Search NASA⌕ Search

SEARCH · Search NASA

Results for “Randomized methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6

Modelling Sonic Boom Propagation through Planetary Boundary Layer Turbulence near the Lateral Extent of the Carpet

Nonlinear acoustic propagation of sonic booms in the atmospheric boundary layer is considered in the context of a one-way solution to a third order wave equation. A split-step approach is utilized to compute different physical effects efficiently. Unlike previous approaches, the diffraction effects are computed exactly in the forward direction with no restriction on the angle of propagation. This results in more accurate modelling of sonic boom near the carpet edge. Heterogenous flow effects are incorporated with a wide-angle parabolic approximation. Nonlinear propagation is computed with a Burgers-Hayes method. Turbulence in the medium is constructed by the method of random Fourier modes. The turbulence spectra are constructed using an altitude dependent 3-dimensional von Karman spectrum. The turbulence field is considered frozen, as the eddy turnover time in the atmospheric boundary layer is generally much larger than the propagation time of the acoustic wave. Comparisons with benchmark predictions from the PCBoom software are conducted. The benchmark cases provide insight into the accuracy of the current prediction code for non-turbulent atmospheres. Future work is discussed regarding the prediction of shaped booms, boundary conditions, and predictions near the lateral extent of the boom carpet where previous approaches fail to capture the diffraction effects.

sonic boom↗

The correlation structure of several popular pseudorandom number generators

One of the desirable properties of a pseudorandom number generator is that the sequence of numbers it generates should have very low autocorrelation for all shifts except for zero shift and those that are multiples of its cycle length. Due to the simple methods of constructing random numbers, the ideal is often not quite fulfilled. A simple method of examining any random generator for previously unsuspected regularities is discussed. Once they are discovered it is often easy to derive the mathematical relationships, which describe the mathematical relationships, which describe the regular behavior. As examples, it is shown that high correlation exists in mixed and multiplicative congruential random number generators and prime moduli Lehmer generators for shifts a fraction of their cycle lengths.

Neuman, F.↗

Digital random-number generator

For binary digit array of N bits, use N noise sources to feed N nonlinear operators; each flip-flop in digit array is set by nonlinear operator to reflect whether amplitude of generator which feeds it is above or below mean value of generated noise. Fixed-point uniform distribution random number generation method can also be used to generate random numbers with other than uniform distribution.

Brocker, D. H.↗

Computing Response Of A Structure To Random Transient Pressures

Improved method of computing vibrational response of structure to transient random acoustic excitation at predominantly low frequencies devised, called "deterministic". Motivated by need to analyze more accurately vibro/acoustic responses of structures at spacecraft-launching facilities and determine whether need for reinforcement or redesign to withstand launch environment. Also used to study such phenomena as earthquake motions, ocean waves, aircraft pressure gusts, responses of bridges to winds, and effects to jet-engine noise on aircraft structures.

Sepcenko, Valentin↗

Application of the extended boundary condition method to Monte Carlo simulations of scattering of waves by two-dimensional random rough surfaces

The extended boundary condition method is applied to Monte Carlo simulations of two-dimensional random rough surface scattering. The numerical results are compared with one-dimensional random rough surfaces obtained from the finite-element method. It is found that the mean scattered intensity from two-dimensional rough surfaces differs from that of one dimension for rough surfaces with large slopes.

Tsang, L.↗

A numerical study of rays in random media

Statistics of electromagnetic rays in a random medium are studied numerically by the Monte Carlo method. Two dimensional random surfaces with prescribed correlation functions are used to simulate the random media. Rays are then traced in these sample media. Statistics of the ray properties such as the ray positions and directions are computed. Histograms showing the distributions of the ray positions and directions at different points along the ray path as well as at given points in space are given. The numerical experiment is repeated for different cases corresponding to weakly and strongly random media with isotropic and anisotropic irregularities. Results are compared with those derived from theoretical investigations whenever possible.

