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A computer program used to process the equations is presented, and a full description of equation implementation is given. The model was implemented in the IBM 360 and CDC series computer systems.
A methodology is presented for using the Volterra-Wiener theory of nonlinear systems in aeroservoelastic (ASE) analyses and design. The theory is applied to the development of nonlinear aerodynamic response models that can be defined in state-space form and are, therefore, appropriate for use in modern control theory. The theory relies on the identification of nonlinear kernels that can be used to predict the response of a nonlinear system due to an arbitrary input. A numerical kernel identification technique, based on unit impulse responses, is presented and applied to a simple bilinear, single-input single-output (SISO) system. The linear kernel (unit impulse response) and the nonlinear second-order kernel of the system are numerically-identified and compared with the exact, analytically-defined and linear and second-order kernels. This kernel identification technique is then applied to the CAP-TSD (Computational Aeroelasticity Program-Transonic Small Disturbance) code for identification of the linear and second-order kernels of a NACA64A010 rectangular wing undergoing pitch at M = 0.5, M = 8.5 (transonic), and M = 0.93 (transonic). Results presented demonstrate the feasibility of this approach for use with nonlinear, unsteady aerodynamic responses.
A digital computer program (ORACLS) for implementing the optimal regulator theory approach to the design of controllers for linear time-invariant systems is described. The user-oriented program employs the latest numerical techniques and is applicable to both the digital and continuous control problems.
The benefits of linear quadratic regulator synthesis methods in designing a multivariable engine control capable of operating an engine throughout its flight envelope were demonstrated. The entire multivariable control synthesis program is reviewed with particular emphasis on engine tests conducted in the NASA Lewis propulsion systems laboratory altitude facility. The multivariable control has basically a proportional plus integral, model following structure with gains scheduled as functions of flight condition. The multivariable control logic design is described, along with control computer implementation aspects. Altitude tests demonstrated that the multivariable control logic could control an engine over a wide range of test conditions. Representative transient responses are presented to demonstrate engine behavior and the functioning of the control logic.
Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.
Five individual 5 year mini-batch geomagnetic models were generated and two computer programs were developed to process the models. The first program computes statistics (mean sigma, weighted sigma) on the changes in the first derivatives (linear terms) of the spherical harmonic coefficients between mini-batches. The program ran successfully. The statistics are intended for use in computing the state noise matrix required in the information filter. The second program is the information filter. Most subroutines used in the filter were tested, but the coefficient statistics must be analyzed before the filter is run.
Engineering problems sometimes involve the numerical solution of boundary value problems over domains containing geometric feature with widely varying scales. Often, a detailed solution is required at one or more of these features. Small details in large structures may have profound effects upon global performance. Conversely, large-scale conditions may effect local performance. Many man-hours and CPU-hours are currently spent in modeling such problems. With the structural zooming technique, it is now possible to design an integrated program which allows the analyst to interactively focus upon a small region of interest, to modify the local geometry, and then to obtain highly accurate responses in that region which reflect both the properties of the overall structure and the local detail. A boundary integral equation analysis program, called BOAST, was recently developed for the stress analysis of cracks. This program can accurately analyze two-dimensional linear elastic fracture mechanics problems with far less computational effort than existing finite element codes. An interactive computer graphical interface to BOAST was written. The graphical interface would have several requirements: it would be menu-driven, with mouse input; all aspects of input would be entered graphically; the results of a BOAST analysis would be displayed pictorially but also the user would be able to probe interactively to get numerical values of displacement and stress at desired locations within the analysis domain; the entire procedure would be integrated into a single, easy to use package; and it would be written using calls to the graphic package called HOOPS. The program is nearing completion. All of the preprocessing features are working satisfactorily and were debugged. The postprocessing features are under development, and rudimentary postprocessing should be available by the end of the summer. The program was developed and run on a VAX workstation, and must be ported to the SUN workstation. This activity is currently underway.
