Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “time discretization”

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 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Low Dissipative High Order Shock-Capturing Methods Using Characteristic-Based Filters

An approach which closely maintains the non-dissipative nature of classical fourth or higher- order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient and fine scale turbulent structures in a stable and efficient manner is described. The approach is a generalization of the method of Gustafsson and Oisson and the artificial compression method (ACM) of Harten. Spatially non-dissipative fourth or higher-order compact and non-compact spatial differencings are used as the base schemes. Instead of applying a scalar filter as in Gustafsson and Olsson, an ACM like term is used to signal the appropriate amount of second or third-order TVD or ENO types of characteristic based numerical dissipation. This term acts as a characteristic filter to minimize numerical dissipation for the overall scheme. For time-accurate computations, time discretizations with low dissipation are used. Numerical experiments on 2-D vortical flows, vortex-shock interactions and compressible spatially and temporally evolving mixing layers showed that the proposed schemes have the desired property with only a 10% increase in operations count over standard second-order TVD schemes. Aside from the ability to accurately capture shock-turbulence interaction flows, this approach is also capable of accurately preserving vortex convection. Higher accuracy is achieved with fewer grid points when compared to that of standard second-order TVD or ENO schemes. To demonstrate the applicability of these schemes in sustaining turbulence where shock waves are absent, a simulation of 3-D compressible turbulent channel flow in a small domain is conducted.

Yee, H. C.↗
NASA NTRS1998

Dictionary Approaches to Image Compression and Reconstruction

This paper proposes using a collection of parameterized waveforms, known as a dictionary, for the purpose of medical image compression. These waveforms, denoted as lambda, are discrete time signals, where y represents the dictionary index. A dictionary with a collection of these waveforms Is typically complete or over complete. Given such a dictionary, the goal is to obtain a representation Image based on the dictionary. We examine the effectiveness of applying Basis Pursuit (BP), Best Orthogonal Basis (BOB), Matching Pursuits (MP), and the Method of Frames (MOF) methods for the compression of digitized radiological images with a wavelet-packet dictionary. The performance of these algorithms is studied for medical images with and without additive noise.

Ziyad, Nigel A.↗
NASA NTRS1998

Dictionary Approaches to Image Compression and Reconstruction

This paper proposes using a collection of parameterized waveforms, known as a dictionary, for the purpose of medical image compression. These waveforms, denoted as phi(sub gamma), are discrete time signals, where gamma represents the dictionary index. A dictionary with a collection of these waveforms is typically complete or overcomplete. Given such a dictionary, the goal is to obtain a representation image based on the dictionary. We examine the effectiveness of applying Basis Pursuit (BP), Best Orthogonal Basis (BOB), Matching Pursuits (MP), and the Method of Frames (MOF) methods for the compression of digitized radiological images with a wavelet-packet dictionary. The performance of these algorithms is studied for medical images with and without additive noise.

Ziyad, Nigel A.↗
NASA NTRS1999

Video Imaging System Particularly Suited for Dynamic Gear Inspection

A digital video imaging system that captures the image of a single tooth of interest of a rotating gear is disclosed. The video imaging system detects the complete rotation of the gear and divide that rotation into discrete time intervals so that each tooth of interest of the gear is precisely determined when it is at a desired location that is illuminated in unison with a digital video camera so as to record a single digital image for each tooth. The digital images are available to provide instantaneous analysis of the tooth of interest, or to be stored and later provide images that yield a history that may be used to predict gear failure, such as gear fatigue. The imaging system is completely automated by a controlling program so that it may run for several days acquiring images without supervision from the user.

Broughton, Howard↗
NASA NTRS2000

Precision of Four Acoustic Bone Measurement Devices

Though many studies have quantified the precision of various acoustic bone measurement devices, it is difficult to directly compare the results among the studies, because they used disparate subject pools, did not specify the estimation methodology, or did not use consistent definitions for various precision characteristics. In this study, we used a repeated measures design protocol to directly determine the precision characteristics of four acoustic bone measurement devices: the Mechanical Response Tissue Analyzer (MRTA), the UBA-575+, the SoundScan 2000 (S2000), and the Sahara Ultrasound Done Analyzer. Ten men and ten women were scanned on all four devices by two different operators at five discrete time points: Week 1, Week 2, Week 3, Month 3 and Month 6. The percent coefficient of variation (%CV) and standardized coefficient of variation were computed for the following precision characteristics: interoperator effect, operator-subject interaction, short-term error variance, and long-term drift, The MRTA had high interoperator errors for its ulnar and tibial stiffness measures and a large long-term drift in its tibial stiffness measurement. The UBA-575+ exhibited large short-term error variances and long-term drift for all three of its measurements. The S2000's tibial speed of sound measurement showed a high short-term error variance and a significant operator-subject interaction but very good values ( < 1%) for the other precision characteristics. The Sahara seemed to have the best overall performance, but was hampered by a large %CV for short-term error variance in its broadband ultrasound attenuation measure.

