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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 NTRS1991

Identification of observer/Kalman filter Markov parameters: Theory and experiments

An algorithm to compute Markov parameters of an observer or Kalman filter from experimental input and output data is discussed. The Markov parameters can then be used for identification of a state space representation, with associated Kalman gain or observer gain, for the purpose of controller design. The algorithm is a non-recursive matrix version of two recursive algorithms developed in previous works for different purposes. The relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and gives bounds on the proper choice of observer order. It is shown that if one uses data containing noise, and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. Results are demonstrated in numerical studies and in experiments on an ten-bay truss structure.

Juang, Jer-Nan↗
NASA NTRS1991

Identification of observer/Kalman filter Markov parameters - Theory and experiments

An algorithm to compute Markov parameters of an observer or Kalman filter from experimental input and output data is discussed. The Markov parameters can then be used for identification of a state space representation, with associated Kalman gain or observer gain, for the purpose of controller design. The algorithm is a non-recursive matrix version of two recursive algorithms developed in previous works for different purposes. The relationship between these other algorithms is developed. The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and gives bounds on the proper choice of observer order. It is shown that if one uses data containing noise, and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment. Results are demonstrated in numerical studies and in experiments on a ten-bay truss structure.

Juang, Jer-Nan↗
NASA NTRS1988

Designing Estimator/Predictor Digital Phase-Locked Loops

Signal delays in equipment compensated automatically. New approach to design of digital phase-locked loop (DPLL) incorporates concepts from estimation theory and involves decomposition of closed-loop transfer function into estimator and predictor. Estimator provides recursive estimates of phase, frequency, and higher order derivatives of phase with respect to time, while predictor compensates for delay, called "transport lag," caused by PLL equipment and by DPLL computations.

Statman, J. I.↗
NASA NTRS2011

Graph Theory Roots of Spatial Operators for Kinematics and Dynamics

Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.

Jain, Abhinandan↗
NASA NTRS1999

Signal Prediction With Input Identification

A novel coding technique is presented for signal prediction with applications including speech coding, system identification, and estimation of input excitation. The approach is based on the blind equalization method for speech signal processing in conjunction with the geometric subspace projection theory to formulate the basic prediction equation. The speech-coding problem is often divided into two parts, a linear prediction model and excitation input. The parameter coefficients of the linear predictor and the input excitation are solved simultaneously and recursively by a conventional recursive least-squares algorithm. The excitation input is computed by coding all possible outcomes into a binary codebook. The coefficients of the linear predictor and excitation, and the index of the codebook can then be used to represent the signal. In addition, a variable-frame concept is proposed to block the same excitation signal in sequence in order to reduce the storage size and increase the transmission rate. The results of this work can be easily extended to the problem of disturbance identification. The basic principles are outlined in this report and differences from other existing methods are discussed. Simulations are included to demonstrate the proposed method.

Juang, Jer-Nan↗
NASA NTRS1993

Development of a recursion RNG-based turbulence model

Reynolds stress closure models based on the recursion renormalization group theory are developed for the prediction of turbulent separated flows. The proposed model uses a finite wavenumber truncation scheme to account for the spectral distribution of energy. In particular, the model incorporates effects of both local and nonlocal interactions. The nonlocal interactions are shown to yield a contribution identical to that from the epsilon-renormalization group (RNG), while the local interactions introduce higher order dispersive effects. A formal analysis of the model is presented and its ability to accurately predict separated flows is analyzed from a combined theoretical and computational stand point. Turbulent flow past a backward facing step is chosen as a test case and the results obtained based on detailed computations demonstrate that the proposed recursion -RNG model with finite cut-off wavenumber can yield very good predictions for the backstep problem.

Zhou, YE↗
NASA NTRS1975

Chandrasekhar-type algorithms for fast recursive estimation in linear systems with constant parameters

In this recursive method proposed, the gain matrix for the Kalman filter and the convariance of the state vector are computed not via the Riccati equation, but from certain other equations. These differential equations are of Chandrasekhar-type. The 'invariant imbedding' idea resulted in the reduction of the basic boundary value problem of transport theory to an equivalent initial value system, a significant computational advance. Initial value experience showed that there is some computational savings in the method and the loss of positive definiteness of the covariance matrix is less vulnerable.

Choudhury, A. K.↗
NASA NTRS1986

Kalman filtering, smoothing and recursive robot arm forward and inverse dynamics

The inverse and forward dynamics problems for multi-link serial manipulators are solved by using recursive techniques from linear filtering and smoothing theory. The pivotal step is to cast the system dynamics and kinematics as a two-point boundary-value problem. Solution of this problem leads to filtering and smoothing techniques identical to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The solutions prescribe an inward filtering recursion to compute a sequence of constraint moments and forces followed by an outward recursion to determine a corresponding sequence of angular and linear accelerations. In addition to providing techniques to compute joint accelerations from applied joint moments (and vice versa), the report provides an approach to evaluate recursively the composite multi-link system inertia matrix and its inverse. The report lays the foundation for the potential use of filtering and smoothing techniques in robot inverse and forward dynamics and in robot control design.

