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NASA NTRS1983

A posteriori error indicators for the p-version of the finite element method

The existence of local a posteriori error indicators for the p-version of the finite element method is demonstrated through numerical examples. It is shown that it is possible to construct reliable error indicators from the residuums and tractions which have the same rate of convergence as the strain energy. The error indicators contribution of an element can be estimated by considering only the element and its immediate neighbors. The optimal sequence of p-distributions can be closely followed by the indicators even when there are only a very few elements, the elements vary greatly in size, the polynomial orders vary, the mesh grading is poor, and the smoothness indices and relative errors vary between wide limits.

Dunavant, D. A.↗

NASA NTRS1984

Probability of error and radiometric resolution for target discrimination in radar images

A straightforward statistical analysis is presented of the problem of discriminating between two distributed targets in a radar image. The probability of making an error is calculated as a function of the target contrast, the number of samples averaged to form each observation, and the system noise. In the absence of system noise, it is observed that a target contrast of 1 dB could not be detected with less than 10 samples averaged; it is also seen that the error probability is sensitive to the number of samples averaged, as expected. Setting the target contrast at the radiometric resolution, a comparison is made of different definitions for this resolution. The comparison shows that each definition yields a different error probability, ranging from less than 0.05 to 0.35. Attention is also given to the effect of system noise, and it is shown that thermal noise does not have a significant effect on the error probability for a fixed target contrast.

Frost, V. S.↗

NASA NTRS1984

The undetected error probability for shortened hamming codes

Hamming or shortened Hamming codes are widely used for error detection in data communications. For example, the CCITT (International Telegraph and Telephone Consultative Committee) recommendation X.25 for packet-switched data networks adopts a distance-4 cyclic Hamming code with 16 parity-check bits for error detection. The natural length of this code is n = 2(15)-1 = 32,767. In practice the length of a data packet is no more than a few thousand bits which is much shorter than the natural length of the code. Consequently, a shortened version of thecode is used. Often the length of a data packet varies, say from a few hundred bits to a few thousand bits, hence the code must be shortened by various degrees. Shortening affects the performance of the code. The error-detection performance of shortened Hamming codes, particularly the codes obtained from the distance-4 Hamming codes adopted by CCITT recommendation X.25, is investigated. A method for computing the probability of an undetected error is presented.

Costello, D. J., Jr.↗

NASA NTRS1984

Submilliarcsecond VLBI Using Compact Close Pairs of Radio Sources: Error Analysis

The potential accuracy attainable for (delta) VLBI positional measurements (submilliarc second level) is reached by simultaneously observing pairs of compact radio sources whose angular separation are smaller than the beamwidth of each antenna. Simultaneous (delta) VLBI (SVLBI) enables significant cancellation of measurement errors. Solar plasma is the dominant fluctuating error source in SVLBI positional measurements since there is enhanced cancellation of the troposphere and ionosphere, and complete cancellation of oscillator instabilities. Of the nonfluctuating error sources, errors due to universal time predominate. By performing SVLBI experiments over several years with many different close pairs of radio sources, limits can be placed on reference frame stability. Intrinsic properties of the sources, such as source structure and proper motion, will limit measurements. The SVLBI differential phase and corruptive noise sources will be discussed here along with estimated results.

Morabito, D. D.↗

NASA NTRS1984

Structure Errors in System Identification

An approach to system identification is presented which explicitly takes structure errors into account and hence provides a systematic way for answering questions concerning the magnitude of estimated parameter errors resulting from structural errors. It is indicated that, from this point of view, it is possible to define near equivalence between process and model and to obtain meaningful theoretical results on solution error system identification. It remains to apply these results to large realistic problems such as those involving models of complex man machine systems.

Bekey, G. A.↗

NASA NTRS1985

A theoretical basis for the analysis of redundant software subject to coincident errors

Fundamental to the development of redundant software techniques fault-tolerant software, is an understanding of the impact of multiple-joint occurrences of coincident errors. A theoretical basis for the study of redundant software is developed which provides a probabilistic framework for empirically evaluating the effectiveness of the general (N-Version) strategy when component versions are subject to coincident errors, and permits an analytical study of the effects of these errors. The basic assumptions of the model are: (1) independently designed software components are chosen in a random sample; and (2) in the user environment, the system is required to execute on a stationary input series. The intensity of coincident errors, has a central role in the model. This function describes the propensity to introduce design faults in such a way that software components fail together when executing in the user environment. The model is used to give conditions under which an N-Version system is a better strategy for reducing system failure probability than relying on a single version of software. A condition which limits the effectiveness of a fault-tolerant strategy is studied, and it is posted whether system failure probability varies monotonically with increasing N or whether an optimal choice of N exists.

