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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Parameter estimation in nonlinear distributed systems - Approximation theory and convergence results

An abstract approximation framework and convergence theory is described for Galerkin approximations applied to inverse problems involving nonlinear distributed parameter systems. Parameter estimation problems are considered and formulated as the minimization of a least-squares-like performance index over a compact admissible parameter set subject to state constraints given by an inhomogeneous nonlinear distributed system. The theory applies to systems whose dynamics can be described by either time-independent or nonstationary strongly maximal monotonic operators defined on a reflexive Banach space which is densely and continuously embedded in a Hilbert space. It is demonstrated that if readily verifiable conditions on the system's dependence on the unknown parameters are satisfied, and the usual Galerkin approximation assumption holds, then solutions to the approximating problems exist and approximate a solution to the original infinite-dimensional identification problem.

Banks, H. T.↗
NASA NTRS1988

Statistical analysis of censored motion sickness latency data using the two-parameter Weibull distribution

The suitability of the two-parameter Weibull distribution for describing highly censored cat motion sickness latency data was evaluated by estimating the parameters with the maximum likelihood method and testing for goodness of fit with the Kolmogorov-Smirnov statistic. A procedure for determining confidence levels and testing for significance of the difference between Weibull parameters is described. Computer programs for these procedures may be obtained from an archival source.

Park, Won J.↗
NASA NTRS1991

On the use of maximum likelihood estimation for the assembly of Space Station Freedom

Distributed parameter models of the Solar Array Flight Experiment, the Mini-MAST truss, and Space Station Freedom assembly are discussed. The distributed parameter approach takes advantage of (1) the relatively small number of model parameters associated with partial differential equation models of structural dynamics, (2) maximum-likelihood estimation using both prelaunch and on-orbit test data, (3) the inclusion of control system dynamics in the same equations, and (4) the incremental growth of the structural configurations. Maximum-likelihood parameter estimates for distributed parameter models were based on static compliance test results and frequency response measurements. Because the Space Station Freedom does not yet exist, the NASA Mini-MAST truss was used to test the procedure of modeling and parameter estimation. The resulting distributed parameter model of the Mini-MAST truss successfully demonstrated the approach taken. The computer program PDEMOD enables any configuration that can be represented by a network of flexible beam elements and rigid bodies to be remodeled.

Taylor, Lawrence W., Jr.↗
NASA NTRS1972

Methods of computing vocabulary size for the two-parameter rank distribution

A summation method is described for computing the vocabulary size for given parameter values in the 1- and 2-parameter rank distributions. Two methods of determining the asymptotes for the family of 2-parameter rank-distribution curves are also described. Tables are computed and graphs are drawn relating paris of parameter values to the vocabulary size. The partial product formula for the Riemann zeta function is investigated as an approximation to the partial sum formula for the Riemann zeta function. An error bound is established that indicates that the partial product should not be used to approximate the partial sum in calculating the vocabulary size for the 2-parameter rank distribution.

Edmundson, H. P.↗
NASA NTRS1992

Reliability analysis of structural ceramic components using a three-parameter Weibull distribution

Described here are nonlinear regression estimators for the three-parameter Weibull distribution. Issues relating to the bias and invariance associated with these estimators are examined numerically using Monte Carlo simulation methods. The estimators were used to extract parameters from sintered silicon nitride failure data. A reliability analysis was performed on a turbopump blade utilizing the three-parameter Weibull distribution and the estimates from the sintered silicon nitride data.

Duffy, Stephen F.↗
NASA NTRS1979

A distributed system adaptive control strategy

One attitude control device being studied for large spacecraft consists of two counter-rotating rings, each designated as an annular momentum control device (AMCD), that are attached to a spacecraft using several magnetic bearings distributed along the circumference of the rings. For large spacecraft large rings are desirable. Unfortunately, for large rings flexibility is appreciable and it becomes necessary to account for the distributed nature of the rings in the design of the magnetic bearing controllers. Also ring behavior is unpredictably sensitive to ring temperature, spin rate, manufacturing imperfections, and other variables. For that reason a distributed adaptive microcomputer-based control system is being sought for ring stabilization and maneuvering. An original adaptive-control methodology for distributed-parameter systems is detailed and application to spinning ring, i.e., AMCD, stabilization is used as an illustration. The proposed methodology, presented as a step-by-step procedure, combines a lumped-parameter expansion description of distributed parameter systems with a fundamental simultaneous identification and control strategy. Simulations are presented providing preliminary evidence of the capabilities of the proposed procedure.

Johnson, C. R., Jr.↗
NASA NTRS1979

Approaches to adaptive digital control focusing on the second order modal descriptions of large, flexible spacecraft dynamics

The widespread modal analysis of flexible spacecraft and recognition of the poor a priori parameterization possible of the modal descriptions of individual structures have prompted the consideration of adaptive modal control strategies for distributed parameter systems. The current major approaches to computationally efficient adaptive digital control useful in these endeavors are explained in an original, lucid manner using modal second order structure dynamics for algorithm explication. Difficulties in extending these lumped-parameter techniques to distributed-parameter system expansion control are cited.