Miller, Christopher↗
NASA NTRS2000

Precision of Four Acoustic Bone Measurement Devices

Though many studies have quantified the precision of various acoustic bone measurement devices, it is difficult to directly compare the results among the studies, because they used disparate subject pools, did not specify the estimation methodology, or did not use consistent definitions for various precision characteristics. In this study, we used a repeated measures design protocol to directly determine the precision characteristics of four acoustic bone measurement devices: the Mechanical Response Tissue Analyzer (MRTA), the UBA-575+, the SoundScan 2000 (S2000), and the Sahara Ultrasound Bone Analyzer. Ten men and ten women were scanned on all four devices by two different operators at five discrete time points: Week 1, Week 2, Week 3, Month 3 and Month 6. The percent coefficient of variation (%CV) and standardized coefficient of variation were computed for the following precision characteristics: interoperator effect, operator-subject interaction, short-term error variance, and long-term drift. The MRTA had high interoperator errors for its ulnar and tibial stiffness measures and a large long-term drift in its tibial stiffness measurement. The UBA-575+ exhibited large short-term error variances and long-term drift for all three of its measurements. The S2000's tibial speed of sound measurement showed a high short-term error variance and a significant operator-subject interaction but very good values (less than 1%) for the other precision characteristics. The Sahara seemed to have the best overall performance, but was hampered by a large %CV for short-term error variance in its broadband ultrasound attenuation measure.

Miller, Christopher↗
NASA NTRS1994

Assessment of Psychophysiological Responses During Motion Sickness Testing

The purpose of this investigation is to evaluate a methodology designed to accurately trace the temporal progression of motion sickness and space motion sickness symptoms. With this method, subjects continuously monitor their own motion sickness symptoms during exposure to a provocative stimulus as symptoms occur, in contrast to previous methods during which subjects report symptoms verbally at discrete time intervals. This method not only is comparable to previous methods in the type of symptoms that subjects report, but subjects report symptoms more frequently. Frequent reporting of motion sickness symptoms allows researchers to detail the waxing and waning of motion sickness symptoms for each individual. Previous research has shown that physiological responses to motion sickness stimuli are characterized by unique individual differences in response patterns. By improving our assessment of motion sickness symptoms with continuous monitoring of symptoms, the relationship between specific physiological responses and sickness levels can be more accurately determined for each individual. Results from this study show significant positive relationships between skin conductance levels and symptom levels for ten individuals; a significant positive relationship between temperature and symptom levels for 5 of 10 individuals; and both positive and negative relationships between respiration, heart rate, blood volume pulse and symptom levels. Continuous monitoring of motion sickness symptoms can be used to more accurately assess motion sickness to aid in the evaluation of countermeasures. In addition, recognition of the onset of symptoms that are strongly related to specific physiological responses could be used as cues to initiate procedures (e.g., Autogenic Feedback Training) to prevent the development of severe motion sickness symptoms.

Stoud, Cynthia S.↗
NASA NTRS2002

Experimental Feedback Control of Flow Induced Cavity Tones

An experimental study of the application of discrete-time, linear quadratic control design methods to the cavity tone problem is described. State space models of the dynamics from a synthetic jet actuator at the leading edge of the cavity to two pressure sensors in the cavity were computed from experimental data. Variations in model order, control order, control bandwidth, and properties of a Kalman state estimator were studied. Feedback control reduced the levels of multiple cavity tones at Mach 0.275, 0.35, and 0.45. Closed loop performance was often limited by excitation of sidebands of cavity tones, and creation of new tones in the spectrum. State space models were useful for explaining some of these limitations, but were not able to account for non-linear dynamics, such as interactions between tones at different frequencies.

