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At least 541 records · Page 30

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NASA NTRS1972

A survey of methods of feasible directions for the solution of optimal control problems

Three methods of feasible directions for optimal control are reviewed. These methods are an extension of the Frank-Wolfe method, a dual method devised by Pironneau and Polack, and a Zontendijk method. The categories of continuous optimal control problems are shown as: (1) fixed time problems with fixed initial state, free terminal state, and simple constraints on the control; (2) fixed time problems with inequality constraints on both the initial and the terminal state and no control constraints; (3) free time problems with inequality constraints on the initial and terminal states and simple constraints on the control; and (4) fixed time problems with inequality state space contraints and constraints on the control. The nonlinear programming algorithms are derived for each of the methods in its associated category.

Polak, E.↗

NASA NTRS1972

The computation of optimal control programmes using a modified successive sweep method.

A second-order method for numerically solving control optimization problems has been developed. The method, referred to as the modified sweep method (MSM), differs from the successive sweep method (SSM) proposed by McReynolds and Bryson (1965) in that the conditions for local control optimality are used to determine the control as an explicit function of the state variables and time. The control is eliminated from the problem and the solution to the resulting two-point boundary value problem can be obtained by linear perturbation methods. The modified sweep method proposed here uncouples the perturbation equations for the state variables and the Lagrange multipliers by using a generalized matrix-Riccati transformation of variables. The resulting algorithm for the numerical iteration process is concerned with determining the initial values of a set of Lagrange multipliers rather than correcting a numerical control programme over the entire time interval of interest.

Colunga, D.↗

NASA NTRS1972

A generalized method for the identification of aircraft stability and control derivatives from flight test data.

This paper discusses the application of a generalized identification method for flight test data analysis. The method is based on the maximum likelihood (ML) criterion and includes output error and equation error methods as special cases. Both the linear and nonlinear models with and without process noise are considered. The flight test data from lateral maneuvers of HL-10 and M2/F3 lifting bodies are processed to determine the lateral stability and control derivatives, instrumentation accuracies and biases. A comparison is made between the results of the output error method and the generalized ML method for M2/F3 data containing gusts. It is shown that better fits to time histories are obtained by using the generalized ML method.

Mehra, R. K.↗

NASA NTRS1973

Feasibility study of the numerical integration of shell equations using the field method

The field method is developed for arbitrary open branch domains subjected to general linear boundary conditions. Although closed branches are within the scope of the method, they are not treated here. The numerical feasibility of the method has been demonstrated by implementing it in a computer program for the linear static analysis of open branch shells of revolution under asymmetric loads. For such problems the field method eliminates the well-known numerical problem of long subintervals associated with the rapid growth of extraneous solutions. Also, the method appears to execute significantly faster than other numerical integration methods.

Cohen, G. A.↗

NASA NTRS1973

Detection of fatigue cracks by nondestructive testing methods

The effectiveness was assessed of various NDT methods to detect small tight cracks by randomly introducing fatigue cracks into aluminum sheets. The study included optimizing NDT methods calibrating NDT equipment with fatigue cracked standards, and evaluating a number of cracked specimens by the optimized NDT methods. The evaluations were conducted by highly trained personnel, provided with detailed procedures, in order to minimize the effects of human variability. These personnel performed the NDT on the test specimens without knowledge of the flaw locations and reported on the flaws detected. The performance of these tests was measured by comparing the flaws detected against the flaws present. The principal NDT methods utilized were radiographic, ultrasonic, penetrant, and eddy current. Holographic interferometry, acoustic emission monitoring, and replication methods were also applied on a reduced number of specimens. Generally, the best performance was shown by eddy current, ultrasonic, penetrant and holographic tests. Etching provided no measurable improvement, while proof loading improved flaw detectability. Data are shown that quantify the performances of the NDT methods applied.

Anderson, R. T.↗

NASA NTRS1973

Application of the generalized Galerkin method to the computation of fluid flows.

