SEARCH · Search NASA

Results for “collocation”

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.

SourceResearch connectionFrom yearThrough year

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

At least 163 records · Page 9

All sources NASA NTRS DOE OSTI

NASA NTRS1990

Numerical methods for hypersonic boundary layer stability

Four different schemes for solving compressible boundary layer stability equations are developed and compared, considering both the temporal and spatial stability for a global eigenvalue spectrum and a local eigenvalue search. The discretizations considered encompass: (1) a second-order-staggered finite-difference scheme; (2) a fourth-order accurate, two-point compact scheme; (3) a single-domain Chebychev spectral collocation scheme; and (4) a multidomain spectral collocation scheme. As Mach number increases, the performance of the single-domain collocation scheme deteriorates due to the outward movement of the critical layer; a multidomain spectral method is accordingly designed to furnish superior resolution of the critical layer.

Malik, M. R.↗

NASA NTRS1991

Geoid undulations and gravity anomalies over the Aral Sea, the Black Sea and the Caspian Sea from a combined GEOS-3/SEASAT/GEOSAT altimeter data set

Satellite-based altimetric data taken by GOES-3, SEASAT, and GEOSAT over the Aral Sea, the Black Sea, and the Caspian Sea are analyzed and a least squares collocation technique is used to predict the geoid undulations on a 0.25x0.25 deg. grid and to transform these geoid undulations to free air gravity anomalies. Rapp's 180x180 geopotential model is used as the reference surface for the collocation procedure. The result of geoid to gravity transformation is, however, sensitive to the information content of the reference geopotential model used. For example, considerable detailed surface gravity data were incorporated into the reference model over the Black Sea, resulting in a reference model with significant information content at short wavelengths. Thus, estimation of short wavelength gravity anomalies from gridded geoid heights is generally reliable over regions such as the Black Sea, using the conventional collocation technique with local empirical covariance functions. Over regions such as the Caspian Sea, where detailed surface data are generally not incorporated into the reference model, unconventional techniques are needed to obtain reliable gravity anomalies. Based on the predicted gravity anomalies over these inland seas, speculative tectonic structures are identified and geophysical processes are inferred.

Au, Andrew Y.↗

NASA NTRS1991

Analysis of altimetry over the Aral Sea

Satellite based altimetric data taken by GEOS-3, SEASAT, and GEOSAT over the Aral Sea are analyzed and a least squares collocation technique is used to predict the geoid undulations on a 0.25 by 0.25 degree grid and to transform these geoid undulations to free air gravity anomalies. Rapp's 180 by 180 geopotential model is taken as the empirical model. The collocation procedure is performed with a set of local residual empirical covariance functions. For comparison, Rapp's global covariance functions and Jordan's self-consistent theoretical covariance functions based on Jordan's formulation and on locally derived parameters are also used to grid geoid undulations and to predict gravity anomalies. The sensitivity of the collocation results to the choice of covariance functions is discussed.

Au, Andrew Y.↗

NASA NTRS1993

Atmospheric moisture fields derived by satellite observations over the tropical Pacific Ocean

Values of precipitable water are retrieved over the tropical and subtropical Pacific Ocean from TOVS infrared and microwave channel brightness temperature and OLR observations by means of stepwise linear regression. The most useful temperature and moisture sensing channels are pre-selected from sensitivity tests of a radiative transfer model. Numerous models are developed and tested against collocated radiosonde observations and Nimbus-7 SMMR precipitable water estimates. For RAOB comparisons, the best estimator used 15 TOVS predictors and captured 71.1 deg percent of the variance (+0.62 g/sq cm standard error) for column precipitable water; for precipitable water of 700-500 mb bulk layer, these values were 71.7 percent and +/- 0.17 g/sq cm. Little skill of estimated precipitable water was obtained for moisture above 500 mb. Regressions were less skillful against SMMR, unless collocation parameters were tightly controlled; SMMR was less acceptable than RAOB's because of observational drift and errors. Generally, the most skillful predictors were boundary layer brightness temperatures of TOVS channels and satellite estimated stability indices. 'Moisture channels' were hardly useful except for estimating middle and upper tropospheric moisture. Additional regression models were constructed testing the sensitivity to different observational and meteorological characteristics. Models which used some in situ observations surface observations or stabilities calculated from RAOB, were the most successful. The best of these explained 87.5 percent of the variance but the regression selected almost no TOVS channels, relying instead on conventional RAOB and surface observations. A set of four regression models were developed, stratifying atmospheric characteristics on the basis of collocated OLR values. These models improved the variance explained by 5.0 percent; the model associated with the highest OLR values (275 W/sq m less than or equal to OLR; that is, no cloud) showed only marginal skill. Precipitable water fields were generated from the best TOVS-only model for seven days in January 1983 and compared with SMMR-estimated fields. OLR fields and ECMWF precipitable water analysis. The TOVS regression model compared favorably to the SMMR analysis in amplitudes and features. It revealed more evolving synoptic signal than the ECMWF analysis. In synoptically active regions, it differed with respect to the OLR analysis, primarily because of actual differences in the vertical distribution of water vapor.

