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NASA NTRS2003

A Time Integration Algorithm Based on the State Transition Matrix for Structures with Time Varying and Nonlinear Properties

A variable order method of integrating the structural dynamics equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. When the time variation of the system can be modeled exactly by a polynomial it produces nearly exact solutions for a wide range of time step sizes. Solutions of a model nonlinear dynamic response exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with solutions obtained by established methods.

Bartels, Robert E.↗

NASA NTRS2018

Multifidelity Uncertainty Quantification of a Commercial Supersonic Transport

The objective of this work was to develop a multifidelity uncertainty quantification approach for efficient analysis of a commercial supersonic transport. An approach based on non-intrusive polynomial chaos was formulated in which a low-fidelity model could be corrected by any number of high-fidelity models. The formulation and methodology also allows for the addition of uncertainty sources not present in the lower fidelity models. To demonstrate the applicability of the multifidelity polynomial chaos approach, two model problems were explored. The first was supersonic airfoil with three levels of modeling fidelity, each capturing an additional level of physics. The second problem was a commercial supersonic transport. This model had three levels of fidelity that included two different modeling approaches and the addition of physics between the fidelity levels. Both problems illustrate the applicability and significant computational savings of the multifidelity polynomial chaos method.

West, Thomas K., IV↗

NASA NTRS2014

A Generic Nonlinear Aerodynamic Model for Aircraft

A generic model of the aerodynamic coefficients was developed using wind tunnel databases for eight different aircraft and multivariate orthogonal functions. For each database and each coefficient, models were determined using polynomials expanded about the state and control variables, and an othgonalization procedure. A predicted squared-error criterion was used to automatically select the model terms. Modeling terms picked in at least half of the analyses, which totalled 45 terms, were retained to form the generic nonlinear aerodynamic (GNA) model. Least squares was then used to estimate the model parameters and associated uncertainty that best fit the GNA model to each database. Nonlinear flight simulations were used to demonstrate that the GNA model produces accurate trim solutions, local behavior (modal frequencies and damping ratios), and global dynamic behavior (91% accurate state histories and 80% accurate aerodynamic coefficient histories) under large-amplitude excitation. This compact aerodynamics model can be used to decrease on-board memory storage requirements, quickly change conceptual aircraft models, provide smooth analytical functions for control and optimization applications, and facilitate real-time parametric system identification.

Grauer, Jared A.↗

NASA NTRS1987

Identification of large space structures: A state-of-practice report

An outline of this work is presented. It begins with a schematic flow diagram and a logical flow diagram of the identification process for large space structures (LSS). Next, the task is defined by a structure model definition. A matrix polynomial formulation with a node displacement equation and a state variable formulation with node displacement and velocities are outlined. Further outlined is the identification of LSS on orbit; modeling errors and uncertainties; verification and validation of model; and noise, computations, and data collection.

Source record↗

NASA NTRS2017

Applying Graph Theory to Problems in Air Traffic Management

Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it isshown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.

computational complexity↗

NASA NTRS2017

Applying Graph Theory to Problems in Air Traffic Management

Graph theory is used to investigate three different problems arising in air traffic management. First, using a polynomial reduction from a graph partitioning problem, it is shown that both the airspace sectorization problem and its incremental counterpart, the sector combination problem are NP-hard, in general, under several simple workload models. Second, using a polynomial time reduction from maximum independent set in graphs, it is shown that for any fixed e, the problem of finding a solution to the minimum delay scheduling problem in traffic flow management that is guaranteed to be within n1-e of the optimal, where n is the number of aircraft in the problem instance, is NP-hard. Finally, a problem arising in precision arrival scheduling is formulated and solved using graph reachability. These results demonstrate that graph theory provides a powerful framework for modeling, reasoning about, and devising algorithmic solutions to diverse problems arising in air traffic management.

precision arrival scheduling↗

NASA NTRS2011

A Maximum Likelihood Approach to Determine Sensor Radiometric Response Coefficients for NPP VIIRS Reflective Solar Bands