Cabell, Randolph H.↗
NASA NTRS2004

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

Shu, Chi-Wang↗
NASA NTRS2004

Control of Initialized Fractional-Order Systems

Fractional-Order systems, or systems containing fractional derivatives and integrals, have been studied by many in the engineering area. Additionally, very readable discussions, devoted specifically to the subject, are presented by Oldham and Spanier, Miller and Ross, and Pudlubny (1999a). It should be noted that there are a growing number of physical systems whose behavior can be compactly described using fractional system theory. Of specific interest to electrical engineers are long lines, electrochemical processes, dielectric polarization, colored noise, viscoelastic materials, and chaos. With the growing number of applications, it is important to establish a theory of control for these fractional-order systems, and for the potential use of fractional-order systems as feedback compensators. This topic is addressed in this paper. The first section discusses the control of fractional-order systems using a vector space representation, where initialization is included in the discussion. It should be noted that Bagley and Calico and Padovan and Sawicki both present a fractional state-space representation, which do not include the important historic effects. Incorporation of these effects based on the initialized fractional calculus is presented . The control methods presented in this paper are based on the initialized fractional order system theory. The second section presents an input-output approach. Some of the problems encountered in these sections are: a) the need to introduce a new complex plane to study the dynamics of fractional-order systems, b) the need to properly define the Laplace transform of the fractional derivative, and c) the proper inclusion of the initialization response in the system and control formulation. Following this, the next section generalizes the proportional-plus-integral-control (PI-control) and PID-control (PI-plus- derivative) concepts using fractional integrals. This is then further generalized using general fractional- order compensators. Finally the compensator concept is generalized by the use of a continuum of fractions in the compensator via the concept of order-distributions. The last section introduces fractional feedback in discrete-time.

Hartley, Tom T.↗
NASA NTRS2004

Error Analysis for Discontinuous Galerkin Method for Parabolic Problems

In the proposal, the following three objectives are stated: (1) A p-version of the discontinuous Galerkin method for a one dimensional parabolic problem will be established. It should be recalled that the h-version in space was used for the discontinuous Galerkin method. An a priori error estimate as well as a posteriori estimate of this p-finite element discontinuous Galerkin method will be given. (2) The parameter alpha that describes the behavior double vertical line u(sub t)(t) double vertical line 2 was computed exactly. This was made feasible because of the explicitly specified initial condition. For practical heat transfer problems, the initial condition may have to be approximated. Also, if the parabolic problem is proposed on a multi-dimensional region, the parameter alpha, for most cases, would be difficult to compute exactly even in the case that the initial condition is known exactly. The second objective of this proposed research is to establish a method to estimate this parameter. This will be done by computing two discontinuous Galerkin approximate solutions at two different time steps starting from the initial time and use them to derive alpha. (3) The third objective is to consider the heat transfer problem over a two dimensional thin plate. The technique developed by Vogelius and Babuska will be used to establish a discontinuous Galerkin method in which the p-element will be used for through thickness approximation. This h-p finite element approach, that results in a dimensional reduction method, was used for elliptic problems, but the application appears new for the parabolic problem. The dimension reduction method will be discussed together with the time discretization method.

Kaneko, Hideaki↗
NASA NTRS2003

Airport Pricing Strategies

Conventional economic wisdom suggests that congestion pricing would be an appropriate response to cope with the growing congestion levels currently experienced at many airports. Several characteristics of aviation markets, however, may make naive congestion prices equal to the value of marginal travel delays a non-optimal response. This paper has developed a model of airport pricing that captures a number of these features. The model in particular reflects that airlines typically have market power and are engaged in oligopolistic competition at different sub-markets; that part of external travel delays that aircraft impose are internal to an operator and hence should not be accounted for in congestion tolls. We presented an analytical treatment for a simple bi-nodal symmetric network, which through the use of 'hyper-networks' would be readily applicable to dynamic problems (in discrete time) such as peak - off-peak differences, and some numerical exercises for the same symmetric network, which was only designed to illustrate the possible comparative static impacts of tolling, in addition to marginal equilibrium conditions as could be derived for the general model specification. Some main conclusions are that second-best optimal tolls are typically lower than what would be suggested by congestion costs alone and may even be negative, and that the toll as derived by Brueckner (2002) may not lead to an increase in total welfare. While Brueckner (2002) has made clear that congestion tolls on airports may be smaller than expected when congestion costs among aircraft are internal for a firm, our analysis adds to this that a further downward adjustment may be in order due to market power. The presence of market power (which causes prices to exceed marginal costs) may cause the pure congestion toll to be suboptimal, because the resulting decrease in demand is too high (the pure congestion tall does not take into account the decrease in consumer surplus). The various downward adjustments in welfare maximizing tolls may well cause the optimal values of these to be negative. Insofar as subsidization is considered unacceptable for whichever reason, our results warn that the most efficient among the non-negative tolls may actually be a zero toll; the pure congestion toll may actually decrease welfare compared to the base case. The model in this paper contains a few simplifying assumptions that may be relaxed in future work. Load factors and aircraft capacity are fixed in this model for simplicity. In a more advanced version of this model, load factors and aircraft capacity can be endogenized. This makes the derivation of the optimality conditions far more complicated, but it should be feasible in a numerical experiment. One can also add a fourth layer to the model, describing the airport's optimization problem. For example, the airport can maximize profits under a cost recovery constraint. The model then deals with interactions between four types of agents. No distinction is made between peak and off-peak traffic in this paper. Finally, the results of the numerical exercise in this paper need to be checked against an asymmetric equilibrium.

