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NASA NTRS2002

NASA Hybrid Reflectometer Project

Time-domain and frequency-domain reflectometry have been used for about forty years to locate opens and shorts in cables. Interpretation of reflectometry data is as much art as science. Is there information in the data that is being missed? Can the reflectometers be improved to allow us to detect and locate defects in cables that are not outright shorts or opens? The Hybrid Reflectometer Project was begun this year at NASA Ames Research Center, initially to model wire physics, simulating time-domain reflectometry (TDR) signals in those models and validating the models against actual TDR data taken on testbed cables. Theoretical models of reflectometry in wires will give us an understanding of the merits and limits of these techniques and will guide the application of a proposed hybrid reflectometer with the aim of enhancing reflectometer sensitivity to the point that wire defects can be detected. We will point out efforts by some other researchers to apply wire physics models to the problem of defect detection in wires and we will describe our own initial efforts to create wire physics models and report on testbed validation of the TDR simulations.

Lynch, Dana↗

NASA NTRS2017

A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.

Hu, Fang↗

NASA NTRSDate not supplied

NESC GN&C TDT Workshop on 2D Image Motion Optical Transfer Functions, Pointing Performance Analysis, and Requirements

What You Will Learn: The focus is on payload imaging performance due to pointing motion. Some historical background on pointing performance analysis is given. The Optical Transfer Function (OTF) and Modulation Transfer Function (MTF) are defined. The imaging performance due to pointing motion is measured by image motion optical transfer functions (IM OTF). IM OTFs are defined for displacement, smear, and jitter motions, which are all rigorously defined. Deterministic and Statistical IM OTFs are briefly derived and graphically illustrated and compared. The IM OTFs are parameterized by pointing error metrics(PEM), which are means and covariances of displacement, smear, and jitter. Emphasis is on procedures and algorithms to evaluate the image motion optical transfer functions and pointing error metrics. Three procedures are covered, which depend on whether the pointing error data is from time-domain simulation, frequency-domain analysis, or stochastic modeling. A method to evaluate the relative contribution of disturbance sources and to identify the most significant contributors is presented. The presentation includes pertinent discussion of flexible structures and control-structure interaction. No single book can adequately cover this subject, so a book is not required for the course. A list of selected articles, reports, documents, and books is provided for reference and further study. Mathis kept to the minimum necessary to convey principles; lengthy derivations are left to the reference material. Graphics are used to illustrate concepts. As with any such learning endeavor, the knowledge gained will be retained and strengthened through actual practice.c©2019–2021 Mark E. Pittelkau— 5

NASA Engineering and Safety Center (NESC)↗

NASA NTRS2003

Detailed Vibration Analysis of Pinion Gear with Time-Frequency Methods

In this paper, the authors show a detailed analysis of the vibration signal from the destructive testing of a spiral bevel gear and pinion pair containing seeded faults. The vibration signal is analyzed in the time domain, frequency domain and with four time-frequency transforms: the Short Time Frequency Transform (STFT), the Wigner-Ville Distribution with the Choi-Williams kernel (WV-CW), the Continuous Wavelet' Transform (CWT) and the Discrete Wavelet Transform (DWT). Vibration data of bevel gear tooth fatigue cracks, under a variety of operating load levels and damage conditions, are analyzed using these methods. A new metric for automatic anomaly detection is developed and can be produced from any systematic numerical representation of the vibration signals. This new metric reveals indications of gear damage with all of the time-frequency transforms, as well as time and frequency representations, on this data set. Analysis with the CWT detects changes in the signal at low torque levels not found with the other transforms. The WV-CW and CWT use considerably more resources than the STFT and the DWT. More testing of the new metric is needed to determine its value for automatic anomaly detection and to develop fault detection methods for the metric.

