intersample and intrasample variations observed by both bulk isotope ratio mass spectrometry (IRMS) and in-situ secondary ion mass spectrometry (SIMS) methods are difficult to interpret in part because of a paucity of bulk Cl isotope measurements. This lack of high-precision bulk data is due to the relative rarity of IRMS laboratories capable of making these high precision measurements on small samples of precious planetary materials such as those returned by human or robotic exploration. Here we present a new method for performing high precision δ37Cl measurements using the modified Middleton ion source of an existing accelerator mass spectrometer. For samples with as little as 1 μg Cl–the equivalent of 2–4 mm3 of a typical lunar rock sample–the average cathode accuracy is ∼1‰. Cathode reproducibility is typically ∼1‰ (2σ) for samples with at least 10 μg of Cl, increasing to ∼3–6‰ for aliquots with ∼1–2 μg Cl, similar to published SIMS results and sufficient to study astromaterials from the Moon, Mars, or 4 Vesta, which have tens of ‰ observed variations.

Tyler S. Anderson↗

Pseudospectral collocation methods for fourth order differential equations

Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.

Malek, Alaeddin↗

Spherical-earth Gravity and Magnetic Anomaly Modeling by Gauss-legendre Quadrature Integration

The usefulness of long-wavelength potential field anomalies in lithospheric interpretation is greatly increased with spherical Earth modeling techniques. Gauss-Legendre quadrature integration is used to calculate the anomalous potential of gravity and magnetic fields and their spatial derivatives on a spherical Earth for an arbitrary body represented by an equivalent point source distribution of gravity poles or magnetic dipoles. The distribution of equivalent point sources is determined directly from the coordinate limits of the source volume. Variable integration limits for an arbitrarily shaped body are derived from interpolation of points which approximate the body's surface envelope. The versatility of the method is enhanced by the ability to treat physical property variations within the source volume and to consider variable magnetic fields over the source and observation surface. A number of examples verify and illustrate the capabilities of the technique, including preliminary modeling of potential field signatures for Mississippi embayment crustal structure at satellite elevations.

Spherical coordinate gravity modeling↗

Orthogonality broadcasting and quantum position verification

The no-cloning theorem leads to information-theoretic security in various quantum cryptographic protocols. However, this security typically derives from a possibly weaker property that classical information encoded in certain quantum states cannot be broadcast. To formally capture this property, we introduce the study of ‘orthogonality broadcasting.’ When attempting to broadcast the orthogonality of two different qubit bases, we establish that the power of classical and quantum communication is equivalent. However, quantum communication is shown to be strictly more powerful for broadcasting orthogonality in higher dimensions. We then relate orthogonality broadcasting to quantum position verification and provide a new method for establishing error bounds in the no pre-shared entanglement model that can address protocols previous methods could not. Our key technical contribution is an uncertainty relation that uses the geometric relation of the states that undergo broadcasting rather than the non-commutative aspect of the final measurements.

quantum cryptography↗

A digital twin based on OpenFAST linearizations for real-time load and fatigue estimation of land-based turbines

Monitoring a wind turbine requires intensive instrumentation, which would be too cost-prohibitive to deploy to an entire wind plant. This work presents a technique that uses readily available measurements to estimate signals that would otherwise require additional instrumentation. This study presents a digital twin concept with a focus on estimating wind speed, thrust, torque, tower-top position, and loads in the tower using supervisory control and data acquisition (SCADA) measurements. The model combines a linear state-space model obtained using OpenFAST linearizations, a wind speed estimator, and a Kalman filter algorithm that integrates measurements with the state model to perform state estimations. The measurements are: top acceleration, generator torque, pitch, and rotational speed. The article extends previous work that derived the linear state-space model using a different method. The new implementation, based on OpenFAST linearization capability, allows for a systematic extension of the method to more states, inputs, outputs, and to the offshore environment. Results from the two methods are compared, and the validation is made with additional measurements using the GE 1.5-MW turbine located at the National Renewable Energy Laboratory test site. Real-time damage equivalent loads of the tower bottom moment are estimated with an average accuracy of approximately 10%. Overall, the results from this proof of concept are encouraging, and further application of the model will be considered.

