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NASA NTRS1989

Recent activities within the Aeroservoelasticity Branch at the NASA Langley Research Center

The objective of research in aeroservoelasticity at the NASA Langley Research Center is to enhance the modeling, analysis, and multidisciplinary design methodologies for obtaining multifunction digital control systems for application to flexible flight vehicles. Recent accomplishments are discussed, and a status report on current activities within the Aeroservoelasticity Branch is presented. In the area of modeling, improvements to the Minimum-State Method of approximating unsteady aerodynamics are shown to provide precise, low-order aeroservoelastic models for design and simulation activities. Analytical methods based on Matched Filter Theory and Random Process Theory to provide efficient and direct predictions of the critical gust profile and the time-correlated gust loads for linear structural design considerations are also discussed. Two research projects leading towards improved design methodology are summarized. The first program is developing an integrated structure/control design capability based on hierarchical problem decomposition, multilevel optimization and analytical sensitivities. The second program provides procedures for obtaining low-order, robust digital control laws for aeroelastic applications. In terms of methodology validation and application the current activities associated with the Active Flexible Wing project are reviewed.

Noll, Thomas E.↗

NASA NTRS1988

Sampling inhomogeneous turbulent fields

The reconstruction of an inhomogeneous random process from a finite number of discrete samples can be performed in terms of the Karhunen-Loeve (KL) expansion for that process. The n(th) eigenfunction has n - 1 zero crossings which are the sampling points for the inhomogeneous process. The rapid variation of the KL eigenfunctions makes it unnecessary to have a high density of sampling (or grid points) near the wall. However, this result should not be construed to indicate that with spectral simulations significantly fewer grid points are required with the KL expansion as compared to other orthogonal expansions. Moin and Moser (1989) have shown that the advantage of the KL expansion over Chebychev expansion rapidly diminishes when high percentage (say 90 percent) energy recovery is demanded.

Adrian, R. J.↗

NASA NTRS1990

Aeroservoelasticity

Accomplishments and current research projects along four main thrusts in aeroservoelasticity at the NASA Langley Research Center are described. One activity focuses on enhancing the modelling and the analysis procedures to accurately predict aeroservoelastic interactions. In the area of modelling, improvements to the minimum-state method of approximating unsteady aerodynamics are shown to provide precise, low-order models for design and simulation tasks. Recent extensions in aerodynamic correction factor methodology are also described. With respect to analysis procedures, the paper reviews novel enhancements to Matched Filter Theory and Random Process Theory for predicting the critical gust profile and the associated time-correlated gust loads for structural design considerations. In another activity, two research projects leading towards improved design capability are summarized. The first program involves the development of an integrated structure/control design capability; the second provides procedures for obtaining low-order, robust digital control laws for aeroelastic applications. Experimental validation of new theoretical developments is the third activity. As such, a short description of the Active Flexible Wing Project is presented, and recent wind-tunnel test accomplishments are summarized. Finally within the area of application, a study performed to assess the state-of-the-art of aeroelastic and aeroservoelastic analysis and design technology with respect to hot, hypersonic flight vehicles is reviewed.

Noll, Thomas E.↗

NASA NTRS1990

Aeroservoelasticity

The paper describes recent accomplishments and current research projects along four main thrusts in aeroservoelasticity at NASA Langley. One activity focuses on enhancing the modeling and analysis procedures to accurately predict aeroservoelastic interactions. Improvements to the minimum-state method of approximating unsteady aerodynamics are shown to provide precise low-order models for design and simulation tasks. Recent extensions in aerodynamic correction-factor methodology are also described. With respect to analysis procedures, the paper reviews novel enhancements to matched filter theory and random process theory for predicting the critical gust profile and the associated time-correlated gust loads for structural design considerations. Two research projects leading towards improved design capability are also summarized: (1) an integrated structure/control design capability and (2) procedures for obtaining low-order robust digital control laws for aeroelastic applications.

Noll, Thomas E.↗

NASA NTRS1990

Stationary and nonstationary random vibrations of laminated composite plates via a higher order theory

Higher order shear deformation theory is utilized to study he weakly stationary and nonstationary random vibrations of cross-ply laminated plates. Normal mode method, in conjunction with the biorthogonality condition, for the nonsymmetric differential equations is applied. Detailed derivation is given for the governing equations, biorthogonality condition, the generalized mass and the generalized forces. Results are listed for a plate which is simply supported at all the edges, and subjected to a point load which is either timewise stationary or nonstationary random process.