Rodriguez, G.↗
NASA NTRS1993

A multimedia adult literacy program: Combining NASA technology, instructional design theory, and authentic literacy concepts

For a number of years, the Software Technology Branch of the Information Systems Directorate has been involved in the application of cutting edge hardware and software technologies to instructional tasks related to NASA projects. The branch has developed intelligent computer aided training shells, instructional applications of virtual reality and multimedia, and computer-based instructional packages that use fuzzy logic for both instructional and diagnostic decision making. One outcome of the work on space-related technology-supported instruction has been the creation of a significant pool of human talent in the branch with current expertise on the cutting edges of instructional technologies. When the human talent is combined with advanced technologies for graphics, sound, video, CD-ROM, and high speed computing, the result is a powerful research and development group that both contributes to the applied foundations of instructional technology and creates effective instructional packages that take advantage of a range of advanced technologies. Several branch projects are currently underway that combine NASA-developed expertise to significant instructional problems in public education. The branch, for example, has developed intelligent computer aided software to help high school students learn physics and staff are currently working on a project to produce educational software for young children with language deficits. This report deals with another project, the adult literacy tutor. Unfortunately, while there are a number of computer-based instructional packages available for adult literacy instruction, most of them are based on the same instructional models that failed these students when they were in school. The teacher-centered, discrete skill and drill-oriented, instructional strategies, even when they are supported by color computer graphics and animation, that form the foundation for most of the computer-based literacy packages currently on the market may not be the most effective or most desirable way to use computer technology in literacy programs. This project is developing a series of instructional packages that are based on a different instructional model - authentic instruction. The instructional development model used to create these packages is also different. Instead of using the traditional five stage linear, sequential model based on behavioral learning theory, the project uses the recursive, reflective design and development model (R2D2) that is based on cognitive learning theory, particularly the social constructivism of Vygotsky, and an epistemology based on critical theory. Using alternative instructional and instructional development theories, the result of the summer faculty fellowship is LiteraCity, a multimedia adult literacy instructional package that is a simulation of finding and applying for a job. The program, which is about 120 megabytes, is distributed on CD-ROM.

Willis, Jerry W.↗
NASA NTRS1993

Computational strategies in the dynamic simulation of constrained flexible MBS

This research focuses on the computational dynamics of flexible constrained multibody systems. At first a recursive mapping formulation of the kinematical expressions in a minimum dimension as well as the matrix representation of the equations of motion are presented. The method employs Kane's equation, FEM, and concepts of continuum mechanics. The generalized active forces are extended to include the effects of high temperature conditions, such as creep, thermal stress, and elastic-plastic deformation. The time variant constraint relations for rolling/contact conditions between two flexible bodies are also studied. The constraints for validation of MBS simulation of gear meshing contact using a modified Timoshenko beam theory are also presented. The last part deals with minimization of vibration/deformation of the elastic beam in multibody systems making use of time variant boundary conditions. The above methodologies and computational procedures developed are being implemented in a program called DYAMUS.

Amirouche, F. M. L.↗
NASA NTRS1991

Adaptive control of Space Station during nominal operations with CMGs

An adaptive control approach is investigated for the Space Station. The main components of the adaptive controller are the parameter identification scheme, the control gain calculation, and the control law. The control law is the Space Station baseline control law. The control gain calculation is based on linear quadratic regulator theory with eigenvalue placement in a vertical strip. The parameter identification scheme is a real-time recursive extended Kalman filter which estimates the inertias and also provides an estimate of the unmodeled disturbances due to the aerodynamic torques and to the nonlinear effects. An analysis of the inertia estimation problem suggests that it is possible to compute accurate estimates of the Space Station inertias during nominal CMG (control moment gyro) operations. The closed-loop adaptive control law is shown to be capable of stabilizing the Space Station after large inertia changes. Results are presented for the pitch axis.

Bishop, R. H.↗
NASA NTRS1972

A generalized theory for the design of contraction cones and other low speed ducts

A generalization of the Tsien method of contraction cone design is described. The design velocity distribution is expressed in such a form that the required high order derivatives can be obtained by recursion rather than by numerical or analytic differentiation. The method is applicable to the design of diffusers and converging-diverging ducts as well as contraction cones. The computer program is described and a FORTRAN listing of the program is provided.

Barger, R. L.↗
NASA NTRS1992

Experiments with recursive estimation in astronomical image processing

Recursive estimation concepts were applied to image enhancement problems since the 70's. However, very few applications in the particular area of astronomical image processing are known. These concepts were derived, for 2-dimensional images, from the well-known theory of Kalman filtering in one dimension. The historic reasons for application of these techniques to digital images are related to the images' scanned nature, in which the temporal output of a scanner device can be processed on-line by techniques borrowed directly from 1-dimensional recursive signal analysis. However, recursive estimation has particular properties that make it attractive even in modern days, when big computer memories make the full scanned image available to the processor at any given time. One particularly important aspect is the ability of recursive techniques to deal with non-stationary phenomena, that is, phenomena which have their statistical properties variable in time (or position in a 2-D image). Many image processing methods make underlying stationary assumptions either for the stochastic field being imaged, for the imaging system properties, or both. They will underperform, or even fail, when applied to images that deviate significantly from stationarity. Recursive methods, on the contrary, make it feasible to perform adaptive processing, that is, to process the image by a processor with properties tuned to the image's local statistical properties. Recursive estimation can be used to build estimates of images degraded by such phenomena as noise and blur. We show examples of recursive adaptive processing of astronomical images, using several local statistical properties to drive the adaptive processor, as average signal intensity, signal-to-noise and autocorrelation function. Software was developed under IRAF, and as such will be made available to interested users.