Chung, Hyosang↗

NASA NTRS1995

Optimal guidance law development for an advanced launch system

The objective of this research effort was to develop a real-time guidance approach for launch vehicles ascent to orbit injection. Various analytical approaches combined with a variety of model order and model complexity reduction have been investigated. Singular perturbation methods were first attempted and found to be unsatisfactory. The second approach based on regular perturbation analysis was subsequently investigated. It also fails because the aerodynamic effects (ignored in the zero order solution) are too large to be treated as perturbations. Therefore, the study demonstrates that perturbation methods alone (both regular and singular perturbations) are inadequate for use in developing a guidance algorithm for the atmospheric flight phase of a launch vehicle. During a second phase of the research effort, a hybrid analytic/numerical approach was developed and evaluated. The approach combines the numerical methods of collocation and the analytical method of regular perturbations. The concept of choosing intelligent interpolating functions is also introduced. Regular perturbation analysis allows the use of a crude representation for the collocation solution, and intelligent interpolating functions further reduce the number of elements without sacrificing the approximation accuracy. As a result, the combined method forms a powerful tool for solving real-time optimal control problems. Details of the approach are illustrated in a fourth order nonlinear example. The hybrid approach is then applied to the launch vehicle problem. The collocation solution is derived from a bilinear tangent steering law, and results in a guidance solution for the entire flight regime that includes both atmospheric and exoatmospheric flight phases.

Calise, Anthony J.↗

NASA NTRS2001

The Vertical Error Characteristics of GOES-derived Winds: Description and Impact on Numerical Weather Prediction

Errors in the height assignment of some satellite-derived winds exist because the satellites sense radiation emitted from a finite layer of the atmosphere rather than a specific level. Potential problems in data assimilation may arise because the motion of a measured layer is often represented by a single-level value. In this research, cloud and water vapor motion winds that are derived from the Geostationary Operational Environmental Satellites (GOES winds) are compared to collocated rawinsonde observations (RAOBs). An important aspect of this work is that in addition to comparisons at each assigned height, the GOES winds are compared to the entire profile of the collocated RAOB data to determine the vertical error characteristics of the GOES winds. The impact of these results on numerical weather prediction is then investigated. The comparisons at individual vector height assignments indicate that the error of the GOES winds range from approx. 3 to 10 m/s and generally increase with height. However, if taken as a percentage of the total wind speed, accuracy is better at upper levels. As expected, comparisons with the entire profile of the collocated RAOBs indicate that clear-air water vapor winds represent deeper layers than do either infrared or water vapor cloud-tracked winds. This is because in cloud-free regions the signal from water vapor features may result from emittance over a thicker layer. To further investigate characteristics of the clear-air water vapor winds, they are stratified into two categories that are dependent on the depth of the layer represented by the vector. It is found that if the vertical gradient of moisture is smooth and uniform from near the height assignment upwards, the clear-air water vapor wind tends to represent a relatively deep layer. The information from the comparisons is then used in numerical model simulations of two separate events to determine the forecast impacts. Four simulations are performed for each case: 1) A control simulation that assimilates no satellite wind data, 2) assimilation of all GOES winds according to their assigned single level height, 3) assimilation of all GOES winds spread over multiple levels, and 4) assimilation of all GOES winds spread over multiple levels, but with variations in the vertical influence of clear-air water vapor winds based on the moisture profile in the model. In the first case, a strong mid-latitude cyclone is present and the use of the satellite data results in improved storm tracks during the initial approx. 36 h forecast period. This is because the satellite data improves the analysis of the environment into which the storm progresses. Statistics for mean wind vector and height differences show that, with the exception of the height field at later times in the first case, the use of GOES winds improves the simulation with time. The simulation results suggest that it is beneficial to spread the GOES wind information over multiple levels, particularly when the moisture profile is used to define the vertical influence.

