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Results for “error guarantees”

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.

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NASA NTRS1975

Stochastic process approximation for recursive estimation with guaranteed bound on the error covariance

An approach, is proposed for the design of approximate, fixed order, discrete time realizations of stochastic processes from the output covariance over a finite time interval, was proposed. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process covariance; (the difference matrix is nonnegative definite). The design is achieved by minimizing, in one of those classes, a measure of the approximation between the model and the process evaluated by the trace of the difference of the respective covariance matrices. Models belonging to these classes have the notable property that, under the same measurement system and estimator structure, the output estimation error covariance matrix computed on the model is an upper bound of the corresponding covariance on the real process. An application of the approach is illustrated by the modeling of random meteorological wind profiles from the statistical analysis of historical data.

Menga, G.↗

NASA NTRS2010

In Search of Grid Converged Solutions

Assessing solution error continues to be a formidable task when numerically solving practical flow problems. Currently, grid refinement is the primary method used for error assessment. The minimum grid spacing requirements to achieve design order accuracy for a structured-grid scheme are determined for several simple examples using truncation error evaluations on a sequence of meshes. For certain methods and classes of problems, obtaining design order may not be sufficient to guarantee low error. Furthermore, some schemes can require much finer meshes to obtain design order than would be needed to reduce the error to acceptable levels. Results are then presented from realistic problems that further demonstrate the challenges associated with using grid refinement studies to assess solution accuracy.

Lockard, David P.↗

NASA NTRSDate not supplied

Operations and Results from the 200 Gbps Tbird Lasercom Mission

Since launch in May 2022, the TeraByte Infrared Delivery (TBIRD) mission has successfully demonstrated 200 Gbps laser communications from a 6U CubeSat and has transferred >1 TB in a pass from low Earth orbit to ground. To support the narrow downlink beam needed for high rate communications, the payload provides pointing feedback to the host spacecraft to precisely track the ground station throughout the 5-minute pass. The space and ground terminals utilize fiber-coupled coherent transceivers in conjunction with an automatic repeat request (ARQ) system to guarantee error-free communication through an atmospheric fading channel. This paper presents an overview of the link operations and mission results to date.

lasercoms↗

NASA NTRSDate not supplied

Operations and Results from the 200 Gbps TBIRD Laser Communication Mission

Since launch in May 2022, the TeraByte Infrared Delivery (TBIRD) mission has successfully demonstrated 200 Gbps laser communications from a 6U CubeSat and has transferred up to 4.8 terabytes (TB) in a pass from low Earth orbit to ground. To our knowledge, this is the fastest downlink ever achieved from space. To support the narrow downlink beam needed for high rate communications, the payload provides pointing feedback to the host spacecraft to precisely track the ground station throughout the 5-minute pass. The space and ground terminals utilize fiber-coupled coherent transceivers in conjunction with an automatic repeat request (ARQ) system to guarantee error-free communication through an atmospheric fading channel. This paper presents an overview of the link operations and mission results to date, as well as implications for future missions with high rate lasercom.

TBIRD↗

NASA NTRS1991

Test functions for the moment method which yield the minimum mean square error

The method of moments has found extensive applications in the solution of a wide class of electromagnetic problems. Additionally, there are a number of basis functions which have found favor and with them different types of testing methods. This work examines the selection of test functions, given a selected set of basis functions, which serve to minimize the mean square error. These test functions will guarantee equal or lesser error compared with any other test function. Additionally, these test functions provide a monotonic improvement of the approximation as the increase in the order of the system. Hence while these test functions require the application of the differential or integral operator one additional time, they provide an absolute lower bound to the mean square error in the approximation and a means to systematically improve accuracy with each increase in the order of the unknowns.

Shamansky, H.↗

NASA NTRSDate not supplied

Assessment of Numerical and Modeling Errors of RANS based Transition Models for Low-Reynolds Numbers 2-D Flows

