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NASA NTRS1986

Application of parameter estimation to highly unstable aircraft

The application of parameter estimation to highly unstable aircraft is discussed. Included are a discussion of the problems in applying the output error method to such aircraft and demonstrates that the filter error method eliminates these problems. The paper shows that the maximum likelihood estimator with no process noise does not reduce to the output error method when the system is unstable. It also proposes and demonstrates an ad hoc method that is similar in form to the filter error method, but applicable to nonlinear problems. Flight data from the X-29 forward-swept-wing demonstrator is used to illustrate the problems and methods discussed.

Maine, R. E.↗

NASA NTRS1986

Application of parameter estimation to highly unstable aircraft

This paper discusses the application of parameter estimation to highly unstable aircraft. It includes a discussion of the problems in applying the output error method to such aircraft and demonstrates that the filter error method eliminates these problems. The paper shows that the maximum likelihood estimator with no process noise does not reduce to the output error method when the system is unstable. It also proposes and demonstrates an ad hoc method that is similar in form to the filter error method, but applicable to nonlinear problems. Flight data from the X-29 forward-swept-wing demonstrator is used to illustrate the problems and methods discussed.

Maine, R. E.↗

NASA NTRS1998

Development of Polyimides-Based NLO Materials for Electrooptical Applications

Development of thermally stable optical materials for nonlinear optics have recently focused on the covalent incorporation of NLO chromophores into high performance polymers, especially thermally stable and processable polyamides. One key aspect for the incorporation of robust NLO chromophores into high Tg polymers is to sustain poling induced order. Other advantages include high loading level of chromophores, and elimination of possible phase separation as well as chromophore sublimation at processing or working temperature. We have prepared several polyimide based polymers which are covalently linked with thermally stable chromophores that we have developed, since polyamides generally exhibit high Tg and good film transparency. Here, we report the development and subsequent incorporation of indoline based chromophores into polyamides, leading to thermally stable NLO polymers.

Rutherford, Jacqueline↗

NASA NTRS2002

Interface Conditions for Wave Propagation Through Mesh Refinement Boundaries

We study the propagation of waves across fixed mesh refinement boundaries in linear and nonlinear model equations in 1-D and 2-D, and in the 3-D Einstein equations of general relativity. We demonstrate that using linear interpolation to set the data in guard cells leads to the production of reflected waves at the refinement boundaries. Implementing quadratic interpolation to fill the guard cells eliminates these spurious signals.

Choi, Dae-II↗

NASA NTRS1991

Thermal elastic shock and its effect on TOPEX spacecraft attitude control

Thermal elastic shock (TES) is a twice per orbit impulsive disturbance torque experienced by low-Earth orbiting spacecraft. The fundamental equations used to model the TES disturbance torque for typical spacecraft appendages (e.g., solar arrays and antenna booms) are derived in detail. In particular, the attitude-pointing performance of the TOPEX spacecraft, when subjected to the TES disturbance, is analyzed using a three-axis nonlinear time-domain simulation. Results indicate that the TOPEX spacecraft could exceed its roll-axis attitude-control requirement during penumbral transitions, and remain in violation for approximately 150 sec each orbit until the umbra collapses. A localized active-control system is proposed as a solution to minimize and/or eliminate the degrading effects of the TES disturbance.

Zimbelman, Darrell F.↗

NASA NTRS1989

On some numerical schemes for transonic flow problems

New second-order-accurate finite-difference approximations for a class of nonlinear PDEs of mixed type, which includes the two-dimensional low-frequency transonic small-disturbance equation (TSD) and full-potential equation (FP), are presented. For the TSD equation, the scheme is implemented via a time-splitting algorithm; the inclusion of flux limiters keeps the total variation nonincreasing and eliminates spurious oscillations near shocks. Global-linear-stability, TVD, and entropy-stability results are proved. Numerical results for the flow over a thin airfoil are presented. Current techniques used to solve the TSD equation may easily be extended to second-order accuracy by this method. For the FP equation, the new scheme requires no subsonic/supersonic switching and no numerical flux biasing. Global linear stability for all values of the Mach number is proved.

