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NASA NTRS1989

A spatial operator algebra for manipulator modeling and control

A spatial operator algebra for modeling the control and trajectory design of manipulation is discussed, with emphasis on its analytical formulation and implementation in the Ada programming language. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of the manipulator. Inversion is obtained using techniques of recursive filtering and smoothing. The operator alegbra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. Implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection, thus greatly simplifying the transition from an abstract problem formulation and solution to the detailed mechanization of a specific algorithm.

Rodriguez, G.↗

NASA NTRS1997

Least-Squares Spectral Element Solutions to the CAA Workshop Benchmark Problems

This paper presents computed results for some of the CAA benchmark problems via the acoustic solver developed at Rocketdyne CFD Technology Center under the corporate agreement between Boeing North American, Inc. and NASA for the Aerospace Industry Technology Program. The calculations are considered as benchmark testing of the functionality, accuracy, and performance of the solver. Results of these computations demonstrate that the solver is capable of solving the propagation of aeroacoustic signals. Testing of sound generation and on more realistic problems is now pursued for the industrial applications of this solver. Numerical calculations were performed for the second problem of Category 1 of the current workshop problems for an acoustic pulse scattered from a rigid circular cylinder, and for two of the first CAA workshop problems, i. e., the first problem of Category 1 for the propagation of a linear wave and the first problem of Category 4 for an acoustic pulse reflected from a rigid wall in a uniform flow of Mach 0.5. The aim for including the last two problems in this workshop is to test the effectiveness of some boundary conditions set up in the solver. Numerical results of the last two benchmark problems have been compared with their corresponding exact solutions and the comparisons are excellent. This demonstrates the high fidelity of the solver in handling wave propagation problems. This feature lends the method quite attractive in developing a computational acoustic solver for calculating the aero/hydrodynamic noise in a violent flow environment.

Lin, Wen H.↗

NASA NTRS2021

An Approach to Reasoning Service Migration in Data and Reasoning Fabric (DRF) Implementation

In this paper we consider service migration problem for Data and Reasoning Fabric (DRF) enabled airspace operations assuming a fixed cloud/edge infrastructure with allocated computing, storage and power resources, where cloud/edge servers, and communication stations are in a wired connected network, while vehicles use a wireless network for communication. The objective is to automatically select the best location for the requested service execution, which achieves minimum cost while satisfying the user quality of service (QoS) and available resources constraints. To this end, estimates of the response time, consumed energy and total cost are defined for each potential compute location. A mixed-integer linear program is then formulated and solved to identify optimal compute locations given QoS constraints, network infrastructure limitations, with worst-case vehicle positioning. The approach is applied to trajectory re-planning use case to avoid a collision with an emergency vehicle in real time.

Air mobility↗

NASA NTRS1971

Equicontrollability and the model following problem

Equicontrollability and its application to the linear time-invariant model-following problem are discussed. The problem is presented in the form of two systems, the plant and the model. The requirement is to find a controller to apply to the plant so that the resultant compensated plant behaves, in an input-output sense, the same as the model. All systems are assumed to be linear and time-invariant. The basic approach is to find suitable equicontrollable realizations of the plant and model and to utilize feedback so as to produce a controller of minimal state dimension. The concept of equicontrollability is a generalization of control canonical (phase variable) form applied to multivariable systems. It allows one to visualize clearly the effects of feedback and to pinpoint the parameters of a multivariable system which are invariant under feedback. The basic contributions are the development of equicontrollable form; solution of the model-following problem in an entirely algorithmic way, suitable for computer programming; and resolution of questions on system decoupling.

Curran, R. T.↗

NASA NTRS1971

Unsteady flow through compressor stages

The application of the nonsteady Lax-Wendroff technique to problems with asymptotically periodic solution which offers a potentially powerful method for the investigation of the interaction of rotating and stationary blade rows in turbomachinery is reported. A technique for specifying boundary conditions with phase lag was developed to accomplish this. A complete nonlinear analysis is carried out numerically to determine the entire flow field without recourse to the assumption of small disturbances of linear equations which underlie the previous acoustic theories. The result, obtained for the case of equal number of rotor and stator blades shows that transonic flow can be handled without difficulty. In addition, the program is not limited with regard to blade thickness, camber or loading. Extension of this method to incorporate viscous wakes and to analysis of fully three dimensional configuration is feasible, and would greatly expand its utility in practical applications.

