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At least 289 records · Page 16

A theoretical analysis of the round-off propagation in different Kalman filter implementations

A theoretical analysis is made of the error propagation due to numerical round-off for four different Kalman filter implementations: the conventional Kalman filter, the square root covariance filter, the square root information filter and the Chandrasekhar square root filter. From these error models, new insights about the applicability of the different filters and their sensitivity to round-off, is obtained. It is shown that the CKF may become completely unreliable when the original plant is unstable, and that this is easily circumvented by a number of techniques. The square root filters, often quoted to possess a conditioning or sensitivity that is the square root of that of the CKF, are shown to possess this property only for the computation of the covariance of the filtered signal and not for the computation of the Kalman gain or the filtered estimate. Finally, the Chandrasekhar filter is shown to be numerically unstable.

Verhaegen, M.↗

Assessment of numerical techniques for unsteady flow calculations

The characteristics of unsteady flow motions have long been a serious concern in the study of various fluid dynamic and combustion problems. With the advancement of computer resources, numerical approaches to these problems appear to be feasible. The objective of this paper is to assess the accuracy of several numerical schemes for unsteady flow calculations. In the present study, Fourier error analysis is performed for various numerical schemes based on a two-dimensional wave equation. Four methods sieved from the error analysis are then adopted for further assessment. Model problems include unsteady quasi-one-dimensional inviscid flows, two-dimensional wave propagations, and unsteady two-dimensional inviscid flows. According to the comparison between numerical and exact solutions, although second-order upwind scheme captures the unsteady flow and wave motions quite well, it is relatively more dissipative than sixth-order central difference scheme. Among various numerical approaches tested in this paper, the best performed one is Runge-Kutta method for time integration and six-order central difference for spatial discretization.

Hsieh, Kwang-Chung↗

Computation of Gust-Cascade Interaction Using the CE/SE Method

The problem 2 in Category 3 of the 4th Computational Aeroacoustic(CAA) Workshop is solved using the space-time conservation element and solution element (CE/SE) method. This problem models rotor-stator interaction in a 2D cascade. It involves complex geometries and flow physics including vortex shedding and acoustic radiation. The parallel version of the 2D nonlinear Euler solver is used with an unstructured triangular mesh to solve this problem. The Giles approach is incorporated with the CE/SE method to handle non-equal pitches of the rotor and stator. Validation on the Giles approach is performed using Problem 3.1 in the 2nd CAA Workshop. The space-time CE/SE method is a finite volume method with second-order accuracy in both space and time. The flux conservation is enforced in both space and time instead of space only. It has low numerical dissipation and dispersion errors. It uses simple non-reflecting boundary conditions and is compatible with unstructured meshes. It is simple, flexible, and generate reasonably accurate solutions. The CE/SE method has been successfully applied to solve numerous practical problems, especially aeroacoustic problems. Some preliminary numerical results of the benchmark problem 3.2 of the 4th CAA Workshop are shown. The steady-state pressure contour is plotted. The mean pressure distribution on the blade surface is compared with Turbo solution showing a good agreement. The sound pressure level versus the rotor harmonic n at the six designated positions on the blade surface, three locations at inlet plane, and three locations at the outlet plane are plotted. It can be seen that the acoustic response exists only at the excitation frequencies (n = 1,2,3). On the blade surface, the acoustic wave at n = 1 is dominant, while at the inlet and outlet planes, the sound pressure level at n = 2 becomes the largest, which is similar to the results presented. The distribution of sound pressure level at different spatial modes along the z- direction is plotted for n = 1,2,3, respectively. It shows that the spatial modes m = -32 and 22 at n = 1 exponentially decay, and the spatial modes m = 10 at n = 2, m = -42 and 12 at n = 3 propagate both upstream and downstream, which agrees with the prediction based on the linearized theory. Some oscillations are observed, which needs to be investigated further. In the final paper, the numerical results will be compared with a frequency-domain solver LINFLUX solution if it is available.