Mostrel, Marco Mosche↗

NASA NTRS1999

Angular-Rate Estimation Using Delayed Quaternion Measurements

This paper presents algorithms for estimating the angular-rate vector of satellites using quaternion measurements. Two approaches are compared one that uses differentiated quaternion measurements to yield coarse rate measurements, which are then fed into two different estimators. In the other approach the raw quaternion measurements themselves are fed directly into the two estimators. The two estimators rely on the ability to decompose the non-linear part of the rotas rotational dynamics equation of a body into a product of an angular-rate dependent matrix and the angular-rate vector itself. This non unique decomposition, enables the treatment of the nonlinear spacecraft (SC) dynamics model as a linear one and, thus, the application of a PseudoLinear Kalman Filter (PSELIKA). It also enables the application of a special Kalman filter which is based on the use of the solution of the State Dependent Algebraic Riccati Equation (SDARE) in order to compute the gain matrix and thus eliminates the need to compute recursively the filter covariance matrix. The replacement of the rotational dynamics by a simple Markov model is also examined. In this paper special consideration is given to the problem of delayed quaternion measurements. Two solutions to this problem are suggested and tested. Real Rossi X-Ray Timing Explorer (RXTE) data is used to test these algorithms, and results are presented.

Azor, R.↗

NASA NTRS2006

A Reevaluation of Airborne HO(x) Observations from NASA Field Campaigns

In-situ observations of tropospheric HO(x) (OH and HO2) obtained during four NASA airborne campaigns (SUCCESS, SONEX, PEM-Tropics B and TRACE-P) are reevaluated using the NASA Langley time-dependent photochemical box model. Special attention is given to previously diagnosed discrepancies between observed and predicted HO2 which increase with higher NO(x) levels and at high solar zenith angles. This analysis shows that much of the model discrepancy at high NO(x) during SUCCESS can be attributed to modeling observations at time-scales too long to capture the nonlinearity of HO(x) chemistry under highly variable conditions for NO(x). Discrepancies at high NO(x) during SONEX can be moderated to a large extent by complete use of all available precursor observations. Differences in kinetic rate coefficients and photolysis frequencies available for previous studies versus current recommendations also explain some of the disparity. Each of these causes is shown to exert greater influence with increasing NO(x) due to both the chemical nonlinearity between HO(x) and NO(x) and the increased sensitivity of HO(x) to changes in sources at high NO(x). In contrast, discrepancies at high solar zenith angles will persist until an adequate nighttime source of HO(x) can be identified. It is important to note that this analysis falls short of fully eliminating the issue of discrepancies between observed and predicted HO(x) for high NO(x) environments. These discrepancies are not resolved with the above causes in other data sets from ground-based field studies. Nevertheless, these results highlight important considerations in the application of box models to observationally based predictions of HO(x) radicals.

Olson, Jennifer↗

NASA NTRS1976

SRM attrition rate study of the aft motor case segments due to water impact cavity collapse loading

The attrition assessment of the aft segments of Solid Rocket Motor due to water impact requires the establishment of a correlation between loading occurrences and structural capability. Each discrete load case, as identified by the water impact velocities and angle, varies longitudinally and radially in magnitude and distribution of the external pressure. The distributions are further required to be shifted forward or aft one-fourth the vehicle diameter to assure minimization of the effect of test instrumentation location for the load determinations. The asymmetrical load distributions result in large geometric nonlinearities in structural response. The critical structural response is progressive buckling of the case. Discrete stiffeners have been added to these aft segments to aid in gaining maximum structural capability for minimum weight addition for resisting these loads. This report presents the development of the attrition assessment of the aft segments and includes the rationale for eliminating all assessable conservatisms from this assessment.