In this paper we report the outcome of selected workshops organized as part of the NATO Applied Vehicle Technology (AVT)-313 activity Incompressible Laminar-to-Turbulent Flow Transition Study that focused on assessing the numerical and modeling accuracy of the γ−Reθ and γ transition models coupled to the k−ω Shear-Stress Transport (SST) two-equation eddy-viscosity model. Three different test cases involving nominally 2D flow configurations were selected: flow over a flat plate with two different levels of turbulence intensity at the inlet; flow around the Eppler 387 foil at a Reynolds number of 3×10^5 and angles of attack of 1 deg. and 7 deg. flow around the NACA 0015 foil at a Reynolds number of 1.8×10^5 and angles of attack of 5 deg. and10 deg. The flat plate flow conditions correspond to natural and by-pass transition, whereas the other two test cases include laminar separation bubbles that lead to separation-induced transition. For each test case, the selected quantities of interest include both integral and local flow quantities. Geometrically similar grids with a wide range of grid refinement ratios were generated for each of the test cases to allow the estimation of numerical uncertainties for all quantities of interest selected for this study. Several RANS flow solvers were used, employing common grids with the same boundary conditions and mathematical models. Therefore, it is possible to analyze the consistency of the results, i.e., to check if the intervals defined by the different numerical solutions with their respective uncertainties overlap with each other. Modeling errors can also be addressed for the selected flow quantities that have experimental data available. However, the experimental information available in these cases is not sufficient to guarantee that experiments and simulations are performed with the same settings. Nonetheless, the available experimental data is sufficient to guarantee that modeling errors are significantly reduced with the use of the transition models when compared to simulations performed using only the k−ω SST model.

CFD Modeling↗

NASA NTRS2010

SEU/SET Tolerant Phase-Locked Loops

The phase-locked loop (PLL) is an old and widely used circuit for frequency and phase demodulation, carrier and clock recovery, and frequency synthesis [1]. Its implementations range from discrete components to fully integrated circuits and even to firmware or software. Often the PLL is a highly critical component of a system, as for example when it is used to derive the on-chip clock, but as of this writing no definitive single-event upset (SET)/single-event transient (SET) tolerant PLL circuit has been described. This chapter hopes to rectify that situation, at least in regard to PLLs that are used to generate clocks. Older literature on fault-tolerant PLLs deals with detection of a hard failure, which is recovered by replacement, repair, or manual restart of discrete component systems. Several patents exist along these lines (6349391, 6272647, and 7089442). A newer approach is to harden the parts of a PLL system, to one degree or another, such as by using a voltage-based charge pump or a triple modular redundant (TMR) voted voltage-controlled oscillator (VCO). A more comprehensive approach is to harden by triplication and voting (TMR) all the digital pieces (primarily the divider) of a frequency synthesis PLL, but this still leaves room for errors in the VCO and the loop filter. Instead of hardening or voting pieces of a system, such as a frequency synthesis system (i.e., clock multiplier), we will show how the entire system can be voted. There are two main ways of doing this, each with advantages and drawbacks. We will show how each has advantages in certain areas, depending on the lock acquisition and tracking characteristics of the PLL. Because of this dependency on PLL characteristics, we will briefly revisit the theory of PLLs. But first we will describe the characteristics of voters and their correct application, as some literature does not follow the voting procedure that guarantees elimination of errors. Additionally, we will find that voting clocks is a bit trickier than voting data where an infallible clock is assumed. It is our job here to produce (or recover) that assumed infallible clock!

Shuler, Robert L., Jr.↗

NASA NTRS1972

Error-erasure decoding of product codes.

Two error-erasure decoding algorithms for product codes that correct all the error-erasure patterns guaranteed correctable by the minimum Hamming distance of the product code are given. The first algorithm works when at least one of the component codes is majority-logic decodable. The second algorithm works for any product code. Both algorithms use the decoders of the component codes.

Wainberg, S.↗

NASA NTRS1983

A new consistent spatial differencing scheme for the transonic full-potential equation

A new spatial differencing scheme for the transonic full-potential equation in conservative form has been developed. This scheme guarantees zero truncation error on any curvilinear mesh for freestream flows in either two- or three-space dimensions. Solutions obtained with this new differencing scheme, away from freestream regions, exhibit greatly improved accuracy, especially for nonsmooth or singular meshes.

Flores, J.↗

NASA NTRS1989

Efficient computer algebra algorithms for polynomial matrices in control design

The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.

