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A method is described for evaluating the minimum distance parameters of trellis phase codes, including CPFSK, partial response FM, and more importantly, coded CPM (continuous phase modulation) schemes. The algorithm provides dramatically faster execution times and lesser memory requirements than previous algorithms. Results of sample calculations and timing comparisons are included.
A method is described for evaluating the minimum distance parameters of trellis phase codes, including CPFSK, partial response FM, and more importantly, coded CPM (continuous phase modulation) schemes. The algorithm provides dramatically faster execution times and lesser memory requirements than previous algorithms. Results of sample calculations and timing comparisons are included.
There is a wealth of cosmological information encoded in the spatial power spectrum of temperature anisotropies of the cosmic microwave background! Experiments designed to map the microwave sky are returning a flood of data (time streams of instrument response as a beam is swept over the sky) at several different frequencies (from 30 to 900 GHz), all with different resolutions and noise properties. The resulting analysis challenge is to estimate, and quantify our uncertainty in, the spatial power spectrum of the cosmic microwave background given the complexities of "missing data", foreground emission, and complicated instrumental noise. Bayesian formulation of this problem allows consistent treatment of many complexities including complicated instrumental noise and foregrounds, and can be numerically implemented with Gibbs sampling. Gibbs sampling has now been validated as an efficient, statistically exact, and practically useful method for low-resolution (as demonstrated on WMAP 1 and 3 year temperature and polarization data). Continuing development for Planck - the goal is to exploit the unique capabilities of Gibbs sampling to directly propagate uncertainties in both foreground and instrument models to total uncertainty in cosmological parameters.
The effects of several critical assumptions and parameters on the computation of strain energy release rates for delamination and debond configurations modeled with plate elements have been quantified. The method of calculation is based on the virtual crack closure technique (VCCT), and models that model the upper and lower surface of the delamination or debond with two-dimensional (2D) plate elements rather than three-dimensional (3D) solid elements. The major advantages of the plate element modeling technique are a smaller model size and simpler geometric modeling. Specific issues that are discussed include: constraint of translational degrees of freedom, rotational degrees of freedom or both in the neighborhood of the crack tip; element order and assumed shear deformation; and continuity of material properties and section stiffness in the vicinity of the debond front, Where appropriate, the plate element analyses are compared with corresponding two-dimensional plane strain analyses.
This paper describes a method for the identification of the parameters entering into the equations of motion of distributed systems. Because the motion of distributed systems is described in terms of partial differential equations, these parameters are in general continuous functions of the spatial variables. For vibrating systems, these parameters ordinarily represent the mass, stiffness and damping distributions. In this paper, these distributions are expanded in terms of finite series of known functions of the spatial variables multiplied by undetermined coefficients. It is assumed that the nature of the equations of motion is known and that a limited number of eigenvalues and eigenfunctions is identified in advance. Use is then made of the least squares method, in conjunction with the eigenfunctions' orthogonality, to compute the undetermined coefficients, thus identifying the system distributed parameters. A method for the identification of the eigensolution is also presented. The procedure for the identification of the eigensolution and of the system parameters is demonstrated via a numerical example.
The continuously Traversing Microphone System consists of a data acquisition and processing method for obtaining the modal coefficients of the discrete, coherent acoustic field in a fan inlet duct. The system would be used in fan rigs or full scale engine installations where present measurement methods, because of the excessive number of microphones and long test times required, are not feasible. The purpose of the investigation reported here was to develop a method for defining modal structure by means of a continuously traversing microphone system and to perform an evaluation of the method, based upon analytical studies and computer simulated tests. A variety of system parameters were examined, and the effects of deviations from ideal were explored. Effects of traverse speed, digitizing rate, run time, roundoff error, calibration errors, and random noise background level were determined. For constant fan operating speed, the sensitivity of the method to normal errors and deviations was determined to be acceptable. Good recovery of mode coefficients was attainable. Fluctuating fan speed conditions received special attention, and it was concluded that by employing suitable time delay procedures, satisfactory information on mode coefficients can be obtained under realistic conditions. A plan for further development involving fan rig tests was prepared.
The problem of robust stability in linear systems with parametric uncertainties is considered. A method is developed to determine bounds on uncertain parameters in the state-space model of the system, so that stability is preserved. Both continuous- and discrete-time systems are considered. Unlike previous results, the stability bounds are derived in terms of actual parameters instead of their absolute values, and consequently the stable region in the parameter space is not necessarily symmetric with respect to the origin. Furthermore, the uncertain parameters do not have to be linearly independent to each other.
