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Various features of the solutions of Duffing's equation are described using a representation of the solutions in the Laplace-Borel transform domain. An application of this technique is illustrated for the symmetry-breaking bifurcation of a hard spring.
A Lagrange multiplier method using techniques developed by Bertsekas (1982) was applied to solving the problem of enforcing simultaneous conservation of the nonlinear integral invariants of the shallow water equations on a limited area domain. This application of nonlinear constrained optimization is of the large dimensional type and the conjugate gradient method was found to be the only computationally viable method for the unconstrained minimization. Several conjugate-gradient codes were tested and compared for increasing accuracy requirements. Robustness and computational efficiency were the principal criteria.
A deconvolution method is presented for estimating input data from measured output data and a model of the dynamic process involved. The method uses an optimal Wiener filter for separating the measured data into signal and noise components, and a high-accuracy Fourier transform for inverting the model dynamics in the frequency domain. The method is an extension of optimal Fourier smoothing, and uses a technique to enhance the contrast between the signal and noise spectra in designing the Wiener filter. The deconvolution method was applied to simulation and flight test data for the purposes of removing unwanted distortions introduced by signal-conditioning filters and sensor dynamics, and for reconstructing turbulence inputs from measured sensor data. Results indicated hat the method performs well given good signal-to-noise levels and accurate models of the dynamic process.
A computational procedure for describing transport of electrons in condensed media has been formulated for application to effects and exposures from spectral distributions typical of electrons trapped in planetary magnetic fields. The procedure is based on earlier parameterizations established from numerous electron beam experiments. New parameterizations have been derived that logically extend the domain of application to low molecular weight (high hydrogen content) materials and higher energies (approximately 50 MeV). The production and transport of high energy photons (bremsstrahlung) generated in the electron transport processes have also been modeled using tabulated values of photon production cross sections. A primary purpose for developing the procedure has been to provide a means for rapidly performing numerous repetitive calculations essential for electron radiation exposure assessments for complex space structures. Several favorable comparisons have been made with previous calculations for typical space environment spectra, which have indicated that accuracy has not been substantially compromised at the expense of computational speed.
A description is given of UNICORN, a prototype system developed for the purpose of investigating artificial intelligence (AI) concepts supporting spacecraft autonomy. UNICORN employs thematic reasoning, of the type first described by Rodger Schank of Northwestern University, to allow the context-sensitive control of multiple intelligent agents within a blackboard based environment. In its domain of application, UNICORN demonstrates the ability to reason teleologically with focused knowledge. Also presented are some of the lessons learned as a result of this effort. These lessons apply to any effort wherein system level autonomy is the objective.
The 'variation-iteration' method using Green's functions to find the eigenvalues and the corresponding eigenfunctions of a homogeneous Fredholm integral equation is employed for the stability analysis of fluid hydromechanics problems with a semiinfinite (infinite) domain of application. The objective of the study is to develop a suitable numerical approach to the solution of such equations in order to better understand the full set of equations for 'real-world' flow models. The study involves a search for a suitable value of the length of the domain which is a fair finite approximation to infinity, which makes the eigensolution an approximation dependent on the length of the interval chosen. In the examples investigated y = 1 = a seems to be the best approximation of infinity; for y greater than unity this method fails due to the polynomial nature of Green's functions.
Self-adaptive mesh refinement dynamically matches the computational demands of a solver for partial differential equations to the activity in the application's domain. In this paper we present two C++ class libraries, P++ and AMR++, which significantly simplify the development of sophisticated adaptive mesh refinement codes on (massively) parallel distributed memory architectures. The development is based on our previous research in this area. The C++ class libraries provide abstractions to separate the issues of developing parallel adaptive mesh refinement applications into those of parallelism, abstracted by P++, and adaptive mesh refinement, abstracted by AMR++. P++ is a parallel array class library to permit efficient development of architecture independent codes for structured grid applications, and AMR++ provides support for self-adaptive mesh refinement on block-structured grids of rectangular non-overlapping blocks. Using these libraries, the application programmers' work is greatly simplified to primarily specifying the serial single grid application and obtaining the parallel and self-adaptive mesh refinement code with minimal effort. Initial results for simple singular perturbation problems solved by self-adaptive multilevel techniques (FAC, AFAC), being implemented on the basis of prototypes of the P++/AMR++ environment, are presented. Singular perturbation problems frequently arise in large applications, e.g. in the area of computational fluid dynamics. They usually have solutions with layers which require adaptive mesh refinement and fast basic solvers in order to be resolved efficiently.