Rao, P. Anil↗

NASA NTRS2003

Uncertainty Propagation for Turbulent, Compressible Flow in a Quasi-1D Nozzle Using Stochastic Methods

This paper describes a fully spectral, Polynomial Chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow, as well as a novel stochastic collocation algorithm for the same application. The stochastic collocation method is key to the efficient use of stochastic methods on problems with complex nonlinearities, such as those associated with the turbulence model equations in compressible flow and for CFD schemes requiring solution of a Riemann problem. Both methods are applied to compressible flow in a quasi-one-dimensional nozzle. The stochastic collocation method is roughly an order of magnitude faster than the fully Galerkin Polynomial Chaos method on the inviscid problem.

Zang, Thomas A.↗

NASA NTRS2005

Computation of Sound Propagation by Boundary Element Method

This report documents the development of a Boundary Element Method (BEM) code for the computation of sound propagation in uniform mean flows. The basic formulation and implementation follow the standard BEM methodology; the convective wave equation and the boundary conditions on the surfaces of the bodies in the flow are formulated into an integral equation and the method of collocation is used to discretize this equation into a matrix equation to be solved numerically. New features discussed here include the formulation of the additional terms due to the effects of the mean flow and the treatment of the numerical singularities in the implementation by the method of collocation. The effects of mean flows introduce terms in the integral equation that contain the gradients of the unknown, which is undesirable if the gradients are treated as additional unknowns, greatly increasing the sizes of the matrix equation, or if numerical differentiation is used to approximate the gradients, introducing numerical error in the computation. It is shown that these terms can be reformulated in terms of the unknown itself, making the integral equation very similar to the case without mean flows and simple for numerical implementation. To avoid asymptotic analysis in the treatment of numerical singularities in the method of collocation, as is conventionally done, we perform the surface integrations in the integral equation by using sub-triangles so that the field point never coincide with the evaluation points on the surfaces. This simplifies the formulation and greatly facilitates the implementation. To validate the method and the code, three canonic problems are studied. They are respectively the sound scattering by a sphere, the sound reflection by a plate in uniform mean flows and the sound propagation over a hump of irregular shape in uniform flows. The first two have analytical solutions and the third is solved by the method of Computational Aeroacoustics (CAA), all of which are used to compare the BEM solutions. The comparisons show very good agreements and validate the accuracy of the BEM approach implemented here.

Guo, Yueping↗

NASA NTRS2011

Fast Simulators for Satellite Cloud Optical Centroid Pressure Retrievals, 1. Evaluation of OMI Cloud Retrievals

We have developed a relatively simple scheme for simulating retrieved cloud optical centroid pressures (OCP) from satellite solar backscatter observations. We have compared simulator results with those from more detailed retrieval simulators that more fully account for the complex radiative transfer in a cloudy atmosphere. We used this fast simulator to conduct a comprehensive evaluation of cloud OCPs from the two OMI algorithms using collocated data from CloudSat and Aqua MODIS, a unique situation afforded by the A-train formation of satellites. We find that both OMI algorithms perform reasonably well and that the two algorithms agree better with each other than either does with the collocated CloudSat data. This indicates that patchy snow/ice, cloud 3D, and aerosol effects not simulated with the CloudSat data are affecting both algorithms similarly. We note that the collocation with CloudSat occurs mainly on the East side of OMI's swath. Therefore, we are not able to address cross-track biases in OMI cloud OCP retrievals. Our fast simulator may also be used to simulate cloud OCP from output generated by general circulation models (GCM) with appropriate account of cloud overlap. We have implemented such a scheme and plan to compare OMI data with GCM output in the near future.

