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All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

State and model error estimation for distributed parameter systems

In-flight estimation of large structure model errors in order to detect inevitable deficiencies in large structure controller/estimator models is discussed. Such an estimation process is particularly applicable in the area of shape control system design required to maintain a prescribed static structural shape and, in addition, suppress dynamic disturbances due to the vehicle vibrational modes. The paper outlines a solution to the problem of static shape estimation where the vehicle shape must be reconstructed from a set of measurements discretely located throughout the structure. The estimation process is based on the principle of least-squares that inherently contains the definition and explicit computation of model error estimates that are optimal in some sense. Consequently, a solution is provided for the problem of estimation of static model errors (e.g., external loads). A generalized formulation applicable to distributed parameters systems is first worked out and then applied to a one-dimensional beam-like structural configuration.

Rodriguez, G.↗
NASA NTRS1983

Algorithms for estimation in distributed models with applications to large space structures

The author discussed the theoretical and computational results for spline based approximation schemes used in parameter estimation algorithms for distributed systems. Specific applications include beam-like structures described by the Euler-Bernoulli and Timoshenko theories and antenna surfaces such as that in the deployable Maypole Hoop/Column model.

Banks, H. T.↗
NASA NTRS1983

Model error estimation for distributed systems described by elliptic equations

A function space approach is used to develop a theory for estimation of the errors inherent in an elliptic partial differential equation model for a distributed parameter system. By establishing knowledge of the inevitable deficiencies in the model, the error estimates provide a foundation for updating the model. The function space solution leads to a specification of a method for computation of the model error estimates and development of model error analysis techniques for comparison between actual and estimated errors. The paper summarizes the model error estimation approach as well as an application arising in the area of modeling for static shape determination of large flexible systems.

Rodriguez, G.↗
NASA NTRS1991

Distributed parameter estimation for NASA Mini-Mast truss through displacement measurements

Most methods of system identification of large flexible structures by far are based on the lumped parameter approach. Because of the considerable computational burden due to the large number of unknown parameters, distributed parameter approach, which greatly decreases the number of unknowns, has being investigated. In this paper a distributed parameter model for the estimation of modal characteristics of NASA Mini-Mast truss has been formulated. Both Bernoulli-Euler beam and Timoshenko beam equations are used to characterize the lateral bending vibrations of the truss. The measurement of the lateral displacement at the tip of the truss is provided to the maximum likelihood estimator. Closed-form solutions of the partial differential equations and closed-form expressions of the sensitivity functions are derived so that the estimation algorithm is highly efficient. The resulting estimates from test data by using Timoshenko beam model are found to be comparable to those derived from finite element analysis.

Huang, Jen-Kuang↗
NASA NTRS1989

Application of optical distributed sensing and computation to control of a large flexible spacecraft

Advances in real-time holography make possible the development of new distributed optical sensors and processors that may have application to the control of flexible structures. This paper presents the analytic evaluation of control system concepts utilizing this new technology on realistic spacecraft. The design of a distributed estimator based on this new optical sensing technique is targeted to vibration control of a complex spacecraft with multiple optical sensors, each of which views a portion of the spacecraft. A simulation of a complex truss structure that was flown in the Solar Array Flight Experiment is utilized to evaluate the performance of the estimator. It is shown that good performance can be obtained from a distributed estimator even in the presence of significant sensor noise.

Montgomery, R. C.↗
NASA NTRS2011

Observability and Estimation of Distributed Space Systems via Local Information-Exchange Networks

