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NASA NTRS1984

High-resolution frequency determination of discrete signal components

An important problem in many applications involves the determination of the frequency of a limited set of sinusoidal components in a time domain signal. The Fourier transform is used as the fundamental tool for conversion to the frequency domain. In the present investigation, an analysis is conducted of the errors inherent in the use of the Fourier transform without time domain windowing, and an algorithm is developed which makes it possible to obtain the frequency of the component signals with high accuracy. This algorithm combines the advantages of the Gaussian window with the computational efficiency of the Fast Fourier Transform (FFT).

Walton, E. K.↗

DOE OSTI2024

Analysis of Power-Maximizing Region 2 Controllers for Wind and Marine Turbines

Wind and marine energy are rapidly growing and complementary technologies that share some techniques for simplified modeling and control, particularly in below-rated flow speeds. A turbine operator has several choices of controller for maximizing power in Region 2. The simple and ubiquitous KΩ 2 control law is often effective but limited in its flexibility. Alternative controllers use reference tracking to split the control objectives into a low-bandwidth optimal tip-speed ratio tracking loop to maximize steady-state power and a higher-bandwidth proportional-integral control loop to reject inflow turbulence. Several options exist for identifying the slowly varying optimal set point during operation, based on estimating the inflow velocity or filtering the power or torque signals. This study compares the trade-offs between performance and other design priorities for a few choices of reference-tracking controller in the literature for reference wind and marine turbines. Analysis is performed in the frequency domain using the linearization of each controller, and the impact of turbulent disturbances on the closed-loop system is described. The controllers are simulated in OpenFAST to analyze their performance with higher-order nonlinear turbine dynamics.

17 WIND ENERGY↗

NASA NTRS1974

Computer Program for Thin Wire Antenna over a Perfectly Conducting Ground Plane

A computer program is presented for a thin-wire antenna over a perfect ground plane. The analysis is performed in the frequency domain, and the exterior medium is free space. The antenna may have finite conductivity and lumped loads. The output data includes the current distribution, impedance, radiation efficiency, and gain. The program uses sinusoidal bases and Galerkin's method.

Richmond, J. H.↗

NASA NTRS1996

ASTROP2 Users Manual: A Program for Aeroelastic Stability Analysis of Propfans

This manual describes the input data required for using the second version of the ASTROP2 (Aeroelastic STability and Response Of Propulsion systems - 2 dimensional analysis) computer code. In ASTROP2, version 2.0, the program is divided into two modules: 2DSTRIP, which calculates the structural dynamic information; and 2DASTROP, which calculates the unsteady aerodynamic force coefficients from which the aeroelastic stability can be determined. In the original version of ASTROP2, these two aspects were performed in a single program. The improvements to version 2.0 include an option to account for counter rotation, improved numerical integration, accommodation for non-uniform inflow distribution, and an iterative scheme to flutter frequency convergence. ASTROP2 can be used for flutter analysis of multi-bladed structures such as those found in compressors, turbines, counter rotating propellers or propfans. The analysis combines a two-dimensional, unsteady cascade aerodynamics model and a three dimensional, normal mode structural model using strip theory. The flutter analysis is formulated in the frequency domain resulting in an eigenvalue determinant. The flutter frequency and damping can be inferred from the eigenvalues.

Reddy, T. S. R.↗

NASA NTRS1997

Development of a Model Based Technique for Gear Diagnostics using the Wigner-Ville method

Imperfections in gear tooth geometry often result from errors in the manufacturing process or excessive material wear during operation. Such faults in the gear tooth geometry can result in large vibrations in the transmission system, and, in some cases, may lead to early failure of the gear transmission system. This report presents the study of the effects of imperfection in gear tooth geometry on the dynamic characteristics of a gear transmission system. The faults in the gear tooth geometry are modeled numerically as the deviation of the tooth profile from its original involute geometry. The changes in gear mesh stiffness due to various profile and pattern variations are evaluated numerically. The resulting changes in the mesh stiffness are incorporated into a computer code to simulate the dynamics of the gear transmission system. A parametric study is performed to examine the sensitivity of gear tooth geometry imperfections on the vibration of a gear transmission system. The parameters variations in this study consist of the magnitude of the imperfection, the pattern of the profile variation, and the total number of teeth affected. Numerical results from the dynamic simulations are examined in both the time and the frequency domains. A joint time-frequency analysis procedure using the Wigner-Ville Distribution is also introduced to identify the location of the damaged tooth from the vibration signature. Numerical simulations of the system dynamics with gear faults were compared to experimental results. An optimal tracker was introduced to quantify the level of damage in the gear mesh system. Conclusions are drawn from the results of this numerical study.