Joiner, J.↗

NASA NTRS2013

High resolution wind measurements for offshore wind energy development

A method, apparatus, system, article of manufacture, and computer readable storage medium provide the ability to measure wind. Data at a first resolution (i.e., low resolution data) is collected by a satellite scatterometer. Thin slices of the data are determined. A collocation of the data slices are determined at each grid cell center to obtain ensembles of collocated data slices. Each ensemble of collocated data slices is decomposed into a mean part and a fluctuating part. The data is reconstructed at a second resolution from the mean part and a residue of the fluctuating part. A wind measurement is determined from the data at the second resolution using a wind model function. A description of the wind measurement is output.

Nghiem, Son Van↗

NASA NTRS2013

Coherent Uncertainty Analysis of Aerosol Measurements from Multiple Satellite Sensors

Aerosol retrievals from multiple spaceborne sensors, including MODIS (on Terra and Aqua), MISR, OMI, POLDER, CALIOP, and SeaWiFS altogether, a total of 11 different aerosol products were comparatively analyzed using data collocated with ground-based aerosol observations from the Aerosol Robotic Network (AERONET) stations within the Multi-sensor Aerosol Products Sampling System (MAPSS, http://giovanni.gsfc.nasa.gov/mapss/ and http://giovanni.gsfc.nasa.gov/aerostat/). The analysis was performed by comparing quality-screened satellite aerosol optical depth or thickness (AOD or AOT) retrievals during 2006-2010 to available collocated AERONET measurements globally, regionally, and seasonally, and deriving a number of statistical measures of accuracy. We used a robust statistical approach to detect and remove possible outliers in the collocated data that can bias the results of the analysis. Overall, the proportion of outliers in each of the quality-screened AOD products was within 12%. Squared correlation coefficient (R2) values of the satellite AOD retrievals relative to AERONET exceeded 0.6, with R2 for most of the products exceeding 0.7 over land and 0.8 over ocean. Root mean square error (RMSE) values for most of the AOD products were within 0.15 over land and 0.09 over ocean. We have been able to generate global maps showing regions where the different products present advantages over the others, as well as the relative performance of each product over different landcover types. It was observed that while MODIS, MISR, and SeaWiFS provide accurate retrievals over most of the landcover types, multi-angle capabilities make MISR the only sensor to retrieve reliable AOD over barren and snow / ice surfaces. Likewise, active sensing enables CALIOP to retrieve aerosol properties over bright-surface shrublands more accurately than the other sensors, while POLDER, which is the only one of the sensors capable of measuring polarized aerosols, outperforms other sensors in certain smoke-dominated regions, including broadleaf evergreens in Brazil and South-East Asia.

remote sensing↗

NASA NTRS2013

Integrated High-Speed Torque Control System for a Robotic Joint

A control system for achieving high-speed torque for a joint of a robot includes a printed circuit board assembly (PCBA) having a collocated joint processor and high-speed communication bus. The PCBA may also include a power inverter module (PIM) and local sensor conditioning electronics (SCE) for processing sensor data from one or more motor position sensors. Torque control of a motor of the joint is provided via the PCBA as a high-speed torque loop. Each joint processor may be embedded within or collocated with the robotic joint being controlled. Collocation of the joint processor, PIM, and high-speed bus may increase noise immunity of the control system, and the localized processing of sensor data from the joint motor at the joint level may minimize bus cabling to and from each control node. The joint processor may include a field programmable gate array (FPGA).

