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A procedure which provides sonic-boom-minimizing equivalent area distributions for supersonic cruise conditions is described. This work extends previous analyses to permit relaxation of the extreme bluntness required by conventional low-boom shapes and includes propagation in a real atmosphere. The procedure provides area distributions which minimize either shock strength or overpressure.
Exact analytical solutions in terms of induced drag influence coefficients can be attained which define the spanwise loading with minimized induced drag, subject to specified constraint conditions, for any nonplanar wing shape or number of lift plus wing bending moment about a given wing span station. Example applications of the theory are made to a biplane, a wing in ground effect, a cruciform wing, a V-wing, a planar-wing winglet, and linked wingtips in formation flying. For minimal induced drag, the spanwise loading, relative to elliptic, is outboard for the biplane and is inboard for the wing in ground effect and for the planar-wing winglet. A spinoff of the triplane solution provides mathematically exact equations for downwash and sidewash about a planar vorticity sheet having an arbitrary loading distribution.
This paper identifies the potential for unconstrained minimization algorithms of mathematical programming to be cost-effective with other conventional techniques of transient nonlinear structural analysis. With this in mind the authors have attempted to critically evaluate a few of the most commonly used algorithms for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth order, first order and second order depending upon the order of the derivative of the function called for by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives derived on the basis of finite difference operations clearly suggest using analytically derived derivatives to obtain better control on the number of minimizations required for convergence to the exact solution.
The Langley unitary plan unitary plan wind tunnel was used to determine the validity of a sonic-boom-minimization theory. Five models - two reference and three low-boom constrained - were tested at design Mach numbers of 1.5 and 2.7. Results show that the pressure signatures generated by the low-boom models had significantly lower overpressure levels than those produced by the reference models and that small changes in the Mach number and/or the lift caused relatively small changes in the signature shape and overpressure level. Boundary-layer effects were found in the signature shape and overpressure level. Boundary-layer effects were found to be sizable on the low-boom models, and when viscous corrections were included in the analysis, improved agreement between the predicted and the measured signatures was noted. Since this agreement was better at Mach 1.5 than at Mach 2.7, it was concluded that the minimization method was definitely valid at Mach 1.5 and was probably valid at Mach 2.7, with further work needed to resolve the uncertainty.
The formulation basis for establishing the static or dynamic equilibrium configurations of finite element models of structures which may behave in the nonlinear range are provided. With both geometric and time independent material nonlinearities included, the development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. Representations of a rigid link and an impenetrable contact plane are added to the deformation model so that any number of nodes of the finite element model may be connected by a rigid link or may contact the plane. Equilibrium configurations are derived as the stationary conditions of a potential function of the generalized nodal variables of the model. Minimization of the nonlinear potential function is achieved by using the best current variable metric update formula for use in unconstrained minimization. Powell's conjugate gradient algorithm, which offers very low storage requirements at some slight increase in the total number of calculations, is the other alternative algorithm to be used for extremely large scale problems.
The effectiveness of using minimization techniques for the solution of nonlinear structural analysis problems is discussed and demonstrated by comparison with the conventional pseudo force technique. The comparison involves nonlinear problems with a relatively few degrees of freedom. A survey of the state-of-the-art of algorithms for unconstrained minimization reveals that extension of the technique to large scale nonlinear systems is possible.
The relative merits and demerits of the minimization techniques are assessed using globally convergent quasi-Newton algorithms on the one hand and the homotopy algorithms on the other hand for the solution of problems of nonlinear structural analysis. Like the homotopy algorithms, the globally convergent quasi-Newton algorithms are equally suited for the solution of the nonlinear equations of structural analysis directly without having to pose the problem as an equivalent minimization problem. In the close neighborhood of the limit and bifurcation points quasi-Newton algorithms experience difficulties. Homotopy algorithms are robust for practically all types of nonlinear problems but are computationally not as cost effective since they provide an extremely accurate prediction of the response by calculating it as a large number of points. Globally convergent algorithms can perform well with very approximate Hessians, while homotopy algorithms require extremely accurate Hessians. While quasi-Newton algorithms can be very easily structured to exploit sparsity and symmetry, homotopy algorithms are not presently so structured and would require special modifications for exploitation of such features without sacrificing robustness and global convergence.