Busko, I.↗
NASA NTRS2004

Telescoping Mechanics: A New Paradigm for Composite Behavior Simulation

This report reviews the application of telescoping mechanics to composites using recursive laminate theory. The elemental scale is the fiber-matrix slice, the behavior of which propagates to laminate. The results from using applications for typical, hybrid, and smart composites and composite-enhanced reinforced concrete structures illustrate the versatility and generality of telescoping scale mechanics. Comparisons with approximate, single-cell, and two- and three-dimensional finite-element methods demonstrate the accuracy and computational effectiveness of telescoping scale mechanics for predicting complex composite behavior.

Chamis, C. C.↗
NASA NTRS1998

Experiments to Determine Whether Recursive Partitioning (CART) or an Artificial Neural Network Overcomes Theoretical Limitations of Cox Proportional Hazards Regression

New computationally intensive tools for medical survival analyses include recursive partitioning (also called CART) and artificial neural networks. A challenge that remains is to better understand the behavior of these techniques in effort to know when they will be effective tools. Theoretically they may overcome limitations of the traditional multivariable survival technique, the Cox proportional hazards regression model. Experiments were designed to test whether the new tools would, in practice, overcome these limitations. Two datasets in which theory suggests CART and the neural network should outperform the Cox model were selected. The first was a published leukemia dataset manipulated to have a strong interaction that CART should detect. The second was a published cirrhosis dataset with pronounced nonlinear effects that a neural network should fit. Repeated sampling of 50 training and testing subsets was applied to each technique. The concordance index C was calculated as a measure of predictive accuracy by each technique on the testing dataset. In the interaction dataset, CART outperformed Cox (P less than 0.05) with a C improvement of 0.1 (95% Cl, 0.08 to 0.12). In the nonlinear dataset, the neural network outperformed the Cox model (P less than 0.05), but by a very slight amount (0.015). As predicted by theory, CART and the neural network were able to overcome limitations of the Cox model. Experiments like these are important to increase our understanding of when one of these new techniques will outperform the standard Cox model. Further research is necessary to predict which technique will do best a priori and to assess the magnitude of superiority.

Kattan, Michael W.↗
NASA NTRS2018

Far-field Lorenz-Mie Scattering in an Absorbing Host Medium. II: Improved Stability of the Numerical Algorithm

A recently developed FORTRAN program computing far-field optical observables for spherical particles in an absorbing medium has exhibited numerical instability arising when the product of the particle vacuum size parameter and the imaginary part of the refractive index of the host becomes sufficiently large. We offer a simple analytical explanation of this instability and propose a compact numerical algorithm for the stable computation of Lorenz–Mie coefficients based on an upward recursion formula for spherical Hankel functions of a complex argument. Extensive tests confirm an excellent accuracy of this algorithm approaching machine precision. The improved public-domain FORTRAN program is available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html.

Lorenz-Mie theory↗
NASA NTRS1992

Computer aided design of digital controller for radial active magnetic bearings

A five degree of freedom Active Magnetic Bearing (AMB) system is developed which is controlled by digital controllers. The model of the radial AMB system is linearized and the state equation is derived. Based on the state variables feedback theory, digital controllers are designed. The performance of the controllers are evaluated according to experimental results. The Computer Aided Design (CAD) method is used to design controllers for magnetic bearings. The controllers are implemented with a digital signal processing (DSP) system. The control algorithms are realized with real-time programs. It is very easy to change the controller by changing or modifying the programs. In order to identify the dynamic parameters of the controlled magnetic system, a special experiment was carried out. Also, the online Recursive Least Squares (RLS) parameter identification method is studied. It can be realized with the digital controllers. Online parameter identification is essential for the realization of an adaptive controller.

Cai, Zhong↗
NASA NTRS1984

Improved finite-difference vibration analysis of pretwisted, tapered beams

An improved finite difference procedure based upon second order central differences is developed. Several difficulties encountered in earlier works with fictitious stations that arise in using second order central differences, are eliminated by developing certain recursive relations. The need for forward or backward differences at the beam boundaries or other similar procedures is eliminated in the present theory. By using this improved theory, the vibration characteristics of pretwisted and tapered blades are calculated. Results of the second order theory are compared with published theoretical and experimental results and are found to be in good agreement. The present method generally produces close lower bound solutions and shows fast convergence. Thus, extrapolation procedures that are customary with first order finite-difference methods are unnecessary. Furthermore, the computational time and effort needed for this improved method are almost the same as required for the conventional first order finite-difference approach.

Subrahmanyam, K. B.↗