Choy, F.↗

NASA NTRS2003

Microstructural and Defect Characterization in Ceramic Composites Using an Ultrasonic Guided Wave Scan System

In this study, an ultrasonic guided wave scan system was used to characterize various microstructural and flaw conditions in two types of ceramic matrix composites, SiC/SiC and C/SiC. Rather than attempting to isolate specific lamb wave modes to use for characterization (as is desired for many types of guided wave inspection problems), the guided wave scan system utilizes the total (multi-mode) ultrasonic response in its inspection analysis. Several time and frequency-domain parameters are calculated from the ultrasonic guided wave signal at each scan location to form images. Microstructural and defect conditions examined include delamination, density variation, cracking, and pre/ post-infiltration. Results are compared with thermographic imaging methods. Although the guided wave technique is commonly used so scanning can be eliminated, applying the technique in the scanning mode allows a more precise characterization of defect conditions.

Roth, D. J.↗

NASA NTRS2023

Unsteady RANS and Scale Resolving Simulations of Open Rotor Noise

Computational simulations using structured curvilinear overset grids with the Launch Ascent and Vehicle Aerodynamics (LAVA) framework are presented for predicting the aerodynamic and aeroacoustic behavior of a contra-rotating open rotor (CROR) propulsion system using a newly developed and computationally efficient sliding mesh technique. A comprehensive evaluation of two turbulence closure treatments is carried out as part of the scope of this work: Unsteady Reynolds-Averaged Navier-Stokes Simulation (URANS), and Hybrid RANS/LES (HRLES). The computed results are then validated against existing experimental measurements at both the nominal take-off and cruise flight conditions. To propagate the noise generated by the near-field CROR system, aeroacoustic analysis based on a frequency-domain permeable surface Ffowcs Williams-Hawkings (FW-H) approach is applied.

ARMD↗

NASA NTRS2023

Unsteady RANS and Scale Resolving Simulations of Open Rotor Noise

ARMD↗

NASA NTRS1999

Time-Frequency Analysis of the Dispersion of Lamb Modes

Accurate knowledge of the velocity dispersion of Lamb modes is important for ultrasonic nondestructive evaluation methods used in detecting and locating flaws in thin plates and in determining their elastic stiffness coefficients. Lamb mode dispersion is also important in the acoustic emission technique for accurately triangulating the location of emissions in thin plates. In this research, the ability to characterize Lamb mode dispersion through a time-frequency analysis (the pseudo-Wigner-Ville distribution) was demonstrated. A major advantage of time-frequency methods is the ability to analyze acoustic signals containing multiple propagation modes, which overlap and superimpose in the time domain signal. By combining time-frequency analysis with a broadband acoustic excitation source, the dispersion of multiple Lamb modes over a wide frequency range can be determined from as little as a single measurement. In addition, the technique provides a direct measurement of the group velocity dispersion. The technique was first demonstrated in the analysis of a simulated waveform in an aluminum plate in which the Lamb mode dispersion was well known. Portions of the dispersion curves of the AO, A I , So, and S2 Lamb modes were obtained from this one waveform. The technique was also applied for the analysis of experimental waveforms from a unidirectional graphite/epoxy composite plate. Measurements were made both along and perpendicular to the fiber direction. In this case, the signals contained only the lowest order symmetric and antisymmetric modes. A least squares fit of the results from several source to detector distances was used. Theoretical dispersion curves were calculated and are shown to be in good agreement with experimental results.

