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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS2020

Generation and Calibration of Linear Models of Aircraft with Highly Coupled Aeroelastic and Flight Dynamics

The lightweight structures and unconventional configurations being considered for the next generation of aircraft mean that any effort to predict or control the flight dynamics is impacted by the structural dynamics. One of the most severe forms of coupling between aeroelasticity and flight dynamics is an instability called body freedom flutter. The existing tools often assume a relatively weak effect of structural dynamics on the flight dynamics, and are therefore incapable of modeling strong interactions like body freedom flutter. A method of combining different sources of data traditionally used for aeroelasticity and flight dynamics is described by reconciling many of the differences between these models. By building upon past modeling efforts, a level of familiarity in the approach is achieved. Generally the differences from the traditional approaches are subtle but significant. The traditional frequency domain flutter model in a modal coordinate system is converted to a form consistent with a time domain flight dynamics model. The time domain rational function approximation about a non-inertial coordinate system and the unique constraints for the conversion between the inertial and non-inertial coordinate systems are discussed. A consistent transformation of the states of aeroelastic models to flight dynamics models is derived, which enables the integration of data from higher fidelity computational fluid dynamics models or wind-tunnel testing. The present method of integrating multidisciplinary data was used to create models that compare well with X-56A flight-test data, including conditions past the flutter speed.

Ouellette, Jeffrey↗
NASA NTRSDate not supplied

An Interactive MATLAB Program for Fitting Transfer Functions to Frequency Responses

A computer program called FRFit (Frequency Response Fitting) for matching single-input single-output (SISO) transfer function models to empirical frequency response data is described. The program was written in MATLAB and has a graphical user interface (GUI). It is interactive in that the user manually builds the transfer function model using ``elementary factors'' (gain, delay, differentiators and integrators, and first- and second-order poles and zeros) and adjusts their values with sliders or entry fields. A nonlinear optimization can also be used to determine maximum-likelihood estimates of the transfer function parameters and their associated uncertainties. The program has some usefulness as a teaching aid, and can be applied to model structure determination, reduced-order modeling, preliminary analysis, and other system identification problems. FRFit is demonstrated using example problems, including the identification of aircraft transfer functions and rational function approximations of Theodorsen's function.

Frequency response↗
NASA NTRSDate not supplied

Reduced-Order Aerodynamic Modeling Based on CFD Frequency Responses from Multisine Inputs

A system identification analysis was performed to determine a reduced-order model (ROM) of a computational fluid dynamics (CFD) solver in support of linear aeroservoelastic model development and feedback control design. The approach was applied to the FUN3D code for the half-span wind tunnel test article used in the NASA-Boeing collaboration called the Integrated Adaptive Wing Technology Maturation (IAWTM) project. In a transonic flow condition, multiple inputs (11 structural mode displacements and 3 control surface deflections) were simultaneously excited with orthogonal phase-optimized multisines while multiple outputs (the corresponding 14 generalized aerodynamic forces) were recorded. From these recorded times series, the matrix of frequency responses was computed and subsequently fit using rational function approximations (RFAs). It was found that the entire (14 x 14) matrix of frequency responses could be determined from a single CFD run and that results generally followed trends predicted using other methods. Differences were attributed to the modeling fidelity and nonlinearities from structural mode and control surface interactions at higher reduced frequencies. More accurate fits of the RFAs to the frequency response data were obtained by making two CFD runs, one with only structural mode excitations and one with only control surface excitations, which reduced the degree of nonlinearity in the modeling data.

Aeroservoelasticity↗
DOE OSTI2021

Computational Math Problems for a Clean Energy Future

Cutting edge computational mathematics are ubiquitous in renewable energy research. Problems in resilient and reliable electric grid operations, infrastructure planning, wind farm yaw control, and more demand sophisticated and scalable computational tools that enable the transition of renewable energy technologies from proof of concept to deployment into our energy system. The mission of the Computational Science Center at NREL is to lead the lab's efforts to solve energy challenges using high-performance computing (HPC), computational science, applied mathematics, scientific data management, visualization, and informatics. In this poster, we provide a short overview of three areas of computational mathematics research at NREL: wind power scenario generation for stochastic grid operations and infrastructure planning, improved rational function approximations for electromagnetic transients codes, and wind farm yaw control using a combination of the Alternating Direction Method of Multipliers (ADMM) and reinforcement learning (RL). Increasing penetrations of renewable energy into power grids motivate the investigation of new approaches to characterizing uncertainty for five-minute economic dispatch problems. Similarly, as the penetration of distributed energy resources on power grids increases, it becomes important to revisit our methods of modelling transient phenomena, i.e. electromagnetic transients programs. Finally, the combination of ADMM and RL for wind farm yaw control presented here can potentially increase the efficiency of the deployed distributed controllers by orders of magnitude.