Optical sensors aboard Earth orbiting satellites such as the next generation Visible/Infrared Imager/Radiometer Suite (VIIRS) assume that the sensors radiometric response in the Reflective Solar Bands (RSB) is described by a quadratic polynomial, in relating the aperture spectral radiance to the sensor Digital Number (DN) readout. For VIIRS Flight Unit 1, the coefficients are to be determined before launch by an attenuation method, although the linear coefficient will be further determined on-orbit through observing the Solar Diffuser. In determining the quadratic polynomial coefficients by the attenuation method, a Maximum Likelihood approach is applied in carrying out the least-squares procedure. Crucial to the Maximum Likelihood least-squares procedure is the computation of the weight. The weight not only has a contribution from the noise of the sensor s digital count, with an important contribution from digitization error, but also is affected heavily by the mathematical expression used to predict the value of the dependent variable, because both the independent and the dependent variables contain random noise. In addition, model errors have a major impact on the uncertainties of the coefficients. The Maximum Likelihood approach demonstrates the inadequacy of the attenuation method model with a quadratic polynomial for the retrieved spectral radiance. We show that using the inadequate model dramatically increases the uncertainties of the coefficients. We compute the coefficient values and their uncertainties, considering both measurement and model errors.

Lei, Ning↗

NASA NTRS1992

A new model for estimating total body water from bioelectrical resistance

Estimation of total body water (T) from bioelectrical resistance (R) is commonly done by stepwise regression models with height squared over R, H(exp 2)/R, age, sex, and weight (W). Polynomials of H(exp 2)/R have not been included in these models. We examined the validity of a model with third order polynomials and W. Methods: T was measured with oxygen-18 labled water in 27 subjects. R at 50 kHz was obtained from electrodes placed on the hand and foot while subjects were in the supine position. A stepwise regression equation was developed with 13 subjects (age 31.5 plus or minus 6.2 years, T 38.2 plus or minus 6.6 L, W 65.2 plus or minus 12.0 kg). Correlations, standard error of estimates and mean differences were computed between T and estimated T's from the new (N) model and other models. Evaluations were completed with the remaining 14 subjects (age 32.4 plus or minus 6.3 years, T 40.3 plus or minus 8 L, W 70.2 plus or minus 12.3 kg) and two of its subgroups (high and low) Results: A regression equation was developed from the model. The only significant mean difference was between T and one of the earlier models. Conclusion: Third order polynomials in regression models may increase the accuracy of estimating total body water. Evaluating the model with a larger population is needed.

Siconolfi, S. F.↗

NASA NTRS2020

Photometry of Asteroid (101955) Bennu with OVIRS on OSIRIS-REx

NASA’s OSIRIS-REx spacecraft arrived at its sampling target, asteroid (101955) Bennu, in December 2018 and started a series of global observation campaigns. Here we investigate the global photometric properties of Bennu as observed by the OSIRIS-REx Visible and InfraRed Spectrometer (OVIRS) over the time period December 9, 2018, to September 26, 2019. In this study we used observations obtained over wavelengths ranging from 0.4 to 3.7 μm, with a solar phase angle range of 5.3° to 132.6°. Our aim is to characterize the global average disk-resolved photometric properties of Bennu with multiple models. The best-fit model is a McEwen model with an exponential phase function and an exponential polynomial partition function. We use this model to correct the OVIRS spectra of Bennu to a standard reference viewing and illumination geometry at visible to infrared wavelengths for the purposes of global spectral mapping. We derive a bolometric Bond albedo map in which Bennu’s surface values range from 0.021 to 0.027. We find a phase reddening effect, and our model is effective at removing this phase reddening. Our average model albedo shows a blueish spectrum with a >10% absorption feature centered at 2.74 μm. Of all comparisons with previously visited asteroids and comets, only 28P/Neujmin, 2P/Encke, and (162173) Ryugu are darker than Bennu. We find that Bennu is a few percent brighter than Ryugu in the wavelengths respectively observed by the OSIRIS-REx and Hayabusa2 missions (from 0.48 to 0.86 μm). We also compare our spectroscopic photometry of Bennu with the OSIRIS-REx imaging photometry and with ground-based predictions.