Prosser, W. H.↗

NASA NTRS1999

Time-Frequency Analysis of the Dispersion of Lamb Modes

Accurate knowledge of the velocity dispersion of Lamb modes is important for ultrasonic nondestructive evaluation methods used in detecting and locating flaws in thin plates and in determining their elastic stiffness coefficients. Lamb mode dispersion is also important in the acoustic emission technique for accurately triangulating the location of emissions in thin plates. In this research, the ability to characterize Lamb mode dispersion through a time-frequency analysis (the pseudo Wigner-Ville distribution) was demonstrated. A major advantage of time-frequency methods is the ability to analyze acoustic signals containing multiple propagation modes, which overlap and superimpose in the time domain signal. By combining time-frequency analysis with a broadband acoustic excitation source, the dispersion of multiple Lamb modes over a wide frequency range can be determined from as little as a single measurement. In addition, the technique provides a direct measurement of the group velocity dispersion. The technique was first demonstrated in the analysis of a simulated waveform in an aluminum plate in which the Lamb mode dispersion was well known. Portions of the dispersion curves of the A(sub 0), A(sub 1), S(sub 0), and S(sub 2)Lamb modes were obtained from this one waveform. The technique was also applied for the analysis of experimental waveforms from a unidirectional graphite/epoxy composite plate. Measurements were made both along, and perpendicular to the fiber direction. In this case, the signals contained only the lowest order symmetric and antisymmetric modes. A least squares fit of the results from several source to detector distances was used. Theoretical dispersion curves were calculated and are shown to be in good agreement with experimental results.

Prosser, W. H.↗

NASA NTRS1988

Experimental implementation of adaptive control for flexible space structures

On-going research at The Aerospace Corporation studying the feasibility of applying adaptive control methodologies to the control of flexible space structures is described. A laboratory testbed was established to test system identification and control approaches. The laboratory set-up and controller design approach are discussed. The ARX least squares parameter estimation technique is analyzed in terms of frequency domain transfer function bias error. This analysis approach enables the determination of the effects of sampling rate, sensor type, and data prefiltering on the estimation performance. The ability to identify space structure dynamics over a range of frequencies is shown to be heavily dependent on these factors.

Mcgraw, Gary A.↗

NASA NTRS1982

Long term frequency stability analysis of the GPS NAVSTAR 6 Cesium clock

Time domain measurements, taken between the NAVSTAR 6 Spacecraft Vehicle (SV) and the Vandenberg Global Positioning System (GPS) Monitor Site, by a pseudo random noise receiver, were collected over an extended period of time and analyzed to estimate the long term frequency stability of the NAVSTAR 6 onboard frequency standard, referenced to the Vandenberg MS frequency standard. The technique employed separates the clock offset from the composite signal by first applying corrections for equipment delays, ionospheric delay, tropospheric delay, Earth rotation and the relativistic effect. The data are edited and smoothed using the predicted SV ephemeris to calculate the geometric delay. Then all available passes from each of the four GPS monitor stations, are collected at 1-week intervals and used to calculate the NAVSTAR orbital elements. The procedure is then completed by subtracting the corrections and the geometric delay, using the final orbital elements, from the composite signal, thus leaving the clock offset and random error.

Mccaskill, T. B.↗

NASA NTRS1978

Stability of constant gain systems with vector feedback

The state space, the controllability, and the observability concepts are discussed in connection with the proposed stability analysis which permits drastic dimensional reductions for a vector feedback problem. Any constant gain system's stability can thus be analyzed in the frequency domain with a single Nyquist plot. The analysis considers the total system with all loops closed, a disturbance vector as input, and the feedback vector as output. All constant gain systems are shown to be decomposable into stable subsystems where the degree of the decomposition determines the dimensions. The maximum decomposition results in the state-space approach which is the limit case. The method is demonstrated with the stability analysis of the pogo phenomenon, an oscillatory interaction between the propulsion and the structure of a space vehicle. This problem, with eigenvalues over a hundred, was drastically but rigorously reduced to a stability analysis of a 4x4 matrix.