ADMM↗
NASA NTRS1990

Neural computation of arithmetic functions

An area of application of neural networks is considered. A neuron is modeled as a linear threshold gate, and the network architecture considered is the layered feedforward network. It is shown how common arithmetic functions such as multiplication and sorting can be efficiently computed in a shallow neural network. Some known results are improved by showing that the product of two n-bit numbers and sorting of n n-bit numbers can be computed by a polynomial-size neural network using only four and five unit delays, respectively. Moreover, the weights of each threshold element in the neural networks require O(log n)-bit (instead of n-bit) accuracy. These results can be extended to more complicated functions such as multiple products, division, rational functions, and approximation of analytic functions.

Siu, Kai-Yeung↗
NASA NTRS1993

Aeroservoelasticity

An overview of some research activities being conducted on aeroservoelasticity (ASE) in flight vehicles is given. Modeling procedures involving rational functions for approximating unsteady aerodynamics are briefly examined along with analysis methods using the ISAC and ADAM codes. The use of ASE in integrated structure/control law design methodology, control design using constrained optimization/singular value constraints, and adaptive structures is addressed. Test demonstrations of aeroelastic wind-tunnel models or full-scale flight vehicles with active control concepts are described which have significantly enhanced the state of the art in active control technology. The Active Flexible Wing wind-tunnel test project is discussed in detail to emphasize today's activities and accomplishments. Finally, recent activities illustrating the state of the art of ASE in high-speed aircraft are examined.

Noll, Thomas E.↗
NASA NTRS1997

Application of AWE Along with a Combined FEM/MoM Technique to Compute RCS of a Cavity-Backed Aperture in an Infinite Ground Plane Over a Frequency Range

A hybrid Finite Element Method (FEM)/Method of Moments (MoM) technique in conjunction with the Asymptotic Waveform Evaluation (AWE) technique is applied to obtain radar cross section (RCS) of a cavity-backed aperture in an infinite ground plane over a frequency range. The hybrid FEM/MoM technique when applied to the cavity-backed aperture results in an integro-differential equation with electric field as the unknown variable, the electric field obtained from the solution of the integro-differential equation is expanded in Taylor series. The coefficients of the Taylor series are obtained using the frequency derivatives of the integro-differential equation formed by the hybrid FEM/MoM technique. The series is then matched via the Pade approximation to a rational polynomial, which can be used to extrapolate the electric field over a frequency range. The RCS of the cavity-backed aperture is calculated using the electric field at different frequencies. Numerical results for a rectangular cavity, a circular cavity, and a material filled cavity are presented over a frequency range. Good agreement between AWE and the exact solution over the frequency range is obtained.

Reddy, C.J.↗
NASA NTRS1976

On the use of Pade approximants to represent unsteady aerodynamic loads for arbitrarily small motions of wings

The general behavior of unsteady airloads in the frequency domain is explained. Based on this, a systematic procedure is described whereby the airloads, produced by completely arbitrary, small, time-dependent motions of a thin lifting surface in an airstream, can be predicted. This scheme employs as raw materials any of the unsteady linearized theories that have been mechanized for simple harmonic oscillations. Each desired aerodynamic transfer function is approximated by means of an appropriate Pade approximant, that is, a rational function of finite degree polynomials in the Laplace transform variable. Although these approximations have many uses, they are proving especially valuable in the design of automatic control systems intended to modify aeroelastic behavior.

Vepa, R.↗
NASA NTRS1994

An Efficient Spectral Method for Ordinary Differential Equations with Rational Function Coefficients

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple three-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e. matrix representations of multiplication by a function) are banded for polynomials, we are able to obtain a banded representation for linear differential operators with rational coefficients. This leads to a method of solution of initial or boundary value problems that, besides having an operation count that scales linearly with the order of truncation N, is computationally well conditioned. Among the applications considered is the use of rational maps for the resolution of sharp interior layers.

Coutsias, Evangelos A.↗
NASA NTRS1975

Quantitative water quality with LANDSAT and Skylab

Correlation studies were completed between LANDSAT Multispectral Scanner (MSS) band ratios derived from computer compatible tape (CCT) and 170 water samples taken from three large Kansas reservoirs, coincident with 16 different LANDSAT passes over a 13 month period. The following conclusions were obtained: (1) LANDSAT MSS reflectance levels are useful for quantitative measurement of suspended solids up to at least 900 ppm, (2) MSS band ratios derived from CCT can measure suspended solids with 67% confidence level accuracy of 12 ppm over the range 0-80 ppm and 35 ppm over the range 0900 ppm, (3) suspended solids contour maps can be easily constructed from CCT for water bodies larger than approximately 100 acres, (4) rationing suppresses MSS reflectance level dependence on seasonal sun angle variation and permits measurement of suspended load the year round in the middle latitudes. SKYLAB imagery from a single pass over three reservoirs compares favorably to LANDSAT results up to 100 ppm.