Elishakoff, Isaac↗

NASA NTRS1989

Recent activities within the aeroservoelasticity branch at the NASA Langley Research Center

Noll, Thomas↗

NASA NTRS1990

Noise power spectral density of the Sundstrand QA-2000 accelerometer

There are no good data on low frequency (less than 0.1 Hz) power spectral density (PSD) for the Q-Flex accelerometer. However, some preliminary stability measurements were made over periods of 12 to 24 hours and demonstrated stability less than 0.5 micro-g over greater than 12 hours. The test data appear to contain significant contributions from temperature variations at that level, so the true sensor contribution may be less than that. If what was seen could be construed as a true random process, it would correspond to about 0.1 micro-g rms over a bandwidth from 10(exp -5) Hz to about 1 Hz. Other studies of low frequency PSD in flexure accelerometers have indicated that material aging effects tend to approximate a first order Markhov process. If we combine such a model with the spectrum obtained at higher frequencies, it suggests the spectrum shown here as a conservative estimate of Q-Flex noise performance.

Peters, Rex↗

NASA NTRS1991

Digital test signal generation: An accurate SNR calibration approach for the DSN

A new method of generating analog test signals with accurate signal to noise ratios (SNRs) is described. High accuracy will be obtained by simultaneous generation of digital noise and signal spectra at a given baseband or bandpass limited bandwidth. The digital synthesis will provide a test signal embedded in noise with the statistical properties of a stationary random process. Accuracy will only be dependent on test integration time with a limit imposed by the system quantization noise (expected to be 0.02 dB). Setability will be approximately 0.1 dB. The first digital SNR generator to provide baseband test signals is being built and will be available in early 1991.

Gutierrez-Luaces, B. O.↗

NASA NTRS1991

Limits on the isolation of stochastic vibration for microgravity space experiments

The limitations on the isolation of stochastic vibrations for microgravity space experiments are explored. These limitations result from the restricted interior space available for vibration isolation. A one-degree-of-freedom representation of the experiment-spacecraft system is used, and an ideal vibration actuator is assumed. A kinematic representation results, and the problem becomes one of finding the minimum acceleration trajectory within a pair of stochastic walls. The wall motion is characterized by an ergodic, stationary, zero-mean, Gaussian random process with known power spectral density. The geometry of the wall trajectories is defined in terms of their significant extrema and zero crossings. This geomemtry is used in defining a composite trajectory that has a mean square acceleratiaon lower than that on the optimal path satisfying the stochastic wall inequality constraints. The optimal control problem is solved on a return path yielding the mean square acceleration in terms of the distributions of significant maxima and first-passage time of the wall process. The methodology is applied to a microgravity isolation problem to find the lower bounds on root-mean-square acceleration given the disturbance power spectral density.

Knospe, C. R.↗

NASA NTRS1990

Accounting for crustal magnetization in models of the core magnetic field

The problem of determining the magnetic field originating in the earth's core in the presence of remanent and induced magnetization is considered. The effect of remanent magnetization in the crust on satellite measurements of the core magnetic field is investigated. The crust as a zero-mean stationary Gaussian random process is modelled using an idea proposed by Parker (1988). It is shown that the matrix of second-order statistics is proportional to the Gram matrix, which depends only on the inner-products of the appropriate Green's functions, and that at a typical satellite altitude of 400 km the data are correlated out to an angular separation of approximately 15 deg. Accurate and efficient means of calculating the matrix elements are given. It is shown that the variance of measurements of the radial component of a magnetic field due to the crust is expected to be approximately twice that in horizontal components.

Jackson, Andrew↗

NASA NTRS1990

Maximum likelihood estimates of polar motion parameters

Two estimators developed by Jeffreys (1940, 1968) are described and used in conjunction with polar-motion data to determine the frequency (Fc) and quality factor (Qc) of the Chandler wobble. Data are taken from a monthly polar-motion series, satellite laser-ranging results, and optical astrometry and intercompared for use via interpolation techniques. Maximum likelihood arguments were employed to develop the estimators, and the assumption that polar motion relates to a Gaussian random process is assessed in terms of the accuracies of the estimators. The present results agree with those from Jeffreys' earlier study but are inconsistent with the later estimator; a Monte Carlo evaluation of the estimators confirms that the 1968 method is more accurate. The later estimator method shows good performance because the Fourier coefficients derived from the data have signal/noise levels that are superior to those for an individual datum. The method is shown to be valuable for general spectral-analysis problems in which isolated peaks must be analyzed from noisy data.