17 WIND ENERGY↗

Lifetime fatigue response due to wake steering on a pair of utility-scale wind turbines

Quantifying the impacts on turbine loads during wind farm control is an important consideration in assessing power production benefits. Wake steering controls aim to improve total wind farm performance by coordinating the control actions of individual turbines, wherein an upstream turbine is intentionally yawed at an offset angle from the measured wind direction. Consequently, this redirects its wake for improved power production and potentially reduces fatigue loads of the downstream turbines. This paper studies the lifetime fatigue loads associated with wake steering by using utility-scale wind turbine experimental data to conduct an analysis on a pair of wind turbines. This study was part of a large field experiment in which a group of five GE 1.5-MW SLE CWE turbines were selected as targets for conducting wake steering research. A standard loads instrumentation package and data acquisition system were installed on two turbines within the cluster to measure turbine fundamental loads. The time-series databases were used to calculate loads statistics as well as short-term and lifetime damage equivalent loads. Fatigue calculations followed the guidance in Annex H of the International Electrotechnical Commission standard 61400-1, Edition 4. Lifetime fatigue calculation results are presented in this analysis; three methods of assessing lifetime fatigue were used to determine percent difference for blade root moments, main shaft moments, main shaft torque, and tower top torque. For all three fatigue treatments, some components’ lifetime fatigue increases for the controlled turbine; however, the downwind turbine experienced a reduction in lifetime fatigue and combined effect for the turbine pair results in a reduction of fatigue when wake steering controls are applied.

17 WIND ENERGY↗

Quantifying Uncertainty in Tortuosity Estimates for Porous Electrodes

Measuring tortuosity in porous electrodes is important for understanding rate capability and optimizing design. Here, we describe an approach to determine electrode tortuosities and quantify the associated uncertainties by fitting a P2D model to discharge profiles from a standard rate capability test. A dimensionless current is identified as a design-of-experiment parameter that can be used to identify experiments that return confident estimates of tortuosity, even when other model parameters are not known with certainty. This approach is applied to analysis of L i x V 3 O 8 (LVO) electrodes and L i x N i 0.33 M n 0.33 C o 0.33 O 2 (NMC) electrodes. The details of the assumptions made in these measurements and their impact on the reported uncertainties are discussed. We also perform an uncertainty analysis on the standard method for quantifying tortuosity in the literature: electrochemical impedance spectroscopy collected under blocking electrolyte conditions. We find that confident estimates can be obtained using this approach even when uncertainties in equivalent circuit model parameters are considered.

25 ENERGY STORAGE↗

Maximum likelihood method for estimating airplane stability and control parameters from flight data in frequency domain

A frequency domain maximum likelihood method is developed for the estimation of airplane stability and control parameters from measured data. The model of an airplane is represented by a discrete-type steady state Kalman filter with time variables replaced by their Fourier series expansions. The likelihood function of innovations is formulated, and by its maximization with respect to unknown parameters the estimation algorithm is obtained. This algorithm is then simplified to the output error estimation method with the data in the form of transformed time histories, frequency response curves, or spectral and cross-spectral densities. The development is followed by a discussion on the equivalence of the cost function in the time and frequency domains, and on advantages and disadvantages of the frequency domain approach. The algorithm developed is applied in four examples to the estimation of longitudinal parameters of a general aviation airplane using computer generated and measured data in turbulent and still air. The cost functions in the time and frequency domains are shown to be equivalent; therefore, both approaches are complementary and not contradictory. Despite some computational advantages of parameter estimation in the frequency domain, this approach is limited to linear equations of motion with constant coefficients.

Klein, V.↗

Complete solution of Boolean equations

A method is presented for generating a single formula involving arbitary Boolean parameters, which includes in it each and every possible solution of a system of Boolean equations. An alternate condition equivalent to a known necessary and sufficient condition for solving a system of Boolean equations is given.