Baras, J. S.↗

NASA NTRS2003

A Nonlinear, Six-Degree of Freedom Precision Formation Control Algorithm, Based on Restricted Three Body Dynamics

Precision Formation Flying is an enabling technology for a variety of proposed space-based observatories, including the Micro-Arcsecond X-ray Imaging Mission (MAXIM), the associated MAXIM pathfinder mission, and the Stellar Imager. An essential element of the technology is the control algorithm. This paper discusses the development of a nonlinear, six-degree of freedom (6DOF) control algorithm for maintaining the relative position and attitude of a spacecraft within a formation. The translation dynamics are based on the equations of motion for the restricted three body problem. The control law guarantees the tracking error convergences to zero, based on a Lyapunov analysis. The simulation, modelled after the MAXIM Pathfinder mission, maintains the relative position and attitude of a Follower spacecraft with respect to a Leader spacecraft, stationed near the L2 libration point in the Sun-Earth system.

Bauer, Frank↗

NASA NTRS1981

Practical robustness measures in multivariable control system analysis

The robustness of the stability of multivariable linear time invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point on a single input, single output Nyquist diagram. Using the return difference transfer matrix, a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness tests that explicitly utilized model error structure are able to guarantee feedback system stability in the face of model errors of larger magnitude than those robustness tests that do not. The robustness of linear quadratic Gaussian control systems are analyzed.

Lehtomaki, N. A.↗

NASA NTRS1991

On the capacity of ternary Hebbian networks

Networks of ternary neurons storing random vectors over the set -1,0,1 by the so-called Hebbian rule are considered. It is shown that the maximal number of stored patterns that are equilibrium states of the network with probability tending to one as N tends to infinity is at least on the order of (N exp 2-1/alpha)/K, where N is the number of neurons, K is the number of nonzero elements in a pattern, and t = alpha x K, alpha between 1/2 and 1, is the threshold in the neuron function. While, for small K, this bound is similar to that obtained for fully connected binary networks, the number of interneural connections required in the ternary case is considerably smaller. Similar bounds, incorporating error probabilities, are shown to guarantee, in the same probabilistic sense, the correction of errors in the nonzero elements and in the location of these elements.

Baram, Yoram↗

NASA NTRS2005

Precise and Scalable Static Program Analysis of NASA Flight Software

Recent NASA mission failures (e.g., Mars Polar Lander and Mars Orbiter) illustrate the importance of having an efficient verification and validation process for such systems. One software error, as simple as it may be, can cause the loss of an expensive mission, or lead to budget overruns and crunched schedules. Unfortunately, traditional verification methods cannot guarantee the absence of errors in software systems. Therefore, we have developed the CGS static program analysis tool, which can exhaustively analyze large C programs. CGS analyzes the source code and identifies statements in which arrays are accessed out of bounds, or, pointers are used outside the memory region they should address. This paper gives a high-level description of CGS and its theoretical foundations. It also reports on the use of CGS on real NASA software systems used in Mars missions (from Mars PathFinder to Mars Exploration Rover) and on the International Space Station.

Brat, G.↗

NASA NTRS1973

On 'Type L' multivariable linear systems.

The purpose of this paper is to summarize results for linear multivariable systems that are analogous to those single input single output systems which are 'type l', i.e., that contain l integrators. Both frequency domain and time-domain properties are given. Appropriate conditions that guarantee zero steady state error in tracking vector polynomial inputs are presented.

Sandell, N., Jr.↗

NASA NTRS1988

On the design of the dissipative LQG-type controllers

The design of dissipative linear-quadratic-Gaussian-type compensators for positive real plants is considered. It is shown that if the noise covariance matrices (used as weighting matrices) satisfy certain conditions, the compensator has a strictly positive real transfer function matrix. The stability of the resulting closed-loop system is guaranteed regardless of modeling errors as long as the plant remains positive real. In view of this property, the controller is expected to be useful for vibration suppression in large, flexible space structures.

Lozano-Leal, R.↗

NASA NTRS1992

Dominant modes of mechanical systems

To obtain a reduced model of a mechanical system, one can identify the dominant modes and retain those as the reduced model. Two widely used schemes for selection of dominant modes are modal cost analysis (MCA) and balancing, but neither of these methods guarantees that the model error is small, where model error measures the difference between the output of the full model and the output of the reduced model. The authors introduce a set of coordinates called pseudo uncorrelated modal coordinates (PUnc) that can be used in conjunction with component cost analysis to select dominant modes yielding a reduced model with minimum model error. Furthermore, unlike MCA and balancing, the accuracy of the reduced model (the model error) in PUnc coordinates can be evaluated before reduction.

Breida, M.↗

NASA NTRS1993

Indirect learning control for nonlinear dynamical systems

In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.

Ryu, Yeong Soon↗