Wang, X.-Y.↗

The use of self checks and voting in software error detection - An empirical study

The results of an empirical study of software error detection using self checks and N-version voting are presented. Working independently, each of 24 programmers first prepared a set of self checks using just the requirements specification of an aerospace application, and then each added self checks to an existing implementation of that specification. The modified programs were executed to measure the error-detection performance of the checks and to compare this with error detection using simple voting among multiple versions. The analysis of the checks revealed that there are great differences in the ability of individual programmers to design effective checks. It was found that some checks that might have been effective failed to detect an error because they were badly placed, and there were numerous instances of checks signaling nonexistent errors. In general, specification-based checks alone were not as effective as specification-based checks combined with code-based checks. Self checks made it possible to identify faults that had not been detected previously by voting 28 versions of the program over a million randomly generated inputs. This appeared to result from the fact that the self checks could examine the internal state of the executing program, whereas voting examines only final results of computations. If internal states had to be identical in N-version voting systems, then there would be no reason to write multiple versions.

Leveson, Nancy G.↗

Adiabatic properties of pulsating DA white dwarfs. I - The treatment of the Brunt-Vaisala frequency and the region of period formation

The fundamental issue of the region of period formaton in a degenerate star is examined, with special attention given to the treatment of the Brunt-Vaisala frequency. It is shown that, in order to obtain reliable numerical results in degenerate stellar models, the Brunt-Vaisala frequency must be appropriately transformed, because it is defined in terms of a difference between two numbers which become nearly equal in highly degenerate matter, causing serious numerical problems and systematic errors. An alternative expression is derived, which is valid for multicomponent nonideal partially degenerate and partially ionized plasmas such as those encountered in white dwarf envelopes. This expression is used to compute the period structure of the same white dwarf considered by Pesnell (1987). It is shown that the implicit numerical differencing used in the Lagrangian pulsation code of Pesnell leads to very serious difficulties when used with models of degenerate stars.

Brassard, P.↗

L-orthogonal signal transmission and detection.

Investigation of the detailed capabilities and performance characterization of systems that employ L-orthogonal signaling techniques. L-orthogonal signals represent a unified set of signals wherein the polyphase and orthogonal (bi-orthogonal) signal sets are included as special cases. This fact is important, since orthogonal (bi-orthogonal) and polyphase signaling sets represent opposing forces as far as tradeoffs between error probability, energy-to-noise ratio, and bandwidth requirements are concerned. Bounds on the performance of the optimum receiver and the performance of various suboptimum (practical) receiver structures are given. Coherent and differentially coherent detection of differentially encoded signals are also pursued. Various comparisons and tradeoffs are made by means of numerical evaluation of the error probability expressions.

Lindsey, W. C.↗

Numerical algorithms for computations of feedback laws arising in control of flexible systems

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

Lasiecka, Irena↗

Wind Retrieval Algorithms for the IWRAP and HIWRAP Airborne Doppler Radars with Applications to Hurricanes

Algorithms for the retrieval of atmospheric winds in precipitating systems from downward-pointing, conically-scanning airborne Doppler radars are presented. The focus in the paper is on two radars: the Imaging Wind and Rain Airborne Profiler(IWRAP) and the High-altitude IWRAP (HIWRAP). The IWRAP is a dual-frequency (Cand Ku band), multi-beam (incidence angles of 30 50) system that flies on the NOAAWP-3D aircraft at altitudes of 2-4 km. The HIWRAP is a dual-frequency (Ku and Kaband), dual-beam (incidence angles of 30 and 40) system that flies on the NASA Global Hawk aircraft at altitudes of 18-20 km. Retrievals of the three Cartesian wind components over the entire radar sampling volume are described, which can be determined using either a traditional least squares or variational solution procedure. The random errors in the retrievals are evaluated using both an error propagation analysis and a numerical simulation of a hurricane. These analyses show that the vertical and along-track wind errors have strong across-track dependence with values of 0.25 m s-1 at nadir to 2.0 m s-1 and 1.0 m s-1 at the swath edges, respectively. The across-track wind errors also have across-track structure and are on average, 3.0 3.5 m s-1 or 10 of the hurricane wind speed. For typical rotated figure four flight patterns through hurricanes, the zonal and meridional wind speed errors are 2 3 m s-1.Examples of measured data retrievals from IWRAP during an eyewall replacement cycle in Hurricane Isabel (2003) and from HIWRAP during the development of Tropical Storm Matthew (2010) are shown.

atmospheric winds↗

Technical Evaluation Report for Symposium AVT-147: Computational Uncertainty in Military Vehicle Design