Eckhardt, D. E., Jr.↗

NASA NTRS1984

Geometric error analysis for shuttle imaging spectrometer experiment

The demand of more powerful tools for remote sensing and management of earth resources steadily increased over the last decade. With the recent advancement of area array detectors, high resolution multichannel imaging spectrometers can be realistically constructed. The error analysis study for the Shuttle Imaging Spectrometer Experiment system is documented for the purpose of providing information for design, tradeoff, and performance prediction. Error sources including the Shuttle attitude determination and control system, instrument pointing and misalignment, disturbances, ephemeris, Earth rotation, etc., were investigated. Geometric error mapping functions were developed, characterized, and illustrated extensively with tables and charts. Selected ground patterns and the corresponding image distortions were generated for direct visual inspection of how the various error sources affect the appearance of the ground object images.

Wang, S. J.↗

NASA NTRS1985

The effect of sensor and actuator errors on static shape control for large space structures

An analytical study was performed to predict and assess the effect of actuator and sensor errors on the performance of a shape control procedure for flexible space structures using applied temperatures. Approximate formulas were derived for the expected value and variance of the rms distortion ratio (ratio of rms distortions with and without corrections) based on the assumption of zero-mean normally distributed random errors in measured distortions and actuator output temperatures. Studies were carried out for a 55-meter radiometer antenna reflector distorted from its ideal parabolic shape by nonuniform orbital heating. The first study consisted of varying the sensor and actuator errors for the case of 12 actuators and computing the distortion ratio. In the second study, sensor and actuator errors were prescribed and the effect of increasing the number of actuators was evaluated.

Haftka, R. T.↗

NASA NTRS1985

The design and analysis of single flank transmission error testor for loaded gears

Due to geometrical imperfections in gears and finite tooth stiffnesses, the motion transmitted from an input gear shaft to an output gear shaft will not have conjugate action. In order to strengthen the understanding of transmission error and to verify mathematical models of gear transmission error, a test stand that will measure the transmission error of a gear pair at operating loads, but at reduced speeds would be desirable. This document describes the design and development of a loaded transmission error tester. For a gear box with a gear ratio of one, few tooth meshing combinations will occur during a single test. In order to observe the effects of different tooth mesh combinations and to increase the ability to load test gear pairs with higher gear ratios, the system was designed around a gear box with a gear ratio of two.

Houser, D. R.↗

NASA NTRS1984

Method for estimating errors for radiation budget based on a scanning radiometer

The conduction of the Earth Radiation Budget Experiment (ERBE) will involve the utilization of three sets of instruments. Each set consists of a nonscanning package and a scanning radiometer. The instruments will fly on the NOAA F and G operational satellites and on a dedicated spacecraft, the Earth Radiation Budget Satellite (ERBS). The ERBS will be in a 57 deg inclination orbit and will precess around the earth to provide sampling of the diurnal cycle of regions between + or - 57 deg latitude. The primary function of the scanning radiometer is to provide measurements for the calculation of the earth-emitted and absorbed solar radiation at the top of the earth-atmosphere system, averaged over 250 x 250 km regions. The present paper is concerned with errors found in these regional averages. Attention is given to details regarding the problem, scene identification probabilities, scene identification error effects, total pixel error, and errors due to regional averaging.

Smith, G. L.↗

NASA NTRS1985

A water-vapor radiometer error model

The water-vapor radiometer (WVR) is used to calibrate unpredictable delays in the wet component of the troposphere in geodetic microwave techniques such as very-long-baseline interferometry (VLBI) and Global Positioning System (GPS) tracking. Based on experience with Jet Propulsion Laboratory (JPL) instruments, the current level of accuracy in wet-troposphere calibration limits the accuracy of local vertical measurements to 5-10 cm. The goal for the near future is 1-3 cm. Although the WVR is currently the best calibration method, many instruments are prone to systematic error. In this paper, a treatment of WVR data is proposed and evaluated. This treatment reduces the effect of WVR systematic errors by estimating parameters that specify an assumed functional form for the error. The assumed form of the treatment is evaluated by comparing the results of two similar WVR's operating near each other. Finally, the observability of the error parameters is estimated by covariance analysis.