Vonpragenau, G. L.↗

NASA NTRS1992

Flutter analysis of supersonic axial flow cascades using a high resolution Euler solver. Part 1: Formulation and validation

This report presents, in two parts, a dynamic aeroelastic stability (flutter) analysis of a cascade of blades in supersonic axial flow. Each blade of the cascade is modeled as a typical section having pitching and plunging degrees of freedom. Aerodynamic forces are obtained from a time accurate, unsteady, two-dimensional cascade solver based on the Euler equations. The solver uses a time marching flux-difference splitting (FDS) scheme. Flutter stability is analyzed in the frequency domain. The unsteady force coefficients required in the analysis are obtained by harmonically oscillating (HO) the blades for a given flow condition, oscillation frequency, and interblade phase angle. The calculated time history of the forces is then Fourier decomposed to give the required unsteady force coefficients. An influence coefficient (IC) method and a pulse response (PR) method are also implemented to reduce the computational time for the calculation of the unsteady force coefficients for any phase angle and oscillation frequency. Part 1, this report, presents these analysis methods and their validation by comparison with results obtained from linear theory for a selected flat plate cascade geometry. A typical calculation for a rotor airfoil is also included to show the applicability of the present solver for airfoil configurations. The predicted unsteady aerodynamic forces for a selected flat plate cascade geometry and flow conditions correlated well with those obtained from linear theory for different interblade phase angles and oscillation frequencies. All the three methods of predicting unsteady force coefficients, namely, HO, IC, and PR, showed good correlations with each other. It was established that only a single calculation with four blade passages is required to calculate the aerodynamic forces for any phase angle for a cascade consisting of any number of blades, for any value of the oscillation frequency. Flutter results, including mistuning effects, for a cascade of stator airfoils are presented in Part 2 of the report.

Reddy, T. S. R.↗

NASA NTRS1996

RSRM Chamber Pressure Oscillations: Transit Time Models and Unsteady CFD

Space Shuttle solid rocket motor low frequency internal pressure oscillations have been observed since early testing. The same type of oscillations also are present in the redesigned solid rocket motor (RSRM). The oscillations, which occur during RSRM burn, are predominantly at the first three motor cavity longitudinal acoustic mode frequencies. Broadband flow and combustion noise provide the energy to excite these modes at low levels throughout motor burn, however, at certain times during burn the fluctuating pressure amplitude increases significantly. The increased fluctuations at these times suggests an additional excitation mechanism. The RSRM has inhibitors on the propellant forward facing surface of each motor segment. The inhibitors are in a slot at the segment field joints to prevent burning at that surface. The aft facing segment surface at a field joint slot burns and forms a cavity of time varying size. Initially the inhibitor is recessed in the field joint cavity. As propellant burns away the inhibitor begins to protrude into the bore flow. Two mechanisms (transit time models) that are considered potential pressure oscillation excitations are cavity-edge tones, and inhibitor hole-tones. Estimates of frequency variation with time of longitudinal acoustic modes, cavity edge-tones, and hole-tones compare favorably with frequencies measured during motor hot firing. It is believed that the highest oscillation amplitudes occur when vortex shedding frequencies coincide with motor longitudinal acoustic modes. A time accurate computational fluid dynamic (CFD) analysis was made to replicate the observations from motor firings and to observe the transit time mechanisms in detail. FDNS is the flow solver used to detail the time varying aspects of the flow. The fluid is approximated as a single-phase ideal gas. The CFD model was an axisymmetric representation of the RSRM at 80 seconds into burn.Deformation of the inhibitors by the internal flow was determined through an iterative structural and CFD analysis. The analysis domain ended just upstream of the nozzle throat. This is an acoustic boundary condition that caused the motor to behave as a closed-open organ pipe. This differs from the RSRM which behaves like a closed-closed organ pipe. The unsteady CFD solution shows RSRM chamber pressure oscillations predominately at the longitudinal acoustic mode frequencies of a closed-open organ pipe. Vortex shedding in the joint cavities and at the inhibitors contribute disturbances to the flow at the second longitudinal acoustic mode frequency. Further studies are planned using an analysis domain that extends downstream of the nozzle throat.