Tapia, M. A.↗

An efficient method for computing the absorption of solar radiation by water vapor

Chou and Arking (1980) have developed a fast but accurate method for computing the IR cooling rate due to water vapor. Using a similar approach, the considered investigation develops a method for computing the heating rates due to the absorption of solar radiation by water vapor in the wavelength range from 4 to 8.3 micrometers. The validity of the method is verified by comparison with line-by-line calculations. An outline is provided of an efficient method for transmittance and flux computations based upon actual line parameters. High speed is achieved by employing a one-parameter scaling approximation to convert an inhomogeneous path into an equivalent homogeneous path at suitably chosen reference conditions.

Chou, M.-D.↗

Radiometric performance of the test-bed aircraft multispectral scanner /TBAMS/ system

Laboratory and flight radiometric performance testing of an experimental multispectral scanner system is described. High sensitivity performance is confirmed by test results using noise equivalent spectral radiance as the primary figure of merit. A performance comparison between the test-bed aircraft multispectral scanner (TBAMS) and the Bendix modular multispectral scanner (M2S) is presented. Methods for achieving high sensitivity operation are discussed as well as some of the practical implications of such operation for flight remote sensing experiments.

Jobson, D. J.↗

Multilevel optimum design of structures with fiber-composite stiffened-panel components

The multilevel approach to minimum weight structural design is extended to wing box structures with fiber-composite stiffened-panel components. Strength, deflection, and panel buckling constraints are treated at the system level with equivalent-thickness-type design variables. Local buckling and panel buckling constraints are guarded against at the component level, employing detailed component dimensions as design variables. A key feature of the method is selection of change in stiffness as the component level objective function to be minimized. Numerical results are given for wing box structures with sandwich and hat-stiffened fiber-composite panels.

Schmit, L. A.↗

Approaches to optimization of SS/TDMA time slot assignment

Reduction techniques for traffic matrices are explored in some detail. These matrices arise in satellite switched time-division multiple access (SS/TDMA) techniques whereby switching of uplink and downlink beams is required to facilitate interconnectivity of beam zones. A traffic matrix is given to represent that traffic to be transmitted from n uplink beams to n downlink beams within a TDMA frame typically of 1 ms duration. The frame is divided into segments of time and during each segment a portion of the traffic is represented by a switching mode. This time slot assignment is characterized by a mode matrix in which there is not more than a single non-zero entry on each line (row or column) of the matrix. Investigation is confined to decomposition of an n x n traffic matrix by mode matrices with a requirement that the decomposition be 100 percent efficient or, equivalently, that the line(s) in the original traffic matrix whose sum is maximal (called critical line(s)) remain maximal as mode matrices are subtracted throughout the decomposition process. A method of decomposition of an n x n traffic matrix by mode matrices results in a number of steps that is bounded by n(2) - 2n + 2. It is shown that this upper bound exists for an n x n matrix wherein all the lines are maximal (called a quasi doubly stochastic (QDS) matrix) or for an n x n matrix that is completely arbitrary. That is, the fact that no method can exist with a lower upper bound is shown for both QDS and arbitrary matrices, in an elementary and straightforward manner.

Wade, T. O.↗

Rare isotope studies involving catalytic oxidation of CO over platinum-tin oxide

Results of studies utilizing normal and rare oxygen isotopes in the catalytic oxidation of carbon monoxide over a platinum-tin oxide catalyst substrate are presented. Chemisorption of labeled carbon monoxide on the catalyst followed by thermal desorption yielded a carbon dioxide product with an oxygen-18 composition consistent with the formation of a carbonate-like intermediate in the chemisorption process. The efficacy of a method developed for the oxygen-18 labeling of the platinum-tin oxide catalyst surface for use in closed cycle pulsed care isotope carbon dioxide lasers is demonstrated for the equivalent of 10 to the 6th power pulses at 10 pulses per second.

Upchurch, Billy T.↗