Beckman, B.↗

NASA NTRS1985

A cascaded coding scheme for error control

A cascaded coding scheme for error control was investigated. The scheme employs a combination of hard and soft decisions in decoding. Error performance is analyzed. If the inner and outer codes are chosen properly, extremely high reliability can be attained even for a high channel bit-error-rate. Some example schemes are studied which seem to be quite suitable for satellite down-link error control.

Kasami, T.↗

NASA NTRS1982

Scout trajectory error propagation computer program

Since 1969, flight experience has been used as the basis for predicting Scout orbital accuracy. The data used for calculating the accuracy consists of errors in the trajectory parameters (altitude, velocity, etc.) at stage burnout as observed on Scout flights. Approximately 50 sets of errors are used in Monte Carlo analysis to generate error statistics in the trajectory parameters. A covariance matrix is formed which may be propagated in time. The mechanization of this process resulted in computer program Scout Trajectory Error Propagation (STEP) and is described herein. Computer program STEP may be used in conjunction with the Statistical Orbital Analysis Routine to generate accuracy in the orbit parameters (apogee, perigee, inclination, etc.) based upon flight experience.

Myler, T. R.↗

NASA NTRS1985

A cascaded coding scheme for error control

A cascade coding scheme for error control is investigated. The scheme employs a combination of hard and soft decisions in decoding. Error performance is analyzed. If the inner and outer codes are chosen properly, extremely high reliability can be attained even for a high channel bit-error-rate. Some example schemes are evaluated. They seem to be quite suitable for satellite down-link error control.

Shu, L.↗

NASA NTRS1985

An analysis of the effects of coincident errors on multi-version software

The present study is concerned with the application of a model which provides a basis for analytical investigations of redundant software. The model links certain basic quantities with the experimental process of testing independently designed software components. The model is employed to provide insight into the effects of coincident errors on an N-version software structure in which the structure fails if at least a majority of its components fail. Attention is given to coincident errors, the intensity distribution for coincident errors, the coincident errors model, and a condition for redundancy to improve reliability.

Eckhardt, D. E., Jr.↗

NASA NTRS1985

Errors in reduction methods

A mathematical basis is given for comparing the relative merits of various techniques used to reduce the order of large linear and nonlinear dynamics problems during their numerical integration. In such techniques as Guyan-Irons, path derivatives, selected eigenvectors, Ritz vectors, etc., the nth order initial value problem of /y(dot) = f(y) for t greater than 0, y(0) given/ is typically reduced to the mth order (m is much less than n) problem of /z(dot) = g(z) for t greater than 0, z(0) given/ by the transformation y = Pz where P changes from technique to technique. This paper gives an explicit approximate expression for the reduction error e-i in terms of P and the Jacobian of f. It is shown that: (a) reduction techniques are more accurate when the time rate of change of the response y is relatively small; (b) the change in response between two successive stations contributes to the errors at future stations after the change in response is transformed by a filtering matrix H, defined in terms of P; (c) the error committed at a station propagates to future stations by a mixing and scaling matrix G, defined in terms of P, Jacobian and of f, and time increment h. The paper discusses the conditions under which the reduction errors may be minimized and gives guidelines for selecting the reduction basis vector, i.e., the columns of P.

Utku, S.↗

NASA NTRS1985

An experimental approach to validating a theory of human error in complex systems

The problem of 'human error' is pervasive in engineering systems in which the human is involved. In contrast to the common engineering approach of dealing with error probabilistically, the present research seeks to alleviate problems associated with error by gaining a greater understanding of causes and contributing factors from a human information processing perspective. The general approach involves identifying conditions which are hypothesized to contribute to errors, and experimentally creating the conditions in order to verify the hypotheses. The conceptual framework which serves as the basis for this research is discussed briefly, followed by a description of upcoming research. Finally, the potential relevance of this research to design, training, and aiding issues is discussed.

Morris, N. M.↗

NASA NTRS1986

The impact of experimental measurement errors on long-term viscoelastic predictions

The impact of flight error in measured viscoelastic parameters on subsequent long-term viscoelastic predictions is numerically evaluated using the Schapery nonlinear viscoelastic model. Of the seven Schapery parameters, the results indicated that long-term predictions were most sensitive to errors in the power law parameter n. Although errors in the other parameters were significant as well, errors in n dominated all other factors at long times. The process of selecting an appropriate short-term test cycle so as to insure an accurate long-term prediction was considered, and a short-term test cycle was selected using material properties typical for T300/5208 graphite-epoxy at 149 C. The process of selection is described, and its individual steps are itemized.

Tuttle, M. E.↗