Spacecraft formation flying involves the coordination of states among multiple spacecraft through relative sensing, inter-spacecraft communication, and control. Most existing formation-flying estimation algorithms can only be supported via highly centralized, all-to-all, static relative sensing. New algorithms are proposed that are scalable, modular, and robust to variations in the topology and link characteristics of the formation exchange network. These distributed algorithms rely on a local information exchange network, relaxing the assumptions on existing algorithms. Distributed space systems rely on a signal transmission network among multiple spacecraft for their operation. Control and coordination among multiple spacecraft in a formation is facilitated via a network of relative sensing and interspacecraft communications. Guidance, navigation, and control rely on the sensing network. This network becomes more complex the more spacecraft are added, or as mission requirements become more complex. The observability of a formation state was observed by a set of local observations from a particular node in the formation. Formation observability can be parameterized in terms of the matrices appearing in the formation dynamics and observation matrices. An agreement protocol was used as a mechanism for observing formation states from local measurements. An agreement protocol is essentially an unforced dynamic system whose trajectory is governed by the interconnection geometry and initial condition of each node, with a goal of reaching a common value of interest. The observability of the interconnected system depends on the geometry of the network, as well as the position of the observer relative to the topology. For the first time, critical GN&C (guidance, navigation, and control estimation) subsystems are synthesized by bringing the contribution of the spacecraft information-exchange network to the forefront of algorithmic analysis and design. The result is a formation estimation algorithm that is modular and robust to variations in the topology and link properties of the underlying formation network.

Fathpour, Nanaz↗
NASA NTRS1983

Cubic spline approximation techniques for parameter estimation in distributed systems

Approximation schemes employing cubic splines in the context of a linear semigroup framework are developed for both parabolic and hyperbolic second-order partial differential equation parameter estimation problems. Convergence results are established for problems with linear and nonlinear systems, and a summary of numerical experiments with the techniques proposed is given.

Banks, H. T.↗
NASA NTRS1989

Maximum likelihood estimation for distributed parameter models of flexible spacecraft

A distributed-parameter model of the NASA Solar Array Flight Experiment spacecraft structure is constructed on the basis of measurement data and analyzed to generate a priori estimates of modal frequencies and mode shapes. A Newton-Raphson maximum-likelihood algorithm is applied to determine the unknown parameters, using a truncated model for the estimation and the full model for the computation of the higher modes. Numerical results are presented in a series of graphs and briefly discussed, and the significant improvement in computation speed obtained by parallel implementation of the method on a supercomputer is noted.

Taylor, L. W., Jr.↗
NASA NTRS1991

Parameter estimation for distributed parameter models of complex, flexible structures

Distributed parameter modeling of structural dynamics has been limited to simple spacecraft configurations because of the difficulty of handling several distributed parameter systems linked at their boundaries. Although there is other computer software able to generate such models or complex, flexible spacecraft, unfortunately, neither is suitable for parameter estimation. Because of this limitation the computer software PDEMOD is being developed for the express purposes of modeling, control system analysis, parameter estimation and structure optimization. PDEMOD is capable of modeling complex, flexible spacecraft which consist of a three-dimensional network of flexible beams and rigid bodies. Each beam has bending (Bernoulli-Euler or Timoshenko) in two directions, torsion, and elongation degrees of freedom. The rigid bodies can be attached to the beam ends at any angle or body location. PDEMOD is also capable of performing parameter estimation based on matching experimental modal frequencies and static deflection test data. The underlying formulation and the results of using this approach for test data of the Mini-MAST truss will be discussed. The resulting accuracy of the parameter estimates when using such limited data can impact significantly the instrumentation requirements for on-orbit tests.

Taylor, Lawrence W., Jr.↗
NASA NTRS2017

Estimating the Distribution of Colored Dissolved Organic Matter During the Southern Ocean Gas Exchange Experiment Using Four-Dimensional Variational Data Assimilation

We diagnosed the effect of various physical processes on the distribution of mixed-layer colored dissolved organic matter (CDOM) and a sulfur hexauoride (SF6) tracer during the Southern Ocean Gas Exchange Experiment (SO GasEx). The biochemical upper ocean state estimate uses in situ and satellite biochemical and physical data in the study region, including CDOM (absorption coefcient and spectral slope), SF6, hydrography, and sea level anomaly. Modules for photobleaching of CDOM and surface transport of SF6 were coupled with an ocean circulation model for this purpose. The observed spatial and temporal variations in CDOM were captured by the state estimate without including any new biological source term for CDOM, assuming it to be negligible over the 26 days of the state estimate. Thermocline entrainment and photobleaching acted to diminish the mixed-layer CDOM with time scales of 18 and 16 days, respectively. Lateral advection of CDOM played a dominant role and increased the mixed-layer CDOM with a time scale of 12 days, whereas lateral diffusion of CDOM was negligible. A Lagrangian view on the CDOM variability was demonstrated by using the SF6 as a weighting function to integrate the CDOM elds. This and similar data assimilation methods can be used to provide reasonable estimates of optical properties, and other physical parameters over the short-term duration of a research cruise, and help in the tracking of tracer releases in large-scale oceanographic experiments, and in oceanographic process studies.