Nesman, Tom↗

NASA NTRS1997

Accelerometer Data Analysis and Presentation Techniques

The NASA Lewis Research Center's Principal Investigator Microgravity Services project analyzes Orbital Acceleration Research Experiment and Space Acceleration Measurement System data for principal investigators of microgravity experiments. Principal investigators need a thorough understanding of data analysis techniques so that they can request appropriate analyses to best interpret accelerometer data. Accelerometer data sampling and filtering is introduced along with the related topics of resolution and aliasing. Specific information about the Orbital Acceleration Research Experiment and Space Acceleration Measurement System data sampling and filtering is given. Time domain data analysis techniques are discussed and example environment interpretations are made using plots of acceleration versus time, interval average acceleration versus time, interval root-mean-square acceleration versus time, trimmean acceleration versus time, quasi-steady three dimensional histograms, and prediction of quasi-steady levels at different locations. An introduction to Fourier transform theory and windowing is provided along with specific analysis techniques and data interpretations. The frequency domain analyses discussed are power spectral density versus frequency, cumulative root-mean-square acceleration versus frequency, root-mean-square acceleration versus frequency, one-third octave band root-mean-square acceleration versus frequency, and power spectral density versus frequency versus time (spectrogram). Instructions for accessing NASA Lewis Research Center accelerometer data and related information using the internet are provided.

Rogers, Melissa J. B.↗

NASA NTRS1984

Comparison of frequency-domain and time-domain rotorcraft vibration control methods

Active control of rotor-induced vibration in rotorcraft has received significant attention recently. Two classes of techniques have been proposed. The more developed approach works with harmonic analysis of measured time histories and is called the frequency-domain approach. The more recent approach computes the control input directly using the measured time history data and is called the time-domain approach. The report summarizes the results of a theoretical investigation to compare the two approaches. Five specific areas were addressed: (1) techniques to derive models needed for control design (system identification methods), (2) robustness with respect to errors, (3) transient response, (4) susceptibility to noise, and (5) implementation difficulties. The system identification methods are more difficult for the time-domain models. The time-domain approach is more robust (e.g., has higher gain and phase margins) than the frequency-domain approach. It might thus be possible to avoid doing real-time system identification in the time-domain approach by storing models at a number of flight conditions. The most significant error source is the variation in open-loop vibrations caused by pilot inputs, maneuvers or gusts. The implementation requirements are similar except that the time-domain approach can be much simpler to implement if real-time system identification were not necessary.

Gupta, N. K.↗

NASA NTRS1999

Cardiac interbeat interval dynamics from childhood to senescence : comparison of conventional and new measures based on fractals and chaos theory

BACKGROUND: New methods of R-R interval variability based on fractal scaling and nonlinear dynamics ("chaos theory") may give new insights into heart rate dynamics. The aims of this study were to (1) systematically characterize and quantify the effects of aging from early childhood to advanced age on 24-hour heart rate dynamics in healthy subjects; (2) compare age-related changes in conventional time- and frequency-domain measures with changes in newly derived measures based on fractal scaling and complexity (chaos) theory; and (3) further test the hypothesis that there is loss of complexity and altered fractal scaling of heart rate dynamics with advanced age. METHODS AND RESULTS: The relationship between age and cardiac interbeat (R-R) interval dynamics from childhood to senescence was studied in 114 healthy subjects (age range, 1 to 82 years) by measurement of the slope, beta, of the power-law regression line (log power-log frequency) of R-R interval variability (10(-4) to 10(-2) Hz), approximate entropy (ApEn), short-term (alpha(1)) and intermediate-term (alpha(2)) fractal scaling exponents obtained by detrended fluctuation analysis, and traditional time- and frequency-domain measures from 24-hour ECG recordings. Compared with young adults (<40 years old, n=29), children (<15 years old, n=27) showed similar complexity (ApEn) and fractal correlation properties (alpha(1), alpha(2), beta) of R-R interval dynamics despite lower spectral and time-domain measures. Progressive loss of complexity (decreased ApEn, r=-0.69, P<0.001) and alterations of long-term fractal-like heart rate behavior (increased alpha(2), r=0.63, decreased beta, r=-0.60, P<0.001 for both) were observed thereafter from middle age (40 to 60 years, n=29) to old age (>60 years, n=29). CONCLUSIONS: Cardiac interbeat interval dynamics change markedly from childhood to old age in healthy subjects. Children show complexity and fractal correlation properties of R-R interval time series comparable to those of young adults, despite lower overall heart rate variability. Healthy aging is associated with R-R interval dynamics showing higher regularity and altered fractal scaling consistent with a loss of complex variability.

NASA Discipline Cardiopulmonary↗