Alzner, E.↗

NASA NTRS1976

Survey and development of finite elements for nonlinear structural analysis. Volume 2: Nonlinear shell finite elements

The development of two new shell finite elements for applications to large deflection problems is considered. The elements in question are doubly curved and of triangular and quadrilateral planform. They are restricted to small strains of elastic materials, and can accommodate large rotations. The elements described, which are based on relatively simple linear elements, make use of a new displacement function approach specifically designed for strongly nonlinear problems. The displacement function development for nonlinear applications is based on certain beam element formulations, and the strain-displacement equations are of a shallow shell type. Additional terms were included in these equations in an attempt to avoid the large errors characteristic of shallow shell elements in certain types of problems. An incremental nonlinear solution procedure specifically adopted to the element formulation was developed. The solution procedure is of combined incremental and total Lagrangian type, and uses a new updating scheme. A computer program was written to evaluate the developed formulations. This program can accommodate small element groups in arbitrary arrangements. Two simple programs were successfully solved. The results indicate that this new type of element has definite promise and should be a fruitful area for further research.

Source record↗

NASA NTRS1986

Evaluation and Improvement of Liquid Propellant Rocket Chugging Analysis Techniques. Part 1: A One-Dimensional Analysis of Low Frequency Combustion Instability in the Fuel Preburner of the Space Shuttle Main Engine

Low frequency combustion instability, known as chugging, is consistently experienced during shutdown in the fuel and oxidizer preburners of the Space Shuttle Main Engines. Such problems always occur during the helium purge of the residual oxidizer from the preburner manifolds during the shutdown sequence. Possible causes and triggering mechanisms are analyzed and details in modeling the fuel preburner chug are presented. A linearized chugging model, based on the foundation of previous models, capable of predicting the chug occurrence is discussed and the predicted results are presented and compared to experimental work performed by NASA. Sensitivity parameters such as chamber pressure, fuel and oxidizer temperatures, and the effective bulk modulus of the liquid oxidizer are considered in analyzing the fuel preburner chug. The computer program CHUGTEST is utilized to generate the stability boundary for each sensitivity study and the region for stable operation is identified.

Lim, Kair Chuan↗

NASA NTRS1985

Modal forced vibration analysis of aerodynamically excited turbosystems

Theoretical aspects of a new capability to determine the vibratory response of turbosystems subjected to aerodynamic excitation are presented. Turbosystems such as advanced turbopropellers with highly swept blades, and axial-flow compressors and turbines can be analyzed using this capability. The capability has been developed and implemented in the April 1984 release of the general purpose finite element program NASTRAN. The dynamic response problem is addressed in terms of the normal modal coordinates of these tuned rotating cyclic structures. Both rigid and flexible hubs/disks are considered. Coriolis and centripetal accelerations, as well as differential stiffness effects are included. Generally non-uniform steady inflow fields and uniform flow fields arbitrarily inclined at small angles with respect to the axis of rotation of the turbosystem are considered sources of aerodynamic excitation. The spatial non-uniformities are considered to be small deviations from a principally uniform inflow. Subsonic and supersonic relative inflows are addressed, with provision for linearly interpolating transonic airloads.

Elchuri, V.↗

NASA NTRS1991

Applications of singular value analysis and partial-step algorithm for nonlinear orbit determination

An adaptive method in which cruise and nonlinear orbit determination problems can be solved using a single program is presented. It involves singular value decomposition augmented with an extended partial step algorithm. The extended partial step algorithm constrains the size of the correction to the spacecraft state and other solve-for parameters. The correction is controlled by an a priori covariance and a user-supplied bounds parameter. The extended partial step method is an extension of the update portion of the singular value decomposition algorithm. It thus preserves the numerical stability of the singular value decomposition method, while extending the region over which it converges. In linear cases, this method reduces to the singular value decomposition algorithm with the full rank solution. Two examples are presented to illustrate the method's utility.