Del Castillo, C. E.↗
NASA NTRS1988

Estimation of distributed acoustic lasers

The purpose of this paper is to present the results of a preliminary investigation of an indirect method which can be used to generate a set of equivalent point loads approximating an applied distributed acoustic load. The method combines the source information with the structure's modal characteristics and forces which give the same response as the applied acoustic load. The technique is demonstrated by predicting a set of point forces acting on a thin aluminum panel which simulate a normally-incident random pressure. The technique is verified by comparing measured strain autospectrums with estimated strain autospectrums generated using the predicting forces. Strain errors within 5 dB were achieved. A limited amount of information about the acoustic load could be deduced using the predicted force autospectrums and phase differences between these forces.

Elliott, K. B.↗
NASA NTRS1987

Estimating the distribution of fault latency in a digital processor

Presented is a statistical approach to measuring fault latency in a digital processor. The method relies on the use of physical fault injection where the duration of the fault injection can be controlled. Although a specific fault's latency period is never directly measured, the method indirectly determines the distribution of fault latency.

Ellis, Erik L.↗
NASA NTRS1991

Distributed parameter estimation for NASA Mini-Mast truss using Timoshenko beam model

A more accurate Timoshenko beam model is used to characterize the bending behavior of the truss. A maximum likelihood estimator for the Timoshenko beam model has been formulated. A closed-form solution of the Timoshenko beam equation, for a uniform cantilevered beam with two concentrated masses, is derived so that the procedure for the estimation of modal characteristics is much improved. The updated model to the NASA Mini-Mast test data is demonstrated.

Shen, Ji-Yao↗
NASA NTRS1981

Contextual classification of multispectral image data: An unbiased estimator for the context distribution

A key input to a statistical classification algorithm, which exploits the tendency of certain ground cover classes to occur more frequently in some spatial context than in others, is a statistical characterization of the context: the context distribution. An unbiased estimator of the context distribution is discussed which, besides having the advantage of statistical unbiasedness, has the additional advantage over other estimation techniques of being amenable to an adaptive implementation in which the context distribution estimate varies according to local contextual information. Results from applying the unbiased estimator to the contextual classification of three real LANDSAT data sets are presented and contrasted with results from non-contextual classifications and from contextual classifications utilizing other context distribution estimation techniques.

Tilton, J. C.↗
NASA NTRS1982

Estimation of atmospheric species concentrations from remote sensing data

The atmospheric species concentration distribution-estimation problem that arises from the measurement configuration of remote sensing, which involves a field of view that moves across the region, is solved by means of the partial differential equation for atmospheric diffusion and the Wiener-Hopf theory. A numerical study is also undertaken for the estimation of concentration distribution downwind of a hypothetical, continuous ground-level source of pollutants.

Omatu, S.↗
NASA NTRS1972

A Bayesian approach to parameter and reliability estimation in the Poisson distribution.

For life testing procedures, a Bayesian analysis is developed with respect to a random intensity parameter in the Poisson distribution. Bayes estimators are derived for the Poisson parameter and the reliability function based on uniform and gamma prior distributions of that parameter. A Monte Carlo procedure is implemented to make possible an empirical mean-squared error comparison between Bayes and existing minimum variance unbiased, as well as maximum likelihood, estimators. As expected, the Bayes estimators have mean-squared errors that are appreciably smaller than those of the other two.

Canavos, G. C.↗