Crockett, C. D.↗

NASA NTRS1984

Two-dimensional computer simulation of EMVJ and grating solar cells under AMO illumination

A computer program, SCAP2D (Solar Cell Analysis Program in 2-Dimensions), is used to evaluate the Etched Multiple Vertical Junction (EMVJ) and grating solar cells. The aim is to demonstrate how SCAP2D can be used to evaluate cell designs. The cell designs studied are by no means optimal designs. The SCAP2D program solves the three coupled, nonlinear partial differential equations, Poisson's Equation and the hole and electron continuity equations, simultaneously in two-dimensions using finite differences to discretize the equations and Newton's Method to linearize them. The variables solved for are the electrostatic potential and the hole and electron concentrations. Each linear system of equations is solved directly by Gaussian Elimination. Convergence of the Newton Iteration is assumed when the largest correction to the electrostatic potential or hole or electron quasi-potential is less than some predetermined error. A typical problem involves 2000 nodes with a Jacobi matrix of order 6000 and a bandwidth of 243.

Gray, J. L.↗

NASA NTRS1984

A comparison of the spectral energy and enstrophy budgets of blocking versus nonblocking periods

Data from the winters of 1978-79 and 1976-77 are analyzed in an attempt to identify any systematic differences in the time mean spectral energy and enstrophy budgets of blocking events in comparison with nonblocking periods. It is found that the most noteworthy differences between the spectral energy and enstrophy budgets of blocking versus nonblocking periods are in the nonlinear interaction terms. It is suggested that an explanation of the greater predictability of the Rex-type blocking found by Bengtsson (1981) might be found in the reversal of low wavenumber enstrophy cascade. This may indicate that the destruction of large-scale vorticity by down-scale cascade and eventual dissipation is greatly reduced or eliminated during blocking events. As a result, blocking patterns may be more persistent and therefore more predictable.

Hansen, A. R.↗

NASA NTRS1986

Multiple grid problems on concurrent-processing computers

Three computer codes were studied which make use of concurrent processing computer architectures in computational fluid dynamics (CFD). The three parallel codes were tested on a two processor multiple-instruction/multiple-data (MIMD) facility at NASA Ames Research Center, and are suggested for efficient parallel computations. The first code is a well-known program which makes use of the Beam and Warming, implicit, approximate factored algorithm. This study demonstrates the parallelism found in a well-known scheme and it achieved speedups exceeding 1.9 on the two processor MIMD test facility. The second code studied made use of an embedded grid scheme which is used to solve problems having complex geometries. The particular application for this study considered an airfoil/flap geometry in an incompressible flow. The scheme eliminates some of the inherent difficulties found in adapting approximate factorization techniques onto MIMD machines and allows the use of chaotic relaxation and asynchronous iteration techniques. The third code studied is an application of overset grids to a supersonic blunt body problem. The code addresses the difficulties encountered when using embedded grids on a compressible, and therefore nonlinear, problem. The complex numerical boundary system associated with overset grids is discussed and several boundary schemes are suggested. A boundary scheme based on the method of characteristics achieved the best results.

Eberhardt, D. S.↗

NASA NTRS1999

Angular-Rate Estimation Using Star Tracker Measurements

This paper presents algorithms for estimating the angular-rate vector of satellites using quaternion measurements. Two approaches are compared, one that uses differentiated quatemion measurements to yield coarse rate measurements which are then fed into two different estimators. In the other approach the raw quatemion measurements themselves are fed directly into the two estimators. The two estimators rely on the ability to decompose the non-linear rate dependent part of the rotational dynamics equation of a rigid body into a product of an angular-rate dependent matrix and the angular-rate vector itself This decomposition, which is not unique, enables the treatment of the nonlinear spacecraft dynamics model as a linear one and, consequently, the application of a Pseudo-Linear Kalman Filter (PSELIKA). It also enables the application of a special Kalman filter which is based on the use of the solution of the State Dependent Algebraic Riccati Equation (SDARE) in order to compute the Kalman gain matrix and thus eliminates the need to propagate and update the filter covariance matrix. The replacement of the elaborate rotational dynamics by a simple first order Markov model is also examined. In this paper a special consideration is given to the problem of delayed quatemion measurements. Two solutions to this problem are suggested and tested. Real Rossi X-Ray Timing Explorer (RXTE) data is used to test these algorithms, and results of these tests are presented.