Ryne, Mark S.↗

NASA NTRS1985

On the factorization of block-tridiagonals without storage constraints

In many programs solving difference equations, problem size is restricted by the number of available memory cells. A strategy has been developed to permit trade-offs between the number of floating point operations required and storage requirements for the solution of certain problems such as block tridiagonal systems of equations. This is done by recomputing some intermediate results instead of storing them. Reducing the storage to the square root of the current requirement will roughly double the number of computations. In theory, if m is the order of each sub-matrix in the block tridiagonal matrix, one can solve any linear system with only 5 sq m + 1 temporary storage cells. This method lends itself to efficient use on computers with parallel processing or vector processing architectures. On these computers the larger number of floating point operations is more than offset by the decrease in I/O and the increased percentage of vector operations made possible by this algorithm.

Merriam, M. L.↗

NASA NTRS1988

Comparison of aerobic fitness and space motion sickness during the Shuttle program

Space motion sickness (SMS) is an important problem for short-duration space flight; 71 percent of STS crewmembers develop SMS symptoms. The search for effective countermeasures and factors that correlate with sensitivity has been extensive. Recently, several investigators have linked aerobic fitness with motion sickness sensitivity in the 1-G or high-G environment. This paper compares the aerobic fitness of 125 Shuttle crewmembers with their SMS symptom category. Aerobic fitness data were obtained from the exercise tolerance test conducted nearest the time of launch. SMS data were derived from the medical debrief summaries. Mean maximum oxygen consumption values for crewmembers in four SMS categories (none, mild, moderate, severe) were 44.55, 44.08, 46.5, and 44.24 ml/kg per min, respectively. Scattergrams with linear regression analysis, comparing aerobic fitness and SMS symptom classification are presented. Correlation coefficients comparing SMS categories vs. aerobic fitness for men and women reveal no definite relationship between the two factors.

Jennings, Richard T.↗

NASA NTRS1985

Three-dimensional elastic-plastic finite-element analysis of fatigue crack propagation

Fatigue cracks are a major problem in designing structures subjected to cyclic loading. Cracks frequently occur in structures such as aircraft and spacecraft. The inspection intervals of many aircraft structures are based on crack-propagation lives. Therefore, improved prediction of propagation lives under flight-load conditions (variable-amplitude loading) are needed to provide more realistic design criteria for these structures. The main thrust was to develop a three-dimensional, nonlinear, elastic-plastic, finite element program capable of extending a crack and changing boundary conditions for the model under consideration. The finite-element model is composed of 8-noded (linear-strain) isoparametric elements. In the analysis, the material is assumed to be elastic-perfectly plastic. The cycle stress-strain curve for the material is shown Zienkiewicz's initial-stress method, von Mises's yield criterion, and Drucker's normality condition under small-strain assumptions are used to account for plasticity. The three-dimensional analysis is capable of extending the crack and changing boundary conditions under cyclic loading.

Goglia, G. L.↗

NASA NTRS1973

Synthesis of multiple shaped beam antenna patterns

Results are presented of research into the problem of finding an excitation of a given antenna such that the desired radiation pattern is approximated to within acceptable limits. This is to be done in such a fashion that boundary conditions involving hardware limitations may be inserted into the problem. The intended application is synthesis of multiple shaped beam antennas. Since this is perhaps the most difficult synthesis problem an antenna engineer is likely to encounter, the approach taken was to include as a by-product capability for synthesizing simpler patterns. The synthesis technique has been almost totally computerized. The class of antennas which may be synthesized with the computer program are those which may be represented as planar (continuous or discrete) current distributions. The technique is not limited in this sense and could indeed by extended to include, for example, the synthesis of conformal arrays or current distributions on the surface of reflectors. The antenna types which the program is set up to synthesize are: line source, rectangular aperture, circular aperture, linear array, rectangular array, and arbitrary planar array.