Low clouds continue to contribute greatly to the uncertainty in cloud feedback estimates. Depending on whether a region is dominated by cumulus (Cu) or stratocumulus (Sc) clouds, the interannual low-cloud feedback is somewhat different in both spaceborne and large-eddy simulation studies. Therefore, simulating the correct amount and variation of the Cu and Sc cloud distributions could be crucial to predict future cloud feedbacks. Here we document spatial distributions and profiles of Sc and Cu clouds derived from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) and CloudSat measurements. For this purpose, we create a new dataset called the Cumulus And Stratocumulus CloudSat-CALIPSO Dataset (CASCCAD), which identifies Sc, broken Sc, Cu under Sc, Cu with stratiform outflow and Cu. To separate the Cu from Sc, we design an original method based on the cloud height, horizontal extent, vertical variability and horizontal continuity, which is separately applied to both CALIPSO and combined CloudSat–CALIPSO observations. First, the choice of parameters used in the discrimination algorithm is investigated and validated in selected Cu, Sc and Sc–Cu transition case studies. Then, the global statistics are compared against those from existing passive- and active-sensor satellite observations. Our results indicate that the cloud optical thickness – as used in passive-sensor observations – is not a sufficient parameter to discriminate Cu from Sc clouds, in agreement with previous literature. Using clustering-derived datasets shows better results although one cannot completely separate cloud types with such an approach. On the contrary, classifying Cu and Sc clouds and the transition between them based on their geometrical shape and spatial heterogeneity leads to spatial distributions consistent with prior knowledge of these clouds, from ground-based, ship-based and field campaigns. Furthermore, we show that our method improves existing Sc–Cu classifications by using additional information on cloud height and vertical cloud fraction variation. Finally, the CASCCAD datasets provide a basis to evaluate shallow convection and stratocumulus clouds on a global scale in climate models and potentially improve our understanding of low-level cloud feedbacks. The CASCCAD dataset (Cesana, 2019, https://doi.org/10.5281/zenodo.2667637) is available on the Goddard Institute for Space Studies (GISS) website at https://data.giss.nasa.gov/clouds/casccad/ (last access: 5 November 2019) and on the zenodo website at https://zenodo.org/record/2667637 (last access: 5 November 2019).
A method for determining highly accurate approximations to families of strongly nonlinear solutions which are either continuous or discontinuous, and which represent variations in some arbitrary parameters, is developed and evaluated. The procedure consists of defining a unit perturbation by employing two or more nonlinear solutions which differ from one another by a nominal change in some geometric or flow parameter, and then using that unit perturbation to predict a family of related nonlinear solutions over a range of parameter variation. Coordinate straining is used in determining the unit perturbation to account for the movement of discontinuities and maxima of high-gradient regions due to the perturbation. Although the procedure is generally applicable, results are presented here for nonlinear aerodynamic applications. Attention is focused in particular on transonic flows which are strongly supercritical and exhibit large surface shock movement over the parametric range studied; and on subsonic flows which display large pressure variations in the stagnation and peak suction pressure regions. Flows past both isolated airfoils and compressor cascades involving a variety of flow and geometry parameter changes are considered. Comparisons with the corresponding 'exact' nonlinear solutions indicate a remarkable accuracy and range of validity of such a procedure. Computational time is trivial.
Nonlinear properties of the stratospheric vacillation model of Holton and Mass (1976) are studied numerically using bifurcation theory. Severe truncation and vertical differencing are used to obtain 81 nonlinear ordinary differential equations with time-dependent variables. Three branches of the steady solutions are determined using Powell's hybrid method and the pseudoarclength continuation method, and a multiplicity of stable steady-state solutions with different vertical structures are found to exist in some range of the bifurcation parameter. Periodic solutions are found which branch off from a steady solution by a Hopf bifurcation. It is suggested that the interannual variability of the stratospheric circulation in the middle and high latitudes during winter may be explained by the multiplicity of steady and periodic stable solutions.
Sampled-data theory, using the Z transformation, is applied to the design of a digital controller for an aircraft-altitude autopilot. Particular attention is focused on the sensitivity of the design to parameter variations and the abruptness of the response, that is, the normal acceleration required to carry out a transient maneuver. Consideration of these two characteristics of the system has shown that the finite settling time design method produces an unacceptable system, primarily because of the high sensitivity of the response to parameter variations, although abruptness can be controlled by increasing the sampling period. Also demonstrated is the importance of having well-damped poles or zeros if cancellation is attempted in the design methods. A different method of smoothing the response and obtaining a design which is not excessively sensitive is proposed, and examples are carried through to demonstrate the validity of the procedure. This method is based on design concepts of continuous systems, and it is shown that if no pole-zero cancellations are allowed in the design, one can obtain a response which is not too abrupt, is relatively insensitive to parameter variations, and is not sensitive to practical limits on control-surface rate. This particular design also has the simplest possible pulse transfer function for the digital controller. Simulation techniques and root loci are used for the verification of the design philosophy.
Adaptive systems under slow parameter adaption can be analyzed by the method of averaging. This provides a means to assess stability (and instability) properties of most adaptive systems, either continuous-time or (more importantly for practice) discrete-time, as well as providing an estimate of the region of attraction. Although the method of averaging is conceptually straightforward, even simple examples are well beyond hand calculations. Specific software tools are proposed which can provide the basis for user-friendly environment to perform the necessary computations involved in the averaging analysis.