Youakim, M. Y.↗

A Multivariate Randomization Text of Association Applied to Cognitive Test Results

Randomization tests provide a conceptually simple, distribution-free way to implement significance testing. We have applied this method to the problem of evaluating the significance of the association among a number (k) of variables. The randomization method was the random re-ordering of k-1 of the variables. The criterion variable was the value of the largest eigenvalue of the correlation matrix.

Ahumada, Albert↗

An efficient computational method for characterizing the effects of random surface errors on the average power pattern of reflectors

Based on the works of Ruze (1966) and Vu (1969), a novel mathematical model has been developed to determine efficiently the average power pattern degradations caused by random surface errors. In this model, both nonuniform root mean square (rms) surface errors and nonuniform illumination functions are employed. In addition, the model incorporates the dependence on F/D in the construction of the solution. The mathematical foundation of the model rests on the assumption that in each prescribed annular region of the antenna, the geometrical rms surface value is known. It is shown that closed-form expressions can then be derived, which result in a very efficient computational method for the average power pattern. Detailed parametric studies are performed with these expressions to determine the effects of different random errors and illumination tapers on parameters such as gain loss and sidelobe levels. The results clearly demonstrate that as sidelobe levels decrease, their dependence on the surface rms/wavelength becomes much stronger and, for a specified tolerance level, a considerably smaller rms/wavelength is required to maintain the low sidelobes within the required bounds.

Rahmat-Samii, Y.↗

Physical Principle for Generation of Randomness

A physical principle (more precisely, a principle that incorporates mathematical models used in physics) has been conceived as the basis of a method of generating randomness in Monte Carlo simulations. The principle eliminates the need for conventional random-number generators. The Monte Carlo simulation method is among the most powerful computational methods for solving high-dimensional problems in physics, chemistry, economics, and information processing. The Monte Carlo simulation method is especially effective for solving problems in which computational complexity increases exponentially with dimensionality. The main advantage of the Monte Carlo simulation method over other methods is that the demand on computational resources becomes independent of dimensionality. As augmented by the present principle, the Monte Carlo simulation method becomes an even more powerful computational method that is especially useful for solving problems associated with dynamics of fluids, planning, scheduling, and combinatorial optimization. The present principle is based on coupling of dynamical equations with the corresponding Liouville equation. The randomness is generated by non-Lipschitz instability of dynamics triggered and controlled by feedback from the Liouville equation. (In non-Lipschitz dynamics, the derivatives of solutions of the dynamical equations are not required to be bounded.)

Zak, Michail↗

Stochastic Optimal Control via Bellman's Principle

This paper presents a method for finding optimal controls of nonlinear systems subject to random excitations. The method is capable to generate global control solutions when state and control constraints are present. The solution is global in the sense that controls for all initial conditions in a region of the state space are obtained. The approach is based on Bellman's Principle of optimality, the Gaussian closure and the Short-time Gaussian approximation. Examples include a system with a state-dependent diffusion term, a system in which the infinite hierarchy of moment equations cannot be analytically closed, and an impact system with a elastic boundary. The uncontrolled and controlled dynamics are studied by creating a Markov chain with a control dependent transition probability matrix via the Generalized Cell Mapping method. In this fashion, both the transient and stationary controlled responses are evaluated. The results show excellent control performances.

Crespo, Luis G.↗

Computed lateral power spectral density response of conventional and STOL airplanes to random atmospheric turbulence

A method of computing the power spectral densities of the lateral response of airplanes to random atmospheric turbulence was adapted to an electronic digital computer. By use of this program, the power spectral densities of the lateral roll, yaw, and sideslip angular displacement of several conventional and STOL airplanes were computed. The results show that for the conventional airplanes, the roll response is more prominent than that for yaw or sideslip response. For the STOL airplanes, on the other hand, the yaw and sideslip responses were larger than the roll response. The response frequency of the STOL airplanes generally is higher than that for the conventional airplanes. This combination of greater sensitivity of the STOL airplanes in yaw and sideslip and the frequency at which they occur could be a factor causing the poor riding qualities of this class of airplanes.