The purpose of this paper is to show that most existing methods for the calculation of fluid flows can be interpreted as special applications of a single mathematical formalism. This formalism, called the generalized Galerkin method, then provides a single conceptual framework for comparing various methods in terms of convergence and accuracy. The method is presented in sufficient mathematical detail to permit its interpretation as a projection in function space. In order to demonstrate the basic thesis, finite difference, finite element, strip integral, and classical integral methods of boundary layer theory are developed by application of the method.

Murphy, J. D.↗

NASA NTRS1975

New methods for the numerical integration of ordinary differential equations and their application to the equations of motion of spacecraft

A number of hybrid methods for solving Cauchy problems are described on the basis of an evaluation of advantages of single and multiple-point numerical integration methods. The selection criterion is the principle of minimizing computer time. The methods discussed include the Nordsieck method, the Bulirsch-Stoer extrapolation method, and the method of recursive Taylor-Steffensen power series.

Banyukevich, A.↗

NASA NTRS1975

Computer analysis of multicircuit shells of revolution by the field method

The field method, presented previously for the solution of even-order linear boundary value problems defined on one-dimensional open branch domains, is extended to boundary value problems defined on one-dimensional domains containing circuits. This method converts the boundary value problem into two successive numerically stable initial value problems, which may be solved by standard forward integration techniques. In addition, a new method for the treatment of singular boundary conditions is presented. This method, which amounts to a partial interchange of the roles of force and displacement variables, is problem independent with respect to both accuracy and speed of execution. This method was implemented in a computer program to calculate the static response of ring stiffened orthotropic multicircuit shells of revolution to asymmetric loads. Solutions are presented for sample problems which illustrate the accuracy and efficiency of the method.

Cohen, G. A.↗

NASA NTRS1976

Shuttle onboard IMU alignment methods

The current approach to the shuttle IMU alignment is based solely on the Apollo Deterministic Method. This method is simple, fast, reliable and provides an accurate estimate for the present cluster to mean of 1,950 transformation matrix. If four or more star sightings are available, the application of least squares analysis can be utilized. The least squares method offers the next level of sophistication to the IMU alignment solution. The least squares method studied shows that a more accurate estimate for the misalignment angles is computed, and the IMU drift rates are a free by-product of the analysis. Core storage requirements are considerably more; estimated 20 to 30 times the core required for the Apollo Deterministic Method. The least squares method offers an intermediate solution utilizing as much data that is available without a complete statistical analysis as in Kalman filtering.

Henderson, D. M.↗

NASA NTRS1976

Aircraft digital control design methods

Variations in design methods for aircraft digital flight control are evaluated and compared. The methods fall into two categories; those where the design is done in the continuous domain (or s plane) and those where the design is done in the discrete domain (or z plane). Design method fidelity is evaluated by examining closed loop root movement and the frequency response of the discretely controlled continuous aircraft. It was found that all methods provided acceptable performance for sample rates greater than 10 cps except the uncompensated s plane design method which was acceptable above 20 cps. A design procedure based on optimal control methods was proposed that provided the best fidelity at very slow sample rates and required no design iterations for changing sample rates.

Powell, J. D.↗

NASA NTRS1976

Conservation properties of numerical integration methods for systems of ordinary differential equations

If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

Rosenbaum, J. S.↗

NASA NTRS1976

A comparison of digital flight control design methods

Many variations in design methods for aircraft digital flight control have been proposed in the literature. In general, the methods fall into two categories: those where the design is done in the continuous domain (or s-plane), and those where the design is done in the discrete domain (or z-plane). This paper evaluates several variations of each category and compares them for various flight control modes of the Langley TCV Boeing 737 aircraft. Design method fidelity is evaluated by examining closed loop root movement and the frequency response of the discretely controlled continuous aircraft. It was found that all methods provided acceptable performance for sample rates greater than 10 cps except the 'uncompensated s-plane design' method which was acceptable above 20 cps. A design procedure based on optimal control methods was proposed that provided the best fidelity at very slow sample rates and required no design iterations for changing sample rates.