Azor, R.↗

NASA NTRS1999

Angular-Rate Estimation using Star Tracker Measurements

This paper presents algorithms for estimating the angular-rate vector of satellites using quaternion measurements. Two approaches are compared, one that uses differentiated quaternion measurements to yield coarse rate measurements which are then fed into two different estimators. In the other approach the raw quaternion measurements themselves are fed directly into the two estimators. The two estimators rely on the ability to decompose the non-linear rate dependent part of the rotational dynamics equation of a rigid body into a product of an angular-rate dependent matrix and the angular-rate vector itself. This decomposition, which is not unique, enables the treatment of the nonlinear spacecraft dynamics model as a linear one and, consequently, the application of a Pseudo-Linear Kalman Filter (PSELIKA). It also enables the application of a special Kalman filter which is based on the use of the solution of the State Dependent Algebraic Riccati Equation (SDARE) in order to compute the Kalman gain matrix and thus eliminates the need to propagate and update the filter covariance matrix. The replacement of the elaborate rotational dynamics by a simple first order Markov model is also examined. In this paper a special consideration is given to the problem of delayed quaternion measurements. Two solutions to this problem are suggested and tested. Real Rossi X-Ray Timing Explorer (RXTE) data is used to test these algorithms, and results of these tests are presented.

Azor, R.↗

NASA NTRS1992

Turbulent transport of a passive-scalar field by using a renormalization-group method

A passive-scalar field is considered to evolve under the influence of a turbulent fluid governed by the Navier-Stokes equation. Turbulent-transport coefficients are calculated by small-scale elimination using a renormalization-group method. Turbulent processes couple both the viscosity and the diffusivity. In the absence of any correlation between the passive-scalar fluctuations and any component of the fluid velocity, the renormalized diffusivity is essentially the same as if the fluid velocity were frozen, although the renormalized equation does contain higher-order nonlinear terms involving viscosity. This arises due to the nonlinear interaction of the velocity with itself. In the presence of a finite correlation, the turbulent diffusivity becomes coupled with both the velocity field and the viscosity. There is then a dependence of the turbulent decay of the passive scalar on the turbulent Prandtl number.

Hossain, Murshed↗

NASA NTRS1992

Direct model reference adaptive control with application to flexible robots

A modification to a direct command generator tracker-based model reference adaptive control (MRAC) system is suggested in this paper. This modification incorporates a feedforward into the reference model's output as well as the plant's output. Its purpose is to eliminate the bounded model following error present in steady state when previous MRAC systems were used. The algorithm was evaluated using the dynamics for a single-link flexible-joint arm. The results of these simulations show a response with zero steady state model following error. These results encourage further use of MRAC for various types of nonlinear plants.

Steinvorth, Rodrigo↗

NASA NTRS1992

A geometrically nonlinear theory of elastic plates

A set of kinematic and intrinsic equilibrium equations is derived for plates undergoing large deflection and rotation but with small strain. The large rotation is treated by the general finite rotation of a frame in which the material points that are originally along a normal line in the undeformed plate undergo only small displacements. Exact intrinsic virtual strain-displacement relations are derived; using a reduced 2-D strain energy function from which the warping has been systematically eliminated, a set of intrinsic equilibrium equations follows. It is demonstrated that only five equilibrium equations can be derived in this way, because the component of virtual rotation about the normal is not independent. These equations include terms which cannot be obtained without the use of a finite rotation vector which contains three nonzero components. These extra terms correspond to the difference of in-plane shear stress resultants in other theories.

Hodges, Dewey H.↗

NASA NTRS1987

Development and evaluation of improved numerical schemes for recirculating flows

The paper examines the performance of the flux-spline scheme for convection-diffusion. Computations are presented for a number of test cases, both linear and nonlinear. It is shown that in all cases the flux-spline scheme yields results which are superior to those obtained with the lower-order formulations such as hybrid differencing. In order to improve the computational efficiency, the flux-spline scheme has been combined with a direct solution algorithm for the continuity and momentum equations. Such an approach eliminates the need for an equation for pressure or pressure correction and is found to be rapidly convergent.

Patankar, S. V.↗