Lichtenstein, J. H.↗

A satellite-based radar wind sensor

The objective is to investigate the application of Doppler radar systems for global wind measurement. A model of the satellite-based radar wind sounder (RAWS) is discussed, and many critical problems in the designing process, such as the antenna scan pattern, tracking the Doppler shift caused by satellite motion, and backscattering of radar signals from different types of clouds, are discussed along with their computer simulations. In addition, algorithms for measuring mean frequency of radar echoes, such as the Fast Fourier Transform (FFT) estimator, the covariance estimator, and the estimators based on autoregressive models, are discussed. Monte Carlo computer simulations were used to compare the performance of these algorithms. Anti-alias methods are discussed for the FFT and the autoregressive methods. Several algorithms for reducing radar ambiguity were studied, such as random phase coding methods and staggered pulse repitition frequncy (PRF) methods. Computer simulations showed that these methods are not applicable to the RAWS because of the broad spectral widths of the radar echoes from clouds. A waveform modulation method using the concept of spread spectrum and correlation detection was developed to solve the radar ambiguity. Radar ambiguity functions were used to analyze the effective signal-to-noise ratios for the waveform modulation method. The results showed that, with suitable bandwidth product and modulation of the waveform, this method can achieve the desired maximum range and maximum frequency of the radar system.

Xin, Weizhuang↗

Review of probabilistic analysis of dynamic response of systems with random parameters

The various methods that have been studied in the past to allow probabilistic analysis of dynamic response for systems with random parameters are reviewed. Dynamic response may have been obtained deterministically if the variations about the nominal values were small; however, for space structures which require precise pointing, the variations about the nominal values of the structural details and of the environmental conditions are too large to be considered as negligible. These uncertainties are accounted for in terms of probability distributions about their nominal values. The quantities of concern for describing the response of the structure includes displacements, velocities, and the distributions of natural frequencies. The exact statistical characterization of the response would yield joint probability distributions for the response variables. Since the random quantities will appear as coefficients, determining the exact distributions will be difficult at best. Thus, certain approximations will have to be made. A number of techniques that are available are discussed, even in the nonlinear case. The methods that are described were: (1) Liouville's equation; (2) perturbation methods; (3) mean square approximate systems; and (4) nonlinear systems with approximation by linear systems.

Kozin, F.↗

An inexpensive and effective method for calculating the strength of randomly reinforced fiber composites

Planar randomly reinforced fiber composites (PRRFC) is pseudoisotropic laminate with large number of ply orientation combinations where strength is function of these ply orientation combinations. Laminate theory can be applied to determine strength of PRRFC, and in conjunction with composite micro- and macromechanics can predict mechanical properties of PRRFC's with any fiber/matrix combination.

Chamis, C. C.↗

Verification of the Solar Dynamics Observatory High Gain Antenna Pointing Algorithm Using Flight Data