The complexity of modern military systems, as well as the cost and difficulty associated with experimentally verifying system and subsystem design makes the use of high-fidelity based simulation a future alternative for design and development. The predictive ability of such simulations such as computational fluid dynamics (CFD) and computational structural mechanics (CSM) have matured significantly. However, for numerical simulations to be used with confidence in design and development, quantitative measures of uncertainty must be available. The AVT 147 Symposium has been established to compile state-of-the art methods of assessing computational uncertainty, to identify future research and development needs associated with these methods, and to present examples of how these needs are being addressed and how the methods are being applied. Papers were solicited that address uncertainty estimation associated with high fidelity, physics-based simulations. The solicitation included papers that identify sources of error and uncertainty in numerical simulation from either the industry perspective or from the disciplinary or cross-disciplinary research perspective. Examples of the industry perspective were to include how computational uncertainty methods are used to reduce system risk in various stages of design or development.

Radespiel, Rolf↗

Sea surface determination from space: The GSFC geoid

The determination of the sea surface/geoid and its relative variation were investigated and results of the altimeter experiment on Skylab to test the geoid are discussed. The spaceborne altimeter on Skylab revealed that the sea surface of the world's oceans can be measured with an accuracy in the meter range. Surface variations are discussed as they relate to those computed from satellite orbital dynamics and ground based gravity data. The GSFC geoid was constructed from about 400,000 satellite tracking data (range, range rate, angles) and about 20,000 ground gravity observations. One of the last experiments on Skylab was to measure and/or test this geoid over almost one orbit. It was found that the computed water surface deviates between 5 to 20 m from the measured one. Further outlined are the influence of orbital errors on the sea surface, and numerical examples are given based upon real tracking data. Orbital height error estimates were computed for geodetic type satellites and are found to be in the order of 0.2 to 5 meters.

Vonbun, F. O.↗

Arrival time of satellite-broadened laser pulses

A method for measuring the time of arrival of very narrow laser pulses which have been reflected and randomly broadened by a target is examined. It is known that these return pulses from the target have very small rise times. A threshold detection algorithm that detects the rising edge of the pulse is used for obtaining the pulse arrival times. The errors of the scheme are evaluated numerically for different pulse shapes, and a loose bound on the errors of detecting a typical pulse is obtained. A gamma-density model is used to characterize the random gain processes of the optical receiver, and the effect of such random gains on the errors of threshold detection is analyzed.

Iyer, R. S.↗

Optimizations on Designing High-Resolution Finite-Difference Schemes

We describe a general optimization procedure for both maximizing the resolution characteristics of existing finite differencing schemes as well as designing finite difference schemes that will meet the error tolerance requirements of numerical solutions. The procedure is based on an optimization process. This is a generalization of the compact scheme introduced by Lele in which the resolution is improved for single, one-dimensional spatial derivative, whereas in the present approach the complete scheme, after spatial and temporal discretizations, is optimized on a range of parameters of the scheme and the governing equations. The approach is to linearize and Fourier analyze the discretized equations to check the resolving power of the scheme for various wave number ranges in the solution and optimize the resolution to satisfy the requirements of the problem. This represents a constrained nonlinear optimization problem which can be solved to obtain the nodal weights of discretization. An objective function is defined in the parametric space of wave numbers, Courant number, Mach number and other quantities of interest. Typical criterion for defining the objective function include the maximization of the resolution of high wave numbers for acoustic and electromagnetic wave propagations and turbulence calculations. The procedure is being tested on off-design conditions of non-uniform mesh, non-periodic boundary conditions, and non-constant wave speeds for scalar and system of equations. This includes the solution of wave equations and Euler equations using a conventional scheme with and without optimization and the design of an optimum scheme for the specified error tolerance.

Liu, Yen↗

Predictability of planetary waves - Interhemispheric differences and the effects of stationary forcing

An attempt is made to determine the way in which errors appear in the ultralong waves of numerical weather prediction models, as well as the means by which such errors may be alleviated. Such efforts to improve the numerical forecasting of planetary waves derive their importance from the fact that energetic large scale phenomena are the basis for prospective improvements in extended range forecasting. A simple, linear, quasi-geostrophic and barotropic model is presently used in real data forecast simulations to explore, in an idealized context, several effects that may clarify discrepancies betweeen predictability theory and the performance of current numerical weather prediction models. Attention is given to the degree to which discrepancies may be accounted for by linear theory.