Mosher, Marianne↗

NASA NTRS2002

Scanning Ultrasonic Spectroscopy System Developed for the Inspection of Composite Flywheels

Composite flywheels are being considered as replacements for chemical batteries aboard the International Space Station. A flywheel stores energy in a spinning mass that can turn a generator to meet power demands. Because of the high rotational speeds of the spinning mass, extensive testing of the flywheel system must be performed prior to flight certification. With this goal in mind, a new scanning system has been developed at the NASA Glenn Research Center for the nondestructive inspection of composite flywheels and flywheel subcomponents. The system uses ultrasonic waves to excite a material and examines the response to detect and locate flaws and material variations. The ultrasonic spectroscopy system uses a transducer to send swept-frequency ultrasonic waves into a test material and then receives the returning signal with a second transducer. The received signal is then analyzed in the frequency domain using a fast Fourier transform. A second fast Fourier transform is performed to examine the spacing of the peaks in the frequency domain. The spacing of the peaks is related to the standing wave resonances that are present in the material because of the constructive and destructive interferences of the waves in the full material thickness as well as in individual layers within the material. Material variations and flaws are then identified by changes in the amplitudes and positions of the peaks in both the frequency and resonance spacing domains. This work, conducted under a grant through the Cleveland State University, extends the capabilities of an existing point-by-point ultrasonic spectroscopy system, thus allowing full-field automated inspection. Results of an ultrasonic spectroscopy scan of a plastic cylinder with intentionally seeded flaws. The result of an ultrasonic spectroscopy scan of a plastic cylinder used as a proof-of-concept specimen is shown. The cylinder contains a number of flat bottomed holes of various sizes and shapes. The scanning system was able to successfully detect all the defects in the material. Ultrasonic spectroscopy results for a second specimen are shown along with a conventional ultrasonic C-scan. The second specimen is a section of a flywheel subcomponent that has a series of drilled holes and notches. This specimen is employed as a defect detection standard to evaluate the various nondestructive evaluation methods under consideration. Scanning results demonstrate the ability of the system to detect flaws on the order of 10 mils in the radial direction and 5 mils in the circumferential direction. Work conducted to date has shown that scanning ultrasonic spectroscopy is a viable tool for the inspection of composite flywheel systems. Ongoing development work is focused on refining the system and scanning parameters for improved resolution and defect detection.

Martin, Richard E.↗

NASA NTRS1996

Periodic Time-Domain Nonlocal Nonreflecting Boundary Conditions for Duct Acoustics

Periodic time-domain boundary conditions are formulated for direct numerical simulation of acoustic waves in ducts without flow. Well-developed frequency-domain boundary conditions are transformed into the time domain. The formulation is presented here in one space dimension and time; however, this formulation has an advantage in that its extension to variable-area, higher dimensional, and acoustically treated ducts is rigorous and straightforward. The boundary condition simulates a nonreflecting wave field in an infinite uniform duct and is implemented by impulse-response operators that are applied at the boundary of the computational domain. These operators are generated by convolution integrals of the corresponding frequency-domain operators. The acoustic solution is obtained by advancing the Euler equations to a periodic state with the MacCormack scheme. The MacCormack scheme utilizes the boundary condition to limit the computational space and preserve the radiation boundary condition. The success of the boundary condition is attributed to the fact that it is nonreflecting to periodic acoustic waves. In addition, transient waves can pass rapidly out of the solution domain. The boundary condition is tested for a pure tone and a multitone source in a linear setting. The effects of various initial conditions are assessed. Computational solutions with the boundary condition are consistent with the known solutions for nonreflecting wave fields in an infinite uniform duct.

Watson, Willie R.↗

NASA NTRS1984

Power spectral ensity of markov texture fields

Texture is an important image characteristic. A variety of spatial domain techniques were proposed for extracting and utilizing textural features for segmenting and classifying images. for the most part, these spatial domain techniques are ad hos in nature. A markov random field model for image texture is discussed. A frequency domain description of image texture is derived in terms of the power spectral density. This model is used for designing optimum frequency domain filters for enhancing, restoring and segmenting images based on their textural properties.

Shanmugan, K. S.↗

NASA NTRS1973

An innovative approach to compensator design

The design is considered of a computer-aided-compensator for a control system from a frequency domain point of view. The design technique developed is based on describing the open loop frequency response by n discrete frequency points which result in n functions of the compensator coefficients. Several of these functions are chosen so that the system specifications are properly portrayed; then mathematical programming is used to improve all of these functions which have values below minimum standards. To do this, several definitions in regard to measuring the performance of a system in the frequency domain are given, e.g., relative stability, relative attenuation, proper phasing, etc. Next, theorems which govern the number of compensator coefficients necessary to make improvements in a certain number of functions are proved. After this a mathematical programming tool for aiding in the solution of the problem is developed. This tool is called the constraint improvement algorithm. Then for applying the constraint improvement algorithm generalized, gradients for the constraints are derived. Finally, the necessary theory is incorporated in a Computer program called CIP (compensator Improvement Program). The practical usefulness of CIP is demonstrated by two large system examples.