Davis, Donald R.↗

NASA NTRS2016

Parallel Aircraft Trajectory Optimization with Analytic Derivatives

Trajectory optimization is an integral component for the design of aerospace vehicles, but emerging aircraft technologies have introduced new demands on trajectory analysis that current tools are not well suited to address. Designing aircraft with technologies such as hybrid electric propulsion and morphing wings requires consideration of the operational behavior as well as the physical design characteristics of the aircraft. The addition of operational variables can dramatically increase the number of design variables which motivates the use of gradient based optimization with analytic derivatives to solve the larger optimization problems. In this work we develop an aircraft trajectory analysis tool using a Legendre-Gauss-Lobatto based collocation scheme, providing analytic derivatives via the OpenMDAO multidisciplinary optimization framework. This collocation method uses an implicit time integration scheme that provides a high degree of sparsity and thus several potential options for parallelization. The performance of the new implementation was investigated via a series of single and multi-trajectory optimizations using a combination of parallel computing and constraint aggregation. The computational performance results show that in order to take full advantage of the sparsity in the problem it is vital to parallelize both the non-linear analysis evaluations and the derivative computations themselves. The constraint aggregation results showed a significant numerical challenge due to difficulty in achieving tight convergence tolerances. Overall, the results demonstrate the value of applying analytic derivatives to trajectory optimization problems and lay the foundation for future application of this collocation based method to the design of aircraft with where operational scheduling of technologies is key to achieving good performance.

aircraft↗

NASA NTRS2017

Implicit Formulation of Muscle Dynamics in OpenSim

Astronauts lose bone and muscle mass during spaceflight. Exercise countermeasure is the primary method for counteracting bone and muscle mass loss in space. New spacecraft exercise device concepts are currently being developed for the NASAs new crew exploration vehicle. The NASA Digital Astronaut Project (DAP) uses computational modeling to help determine if the new exercise devices will be effective as countermeasures. The NASA Digital Astronaut Project is developing the ability to utilize predictive simulation to provide insight into the change in kinematics and kinetics with a change in device and gravitational environment (1-g versus 0-g). For example, in space exercise the subject's body weight is applied in addition to the loads prescribed for musculoskeletal maintenance. How and where these loads are applied obviously directly impacts bone and tissue loads. Additionally, due to space vehicle structural requirements, exercise devices are often placed on vibration isolation systems. This changes the apparent impedance or stiffness of the device as seen by the user. Data collection under these conditions is often impractical and limited. Predictive modeling provides a means to have a virtual subject to test hypotheses. Predictive simulation provides a virtual subject for which we are able to perform studies such as sensitivity to device loading and vibration isolation without the need for laboratory kinematic or kinetic test data.Direct Collocation optimization provides an efficient means to perform task based optimization and predictive modeling. It is relatively straight forward to structure a physical exercise task in a Direct Collocation mathematical formulation: perform a motion such that you start at an initial pose, achieve a given amount of deflection i.e a squat, return to the initial pose, and minimize muscle activation cost. Direct Collocation is advantageous in that it does not require numerical integration to evaluate the objective function. Instead, the system dynamics are transformed to discrete time and the optimizer is constrained such that the solution is not considered to be a valid unless the dynamic equations are satisfied at all time points. The simulation and optimization are effectively done simultaneously. Due to the implicit integration, time steps can be more coarse than in a differential equation solver. In a gait scenario this means that that the model constraints and cost function are evaluated at 100 nodes in the gait cycle versus 10,000 integration steps in a variable-step forward dynamic simulation. Furthermore, no time is wasted on accurate simulations of movements that are far from the optimum. Constrained optimization algorithms require a Jacobian matrix that contains the partial derivatives of each of the dynamic constraints with respect to of each of the state and control variables at all time points. This is a large but sparse matrix. An implicit dynamics formulation requires computation of the dynamic residuals f as a function of the states x and their derivatives, and controls u:f(x, dxdt, u) 0If the dynamics of musculoskeletal system are formulated implicitly, the Jacobian elements are often available analytically, eliminating the need for numerical differentiation; this is obviously computationally advantageous. Additionally, implicit formulation of musculoskeletal dynamics do not suffer from singularities from low mass bodies, zero muscle activation, or other stiff system or

physical exercise↗

NASA NTRS2019

Low-Thrust Trajectory Design for a Cislunar CubeSat Leveraging Structures from the Bicircular Restricted Four-Body Problem

The upcoming Lunar IceCube (LIC) mission will deliver a 6U CubeSat to a low lunar orbit via a ride-share opportunity during NASAs Artemis 1 mission. This presents a challenging trajectory design scenario, as the vast change in energy required to transfer from the initial deployment state to the destination orbit is compounded by the limitations of the LICs low-thrust engine. This investigation addresses these challenges by developing a trajectory design framework that utilizes dynamical structures available in the Bicircular Restricted Four-Body Problem (BCR4BP) along with a robust direct collocation algorithm. Maps are created that expedite the selection of invariant manifold paths from a periodic staging orbit in the BCR4BP that offer favorable connections between the LIC transfer phases. Initial guesses assembled from these maps are passed to a direct collocation algorithm that corrects them in the BCR4BP while including the variable low-thrust acceleration of the spacecraft engine. Results indicate that the ordered motion provided by the BCR4BP and the robustness of direct collocation combine to offer an efficient and adaptable framework for designing a baseline trajectory for the LIC mission.

