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NASA NTRS1990

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. Part 1: The ODE connection and its implications for algorithm development in computational fluid dynamics

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Yee, H. C.↗

NASA NTRS1991

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I - The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics

Yee, H. C.↗

NASA NTRS1974

The effect of spurious angular accelerations on tracking in dynamic simulation

A laboratory study was conducted to investigate the effect of spurious simulator yaw motions on a pilot's control performance. A second objective was to compare the efficiency of static and dynamic simulator tracking in previously unexamined vehicle dynamics. Twelve airline pilots served as subjects in a moving-base flight simulator under congruent-motion, spurious-motion, and no-motion conditions. The results indicated a significant increase in the amount of error with increasing levels of spurious motion during the initially administered series of trials. The influence of spurious motion, however, was absent in a second series of trials. The data suggest that the pilots learned to compensate in their performance for the spurious inputs. It was also found that congruent visual and rotational cueing produced superior performance to that of tracking with visual information alone.

Beck, L. J.↗

NASA NTRS1993

Spurious symptom reduction in fault monitoring

Previous work accomplished on NASA's Faultfinder concept suggested that the concept was jeopardized by spurious symptoms generated in the monitoring phase. The purpose of the present research was to investigate methods of reducing the generation of spurious symptoms during in-flight engine monitoring. Two approaches for reducing spurious symptoms were investigated. A knowledge base of rules was constructed to filter known spurious symptoms and a neural net was developed to improve the expectation values used in the monitoring process. Both approaches were effective in reducing spurious symptoms individually. However, the best results were obtained using a hybrid system combining the neural net capability to improve expectation values with the rule-based logic filter.

Shontz, William D.↗

NASA NTRS1972

Congruent and spurious motion in the learning and performance of a compensatory tracking task.

Examination of the importance of congruent and spurious yaw motion in compensatory tracking by eight airline pilots. The pilots, seated erect in the Ames man-carrying rotation device(MCRD), tracked with k/s+1 and k/s(s+1) vehicle dynamics in fixed- and moving-base simulation. Following the learning phase of the experiment, five levels of spurious angular acceleration were superimposed on the motion of the MCRD. Learning of the tracking task was found to be a function of both vehicle dynamics and mode of simulation. The presence of congruent motion information reduced learningtime in k/s(s+1) vehicle dynamics and resulted in lower tracking error in both vehicle dynamics. The spurious angular accelerations resulted in an increase in pilot tracking error; however, the relationship between the magnitude of the acceleration and its effect was highly complex. The data suggest that the minimal disturbance level for spurious angular accelerations during tracking is below 0.4 degec.

Guercio, J. G.↗

NASA NTRS1995

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations: Global Asymptotic Behavior of Time Discretizations - 2

The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

Yee, H. C.↗

NASA NTRS1995

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations: Global Asymptotic Behavior of Time Discretizations - Part 2

The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.

Yee, H. C.↗

NASA NTRS2005

"The Design of a Compact, Wide Spurious-Suppression Bandwidth Bandpass Filter Using Stepped Impedance Resonators"

We propose an analytical design for a microstrip broadband spurious-suppression filter. The proposed design uses every section of the transmission lines as both a coupling and a spurious suppression element, which creates a very compact, planar filter. While a traditional filter length is greater than the multiple of the quarter wavelength at the center passband frequency (lambda(sub g)/4), the proposed filter length is less than (order n(Ssup th) + l)center dot lambda(sub g)/8. The filter s spurious response and physical dimension are controlled by the step impedance ratio (R) between two transmission line sections as a lambda(sub g)/4 resonator. The experimental result shows that, with R of 0.2, the out-of-band attenuation is greater than 40 dB; and the first spurious mode is shifted to more than 5 times the fundamental frequency. Moreover, it is the most compact planar filter design to date. The results also indicate a low in-band insertion loss.

U-Yen, Kongpop↗

NASA NTRS1978

Steady state spurious errors in shock-capturing numerical schemes

The behavior of the steady state spurious error modes of the MacCormack scheme and the upwind scheme of Warming and Beam was obtained from a linearized difference equation for the steady state error. It was shown that the spurious errors can exist either as an eigensolution of the homogeneous part of this difference equation or because of excitation from large discretization errors near oblique shocks. It was found that the upwind scheme does not permit spurious oscillations on the upstream side of shocks. Examples are given for the inviscid Burgers' equation and for one and two dimensional gasdynamic flows.

Karlsen, L. K.↗

NASA NTRS1987

Causes of spurious features in spectral reflectance data

Several techniques are becoming common in the analysis of imaging spectrometer data that can lead to spurious absorption features or to changes in the position, width, and shape of actual absorption features. It is a common practice to calibrate AIS or other imaging spectrometer data by averaging each pixel along the flight line. The average is used to calibrate the spectral data by dividing the spectrum at each pixel by the average. If some pixels in the data set contain an absorption, then the average will also show an absorption. Some AIS data has had problems with wavelength stability from one scan line to the next which can produce spurious features with some analysis methods. If a pixel has a spectrum with an absorption having a different position or width than the spectrum used in a ratio, then the ratio can produce a spurious absorption at a different position and width than the true absorption feature. An average spectrum ratioed to each pixel will produce band shifts, and changes in width or shape. If continuum removal is performed by substraction rather than division, band positions can also be shifted.

