Differential games and manual control.
Simulation of pursuit-evasion differential game using variational method, comparing performance of human pilot to optimal pursuer
MANUAL CONTROL↗
SEARCH · Engineering Papers
Results for “Variational methods”
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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Theoretical calculation of ozone vibrational infrared intensities
An ab initio dipole moment function for ozone has been computed using the CASSCF (complete active space self-consistent field) method, and forms the basis for a calculation of ozone infrared band intensities. Vibrational wave functions were generated using the variational method with potential energy surfaces derived from experimental force constants. Computed values of the permanent dipole moment, dipole moment derivatives, and infrared band strengths are all found to be in remarkably good agreement with experiment. Intensities are predicted for hot bands for which experimental values are unavailable, and implications for atmospheric ozone spectroscopy are discussed. As the dipole moment matrix element signs are now established for nearly all of the observed bands, further refinement of the dipole moment function is possible.
Adler-Golden, S. M.↗
Skin Friction Extracted from Surface Pressure in Incident Shock-Wave/Boundary-Layer Interaction
High-resolution skin-friction fields are extracted from pressure-sensitive paint (PSP) data obtained in shock-wave/boundary-layer interaction (SWBLI). The method of extracting skin friction from surface pressure is described, including the fundamental relation between skin friction and surface pressure, the variational method, error analysis, and an approximate iterative method. The proposed method is based on a coupling relation between skin friction and surface pressure, where the boundary enstrophy flux is suitably modeled or approximated. This method is applied to unsteady PSP data obtained in incident SWBLIs at Mach 2.5 for different Reynolds numbers, revealing the skin-friction structures of the flows: particularly, the separation bubble induced by the incident shock wave. The extracted results are in good agreement with the data obtained by the surface-stress-sensitive film.
skin friction↗
Finite element analysis of time-independent superconductivity
The development of electromagnetic (EM) finite elements based upon a generalized four-potential variational principle is presented. The use of the four-potential variational principle allows for downstream coupling of EM fields with the thermal, mechanical, and quantum effects exhibited by superconducting materials. The use of variational methods to model an EM system allows for a greater range of applications than just the superconducting problem. The four-potential variational principle can be used to solve a broader range of EM problems than any of the currently available formulations. It also reduces the number of independent variables from six to four while easily dealing with conductor/insulator interfaces. This methodology was applied to a range of EM field problems. Results from all these problems predict EM quantities exceptionally well and are consistent with the expected physical behavior.
Schuler, James J.↗
Control optimization of a lifting body entry problem by an improved and a modified method of perturbation function
A study of the solution problem of a complex entry optimization was studied. The problem was transformed into a two-point boundary value problem by using classical calculus of variation methods. Two perturbation methods were devised. These methods attempted to desensitize the contingency of the solution of this type of problem on the required initial co-state estimates. Also numerical results are presented for the optimal solution resulting from a number of different initial co-states estimates. The perturbation methods were compared. It is found that they are an improvement over existing methods.
Garcia, F., Jr.↗
Synthesis of spherical minimum-weight proton shields
A systematic method has been developed for minimizing spherical shield weights for protection against proton radiation, including secondary neutron production, subject to various specified dose constraints. Variational methods are applied to a radiation model yielding the choice of optimum shielding materials and their mixtures, together with a prescription for their disposition in a multilayer spherical shield.
Spherical Shell↗
Active Control of Fan Noise-Feasibility Study. Volume 2: Canceling Noise Source-Design of an Acoustic Plate Radiator Using Piezoceramic Actuators
The feasibility of using acoustic plate radiators powered by piezoceramic thin sheets as canceling sources for active control of aircraft engine fan noise is demonstrated. Analytical and numerical models of actuated beams and plates are developed and validated. An optimization study is performed to identify the optimum combination of design parameters that maximizes the plate volume velocity for a given resonance frequency. Fifteen plates with various plate and actuator sizes, thicknesses, and bonding layers were fabricated and tested using results from the optimization study. A maximum equivalent piston displacement of 0.39 mm was achieved with the optimized plate samples tested with only one actuator powered, corresponding to a plate deflection at the center of over 1 millimeter. This is very close to the deflection required for a full size engine application and represents a 160-fold improvement over previous work. Experimental results further show that performance is limited by the critical stress of the piezoceramic actuator and bonding layer rather than by the maximum moment available from the actuator. Design enhancements are described in detail that will lead to a flight-worthy acoustic plate radiator by minimizing actuator tensile stresses and reducing nonlinear effects. Finally, several adaptive tuning methods designed to increase the bandwidth of acoustic plate radiators are analyzed including passive, active, and semi-active approaches. The back chamber pressurization and volume variation methods are investigated experimentally and shown to be simple and effective ways to obtain substantial control over the resonance frequency of a plate radiator. This study shows that piezoceramic-based plate radiators can be a viable acoustic source for active control of aircraft engine fan noise.
Pla, F. G.↗
Determination of optimum nozzle contours for the expansion of dissociated gases by methods of the variational calculus.
Optimum nozzle contours for expansion of Lighthill idealized dissociating gas in one- dimensional flow determined by methods of variational calculus
ONE-DIMENSIONAL FLOW↗
Determination of optimum nozzle contours for the expansion of dissociated gases by methods of the variational calculus.