Pels, Eric↗
NASA NTRS2005

Attitude Sensor Pseudonoise

Even assuming perfect attitude sensors and gyros, sensor measurements on a vibrating spacecraft have apparent errors. These apparent sensor errors, referred to as pseudonoise, arise because gyro and sensor measurements are performed at discrete times. This paper explains the concept of pseudonoise, quantifies its behavior, and discusses the effect of vibrations that are nearly commensurate with measurement periods. Although pseudonoise does not usually affect attitude determination it does affect sensor performance evaluation. Attitude rates are usually computed from differences between pairs of accumulated angle measurements at different times and are considered constant in the periods between measurements. Propagation using these rates does not reproduce exact instantaneous spacecraft attitudes except at the gyro measurement times. Exact sensor measurements will therefore be inconsistent with estimates based on the propagated attitude. This inconsistency produces pseudonoise. The characteristics of pseudonoise were determined using a simple, one-dimensional model of spacecraft vibration. The statistical properties of the deviations of measurements from model truth were determined using this model and a range of different periods of sensor and rate measurements. This analysis indicates that the magnitude of pseudonoise depends on the ratio of the spacecraft vibration period to the time between gyro measurements and can be as much as twice the amplitude of the vibration. In cases where the vibration period and gyro or sensor measurement period are nearly commensurate, unexpected changes in pseudonoise occur.

Hashmall, Joseph A.↗
NASA NTRS2006

A Measure-Theoretic Proof of the Markov Property for Hybrid Systems with Markovian Inputs

The behavior of a general hybrid system in discrete time can be represented by a non-linear difference equation x(k+1) = Fk(x(k), theta(k)), where theta(k) is assumed to be a finite state Markov chain. An important step in the stability analysis of these systems is to establish the Markov property of (x(k), theta(k)). There are, however, no complete proofs of this property which are simple to understand. This paper aims to correct this problem by presenting a complete and explicit proof, which uses only basic measure-theoretical concepts.

Tejada, Arturo↗
NASA NTRS2008

Information Extraction for System-Software Safety Analysis: Calendar Year 2007 Year-End Report

This annual report describes work to integrate a set of tools to support early model-based analysis of failures and hazards due to system-software interactions. The tools perform and assist analysts in the following tasks: 1) extract model parts from text for architecture and safety/hazard models; 2) combine the parts with library information to develop the models for visualization and analysis; 3) perform graph analysis on the models to identify possible paths from hazard sources to vulnerable entities and functions, in nominal and anomalous system-software configurations; 4) perform discrete-time-based simulation on the models to investigate scenarios where these paths may play a role in failures and mishaps; and 5) identify resulting candidate scenarios for software integration testing. This paper describes new challenges in a NASA abort system case, and enhancements made to develop the integrated tool set.

Malin, Jane T.↗
NASA NTRS2005

Experimental Feedback Control of Flow Induced Cavity Tones

Discrete-time, linear quadratic methods were used to design feedback controllers for reducing tones generated by flow over a cavity. The dynamics of a synthetic jet actuator mounted at the leading edge of the cavity as observed by two microphones in the cavity were modeled over a broad frequency range using state space models computed from experimental data. Variations in closed loop performance as a function of model order, control order, control bandwidth, and state estimator design were studied using a cavity in the Probe Calibration Tunnel at NASA Langley. The controller successfully reduced the levels of multiple cavity tones at the tested flow speeds of Mach 0.275, 0.35, and 0.45. In some cases, the closed loop results were limited by excitation of sidebands of the cavity tones, or the creation of new tones at frequencies away from the cavity tones. Nonetheless, the results validate the combination of optimal control and experimentally-generated state space models, and suggest this approach may be useful for other flow control problems. The models were not able to account for non-linear dynamics, such as interactions between tones at different frequencies.

Cabell, Randolph H.↗
NASA NTRS2008

Trajectory Planning by Preserving Flexibility: Metrics and Analysis

In order to support traffic management functions, such as mitigating traffic complexity, ground and airborne systems may benefit from preserving or optimizing trajectory flexibility. To help support this hypothesis trajectory flexibility metrics have been defined in previous work to represent the trajectory robustness and adaptability to the risk of violating safety and traffic management constraints. In this paper these metrics are instantiated in the case of planning a trajectory with the heading degree of freedom. A metric estimation method is presented based on simplifying assumptions, namely discrete time and heading maneuvers. A case is analyzed to demonstrate the estimation method and its use in trajectory planning in a situation involving meeting a time constraint and avoiding loss of separation with nearby traffic. The case involves comparing path-stretch trajectories, in terms of adaptability and robustness along each, deduced from a map of estimated flexibility metrics over the solution space. The case demonstrated anecdotally that preserving flexibility may result in enhancing certain factors that contribute to traffic complexity, namely reducing proximity and confrontation.

Idris, Husni R.↗
NASA NTRS2000

Adjoints and Low-rank Covariance Representation

Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.

Tippett, Michael K.↗