The lethargy-dependent equations of the consistent Pl approximation to the Boltzmann transport equation for slowing down neutrons have been used as the basis of an IBM 704 computer program. Some of the effects included are (1) linearly anisotropic center of mass elastic scattering, (2) heavy element inelastic scattering based on the evaporation model of the nucleus, and (3) optional variation of the buckling with lethargy. The microscopic cross-section data developed for this program covered 473 lethargy points from lethargy u = 0 (10 Mev) to u = 19.8 (0.025 ev). The value of the fission neutron age in water calculated here is 26.5 square centimeters; this value is to be compared with the recent experimental value given as 27.86 square centimeters. The Fourier transform of the slowing-down kernel for water to indium resonance energy calculated here compared well with the Fourier transform of the kernel for water as measured by Hill, Roberts, and Fitch. This method of calculation has been applied to uranyl fluoride - water solution critical assemblies. Theoretical results established for both unreflected and fully reflected critical assemblies have been compared with available experimental data. The theoretical buckling curve derived as a function of the hydrogen to uranium-235 atom concentration for an energy-independent extrapolation distance was successful in predicting the critical heights of various unreflected cylindrical assemblies. The critical dimensions of fully water-reflected cylindrical assemblies were reasonably well predicted using the theoretical buckling curve and reflector savings for equivalent spherical assemblies.
The equations of motion program L217 (EOM) is described. The program formulates the matrix coefficients for a second order linear differential equation which describes the motion of an airplane relative to its level equilibrium flight condition. Aerodynamic data from FLEXSTAB or Doublet Lattice (L216) programs are used to derive the equations for quasi-steady or complete unsteady aerodynamics.
Inverse methods for estimating the surface ciculation of the equatorial Pacific by combining a linear reduced-gravity shallow-water model with the Tropical Ocean-Global Atmosphere ship-of-opportunity expendable bathythermograph (TOGA SOP XBT) observing program are examined. It is demonstrated that a simple linear model of the upper circulation of the equatorial Pacific can be successfully used as a weak constraint when smoothing the TOGA SOP XBT data. A circulation is sought as the weighted least squares fit to the dynamics and the data. The solution method is an expansion in representer functions, and the generalized inverse problem is thereby reduced from a functional problem to an algebraic problem for the coefficients of the representer. A specific inverse calculation using synthetic forcing and data is presented.
Formulations and algorithms implemented in the MHOST finite element program are discussed. The code uses a novel concept of the mixed iterative solution technique for the efficient 3-D computations of turbine engine hot section components. The general framework of variational formulation and solution algorithms are discussed which were derived from the mixed three field Hu-Washizu principle. This formulation enables the use of nodal interpolation for coordinates, displacements, strains, and stresses. Algorithmic description of the mixed iterative method includes variations for the quasi static, transient dynamic and buckling analyses. The global-local analysis procedure referred to as the subelement refinement is developed in the framework of the mixed iterative solution, of which the detail is presented. The numerically integrated isoparametric elements implemented in the framework is discussed. Methods to filter certain parts of strain and project the element discontinuous quantities to the nodes are developed for a family of linear elements. Integration algorithms are described for linear and nonlinear equations included in MHOST program.
Computed tomography (CT) inspection was performed on test articles additively manufactured from metallic materials. Metallic AM and machined wrought alloy test articles with programmed flaws and geometric features were inspected using a 2-megavolt linear accelerator based CT system. Performance of CT inspection on identically configured wrought and AM components and programmed flaws was assessed to determine the impact of additive manufacturing on inspectability of objects with complex geometries.
System of processor programs performs stress, buckling, and vibrational analysis of large linear finite element systems in excess of 50,000 degrees of freedom, while minimizing processing cost, execution time, central memory storage, and secondary data storage requirements. Programs use sparse matrix solution techniques and other computational and data management procedures.