Mitchell, J. R.↗

NASA NTRS1988

An efficient approach for statistical calculations with globally gridded filtered time series

The formulas for performing several statistical calculations based on Fourier coefficients are presented for use in atmospheric observational studies. The calculations discussed include a method for estimating the degree of temporal freedoms of two correlated time series and a method for performing seasonal analyses using a half-year summer/winter projection operator in the frequency domain. A modified lag-correlation calculation is proposed for obtaining lag correlations in the frequency domain. Also, a spectral approach for Empirical Orthogonal Function (EOF) and Extended EOF analysis is given which reduces the size of the matrix to be solved in the eigenproblem.

Gao, X. H.↗

NASA NTRS1972

An innovative approach to compensator design

The primary goal is to present for a control system a computer-aided-compensator design technique from a frequency domain point of view. The thesis for developing this technique is to describe the open loop frequency response by n discrete frequency points which result in n functions of the compensator coefficients. Several of these functions are chosen so that the system specifications are properly portrayed; then mathematical programming is used to improve all of these functions which have values below minimum standards. In order to do this several definitions in regard to measuring the performance of a system in the frequency domain are given. Next, theorems which govern the number of compensator coefficients necessary to make improvements in a certain number of functions are proved. After this a mathematical programming tool for aiding in the solution of the problem is developed. Then for applying the constraint improvement algorithm generalized gradients for the constraints are derived. Finally, the necessary theory is incorporated in a computer program called CIP (compensator improvement program).

Mitchell, J. R.↗

NASA NTRS2003

Modular, Parallel Pulse-Shaping Filter Architectures

Novel architectures based on parallel subconvolution frequency-domain filtering methods have been developed for modular processing rate reduction of discrete-time pulse-shaping filters. Such pulse-shaping is desirable and often necessary to obtain bandwidth efficiency in very-high-rate wireless communications systems. In principle, this processing could be implemented in very-large-scale integrated (VLSI) circuits. Whereas other approaches to digital pulse-shaping are based primarily on time-domain processing concepts, the theory and design rules of the architectures presented here are founded on frequency-domain processing that has advantages in certain systems.

Gray, Andrew A.↗

NASA NTRS2013

Psychoacoustic Analysis of Synthesized Jet Noise

An aircraft noise synthesis capability is being developed so the annoyance caused by proposed aircraft can be assessed during the design stage. To make synthesized signals as realistic as possible, high fidelity simulation is required for source (e.g., engine noise, airframe noise), propagation and receiver effects. This psychoacoustic study tests whether the jet noise component of synthesized aircraft engine noise can be made more realistic using a low frequency oscillator (LFO) technique to simulate fluctuations in level observed in recordings. Jet noise predictions are commonly made in the frequency domain based on models of time-averaged empirical data. The synthesis process involves conversion of the frequency domain prediction into an audible pressure time history. However, because the predictions are time-invariant, the synthesized sound lacks fluctuations observed in recordings. Such fluctuations are hypothesized to be perceptually important. To introduce time-varying characteristics into jet noise synthesis, a method has been developed that modulates measured or predicted 1/3-octave band levels with a (<20Hz) LFO. The LFO characteristics are determined through analysis of laboratory jet noise recordings. For the aft emission angle, results indicate that signals synthesized using a generic LFO are perceived as more similar to recordings than those using no LFO, and signals synthesized with an angle-specific LFO are more similar to recordings than those synthesized with a generic LFO.