The Solar Dynamics Observatory (SDO) is a NASA spacecraft designed to study the Sun. It was launched on February 11, 2010 into a geosynchronous orbit, and uses a suite of attitude sensors and actuators to finely point the spacecraft at the Sun. SDO has three science instruments: the Atmospheric Imaging Assembly (AIA), the Helioseismic and Magnetic Imager (HMI), and the Extreme Ultraviolet Variability Experiment (EVE). SDO uses two High Gain Antennas (HGAs) to send science data to a dedicated ground station in White Sands, New Mexico. In order to meet the science data capture budget, the HGAs must be able to transmit data to the ground for a very large percentage of the time. Each HGA is a dual-axis antenna driven by stepper motors. Both antennas transmit data at all times, but only a single antenna is required in order to meet the transmission rate requirement. For portions of the year, one antenna or the other has an unobstructed view of the White Sands ground station. During other periods, however, the view from both antennas to the Earth is blocked for different portions of the day. During these times of blockage, the two HGAs take turns pointing to White Sands, with the other antenna pointing out to space. The HGAs handover White Sands transmission responsibilities to the unblocked antenna. There are two handover seasons per year, each lasting about 72 days, where the antennas hand off control every twelve hours. The non-tracking antenna slews back to the ground station by following a ground commanded trajectory and arrives approximately 5 minutes before the formerly tracking antenna slews away to point out into space. The SDO Attitude Control System (ACS) runs at 5 Hz, and the HGA Gimbal Control Electronics (GCE) run at 200 Hz. There are 40 opportunities for the gimbals to step each ACS cycle, with a hardware limitation of no more than one step every three GCE cycles. The ACS calculates the desired gimbal motion for tracking the ground station or for slewing, and sends the command to the GCE at 5 Hz. This command contains the number of gimbals steps for that ACS cycle, the direction of motion, the spacing of the steps, and the delay before taking the first step. The AIA and HMI instruments are sensitive to spacecraft jitter. Pre-flight analysis showed that jitter from the motion of the HGAs was a cause of concern. Three jitter mitigation techniques were developed to overcome the effects of jitter from different sources. The first method is the random step delay, which avoids gimbal steps hitting a cadence on a jitter-critical mode by pseudo-randomly delaying the first gimbal step in an ACS cycle. The second method of jitter mitigation is stagger stepping, which forbids the two antennas from taking steps during the same ACS cycle in order to avoid constructively adding jitter from two antennas. The third method is the inclusion of an instrument No Step Request (NSR), which allows the instruments to request a stoppage in gimbal stepping during the times when they are taking images. During the commissioning phase of the mission, a jitter test was performed onboard the spacecraft. Various sources of jitter, such as the reaction wheels, the High Gain Antenna motors, and the motion of the instrument filter wheels, were examined to determine the level of their effect on the instruments. During the HGA portion of the test, the jitter amplitudes from the single step of a gimbal were examined, as well as the amplitudes due to the execution of various gimbal rates. These jitter levels are compared with the gimbal jitter allocations for each instrument. Additionally, the jitter test provided insight into a readback delay that exists with the GCE. Pre-flight analysis suggested that gimbal steps scheduled to occur during the later portion of an ACS cycle would not be read during that cycle, resulting in a delay in the telemetered current gimbal position. Flight data from the jitter test confirmed this expectation. Analysis is presentehat shows the readback delay does not have a negative impact on gimbal control. The decision was made to consider implementing two of the jitter mitigation techniques on board the spacecraft: stagger stepping and the NSR. Flight data from two sets of handovers, one set without jitter mitigation and the other with mitigation enabled, were examined. The trajectory of the predicted handover was compared with the measured trajectory for the two cases, showing that tracking was not negatively impacted with the addition of the jitter mitigation techniques. Additionally, the individual gimbal steps were examined, and it was confirmed that the stagger stepping and NSRs worked as designed. An Image Quality Test was performed to determine the amount of cumulative jitter from the reaction wheels, HGAs, and instruments during various combinations of typical operations. In this paper, the flight results are examined from a test where the HGAs are following the path of a nominal handover with stagger stepping on and HMI NSRs enabled. In this case, the reaction wheels are moving at low speed and the instruments are taking pictures in their standard sequence. The flight data shows the level of jitter that the instruments see when their shutters are open. The HGA-induced jitter is well within the jitter requirement when the stagger step and NSR mitigation options are enabled. The SDO HGA pointing algorithm was designed to achieve nominal antenna pointing at the ground station, perform slews during handover season, and provide three HGA-induced jitter mitigation options without compromising pointing objectives. During the commissioning phase, flight data sets were collected to verify the HGA pointing algorithm and demonstrate its jitter mitigation capabilities.

Bourkland, Kristin L.↗

Simulation of random envelope processes.

Efficient and practical methods of simulating stationary and nonstationary random envelope processes are presented. The stationary envelope processes are simulated by using the fast Fourier transform while the nonstationary envelope processes are simulated as the square root of the sum of a series of cosine functions and a series of sine functions with random phase angles. Typical applications of the envelope simulation are the simulations of peaks and troughs which play an important role in the analyses of the first excursion probability, fatigue and crack propagation. In particular, applications to the crack propagation under random loadings are demonstrated in detail.

Yang, J.-N.↗