Johnson, C. R., Jr.↗
NASA NTRS2005

FIDDLE: A Computer Code for Finite Difference Development of Linear Elasticity in Generalized Curvilinear Coordinates

A three-dimensional numerical solver based on finite-difference solution of three-dimensional elastodynamic equations in generalized curvilinear coordinates has been developed and used to generate data such as radial and tangential stresses over various gear component geometries under rotation. The geometries considered are an annulus, a thin annular disk, and a thin solid disk. The solution is based on first principles and does not involve lumped parameter or distributed parameter systems approach. The elastodynamic equations in the velocity-stress formulation that are considered here have been used in the solution of problems of geophysics where non-rotating Cartesian grids are considered. For arbitrary geometries, these equations along with the appropriate boundary conditions have been cast in generalized curvilinear coordinates in the present study.

Kaul, Upender K.↗
NASA NTRS2013

Ensemble Forecasting of Coronal Mass Ejections Using the WSA-ENLIL with CONED Model

The combination of the Wang-Sheeley-Arge (WSA) coronal model, ENLIL heliospherical model version 2.7, and CONED Model version 1.3 (WSA-ENLIL with CONED Model) was employed to form ensemble forecasts for 15 halo coronal mass ejections (halo CMEs). The input parameter distributions were formed from 100 sets of CME cone parameters derived from the CONED Model. The CONED Model used image processing along with the bootstrap approach to automatically calculate cone parameter distributions from SOHO/LASCO imagery based on techniques described by Pulkkinen et al. (2010). The input parameter distributions were used as input to WSA-ENLIL to calculate the temporal evolution of the CMEs, which were analyzed to determine the propagation times to the L1 Lagrangian point and the maximum Kp indices due to the impact of the CMEs on the Earth's magnetosphere. The Newell et al. (2007) Kp index formula was employed to calculate the maximum Kp indices based on the predicted solar wind parameters near Earth assuming two magnetic field orientations: a completely southward magnetic field and a uniformly distributed clock-angle in the Newell et al. (2007) Kp index formula. The forecasts for 5 of the 15 events had accuracy such that the actual propagation time was within the ensemble average plus or minus one standard deviation. Using the completely southward magnetic field assumption, 10 of the 15 events contained the actual maximum Kp index within the range of the ensemble forecast, compared to 9 of the 15 events when using a uniformly distributed clock angle.

coronal mass↗
NASA NTRS1983

Some properties of a 5-parameter bivariate probability distribution

A five-parameter bivariate gamma distribution having two shape parameters, two location parameters and a correlation parameter was developed. This more general bivariate gamma distribution reduces to the known four-parameter distribution. The five-parameter distribution gives a better fit to the gust data. The statistical properties of this general bivariate gamma distribution and a hypothesis test were investigated. Although these developments have come too late in the Shuttle program to be used directly as design criteria for ascent wind gust loads, the new wind gust model has helped to explain the wind profile conditions which cause large dynamic loads. Other potential applications of the newly developed five-parameter bivariate gamma distribution are in the areas of reliability theory, signal noise, and vibration mechanics.

Tubbs, J. D.↗
NASA NTRS1988

On the problem of modeling for parameter identification in distributed structures

Structures are often characterized by parameters, such as mass and stiffness, that are spatially distributed. Parameter identification of distributed structures is subject to many of the difficulties involved in the modeling problem, and the choice of the model can greatly affect the results of the parameter identification process. Analogously to control spillover in the control of distributed-parameter systems, identification spillover is shown to exist as well and its effect is to degrade the parameter estimates. Moreover, as in modeling by the Rayleigh-Ritz method, it is shown that, for a Rayleigh-Ritz type identification algorithm, an inclusion principle exists in the identification of distributed-parameter systems as well, so that the identified natural frequencies approach the actual natural frequencies monotonically from above.

Norris, Mark A.↗
NASA NTRS1988

A perturbation technique for parameter identification in distributed structures

Structures are often characterized by parameters, such as mass and stiffness, that are spatially distributed. Parameter identification of distributed structures is subject to many of the difficulties involved in the modeling problem, and the choice of the model can greatly affect the results of the parameter identification process. Analogously to control spillover in the control of distributed-parameter systems, identification spillover is shown to exist as well and its effect is to degrade the parameter estimates. Moreover, as in modeling by the Rayleigh-Ritz method, it is shown that, for a Rayleigh-Ritz type identification algorithm, an inclusion principle exists in the identification of distributed-parameter systems as well, so that the identified natural frequencies approach the actual natural frequencies monotonically from above.

Meirovitch, L.↗
NASA NTRS1989

On the problem of modeling for parameter identification in distributed structures

Structures are often characterized by parameters, such as mass and stiffness, that are spatially distributed. Parameter identification of distributed structures is subject to many of the difficulties involved in the modeling problem, and the choice of the model can greatly affect the results of the parameter identification process. Analogously to control spillover in the control of distributed-parameter systems, identification spillover is shown to exist as well and its effect is to degrade the parameter estimates. Moreover, as in modeling by the Rayleigh-Ritz method, it is shown that, for a Rayleigh-Ritz type identification algorithm, an inclusion principle exists in the identification of distributed-parameter systems as well, so that the identified natural frequencies approach the actual natural frequencies monotonically from above.