This software consists of a set of application programs that support ground-based image processing for in situ missions. These programs represent a collection of utility routines that perform miscellaneous functions in the context of the ground data system. Each one fulfills some specific need as determined via operational experience. The most unique aspect to these programs is that they are integrated into the large, in situ image processing system via the PIG (Planetary Image Geometry) library. They work directly with space in situ data, understanding the appropriate image meta-data fields and updating them properly. The programs themselves are completely multimission; all mission dependencies are handled by PIG. This suite of programs consists of: (1)marscahv: Generates a linearized, epi-polar aligned image given a stereo pair of images. These images are optimized for 1-D stereo correlations, (2) marscheckcm: Compares the camera model in an image label with one derived via kinematics modeling on the ground, (3) marschkovl: Checks the overlaps between a list of images in order to determine which might be stereo pairs. This is useful for non-traditional stereo images like long-baseline or those from an articulating arm camera, (4) marscoordtrans: Translates mosaic coordinates from one form into another, (5) marsdispcompare: Checks a Left Right stereo disparity image against a Right Left disparity image to ensure they are consistent with each other, (6) marsdispwarp: Takes one image of a stereo pair and warps it through a disparity map to create a synthetic opposite- eye image. For example, a right eye image could be transformed to look like it was taken from the left eye via this program, (7) marsfidfinder: Finds fiducial markers in an image by projecting their approximate location and then using correlation to locate the markers to subpixel accuracy. These fiducial markets are small targets attached to the spacecraft surface. This helps verify, or improve, the pointing of in situ cameras, (8) marsinvrange: Inverse of marsrange . given a range file, re-computes an XYZ file that closely matches the original. . marsproj: Projects an XYZ coordinate through the camera model, and reports the line/sample coordinates of the point in the image, (9) marsprojfid: Given the output of marsfidfinder, projects the XYZ locations and compares them to the found locations, creating a report showing the fiducial errors in each image. marsrad: Radiometrically corrects an image, (10) marsrelabel: Updates coordinate system or camera model labels in an image, (11) marstiexyz: Given a stereo pair, allows the user to interactively pick a point in each image and reports the XYZ value corresponding to that pair of locations. marsunmosaic: Extracts a single frame from a mosaic, which will be created such that it could have been an input to the original mosaic. Useful for creating simulated input frames using different camera models than the original mosaic used, and (12) merinverter: Uses an inverse lookup table to convert 8-bit telemetered data to its 12-bit original form. Can be used in other missions despite the name.
A simple non-linear circuit model for battery behavior is given. It is based on time-dependent features of the well-known PIN change storage diode, whose behavior is described by equations similar to those associated with electrochemical cells. The circuit simulation computer program ADVICE was used to predict non-linear response from a topological description of the battery analog built from advice components. By a reasonable choice of one set of parameters, the circuit accurately simulates a wide spectrum of measured non-linear battery responses to within a few millivolts.
Trends toward the automation of the design process for airplanes and missiles accentuate the need for analytic techniques for the prediction of aerodynamic characteristics. A number of computer codes have been developed or are under development which show promise of significantly improving the estimation of aerodynamic characteristics for arbitrarily-shaped bodies at supersonic speeds. The programs considered range in complexity from a simple linearized solution employing slender body theory to an exact finite difference solution of the Euler equations. The results from five computer codes are compared with experimental data to determine the accuracy, range of applicability, ease of use, and computer time and cost of the programs. The results provide a useful guide for selecting the appropriate method for treating bodies at the various levels of an automated design process.
Method works for linear and nonlinear systems. Finite-element-based computer program developed to analyze free and forced response of multishaft rotor-bearing systems. Acronym, ARDS, denotes Analysis of Rotor Dynamic Systems. Systems with nonlinear interconnection or support bearings or both analyzed by numerically integrating reduced set of coupledsystem equations. Linear systems analyzed in closed form for steady excitations and treated as equivalent to nonlinear systems for transient excitation. ARDS is FORTRAN program developed on an Amdahl 470 (similar to IBM 370).
Principles for the design and stability of a spacecraft on-orbit attitude control system employing on-off Reaction Control System (RCS) thrusters is presented. Both the vehicle dynamics and the control system actuators are inherently nonlinear, hence traditional linear control system design approaches are not directly applicable. This paper has three main aspects: It summarizes key RCS control System design principles from the Space Shuttle and Space Station programs, it demonstrates a new approach to develop a linear model of a phase plane control system using describing functions, and applies each of these to the initial development of the NASA's next generation of upper stage vehicles. Topics addressed include thruster hardware specifications, phase plane design and stability, jet selection approaches, filter design metrics, and automaneuver logic.