A time-domain finite element method is developed for optimal control problems. The theory derived is general enough to handle a large class of problems including optimal control problems that are continuous in the states and controls, problems with discontinuities in the states and/or system equations, problems with control inequality constraints, problems with state inequality constraints, or problems involving any combination of the above. The theory is developed in such a way that no numerical quadrature is necessary regardless of the degree of nonlinearity in the equations. Also, the same shape functions may be employed for every problem because all strong boundary conditions are transformed into natural or weak boundary conditions. In addition, the resulting nonlinear algebraic equations are very sparse. Use of sparse matrix solvers allows for the rapid and accurate solution of very difficult optimization problems. The formulation is applied to launch-vehicle trajectory optimization problems, and results show that real-time optimal guidance is realizable with this method. Finally, a general problem solving environment is created for solving a large class of optimal control problems. The algorithm uses both FORTRAN and a symbolic computation program to solve problems with a minimum of user interaction. The use of symbolic computation eliminates the need for user-written subroutines which greatly reduces the setup time for solving problems.
An open-source scalar package and associated software tools have been developed in the Scala programming language, including plotting tools based on the free GRACE plotting package. The scalar package represents physical scalars and can help to prevent errors involving physical units in engineering and scientific computation. The scalar package includes a complete implementation of the standard SI metric system of units and many common non-metric units. The design also allows users to easily de ne a specialized or reduced set of physical units for any particular application or domain. The scalar package can be used in two different modes: one mode provides unit compatibility checking but is slower, and the other mode bypasses the compatibility checks but is much faster and still prevents the most common type of unit error. Switching between the two modes requires no changes in the user's code, making it convenient and usable with no significant performance penalty for even the most computationally intensive applications.
The Linked Windows Interactive Data System (LinkWinds) is a prototype visual data exploration system resulting from a NASA Jet Propulsion Laboratory (JPL) program of research into the application of graphical methods for rapidly accessing, displaying, and analyzing large multi variate multidisciplinary data sets. Running under UNIX it is an integrated multi-application executing environment using a data-linking paradigm to dynamically interconnect and control multiple windows containing a variety of displays and manipulators. This paradigm, resulting in a system similar to a graphical spreadsheet, is not only a powerful method for organizing large amounts of data for analysis, but leads to a highly intuitive, easy-to-learn user interface. It provides great flexibility in rapidly interacting with large masses of complex data to detect trends, correlations, and anomalies. The system, containing an expanding suite of non-domain-specific applications, provides for the ingestion of a variety of data base formats and hard -copy output of all displays. Remote networked workstations running LinkWinds may be interconnected, providing a multiuser science environment (MUSE) for collaborative data exploration by a distributed science team. The system is being developed in close collaboration with investigators in a variety of science disciplines using both archived and real-time data. It is currently being used to support the Microwave Limb Sounder (MLS) in orbit aboard the Upper Atmosphere Research Satellite (UARS). This paper describes the application of LinkWinds to this data to rapidly detect features, such as the ozone hole configuration, and to analyze correlations between chemical constituents of the atmosphere.
