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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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This paper presents a framework for the study of the convergence properties of optimal control algorithms and illustrates its use by means of two examples. The framework consists of an algorithm prototype with a convergence theorem, together with some results in relaxed controls theory.
A fast sequency-ordered Walsh transform algorithm is presented; this sequency-ordered fast transform is complementary to the sequency-ordered fast Walsh transform introduced by Manz (1972) and eliminating gray code reordering through a modification of the basic fast Hadamard transform structure. The new algorithm retains the advantages of its complement (it is in place and is its own inverse), while differing in having a decimation-in time structure, accepting data in normal order, and returning the coefficients in bit-reversed sequency order. Applications include estimation of Walsh power spectra for a random process, sequency filtering and computing logical autocorrelations, and selective bit reversing.
Several algorithms have been developed for computing the potential and attraction of a simple density layer. These are numerical cubature, Taylor series, and a mixed analytic and numerical integration using a singularity-matching technique. A computer program has been written to combine these techniques for computing the disturbing acceleration on an artificial earth satellite. A total of 1640 equal-area, constant surface density blocks on an oblate spheroid are used. The singularity-matching algorithm is used in the subsatellite region, Taylor series in the surrounding zone, and numerical cubature on the rest of the earth.
The theory and applications are presented of a new image enhancement algorithm which refines computer classification maps of multispectral data. The refinement eliminates connected sets smaller than a prespecified size and merges them to the surrounding area. Conventional practices in forestry timber stand mapping requires small geographic areas to be absorbed by surrounding large areas to form homogeneous stands. This homogeneity is often incompatible with the statistical formulation of homogeneity. Elements within a timber stand which should be labeled as one feature often correspond to more than one class mapped by existing computer classification techniques. The new algorithm is designed to postprocess classification maps to result in more usable timber stand maps. The new image enhancement technique is compared with an accepted neighbor-checking postprocessing technique, demonstrating the superiority of the new technique for forestry stand mapping.
An algorithm for optimal design is given which incorporates several of the desirable features of both mathematical programming and optimality criteria, while avoiding some of the undesirable features. The algorithm proceeds by approaching the optimal solution through the solutions of an associated set of constrained optimal design problems. The solutions of the constrained problems are recognized at each stage through the application of optimality criteria based on energy concepts. Two examples are described in which the optimal member size and layout of a truss is predicted, given the joint locations and loads.
The author has identified the following significant results. Results show that the new algorithm produced cleaner classification maps in which holes of small predesignated sizes were eliminated and significant boundary information was preserved. These cleaner post-processed maps better resemble true life timber stand maps and are thus more usable products than the pre-post-processing ones: Compared to an accepted neighbor-checking post-processing technique, the new algorithm is more appropriate for timber stand mapping.
A stochastic approximation algorithm for estimating the proportions in a mixture of normal densities is presented. The algorithm is shown to converge to the true proportions in the case of a mixture of two normal densities.
An algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
THe Collins-Loos algorithm for computing isolating intervals for the zeros of an integer polynomial requires the evaluation of polynomials at rational points. This implies the use of arbitrary precision integer arithmetic. It is shown how careful use of single precision, floating point arithmetic within the context of a slightly modified algorithm can make the calculation considerably faster and no less exact. Typically, 95% or more of the evaluations can be done without exact arithmetic. The precise speedup depends on the relative costs of the arithmetic in a given implementation. The implementation on DEC KL-10 computer is some 5 to 10 times faster than the original Univac 1110 implementation in SAC-I.
A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.
A computationally fast algorithm for approximating the amplitude (A) of a quadrature pair (I,Q) has been discovered. The piecewise linear formula, the unbiased estimate of A=X+1/8y when X or = 3Y and 7/8X + 1/2Y when X or = 3Y applies where X is congruent to the maximum absolute value of (I,Q) and Y is congruent to the minimum absolute value of (I,Q). This algorithm has been proven to be far more accurate then currently used approximations. An immediate application is the wideband digital spectrum analyzer under development for monitoring radio frequency interference at Deep Space Network stations.
Minimum time accelerations of aircraft turbofan engines are presented. The calculation of these accelerations was made by using a piecewise linear engine model, and an algorithm based on nonlinear programming. Use of this model and algorithm allows such trajectories to be readily calculated on a digital computer with a minimal expenditure of computer time.
The filtering algorithm for processing integral measurements is extended to include analog type prefilters with infinite memory, and to include sequential processing of prefiltered data in multi-sensor, multi-sample rate systems. The extension to infinite memory prefilters requires serial decorrelation of the prefilter output prior to state estimation. These algorithms provide a technique for investigation of prefilter parameter sensitivities, and provide optimal compensation for any information loss due to prefiltering.
Signature extension is intended to increase the space-time range over which a set of training statistics can be used to classify data without significant loss of recognition accuracy. A first cluster matching algorithm MASC (Multiplicative and Additive Signature Correction) was developed at the Environmental Research Institute of Michigan to test the concept of using associations between training and recognition area cluster statistics to define an average signature transformation. A more recent signature extension module CROP-A (Cluster Regression Ordered on Principal Axis) has shown evidence of making significant associations between training and recognition area cluster statistics, with the clusters to be matched being selected automatically by the algorithm.
Analytical redundancy is applied to the pitch axis of an aircraft to enhance sensor fault detection. Three different designs based on monitoring Kalman filter residuals or likelihood functions were developed. Sensor failures were simulated to evaluate the performance of the algorithms on a nonlinear simulation of an F-8C aircraft. Based on requirements for sensor fault detection and preliminary simulator performance it is concluded that these algorithms have the potential for reducing the level of sensor redundancy in a digital flight control system without compromising performance.
Two methods for stabilizing constant linear systems, namely, the extended Bass algorithm for continuous systems and a discrete system analog, are discussed. For the continuous algorithm, a new result on the degree of stability of the closed-loop eigenvalues is presented, and for both methods, typical results and asymptotic trends in the data are illustrated through an example computation.
A high-radix FFT algorithm for computing transforms over FFT, where q is a Mersenne prime, is developed to implement fast circular convolutions. This new algorithm requires substantially fewer multiplications than the conventional FFT.
A fundamental requirement for ground analysis of onboard attitude control systems is the determination of the time evolution of spacecraft angular orientation and velocity, and of external torques acting on the spacecraft. However, at times, there are limitations on the data received on the ground, and essential but missing variables must be estimated. This paper contains a description of the design and implementation of an algorithm for angular position, velocity, and torque estimation. The algorithm has been used to analyze the performance of the Viking Orbiter attitude control system. Typical results of this analysis are presented.