Clark, Roger N.↗

NASA NTRS1989

Elimination of spurious eigenvalues in the Chebyshev tau spectral method

Spectral methods have been used to great advantage in hydrodynamic stability calculations; the concepts are described in Orszag's seminal application of the Chebyshev tau method to the Orr-Sommerfeld equation for plane Poiseuille flow in 1971. Orszag discusses both the Chebyshev Galerkin and the Chebyshev tau methods, but presents results for the tau method, which is easier to implement than the Galerkin method. The tau method has the disadvantage that two unstable eigenvalues are produced that are artifacts of the discretization. An extremely simple modification to the Chebyshev tau method is presented which eliminates the spurious eigenvalues. First a simplified model of the Orr-Sommerfeld equation discussed by Gottlieb and Orszag was studied. Then the Chebyshev tau method is considered, which has two spurious eigenvalues, and then a modification which eliminates them is described. Finally, results for the Orr-Sommerfeld equation are considered where the modified tau method also eliminates the spurious eigenvalues. The simplicity of the modification makes it a convenient alternative to other approaches to the problem.

Mcfadden, G. B.↗

NASA NTRS1990

Removing spurious reflections from CFD solutions by using the Complex Cepstrum

The Complex Cepstrum is shown to remove spurious reflections from artificial boundaries in computational fluid dynamic (CFD) solutions. First, the Complex Cepstrum theory is presented. A model time sequence consisting of a direct signal and reflections is analyzed theoretically with the Complex Cepstrum, and it is shown that the direct signal uncontaminated by reflections may be recovered in the time domain. Next, the Complex Cepstrum is applied to one- and three-dimensional CFD solutions, and spurious reflections from the boundary conditions are removed. By eliminating spurious reflections introduced by artificial boundary conditions, the applicability of CFD methods to aeroacoustic problems is greatly enhanced.

Meadows, Kristine R.↗

NASA NTRS1990

Elimination of spurious eigenvalues in the Chebyshev tau spectral method

A very simple modification is presented for the Chebyshev tau method which can eliminate spurious eigenvalues, proceeding from a consideration of the vorticity-streamfunction reformulation of the Chebyshev tau method and the Chebyshev-Galerkin method, which have no spurious modes. Consideration of a model problem indicates that these two approaches are equivalent, and that they reduce to the present modification of the tau method. This modified tau method also eliminates spurious eigenvalues from the Orr-Sommerfeld equation.

Mcfadden, G. B.↗

NASA NTRS1992

Spurious Modes in Spectral Collocation Methods with Two Non-Periodic Directions

Collocation implementation of the Kleiser-Schumann's method in geometries with two non-periodic directions is shown to suffer from three spurious modes - line, column and checkerboard - contaminating the computed pressure field. The corner spurious modes are also present but they do not affect evaluation of pressure related quantities. A simple methodology in the inversion of the influence matrix will efficiently filter out these spurious modes.

Balachandar, S.↗

NASA NTRS2005

Ultra-Compact Broadband High-Spurious Suppression Bandpass Filter Using Double Split-end Stepped Impedance Resonators

We propose an ultra compact single-layer spurious suppression band pass filter design which has the following benefit: 1) Effective coupling area can be increased with no fabrication limitation and no effect on the spurious response; 2) Two fundamental poles are introduced to suppress spurs; 3) Filter can be designed with up to 30% bandwidth; 4) The Filter length is reduced by at least 100% when compared to the conventional filter; 5) Spurious modes are suppressed up to at the seven times the fundamental frequency; and 6) It uses only one layer of metallization which minimize the fabrication cost.

U-Yen, Kongpop↗

NASA NTRS2017

Identification of Spurious Signals from Permeable Ffowcs Williams and Hawkings Surfaces

Integral forms of the permeable surface formulation of the Ffowcs Williams and Hawkings (FW-H) equation often require an input in the form of a near field Computational Fluid Dynamics (CFD) solution to predict noise in the near or far field from various types of geometries. The FW-H equation involves three source terms; two surface terms (monopole and dipole) and a volume term (quadrupole). Many solutions to the FW-H equation, such as several of Farassat's formulations, neglect the quadrupole term. Neglecting the quadrupole term in permeable surface formulations leads to inaccuracies called spurious signals. This paper explores the concept of spurious signals, explains how they are generated by specifying the acoustic and hydrodynamic surface properties individually, and provides methods to determine their presence, regardless of whether a correction algorithm is employed. A potential approach based on the equivalent sources method (ESM) and the sensitivity of Formulation 1A (Formulation S1A) is also discussed for the removal of spurious signals.

Lopes, Leonard V.↗

NASA NTRS1965

Spurious signals in satellite command systems

Problems encountered in operation of Relay I satellite generalized to spurious signals in satellite command systems - Error probabilities for command failures and spurious commands

SIGNAL RECEPTION↗

NASA NTRS1975

Scanning Kirkpatrick-Baez X-ray telescope to maximize effective area and eliminate spurious images - Design

We consider the design of a Kirkpatrick-Baez grazing-incidence X-ray telescope to be used in a scan of the sky and analyze the distribution of both properly reflected rays and spurious images over the field of view. To obtain maximum effective area over the field of view, it is necessary to increase the spacing between plates for a scanning telescope as compared to a pointing telescope. Spurious images are necessarily present in this type of lens, but they can be eliminated from the field of view by adding properly located baffles or collimators. Results of a computer design are presented.

Kast, J. W.↗