Roads, J. O.↗

A Novel Protocol for Decoating and Permeabilizing Bacterial Spores for Epifluorescent Microscopy

Based on previously reported procedures for permeabilizing vegetative bacterial cells, and numerous trial-and-error attempts with bacterial endospores, a protocol was developed for effectively permeabilizing bacterial spores, which facilitated the applicability of fluorescent in situ hybridization (FISH) microscopy. Bacterial endospores were first purified from overgrown, sporulated suspensions of B. pumilus SAFR-032. Purified spores at a concentration of approx equals 10 million spores/mL then underwent proteinase-K treatment, in a solution of 468.5 μL of 100 mM Tris-HCl, 30 μL of 10% SDS, and 1.5 microL of 20 mg/mL proteinase-K for ten minutes at 35 ºC. Spores were then harvested by centrifugation (15,000 g for 15 minutes) and washed twice with sterile phosphate-buffered saline (PBS) solution. This washing process consisted of resuspending the spore pellets in 0.5 mL of PBS, vortexing momentarily, and harvesting again by centrifugation. Treated and washed spore pellets were then resuspended in 0.5 mL of decoating solution, which consisted of 4.8 g urea, 3 mL Milli-Q water, 1 mL 0.5M Tris, 1 mL 1M dithiothreitol (DTT), and 2 mL 10% sodium-dodecylsulfate (SDS), and were incubated at 65 ºC for 15 minutes while being shaken at 165 rpm. Decoated spores were then, once again, washed twice with sterile PBS, and subjected to lysozyme/mutanolysin treatment (7 mg/mL lysozyme and 7U mutanolysin) for 15 minutes at 35 C. Spores were again washed twice with sterile PBS, and spore pellets were resuspended in 1-mL of 2% SDS. This treatment, facilitating inner membrane permeabilization, lasted for ten minutes at room temperature. Permeabilized spores were washed two final times with PBS, and were resuspended in 200 mkcroL of sterile PBS. At this point, the spores were permeable and ready for downstream processing, such as oligonucleotideprobe infiltration, hybridization, and microscopic evaluation. FISH-microscopic imagery confirmed the effective and efficient (≈50% successful permeabilization and recovery) permeabilization of numerous spore preparations. The novelty of the technology developed here is in its applicability to bacterial endospores. While protocols abound for the effective permeabilization of bacterial, archaeal, and eukaryotic vegetative cells, there are no such reliable methods for decoating and permeabilizing bacterial endospores in a manner that is amenable to downstream FISH microscopic analyses. This innovation enables the direct visualization and enumeration of spores via FISH-based microscopic techniques, circumventing the complications that accompany previously required germination regimes. The synergistic enzymatic weakening of the many spore layers facilitates a structural compromise that is just enough to render the spores permeable without degrading the spore to a level, which precludes it from recognition.

LaDuc, Myron T.↗

Some effects of bias errors in redundant flight control systems.

The controllability and steady-state response of parallel-redundant flight control systems are examined. It is found that state components which appear in the parallel signal paths, e.g., individual actuator commands, are not controllable, although the sum of the command signals is well-behaved. If the response modes associated with these components are not stable, bias errors can cause the components to diverge, leading to the possibility of 'nuisance trips' in failure detection/isolation logic and eventual control system lockup (at saturation). Combining the inputs to the control computers assures that sensor bias will not cause divergence, while cross-strapping control strings bounds divergent response to all bias error inputs. Results of numerical solutions confirm the problem and its solutions.

Stengel, R. F.↗

Some effects of bias errors in redundant flight control systems

The controllability and steady-state response of parallel-redundant flight control systems are examined. It is found that state components which appear in the parallel signal paths, or individual actuator commands, are not controllable, although the sum of the command signals is well-behaved. If the response modes associated with these components are not stable, bias errors can cause the components to diverge, leading to the possibility of nuisance trips in failure detection/isolation logic and eventual control system lockup (at saturation). Combining the inputs to the control computers assures that sensor bias will not cause divergence, while cross-strapping control strings bounds divergent response to all bias error inputs. Results of numerical solutions confirm the problem and its solutions.

Stengel, R. F.↗