Okcu, Selen↗

NASA NTRS1976

Pulse analysis of acoustic emission signals

A method for the signature analysis of pulses in the frequency domain and the time domain is presented. Fourier spectrum, Fourier transfer function, shock spectrum and shock spectrum ratio are examined in the frequency domain analysis, and pulse shape deconvolution is developed for use in the time domain analysis. To demonstrate the relative sensitivity of each of the methods to small changes in the pulse shape, signatures of computer modeled systems with analytical pulses are presented. Optimization techniques are developed and used to indicate the best design parameters values for deconvolution of the pulse shape. Several experiments are presented that test the pulse signature analysis methods on different acoustic emission sources. These include acoustic emissions associated with: (1) crack propagation, (2) ball dropping on a plate, (3) spark discharge and (4) defective and good ball bearings.

Houghton, J. R.↗

NASA NTRS1977

Pulse analysis of acoustic emission signals

A method for the signature analysis of pulses in the frequency domain and the time domain is presented. Fourier spectrum, Fourier transfer function, shock spectrum and shock spectrum ratio were examined in the frequency domain analysis, and pulse shape deconvolution was developed for use in the time domain analysis. Comparisons of the relative performance of each analysis technique are made for the characterization of acoustic emission pulses recorded by a measuring system. To demonstrate the relative sensitivity of each of the methods to small changes in the pulse shape, signatures of computer modeled systems with analytical pulses are presented. Optimization techniques are developed and used to indicate the best design parameters values for deconvolution of the pulse shape. Several experiments are presented that test the pulse signature analysis methods on different acoustic emission sources. These include acoustic emissions associated with: (1) crack propagation, (2) ball dropping on a plate, (3) spark discharge and (4) defective and good ball bearings. Deconvolution of the first few micro-seconds of the pulse train are shown to be the region in which the significant signatures of the acoustic emission event are to be found.

Houghton, J. R.↗

NASA NTRS1977

The application of the Routh approximation method to turbofan engine models

The Routh approximation technique is applied in the frequency domain to a 16th order state variable turbofan engine model. The results obtained motivate the extension of the frequency domain formulation of the Routh method to the time domain to handle the state variable formulation directly. The time domain formulation is derived, and a characterization, which specifies all possible Routh similarity transformations, is given. The characterization is computed by the solution of two eigenvalue eigenvector problems. The application of the time domain Routh technique to the state variable engine model is described, and some results are given.

Merrill, W. C.↗

NASA NTRS1977

Pulse analysis of acoustic emission signals

A method for the signature analysis of pulses in the frequency domain and the time domain is presented. Fourier spectrum, Fourier transfer function, shock spectrum and shock spectrum ratio were examined in the frequency domain analysis and pulse shape deconvolution was developed for use in the time domain analysis. Comparisons of the relative performance of each analysis technique are made for the characterization of acoustic emission pulses recorded by a measuring system. To demonstrate the relative sensitivity of each of the methods to small changes in the pulse shape, signatures of computer modeled systems with analytical pulses are presented. Optimization techniques are developed and used to indicate the best design parameter values for deconvolution of the pulse shape. Several experiments are presented that test the pulse signature analysis methods on different acoustic emission sources. These include acoustic emission associated with (a) crack propagation, (b) ball dropping on a plate, (c) spark discharge, and (d) defective and good ball bearings. Deconvolution of the first few micro-seconds of the pulse train is shown to be the region in which the significant signatures of the acoustic emission event are to be found.

Houghton, J. R.↗

NASA NTRS1977

The application of the Routh approximation method to turbofan engine models

The Routh approximation technique is applied in the frequency domain to a 16th order state variable turbofan engine model. The results obtained motivate the extension of the frequency domain formulation of the Routh method to the time domain to handle the state variable formulation directly. The time domain formulation is derived and a new characterization, which specifies all possible Routh similarity transformations, is given. This characterization is computed by the solution of two eigenvalue-eigenvector problems. The application of the time domain Routh technique to the state variable engine model is described and some results are given. Additional computational problems are discussed including an optimization procedure which can improve the approximation accuracy by taking advantage of the transformation characterization.

Merrill, W. C.↗

NASA NTRS1988

Development of an adaptive LDV signal processor

Recent attempts at realization of a frequency domain signal processor exhibit practical drawbacks such as manual gain, filter and sampling adjustments, and simplistic adaptations of frequency domain techniques. This paper introduces an adaptive LDV signal processor, one which requires no operator intervention under any circumstances by adapting dynamically to burst characteristics, while surpassing all previous techniques in range and accuracy.

Baker, Glenn D.↗