A method of parameterizing the coefficients of a dynamical system based of a proper orthogonal decomposition (POD) representing the flow dynamics of a viscous fluid has been introduced. (A brief description of POD is presented in the immediately preceding article.) The present parameterization method is intended to enable construction of the dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers. The need for this or a similar method arises as follows: A procedure that includes direct numerical simulation followed by POD, followed by Galerkin projection to a dynamical system has been proven to enable representation of flow dynamics by a low-dimensional model at the Reynolds number of the simulation. However, a more difficult task is to obtain models that are valid over a range of Reynolds numbers. Extrapolation of low-dimensional models by use of straightforward Reynolds-number-based parameter continuation has proven to be inadequate for successful prediction of flows. A key part of the problem of constructing a dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers is the problem of understanding and providing for the variation of the coefficients of the dynamical system with the Reynolds number. Prior methods do not enable capture of temporal dynamics over ranges of Reynolds numbers in low-dimensional models, and are not even satisfactory when large numbers of modes are used. The basic idea of the present method is to solve the problem through a suitable parameterization of the coefficients of the dynamical system. The parameterization computations involve utilization of the transfer of kinetic energy between modes as a function of Reynolds number. The thus-parameterized dynamical system accurately predicts the flow dynamics and is applicable to a range of flow problems in the dynamical regime around the Hopf bifurcation. Parameter-continuation software can be used on the parameterized dynamical system to derive a bifurcation diagram that accurately predicts the temporal flow behavior.
The two-dimensional model of stratospheric constituents is presented in detail. The derivation of pertinent transport parameters and the numerical solution of the species continuity equations, including a technique for treating the stiff differential equations that represent the chemical kinetic terms, and appropriate methods for simulating the diurnal variations of the solar zenith angle and species concentrations are discussed. Predicted distributions of tracer constituents (ozone, carbon 14, nitric acid) are compared with observed distributions.
Report describes accurate method of determining orbit of low-altitude Earth satellite. Method insensitive to clock errors and provides continuous determination of orbit. Report examines effects of employing fewer ground stations, applying different solution strategies, and introducing fictitious thrust parameters to minimize geopotential modeling error - one of major error sources.
A scanning scheme for the laser rangefinder aboard an autonomous Mars Rover is developed. The rover is expected to be able to traverse an incline of slope up to 25% deg positive or negative. The total azimuth angle of the rangefinder is calculated so that the rangefinder can scan a width of 3 m at a distance of 3 m. A combination of two approaches is considered: scanning the field with a data point spacing appropriate for the terrain modeling technique, followed by zoom scanning with reduced spacing aimed at an obstacle location indicated in a previous terrain scan. It is found that the scan time and total number of data points can be reduced by dividing the field into corridors. The scan is divided into two subscans: the initial scan covering the entire field, and a corridor scan. The corridor scan method reduces the core required in the on-board computer. Hardware changes are expected to be small since the parameters of the corridor are fixed and a continuously variable point spacing is not necessary.
This paper presents grid generation techniques available in the Volume Grid Manipulation (VGM) code. The VGM code is designed to manipulate existing line, surface and volume grids to improve the quality of the data. It embodies an easy to read rich language of commands that enables such alterations as topology changes, grid adaption and smoothing. Additionally, the VGM code can be used to construct simplified straight lines, splines, and conic sections which are common curves used in the generation and manipulation of points, lines, surfaces and volumes (i.e., grid data). These simple geometric curves are essential in the construction of domain discretizations for computational fluid dynamic simulations. By comparison to previously established methods of generating these curves interactively, the VGM code provides control of slope continuity and grid point-to-point stretchings as well as quick changes in the controlling parameters. The VGM code offers the capability to couple the generation of these geometries with an extensive manipulation methodology in a scripting language. The scripting language allows parametric studies of a vehicle geometry to be efficiently performed to evaluate favorable trends in the design process. As examples of the powerful capabilities of the VGM code, a wake flow field domain will be appended to an existing X33 Venturestar volume grid; negative volumes resulting from grid expansions to enable flow field capture on a simple geometry, will be corrected; and geometrical changes to a vehicle component of the X33 Venturestar will be shown.
An important goal of NASA's Internal Vehicle Health Management program (IVHM) is to develop and verify methods and technologies for fault detection in critical airframe structures. A particularly promising new technology under development at NASA Langley Research Center is distributed Bragg fiber optic strain sensors. These sensors can be embedded in, for instance, aircraft wings to continuously monitor surface strain during flight. Strain information can then be used in conjunction with well-known vibrational techniques to detect faults due to changes in the wing's physical parameters or to the presence of incipient cracks. To verify the benefits of this technology, the Formal Methods Group at NASA LaRC has proposed the use of formal verification tools such as PVS. The verification process, however, requires knowledge of the physics and mathematics of the vibrational techniques and a clear understanding of the particular fault detection methodology. This report presents a succinct review of the physical principles behind the modeling of vibrating structures such as cantilever beams (the natural model of a wing). It also reviews two different classes of fault detection techniques and proposes a particular detection method for cracks in wings, which is amenable to formal verification. A prototype implementation of these methods using Matlab scripts is also described and is related to the fundamental theoretical concepts.