Direct solvers currently dominate commercial finite element structural software, but do not scale well in the fine granularity regime targeted by emerging parallel processors. Substructure based iterative solvers--often called also domain decomposition algorithms--lend themselves better to parallel processing, but must overcome several obstacles before earning their place in general purpose structural analysis programs. One such obstacle is the solution of systems with many or repeated right hand sides. Such systems arise, for example, in multiple load static analyses and in implicit linear dynamics computations. Direct solvers are well-suited for these problems because after the system matrix has been factored, the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions. On the other hand, iterative solvers in general are ill-suited for these problems because they often must restart from scratch for every different right hand side. In this paper, we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides. Basically, we formulate the overall problem as a series of minimization problems over K-orthogonal and supplementary subspaces, and tailor the preconditioned conjugate gradient algorithm to solve them efficiently. The resulting solution method is scalable, whereas direct factorization schemes and forward and backward substitution algorithms are not. We illustrate the proposed methodology with the solution of static and dynamic structural problems, and highlight its potential to outperform forward and backward substitutions on parallel computers. As an example, we show that for a linear structural dynamics problem with 11640 degrees of freedom, every time-step beyond time-step 15 is solved in a single iteration and consumes 1.0 second on a 32 processor iPSC-860 system; for the same problem and the same parallel processor, a pair of forward/backward substitutions at each step consumes 15.0 seconds.
A technique is described for designing feedback control systems using frequency domain models, a quadratic cost function, and a parameter optimization computer program. FORTRAN listings for the computer program are included. The approach is applied to the design of shock position controllers for a supersonic inlet. Deterministic or random system disturbances, and the presence of random measurement noise are considered. The cost function minimization is formulated in the time domain, but the problem solution is obtained using a frequency domain system description. A scaled and constrained conjugate gradient algorithm is used for the minimization. The approach to a supersonic inlet included the calculations of the optimal proportional-plus integral (PI) and proportional-plus-integral-plus-derivative controllers. A single-loop PI controller was the most desirable of the designs considered.
Application of domain tip logic in designing associative processors for spaceborne use
The question of image distribution reconstruction for coherent illumination of an object located in the aperture far zone is considered from first principles without postulating any particular optical spread function. The object function is mathematically modeled as a complex random function of angular coordinates, and it is assumed that the object distribution of interest is angularly limited to a certain a priori assigned field of view (FOV). A linear reconstruction procedure that is uniformly optimal in the FOV is established by using the methods of statistical estimation. Two special cases are examined: imaging a limited sector of a wide-angle random scene and objects in the FOV immersed in a wide-angle background of angular noise. It is noted that the domain of application of the reconstruction method is restricted to microwave frequencies.
A method is presented for the signature analysis of pulses by reconstructing in the time domain the shape of the pulse prior to its passing through the measurement system. This deconvolution technique is first evaluated using an idealized system and analytical pulse models and is shown to provide improved results. An experimental situation is then treated; system-component models are developed for the digitizer, tape recorder, filter, transducer and mechanical structure. To accommodate both calibration results and manufacturer's data, and to provide stable mathematical models entails considerable effort: some 30 parameters must be identified to model this system - which is still a substantial approximation - albeit of very high order. Experimental pulses generated by a ball drop, spark discharge and a tearing crack are then deconvoluted 'back through' the system as modeled, using this technique. These results are compared and indicate (a) that consistent shapes may be expected from a given type of source and (b) that some sources can be identified with greater clarity using the deconvolution approach.
QATT, a natural language interface developed for the Qualitative Process Engine (QPE) system is presented. The major goal was to evaluate the use of a preexisting natural language understanding system designed to be tailored for query processing in multiple domains of application. The other goal of QATT is to provide a comfortable environment in which to query envisionments in order to gain insight into the qualitative behavior of physical systems. It is shown that the use of the preexisting system made possible the development of a reasonably useful interface in a few months.
This report summarizes the findings and lessons learned from the development of an intelligent user interface for a space flight planning simulation program, in the specific area related to constraint-checking. The different functionalities of the Graphical User Interface part and of the rule-based part of the system have been identified. Their respective domain of applicability for error prevention and error checking have been specified.
The authors have previously introduced the concept of virtual reality worlds governed by artificial intelligence. Creation of an intelligent virtual reality was further proposed as a universal interface for the handicapped. This paper extends consideration of intelligent virtual realty to a context in which fuzzy set principles are explored as a major tool for implementing theory in the domain of applications to the disabled.