Pritchett, Robert↗

NASA NTRS2019

Low-Thrust Trajectory Design for A Cislunar CubeSat Leveraging Structures from the Bicircular Restricted Four-Body Problem

Pritchett, Robert↗

NASA NTRS2020

A Machine Learning-Based Cloud Detection and Thermodynamic Phase Classification Algorithm using Passive Spectral Observations

We trained two Random Forest (RF) machine-learning models for cloud mask and cloud thermodynamic phase detection using spectral observations from VIIRS on Suomi NPP (SNPP). Observations from CALIOP were carefully selected to provide reference labels. The two RF models were trained for all-day and daytime-only conditions using a 4-year collocated VIIRS/CALIOP dataset from 2013 to 2016. Due to the orbit difference, the collocated CALIOP and SNPP VIIRS training samples cover a broad viewing zenith angle range, which is a great benefit to overall model performance. The all-day model uses 3 VIIRS infrared (IR) bands (8.6,11, and 12 μm) and the daytime model uses 5 Near-IR (NIR) and Shortwave-IR (SWIR) bands (0.86, 1.24, 1.38, 1.64 and 2.25 μm) together with the 3 IR bands to detect clear, liquid water, and ice cloud pixels. Up to 7 surface types, namely, ocean/water, forest, cropland, grassland, snow/ice, barren/desert, and shrubland, were considered separately to enhance performance for both models. Detection of cloudy pixels and thermodynamic phase with the two RF models were compared against collocated CALIOP products from 2017. It is shown that, with a conservative screening process that excludes the most challenging cloudy pixels for passive remote sensing, the two RF models have high accuracy rates in comparison with the CALIOP reference for both cloud detection and thermodynamic phase. Other existing SNPP VIIRS and Aqua MODIS cloud mask and phase products are also evaluated, with results showing that the two RF models and the MODIS MYD06 optical property phase product are the top 3 algorithms with respect to lidar observations during the daytime. During the nighttime, the RF all-day model works best for both cloud detection and phase, in particular for pixels over snow/ice surfaces. The present RF models can be extended to other similar passive instruments if training samples can be collected from CALIOP or other lidars. However, the quality of reference labels and potential sampling issues that may impact model performance would need further attention.

cloud detection↗

NASA NTRSDate not supplied

Discontinuous Galerkin and Related Methods for ODE

A defining feature of the discontinuous Galerkin (DG) method for ODE is that the piecewise polynomial solution can have a jump discontinuity at the beginning of each step. Starting from the standard integral formulation, the DG method is derived here in differential form. The key ingredient is a polynomial called the correction function, which helps ‘correct’ the discontinuous solution by approximating the jump and yields a continuous one. Under the right Radau quadrature, this continuous solution is identical to the solutions by the right Radau collocation and the continuous Galerkin (CG) methods. Next, the correction function facilitates the construction of the associated implicit Runge-Kutta schemes (IRK-DG). Different quadratures for DG result in different IRK-DG methods: left Radau quadrature in Radau IA, right Radau quadrature in Radau IIA or right Radau collocation, and Gauss quadrature in a method called DG-Gauss. The construction of IRK-DG clarifies the meaning and facilitates the proofs of various 𝐵(𝑝), 𝐶(𝜂), and 𝐷(𝜁) conditions for accuracy. The two consequences of these conditions are that all 𝑠-stage IRK-DG methods are accurate to order 2𝑠 − 1, and the IRK-DG methods of Radau type are unique. Numerical examples showing the behavior of the DG solutions are provided. In all, the correction function plays a key role and helps establish the relations among the DG, IRK-DG, collocation, and CG schemes.

numerical methods↗