Wilson, Clark R.↗

NASA NTRS1989

Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution, appendix 4

The power spectrum for a stationary random process can be defined with the Wiener-Khintchine Theorem, which says that the power spectrum and the auto correlation function are a Fourier transform pair. To implement this theorem for signals that are discrete and of finite length we can use the Blackman-Tukey method. Blackman and Tukey (1958) show that a function w(tau), called a lag window, can be applied to the auto correlation estimates to obtain power spectrum estimates that are statistically stable. The Fourier transform of w(r) is called a spectral window. Typical choices for spectral windows show a distinct trade-off between the main lobe width and side lobe strength. A new idea for designing windows by taking linear combinations of the standard windows to produce hybrid windows was introduced by Smith (1985). We implement Smith's idea to obtain spectral windows with narrow main lobes and smaller (compared with typical windows) near side lobes. One of the main contributions of this thesis is that we show that Smith's problem is equivalent to a Quadratic Programming (QP) problem with linear equality and inequality constraints. A computer program was written to produce hybrid windows by setting up and solving the QP problem. We also developed and solved two variations of the original problem. The two variations involved changing the inequality constraints in both cases from non negativity on the combination coefficients to non negativity on the hybrid lag window itself. For the second variation, the window functions used to construct the hybrid window were changed to a frequency-variable set of truncated cosinusoids. A series of tests was run with the three computer programs to investigate the behavior of the hybrid spectral and lag windows. Emphasis was put on obtaining spectral windows with both relatively narrow main lobes and the lowest possible (for these algorithms) near side lobes. Some success was achieved for this goal. A 10 dB peak side lobe reduction over the rectangular spectral window without significant main lobe broadening was achieved. Also, average side lobe levels of -117 dB were reached at a cost of doubling the main lobe width (at the -3 dB point).

Ioup, George E.↗

NASA NTRS1957

The response of an airplane to random atmospheric disturbances

The statistical approach to the gust-load problem which consists in considering flight through turbulent air to be a stationary random process is extended by including the effect of lateral variation of the instantaneous gust intensity on the aerodynamic forces. The forces obtained in this manner are used in dynamic analyses of rigid and flexible airplanes free to move vertically, in pitch, and in roll. The effect of the interaction of longitudinal, vertical, and lateral gusts on the wing stresses is also considered.

LOADS, GUST - WINGS↗

NASA NTRS1958

The response of an airplane to random atmospheric disturbances

The statistical approach to the gust-load problem, which consists in considering flight through turbulent air to be a stationary random process, is extended by including the effect of lateral variation of the instantaneous gust intensity on the aerodynamic forces. The forces obtained in this manner are used in dynamic analyses of rigid and flexible airplanes free to move vertically, in pitch, and in roll. The effect of the interaction of longitudinal, normal, and lateral gusts on the wind stresses is also considered.

Diederich, Franklin W↗

NASA NTRS1992

Probabilistic evaluation of uncertainties and risks in aerospace components

This paper summarizes a methodology developed at NASA Lewis Research Center which computationally simulates the structural, material, and load uncertainties associated with Space Shuttle Main Engine (SSME) components. The methodology was applied to evaluate the scatter in static, buckling, dynamic, fatigue, and damage behavior of the SSME turbo pump blade. Also calculated are the probability densities of typical critical blade responses, such as effective stress, natural frequency, damage initiation, most probable damage path, etc. Risk assessments were performed for different failure modes, and the effect of material degradation on the fatigue and damage behaviors of a blade were calculated using a multi-factor interaction equation. Failure probabilities for different fatigue cycles were computed and the uncertainties associated with damage initiation and damage propagation due to different load cycle were quantified. Evaluations on the effects of mistuned blades on a rotor were made; uncertainties in the excitation frequency were found to significantly amplify the blade responses of a mistuned rotor. The effects of the number of blades on a rotor were studied. The autocorrelation function of displacements and the probability density function of the first passage time for deterministic and random barriers for structures subjected to random processes also were computed. A brief discussion was included on the future direction of probabilistic structural analysis.