Optimum nozzle contours for expansion of Lighthill idealized dissociating gas in one- dimensional flow determined by methods of variational calculus
Berns, R. R.↗
Investigation of cosmic ray variations as a method of studying interplanetary space
Cosmic ray variations and interplanetary space
Source record↗
Predicting the Size of Sunspot Cycle 24 on the Basis of Single- and Bi-Variate Geomagnetic Precursor Methods
Examined are single- and bi-variate geomagnetic precursors for predicting the maximum amplitude (RM) of a sunspot cycle several years in advance. The best single-variate fit is one based on the average of the ap index 36 mo prior to cycle minimum occurrence (E(Rm)), having a coefficient of correlation (r) equal to 0.97 and a standard error of estimate (se) equal to 9.3. Presuming cycle 24 not to be a statistical outlier and its minimum in March 2008, the fit suggests cycle 24 s RM to be about 69 +/- 20 (the 90% prediction interval). The weighted mean prediction of 11 statistically important single-variate fits is 116 +/- 34. The best bi-variate fit is one based on the maximum and minimum values of the 12-mma of the ap index; i.e., APM# and APm*, where # means the value post-E(RM) for the preceding cycle and * means the value in the vicinity of cycle minimum, having r = 0.98 and se = 8.2. It predicts cycle 24 s RM to be about 92 +/- 27. The weighted mean prediction of 22 statistically important bi-variate fits is 112 32. Thus, cycle 24's RM is expected to lie somewhere within the range of about 82 to 144. Also examined are the late-cycle 23 behaviors of geomagnetic indices and solar wind velocity in comparison to the mean behaviors of cycles 2023 and the geomagnetic indices of cycle 14 (RM = 64.2), the weakest sunspot cycle of the modern era.
Wilson, Robert M.↗
A Stability Analysis of Cylindrical Panels Using a Finite Element Formulation
A cylindrical finite element suitable for the linear stability analysis of cylindrical shells is developed. Energy principles and variational methods lead to a problem formulation which lends itself to physical interpretations of the governing matrices of the finite element. By properly grouping the terms which result from taking the second variation of the potential energy of the element, it is possible to identify three distinct types of matrices. The first matrix is the conventional stiffness matrix; the second is an initial stress stiffness matrix; and the third is an initial displacement stiffness matrix. With the assumption of linearity, the buckling problem is stated in terms of the classical linear real eigenvalue equation. This problem formulation was programmed on the CDC 6600 series computer. The computer program is used to analyze the buckling of a variety of structures. Columns, arches, flat plates and curved panels with and without cutouts are considered.
Snyder, R. E.↗
Shape integral method for magnetospheric shapes
A method is developed for calculating the shape of any magnetopause to arbitrarily high precision. The method uses an integral equation which is evaluated for a trial shape. The resulting values of the integral equation as a function of auxiliary variables indicate how close one is to the desired solution. A variational method can then be used to improve the trial shape. Some potential applications are briefly mentioned.
Michel, F. C.↗
On the optimal use of fictitious time in variation of parameters methods with application to BG14
The optimal way to use fictitious time in variation of parameter methods is presented. Setting fictitious time to zero at the end of each step is shown to cure the instability associated with some types of problems. Only some parameters are reinitialized, thereby retaining redundant information.
Gottlieb, Robert G.↗
Determination of Flaw Size from Thermographic Data
Conventional methods for reducing the pulsed thermographic responses of delaminations tend to overestimate the size of the flaw. Since the heat diffuses in the plane parallel to the surface, the resulting temperature profile over the flaw is larger than the flaw. A variational method is presented for reducing the thermographic data to produce an estimated size for the flaw that is much closer to the true size of the flaw. The size is determined from the spatial thermal response of the exterior surface above the flaw and a constraint on the length of the contour surrounding the flaw. The technique is applied to experimental data acquired on a flat bottom hole composite specimen.
Winfree, William P.↗
Comparison of some optimal control methods for the design of turbine blades
This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.
Desilva, B. M. E.↗
Indirect methods for measuring variations of the solar constant
The difference between the methods that measure delta S, and those that measure variations in the solar luminosity, delta L, is discussed. It is shown that the past practice of simply relating delta S to delta L by geometrical arguments is not valid because of anisotropy of the solar radiation. It is concluded that direct techniques prove the existence of short term variability that is fully explainable in terms of the passage of active regions (spots and faculae) on the face of the Sun. The obervations of changes in the solar diameter support the existence of structurally induced variations of the solar luminosity on timescales of tens of years, which are significant in the understanding of climatic variations.
Sofia, S.↗
Intermolecular potential for thermal H2O-He collisions
Theoretical potentials for rotational excitation of H2O by He were constructed via several methods, all of which start with a large basis set SCF interaction. The semiempirical Hartree-Fock with damped dispersion model adds a damped long-range attraction with parameters adjusted to fit experimental total differential cross sections. Purely ab initio potentials add correlation energies obtained via perturbation theory (MP2 and MP4) or a variational method (ICF1). Scattering calculations were performed on all surfaces to compare wih available beam scattering and pressure broadening data and to assess sensitivity of state-to-state rates to uncertainties in the potential. From comparison with the limited experimental data, the ICF1 surface appears to be marginally better than the MP4 surface. Thermal rates calculated from this surface should be accurate to better than 50 percent, at least for the larger, more important rates.
Palma, Amedeo↗