Asteroid Bennu↗

NASA NTRS2009

Real-Time Detection of Dust Devils from Pressure Readings

A method for real-time detection of dust devils at a given location is based on identifying the abrupt, temporary decreases in atmospheric pressure that are characteristic of dust devils as they travel through that location. The method was conceived for use in a study of dust devils on the Martian surface, where bandwidth limitations encourage the transmission of only those blocks of data that are most likely to contain information about features of interest, such as dust devils. The method, which is a form of intelligent data compression, could readily be adapted to use for the same purpose in scientific investigation of dust devils on Earth. In this method, the readings of an atmospheric- pressure sensor are repeatedly digitized, recorded, and processed by an algorithm that looks for extreme deviations from a continually updated model of the current pressure environment. The question in formulating the algorithm is how to model current normal observations and what minimum magnitude deviation can be considered sufficiently anomalous as to indicate the presence of a dust devil. There is no single, simple answer to this question: any answer necessarily entails a compromise between false detections and misses. For the original Mars application, the answer was sought through analysis of sliding time windows of digitized pressure readings. Windows of 5-, 10-, and 15-minute durations were considered. The windows were advanced in increments of 30 seconds. Increments of other sizes can also be used, but computational cost increases as the increment decreases and analysis is performed more frequently. Pressure models were defined using a polynomial fit to the data within the windows. For example, the figure depicts pressure readings from a 10-minute window wherein the model was defined by a third-degree polynomial fit to the readings and dust devils were identified as negative deviations larger than both 3 standard deviations (from the mean) and 0.05 mbar in magnitude. An algorithm embodying the detection scheme of this example was found to yield a miss rate of just 8 percent and a false-detection rate of 57 percent when evaluated on historical pressure-sensor data collected by the Mars Pathfinder lander. Since dust devils occur infrequently over the course of a mission, prioritizing observations that contain successful detections could greatly conserve bandwidth allocated to a given mission. This technique can be used on future Mars landers and rovers, such as Mars Phoenix and the Mars Science Laboratory.

Wagstaff, Kiri↗

NASA NTRS1972

Feedline dynamic effects on shuttle POGO stability

The transmission parameters for the dynamic characteristics of a feedline were approximated using both power and product series expansions. The feedline transfer functions of a shuttle orbiter feedline configuration were obtained using power and product series approximations of 60th, 120th, 180th, and 240th, order. Bode plots using the above polynomial approximations were obtained and the results compared with the exact solution. The exact solution to the feedline transfer function was obtained by using the transcendental terms appearing in the transmission parameters. The results show that the shuttle orbiter feedline may be modeled adequately by using polynomial approximations for the transcendental functions appearing in the transmission parameters. The power series approach was shown to be preferable to the product series method.

Dimaggio, O. D.↗

NASA NTRS2020

The GGCMI Phase 2 emulators: global gridded crop model responses to changes in CO2, temperature, water, and nitrogen (version 1.0)

Statistical emulation allows combining advantageous features of statistical and process-based crop models for understanding the effects of future climate changes on crop yields. We describe here the development of emulators for nine process-based crop models and five crops using output from the Global Gridded Model Intercomparison Project (GGCMI) Phase 2. The GGCMI Phase 2 experiment is designed with the explicit goal of producing a structured training dataset for emulator development that samples across four dimensions relevant to crop yields: atmospheric carbon dioxide (CO2) concentrations, temperature, water supply, and nitrogen inputs (CTWN). Simulations are run under two different adaptation assumptions: that growing seasons shorten in warmer climates, and that cultivar choice allows growing seasons to remain fixed. The dataset allows emulating the climatological-mean yield response of all models with a simple polynomial in mean growing-season values. Climatological-mean yields are a central metric in climate change impact analysis; we show here that they can be captured without relying on interannual variations. In general, emulation errors are negligible relative to differences across crop models or even across climate model scenarios; errors become significant only in some marginal lands where crops are not currently grown. We demonstrate that the resulting GGCMI emulators can reproduce yields under realistic future climate simulations, even though the GGCMI Phase 2 dataset is constructed with uniform CTWN offsets, suggesting that the effects of changes in temperature and precipitation distributions are small relative to those of changing means. The resulting emulators therefore capture relevant crop model responses in a lightweight, computationally tractable form, providing a tool that can facilitate model comparison, diagnosis of interacting factors affecting yields, and integrated assessment of climate impacts.

James A Franke↗

NASA NTRS2002

Modeling and control for closed environment plant production systems

A computer program was developed to study multiple crop production and control in controlled environment plant production systems. The program simulates crop growth and development under nominal and off-nominal environments. Time-series crop models for wheat (Triticum aestivum), soybean (Glycine max), and white potato (Solanum tuberosum) are integrated with a model-based predictive controller. The controller evaluates and compensates for effects of environmental disturbances on crop production scheduling. The crop models consist of a set of nonlinear polynomial equations, six for each crop, developed using multivariate polynomial regression (MPR). Simulated data from DSSAT crop models, previously modified for crop production in controlled environments with hydroponics under elevated atmospheric carbon dioxide concentration, were used for the MPR fitting. The model-based predictive controller adjusts light intensity, air temperature, and carbon dioxide concentration set points in response to environmental perturbations. Control signals are determined from minimization of a cost function, which is based on the weighted control effort and squared-error between the system response and desired reference signal.