Shah, A. R.↗

NASA NTRS1993

Application of neural network to remote sensing of soil moisture using theoretical polarimetric backscattering coefficients

This paper investigates the potential application of neural network to inversion of soil moisture using polarimetric remote sensing data. The neural network used for the inversion of soil parameters is multi-layer perceptron trained with the back-propagation algorithm. The training data include the polarimetric backscattering coefficients obtained from theoretical surface scattering models together with an assumed nominal range of soil parameters which are comprised of the soil permittivity and surface roughness parameters. Soil permittivity is calculated from the soil moisture and the assumed soil texture based on an empirical formula at C-, L-, and P-bands. The rough surface parameters for the soil surface, which is described by the Gaussian random process, are the root-mean-square (rms) height and correlation length. For the rough surface scattering, small perturbation method is used for the L-band frequency, and Kirchhoff approximation is used for the C-band frequency to obtain the corresponding backscattering coefficients. During the training, the backscattering coefficients are the inputs to the neural net and the output from the net are compared with the desired soil parameters to adjust the interconnecting weights. The process is repeated for each input-output data entry and then for the entire training data until convergence is reached. After training, the backscattering coefficients are applied to the trained neural net to retrieve the soil parameters which are compared with the desired soil parameters to verify the effectiveness of this technique. Several cases are examined. First, for simplicity, the correlation length and rms height of the soil surface are fixed while soil moisture is varied. Soil moisture obtained using the neural networks with either L-band or C-band backscattering coefficients for the HH and VV polarizations as inputs is in good agreement with the desired soil moisture. The neural net output matches the desired output for the soil moisture range of 16 to 60 percent for the C-band case. The next case investigated is to vary both soil moisture and rms height while keeping the correlation length fixed. For this case, C-band backscattering coefficients are not sufficient for retrieving two parameters because the Kirchhoff approximation gives the same HH and VV backscattering coefficients. Therefore, the backscattering coefficients at two different frequency bands are necessary to find both the soil moisture and rms height. Finally, the neural nets are also applied to simultaneously invert soil moisture, rms height, and correlation length. Overall, the soil moisture retrieved from the neural network agrees very well with the desired soil moisture. This suggests that the neural network shows potential for retrieval of soil parameters from remote sensing data.

Wang, L.↗

NASA NTRS1993

Digital test signal generation: An accurate SNR calibration approach for the DSN

In support of the on-going automation of the Deep Space Network (DSN) a new method of generating analog test signals with accurate signal-to-noise ratio (SNR) is described. High accuracy is obtained by simultaneous generation of digital noise and signal spectra at the desired bandwidth (base-band or bandpass). The digital synthesis provides a test signal embedded in noise with the statistical properties of a stationary random process. Accuracy is dependent on test integration time and limited only by the system quantization noise (0.02 dB). The monitor and control as well as signal-processing programs reside in a personal computer (PC). Commands are transmitted to properly configure the specially designed high-speed digital hardware. The prototype can generate either two data channels modulated or not on a subcarrier, or one QPSK channel, or a residual carrier with one biphase data channel. The analog spectrum generated is on the DC to 10 MHz frequency range. These spectra may be up-converted to any desired frequency without loss on the characteristics of the SNR provided. Test results are presented.

Gutierrez-Luaces, Benito O.↗

NASA NTRS1995

Development and computer implementation of design/analysis techniques for multilayered composite structures. Probabilistic fiber composite micromechanics

Probabilistic composite micromechanics methods are developed that simulate expected uncertainties in unidirectional fiber composite properties. These methods are in the form of computational procedures using Monte Carlo simulation. The variables in which uncertainties are accounted for include constituent and void volume ratios, constituent elastic properties and strengths, and fiber misalignment. A graphite/epoxy unidirectional composite (ply) is studied to demonstrate fiber composite material property variations induced by random changes expected at the material micro level. Regression results are presented to show the relative correlation between predictor and response variables in the study. These computational procedures make possible a formal description of anticipated random processes at the intraply level, and the related effects of these on composite properties.

Stock, Thomas A.↗