Yarger, H. L.↗
NASA NTRS1977

Finite state modeling of aeroelastic systems

A general theory of finite state modeling of aerodynamic loads on thin airfoils and lifting surfaces performing completely arbitrary, small, time-dependent motions in an airstream is developed and presented. The nature of the behavior of the unsteady airloads in the frequency domain is explained, using as raw materials any of the unsteady linearized theories that have been mechanized for simple harmonic oscillations. Each desired aerodynamic transfer function is approximated by means of an appropriate Pade approximant, that is, a rational function of finite degree polynomials in the Laplace transform variable. The modeling technique is applied to several two dimensional and three dimensional airfoils. Circular, elliptic, rectangular and tapered planforms are considered as examples. Identical functions are also obtained for control surfaces for two and three dimensional airfoils.

Vepa, R.↗
NASA NTRS1993

A rational interpolation method to compute frequency response

A rational interpolation method for approximating a frequency response is presented. The method is based on a product formulation of finite differences, thereby avoiding the numerical problems incurred by near-equal-valued subtraction. Also, resonant pole and zero cancellation schemes are developed that increase the accuracy and efficiency of the interpolation method. Selection techniques of interpolation points are also discussed.

Kenney, Charles↗
NASA NTRS2001

Application of Computer Tomography for Life Detection

Perhaps one of the most fundamentally difficult challenges facing those who would search for life is that of scale determination. Spatial scales of life on Earth range over more than 15 orders of magnitude in mass and volume, and more than 8 orders of magnitude in 2 dimensional space. If the distribution of life is sparse in comparison to the background on which it is found, then the choice of the right scale is critical to finding that life. But how does one identify the proper scale? To put this in other words, how does one recognize the "haystacks" in which the needles (biosignatures and evidence of life) might be most profitably searched for? The problem is further exacerbated when conditions get extreme because much of the life moves from the clement surface environment into the pores and more clement environments inside of rocks, minerals and soils. Once encased in their lithic homes, these microbes become nearly impossible to study by standard techniques because of the opacity of the rocks. It is this problem that we propose to address in the work proposed here. Computer Tomography (CT) has been a very valuable tool in medicine, where the best resolution available has typically been of the order of about 0.5 mm. However, to adapt the approach for life detection of microbial endoliths, the resolution needs to be moved to the micrometer and even submicrometer levels. Thus for the studies proposed here, we begin with a commercially available instrument that can yield resolution of approximately 10 micrometers. The rational for this is twofold: first, this is the "state of the art" in laboratory instruments; and second, that while the usual size of a microbial cell is about 1 micron, microorganisms tend to live in communities that usually exceed the 10 micrometer size range. The resolution also depends on the sample size itself, so having a small lab instrument into which small samples can be placed will be beneficial to the resolution. We have now used several different CT systems, beginning with the medical scanners (Arcadia CT group) for the detection of layered communities in sandstone rocks from Antarctica. Even this crude instrument was able to point to the areas of the rock that were dominated by microbial populations - this provides the critical first information that says, "Go back and look at these sites with other methods." We showed that without sample preparation or destruction it was possible to gain knowledge as to the presence of density differences suggestive of life.

Tsapin, A.↗
NASA NTRS1986

Can stochastic, dissipative wave fields be treated as random walk generators

A suggestion by Meek et al. (1985) that the gravity wave field be viewed as stochastic, with significant nonlinearities, is applied to calculate diffusivities. The purpose here is to calculate the diffusivity for stochastic wave model and compare it with previous diffusivity estimates. The researchers do this for an idealized case in which the wind velocity changes but slowly, and for which saturation is the principal mechanism by which wave energy is lost. A related calculation was given in a very brief way (Weinstock, 1976), but the approximations were not fully justified, nor were the physical pre-suppositions clearly explained. The observations of Meek et al. (1985) have clarified the pre-suppositions for the researchers and provided a rationalization and improvement of the approximations employed.

Weinstock, J.↗
NASA NTRS1993

A hybrid Pade-Galerkin technique for differential equations

A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter epsilon associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade approximation in the form of a rational function in the parameter epsilon. In the third step, the various powers of epsilon which appear in the Pade approximation are replaced by new (unknown) parameters (delta(sub j)). These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade approximations fail to do so. The method is discussed and topics for future investigations are indicated.

Geer, James F.↗
NASA NTRS1977

Study of Lubricant Jet Flow Phenomena in Spur Gears: Out of Mesh Condition

Oil jet lubrication on the disengaging side of a gear mesh was analyzed. Results of the analysis were computerized and used to determine the oil jet impingement depth for several gear ratios and oil jet to pitch line velocity ratios. A gear test rig using high speed photography was used to experimentally determine the oil jet impingement depth on the disengaging side of mesh. Impingement depth reached a maximum at gear ratio near 1.5 where chopping by the leading gear tooth limited impingement depth. The pinion impingement depth is zero above a gear ratio of 1.172 for a jet velocity to pitch time velocity ration of 1.0 and is similar for other velocity ratios. The impingement depth for gear and pinion are equal and approximately one half the maximum at a gear ration of 7.0.

Townsend, D. P.↗