Powell, J. D.↗

NASA NTRS1977

A comparison of simple shear characterization methods for composite laminates

Various methods for the shear stress-strain characterization of composite laminates are examined, and their advantages and limitations are briefly discussed. Experimental results and the necessary accompanying analysis are then presented and compared for three simple shear characterization procedures. These are the off-axis tensile test method, the + or - 45 degs tensile test method and the 0 deg/90 degs symmetric rail shear test method. It is shown that the first technique indicates that the shear properties of the G/E laminates investigated are fundamentally brittle in nature while the latter two methods tend to indicate that the G/E laminates are fundamentally ductile in nature. Finally, predictions of incrementally determined tensile stress-strain curves utilizing the various different shear behavior methods as input information are presented and discussed.

Yeow, Y. T.↗

NASA NTRS1976

Free-interface methods of substructure coupling for dynamic analysis

Benfield, et al. (1972) showed that among fixed-interface, free-interface, and hybrid substructure coupling methods, the fixed-interface methods as the most accurate and the free-interface methods are the least accurate. In the present note, a substructure coupling method is proposed which employs free-interface substructure modes supplemented by 'reduced flexibility.' Substructure coupling based on the improved substructure model is discussed, and a numerical comparison with Hou's free-interface method is given. To simplify representation of the method proposed, the substructure equations are developed first for constrained substructures, and then the equations representing substructures with rigid-body modes are given. Finally, the equations for coupling of substructures are derived. Example calculations are included.

Craig, R. R., Jr.↗

NASA NTRS1977

Temperature retrievals from satellite radiance measurements - An empirical method

This paper presents a method for using satellite measurements to interpolate vertical temperature soundings between radiosonde stations. The calculations presented show that especially in the 1000-800 mb layer, where linear methods of temperature retrieval usually contain large errors, the proposed method reduces the errors substantially. The method finds a set of coefficients, which when multiplied by corresponding measured radiance quantities, yield zero temperature error at a radiosonde station. This derived set of coefficients is then applied to satellite radiance measurements at places between the radiosonde stations. The computations show, for example, that the average absolute error in the layer 1000-800 mb is only 0.3 K when the corresponding 'minimum-information' method error was 2.9 K. The method may be most applicable to measurements from geostationary satellites, but should also be applicable to measurements from polar orbiting satellites under certain conditions.

Fritz, S.↗

NASA NTRS1978

Quasi-Newton Methods

The problem to be solved is formulated precisely and the introduction of quasi-Newton methods is motivated by considering the classical Newton and secant methods and their properties. Three highly successful quasi-Newton methods are surveyed: Broyden's method for the solution of general nonlinear equations, and the Davidon-Fletcher-Powell and Broyden-Fletcher-Goldfarb-Shanno procedures for unconstrained minimization. Finally, the properties of these methods are compared to those of Newton's method and UHMLE in potential applications to maximum-likelihood estimation of parameters in mixture distributions.

Walker, H. F.↗

NASA NTRS1978

Solution of axisymmetric and two-dimensional inviscid flow over blunt bodies by the method of lines

Comparisons with experimental data and the results of other computational methods demonstrated that very accurate solutions can be obtained by using relatively few lines with the method of lines approach. This method is semidiscrete and has relatively low core storage requirements as compared with fully discrete methods since very little data were stored across the shock layer. This feature is very attractive for three dimensional problems because it enables computer storage requirements to be reduced by approximately an order of magnitude. In the present study it was found that nine lines was a practical upper limit for two dimensional and axisymmetric problems. This condition limits application of the method to smooth body geometries where relatively few lines would be adequate to describe changes in the flow variables around the body. Extension of the method to three dimensions was conceptually straightforward; however, three dimensional applications would also be limited to smooth body geometries although not necessarily to total of nine lines.

Hamilton, H. H., II↗

NASA NTRS1978

Improved methods for calculating the thickness noise

Advanced methods to compute the rotor thickness noise which is predominant in the case of high speed rotor were developed. These methods were deduced from a previous method by transforming the integral coordinate, commuting the order of integration and differential, and/or performing chordwise integration analytically with some adequate assumption. The necessary computational times and waveforms obtained by the previous and three advanced methods were compared. It was then concluded that the advanced methods could save the computational time compared with the previous method with the same accuracy.

Nakamura, Y.↗