Stutzman, W. L.↗

NASA NTRS1994

Sensitivity Analysis of Flutter Response of a Wing Incorporating Finite-Span Corrections

Flutter analysis of a wing is performed in compressible flow using state-space representation of the unsteady aerodynamic behavior. Three different expressions are used to incorporate corrections due to the finite-span effects of the wing in estimating the lift-curve slope. The structural formulation is based on a Rayleigh-Pitz technique with Chebyshev polynomials used for the wing deflections. The aeroelastic equations are solved as an eigen-value problem to determine the flutter speed of the wing. The flutter speeds are found to be higher in these cases, when compared to that obtained without accounting for the finite-span effects. The derivatives of the flutter speed with respect to the shape parameters, namely: aspect ratio, area, taper ratio and sweep angle, are calculated analytically. The shape sensitivity derivatives give a linear approximation to the flutter speed curves over a range of values of the shape parameter which is perturbed. Flutter and sensitivity calculations are performed on a wing using a lifting-surface unsteady aerodynamic theory using modules from a system of programs called FAST.

Issac, Jason Cherian↗

NASA NTRS1972

Systems identification using a modified Newton-Raphson method: A FORTRAN program

A FORTRAN program is offered which computes a maximum likelihood estimate of the parameters of any linear, constant coefficient, state space model. For the case considered, the maximum likelihood estimate can be identical to that which minimizes simultaneously the weighted mean square difference between the computed and measured response of a system and the weighted square of the difference between the estimated and a priori parameter values. A modified Newton-Raphson or quasilinearization method is used to perform the minimization which typically requires several iterations. A starting technique is used which insures convergence for any initial values of the unknown parameters. The program and its operation are described in sufficient detail to enable the user to apply the program to his particular problem with a minimum of difficulty.

Taylor, L. W., Jr.↗

NASA NTRS2000

Cascade Optimization for Aircraft Engines With Regression and Neural Network Analysis - Approximators

The NASA Engine Performance Program (NEPP) can configure and analyze almost any type of gas turbine engine that can be generated through the interconnection of a set of standard physical components. In addition, the code can optimize engine performance by changing adjustable variables under a set of constraints. However, for engine cycle problems at certain operating points, the NEPP code can encounter difficulties: nonconvergence in the currently implemented Powell's optimization algorithm and deficiencies in the Newton-Raphson solver during engine balancing. A project was undertaken to correct these deficiencies. Nonconvergence was avoided through a cascade optimization strategy, and deficiencies associated with engine balancing were eliminated through neural network and linear regression methods. An approximation-interspersed cascade strategy was used to optimize the engine's operation over its flight envelope. Replacement of Powell's algorithm by the cascade strategy improved the optimization segment of the NEPP code. The performance of the linear regression and neural network methods as alternative engine analyzers was found to be satisfactory. This report considers two examples-a supersonic mixed-flow turbofan engine and a subsonic waverotor-topped engine-to illustrate the results, and it discusses insights gained from the improved version of the NEPP code.

Patnaik, Surya N.↗

NASA NTRS1977

Development of a moderately sized finite element program for nonlinear structural analysis

AGGIE 1 is a computer program for predicting the linear and nonlinear, static and dynamic structural response of two- and three-dimensional continuum solids. The program is based on isoparametric finite elements and allows for 2-D plane stress, plane strain, and axisymmetric analyses and general 3-D analyses. Large strain kinematics is based on the total Lagrangian formulation. Materially nonlinear models include several elastic-plastic work-hardening models as well as an incompressible Mooney-Rivlin model. Included in this report is a brief description of the theoretical bases of the program, the material models used, the element library and the overall program organization. Instructions for data input preparation are given in detail. Several sample problems are given along with the required program input and program generated solutions.

Haisler, W. E.↗

NASA NTRS1986

The expanded LaGrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrainted optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