NASA Discipline Life Support Systems↗

NASA NTRS1994

Analytic Sensitivities for Shape Optimization in Equivalent Plate Structural Wing Models

Equivalent plate modeling techniques based on Ritz analysis with simple polynomials prove to be efficient tools for structural modeling of wings in the preliminary design stage. Accuracy problems are encountered, however, when these models are used to obtain finite difference behavior sensitivities with respect to planform shape. The accuracy problems are associated with the poor numerical conditioning of static and eigenvalue equations. As higher-order polynomials are being used to Improve the analysis itself, the more sensitive is the finite difference derivative to the step size used. This article describes a formulation of wing equivalent plate modeling in which it is simple to obtain analytic, explicit expressions for stiffness and mass matrix elements without the need to perform numerical integration. This formulation leads naturally to analytic expressions for the derivatives of displacements, stresses, and natural frequencies with respect to shape design variables. This article examines the accuracy of finite difference derivatives compared with the analytic derivatives, and shows that In some cases it is impossible to obtain any information of value by finite differences. Analytic sensitivities, in this case, are still sufficiently accurate for design optimization.

Livne, Eli↗

NASA NTRS2003

Wind Tunnel Database Development using Modern Experiment Design and Multivariate Orthogonal Functions

A wind tunnel experiment for characterizing the aerodynamic and propulsion forces and moments acting on a research model airplane is described. The model airplane called the Free-flying Airplane for Sub-scale Experimental Research (FASER), is a modified off-the-shelf radio-controlled model airplane, with 7 ft wingspan, a tractor propeller driven by an electric motor, and aerobatic capability. FASER was tested in the NASA Langley 12-foot Low-Speed Wind Tunnel, using a combination of traditional sweeps and modern experiment design. Power level was included as an independent variable in the wind tunnel test, to allow characterization of power effects on aerodynamic forces and moments. A modeling technique that employs multivariate orthogonal functions was used to develop accurate analytic models for the aerodynamic and propulsion force and moment coefficient dependencies from the wind tunnel data. Efficient methods for generating orthogonal modeling functions, expanding the orthogonal modeling functions in terms of ordinary polynomial functions, and analytical orthogonal blocking were developed and discussed. The resulting models comprise a set of smooth, differentiable functions for the non-dimensional aerodynamic force and moment coefficients in terms of ordinary polynomials in the independent variables, suitable for nonlinear aircraft simulation.

Morelli, Eugene A.↗

NASA NTRS1980

Landsat analysis of tropical forest succession employing a terrain model

Landsat multispectral scanner (MSS) data have yielded a dual classification of rain forest and shadow in an analysis of a semi-deciduous forest on Mindonoro Island, Philippines. Both a spatial terrain model, using a fifth side polynomial trend surface analysis for quantitatively estimating the general spatial variation in the data set, and a spectral terrain model, based on the MSS data, have been set up. A discriminant analysis, using both sets of data, has suggested that shadowing effects may be due primarily to local variations in the spectral regions and can therefore be compensated for through the decomposition of the spatial variation in both elevation and MSS data.

Barringer, T. H.↗

NASA NTRS1984

Determination of equivalent model geometry for tunnel wall interference assessment/correction

A formula for the determination of equivalent model geometry with two variables measured at the interface is derived, based on two dimensional subsonic flow. This predicted model profile is a reasonable initial estimate for transonic flow as long as the sonic region does not reach the interface. A general formula is given in two forms. One is in terms of complex variable functions and the other is an integral equation. The complex-function formula has the advantage of using analytic expressions. The integral equation form requires a numerical solution after assuming the model geometry as a polynomial function. Examples are given to illustrate the application of the formulas.

Lo, C. F.↗

NASA NTRS1985

Comparison of Two Algebraic Methods for Curve/curve Intersection

Most geometric modeling systems use either polynomial or rational functions to represent geometry. In such systems most computational problems can be formulated as systems of polynomials in one or more variables. Classical elimination theory can be used to solve such systems. Here Cayley's method of elimination is summarized and it is shown how it can best be used to solve the curve/curve intersection problem. Cayley's method was found to be a more straightforward approach. Furthermore, it is computationally simpler, since the elements of the Cayley matrix are one variable instead of two variable polynomials. Researchers implemented and tested both methods and found Cayley's to be more efficient. Six pairs of curves, representing mixtures of lines, circles, and cubic arcs were used. Several examples had multiple intersection points. For all six cases Cayley's required less CPU time than the other method. The average time ratio of method 1 to method 2 was 3.13:1, the least difference was 2.33:1, and the most dramatic was 6.25:1. Both of the above methods can be extended to solve the surface/surface intersection problem.

Demontaudouin, Y.↗