Norris, Mark A.↗
NASA NTRS1981

Problems in the application of multivariable adaptive control to flexible spacecraft

The present investigation is concerned with the application of adaptive control to distributed parameter systems (DPS) which arise in the modeling of large space structures (LSS). Distributed parameter and multivariable models for LSS are introduced and the decoupled adaptive control of such models is considered. Possibilities to achieve adaptive control in connection with a more general model are also examined. It is found that, in concept, adaptive control appears to be a natural choice for solving attitude and shape perturbation problems in LSS. However, due to the distributed parameter nature of such structures and the current lack of experience in their control, the problem must be phrased in general terms which are very difficult to deal with. In particular, detailed a priori plant knowledge is currently required so that decoupling and/or reduced order models of sufficient accuracy can be provided.

Lawrence, D. A.↗
NASA NTRS2011

Simultaneous Retrieval of Aerosol and Cloud Properties During the MILAGRO Field Campaign

Estimation of Direct Climate Forcing (DCF) due to aerosols in cloudy areas has historically been a difficult task, mainly because of a lack of appropriate measurements. Recently, passive remote sensing instruments have been developed that have the potential to retrieve both cloud and aerosol properties using polarimetric, multiple view angle, and multi spectral observations, and therefore determine DCF from aerosols above clouds. One such instrument is the Research Scanning Polarimeter (RSP), an airborne prototype of a sensor on the NASA Glory satellite, which unfortunately failed to reach orbit during its launch in March of 2011. In the spring of 2006, the RSP was deployed on an aircraft based in Veracruz, Mexico, as part of the Megacity Initiative: Local and Global Research Observations (MILAGRO) field campaign. On 13 March, the RSP over flew an aerosol layer lofted above a low altitude marine stratocumulus cloud close to shore in the Gulf of Mexico. We investigate the feasibility of retrieving aerosol properties over clouds using these data. Our approach is to first determine cloud droplet size distribution using the angular location of the cloud bow and other features in the polarized reflectance. The selected cloud was then used in a multiple scattering radiative transfer model optimization to determine the aerosol optical properties and fine tune the cloud size distribution. In this scene, we were able to retrieve aerosol optical depth, the fine mode aerosol size distribution parameters and the cloud droplet size distribution parameters to a degree of accuracy required for climate modeling. This required assumptions about the aerosol vertical distribution and the optical properties of the coarse aerosol size mode. A sensitivity study was also performed to place this study in the context of future systematic scanning polarimeter observations, which found that the aerosol complex refractive index can also be observed accurately if the aerosol optical depth is larger than roughly 0.8 at a wavelength of (0.555 m).

Knobelspiesse, K.↗
NASA NTRS1979

An assessment of methods for the control of large space structures

Large flexible spacecraft represent highly complex distributed-parameter systems. In theory, a distributed-parameter system possesses an infinite number of degrees of freedom. For practical reasons, however, it must be discretized, which implies truncation. From a structural dynamics point of view, a mathematical model can be made more accurate by retaining an increasing number of degrees of freedom. From a control theory point of view, however, an increasing number of degrees of freedom places severe demands on the reliability of the various control algorithms. There is a difference of at least one order of magnitude between the structural modeling requirements and control theory capability. One of the challenges of large space structures control technology is to bridge this difference.

Meirovitch, L.↗
NASA NTRS1992

Reliability analysis of structural ceramic components using a three-parameter Weibull distribution

Described here are nonlinear regression estimators for the three-Weibull distribution. Issues relating to the bias and invariance associated with these estimators are examined numerically using Monte Carlo simulation methods. The estimators were used to extract parameters from sintered silicon nitride failure data. A reliability analysis was performed on a turbopump blade utilizing the three-parameter Weibull distribution and the estimates from the sintered silicon nitride data.

Duffy, Stephen F.↗
NASA NTRS2022

Statistical Distribution of Gear Surface Fatigue Lives at High Reliability

The reliability of gears is important for a wide variety of applications, and the gearing community has a desire for better prediction of fatigue life at very high reliability. To improve predictions, a set of 950 NASA-conducted gear surface fatigue test results were gathered, pooled together using the general standardized Weibull variate, and then fit to a Weibull three-parameter distribution. An iterative fitting method was developed and then applied to the gear fatigue data to determine the values of the distribution parameters. Additional analyses were done using bearing and gear data that demonstrate a trend of increasing minimum life coefficient as correlated to the timeframe of the fatigue testing, and material cleanliness is proposed as a primary explanation for such correlation. It is noted that this observed trend supports published findings from analytical modeling and experimental studies that improvements to material cleanliness improves minimum fatigue life. Further use and study of the three-parameter Weibull distribution is recommended as a tool to quantify fatigue life most accurately in the high reliability regime.

gear↗