An objective analysis procedure is presented which combines Seasat-A satellite scatterometer (SASS) data with other available data on wind speeds by minimizing an objective function of gridded wind speed values. The functions are defined as the loss functions for the SASS velocity data, the forecast, the SASS velocity magnitude data, and conventional wind speed data. Only aliases closest to the analysis were included, and a method for improving the first guess while using a minimization technique and slowly changing the parameters of the problem is introduced. The model is employed to predict the wind field for the North Atlantic on Sept. 10, 1978. Dealiased SASS data is compared with available ship readings, showing good agreement between the SASS dealiased winds and the winds measured at the surface. Expansion of the model to take in low-level cloud measurements, pressure data, and convergence and cloud level data correlations is discussed.
Instead of using the criterion of maximum free distance, (df) or the maximum (df) with minimizing a few first distance profiles, short constraint length rate 1/N convolution codes were searched using a criterion of minimizing required bit energy-to-noise density ratio, E(b)/N(o), for a given value of desired bit error rate (BER), for the goodness of a code. The considered channel was binary antipodal signaling over additive white Gaussian noise and no quantization at the channel output. For the BER calculations, the transfer function bounding technique was used. Partial searches were performed using some known facts and a very useful idea that "good codes generate good codes.'' That is, for a given constraint length K, good rate 1/(N + 1) codes can be found by extending the code generator matrices of good rate 1/N codes. The code search results are tabulated for 3 or = K or = 7 and 2 or = N or = 8. For many pairs of K and N, the new codes are shown to save 0.1 to 0.4 dB in the required E(b)/N(o) compared to previously reported codes. Additionally, the benefits of coding bandwidth expansion are confirmed with the new codes.
An automated procedure to lessen the tedium of manual approach currently used to minimize surface distortions in a hoop/column antenna is studied. Three fundamental elements are used for the study: (1) The finite element analysis program is used to calculate the antenna surface distortions due to externally applied loads; (2) a general purpose optimization program is used to determine the set of control cable tensions which minimize the antenna surface distortions; and (3) another program is used to calculate the best fit parabola passing through a distorted antenna shape and to calculate the RMS distortion error. The interim results of this feasibility study are given.
The problem of minimal time detection of abrupt parameter changes in linear stochastic systems considered. The problem is posed as an optimal stopping problem for the detection in change of the induced probability measure. Under the assumption of a prior distribution for the time of change (or disruption) a stopping rule is given which minimizes the average detection delay when there is knowledge of the new measure after the change. When the new induced measure is unknown, a stopping rule is given, based only on the noisy observations and is shown to be better than the a priori knowlege of the disruption time.
The minimal cosmic background radiation (CBR) anisotropy implied by the presence of peculiar motions of a given amplitude on some specified scale is calculated using a new, power spectrum-independent approach. If the tentative evidence for deviations from the Hubble flow of magnitude delta V/V roughly 0.1 at V roughly 5000 km/s is confirmed, microwave background fluctuations with a coherence scale of about 2 deg and dispersion delta T/T greater than 10 to the -5th are predicted. It is found that the existing upper limits on delta T/T are not inconsistent with v(r) = 500 km/s at r = 50/h Mpc. A reduction of the observational limits on the CBR anisotropy below the authors' minimal predictions for delta T/T would challenge the current interpretation of measurements of deviations from the Hubble flow. Gravitational instability without reheating as a mechanism for generation of the large-scale structure of the universe would be in severe difficulty.
Mathematical analysis of the minimization of spacecraft fuel usage for both impulsive and finite motor burns is presented. A high precision integrated trajectory search program (SEPV) and several optimization software libraries are used to solve minimum fuel usage problems. The SEPV program has the capacity to vary either the initial spacecraft state or the finite burn parameters to acquire a specified set of target values. Several test examples for the Voyager 2 Uranus Encounter and the Galileo Jupiter Orbiter are presented to show that spacecraft fuel consumption can be minimized in targeting maneuver strategies. The fuel savings achieved by the optimum solution can be significant.
Results are presented from a computer simulation comparing two statistical fitting techniques on data samples with large and small counts per bin; the results are then related specifically to X-ray astronomy. The Marquardt and Powell minimization techniques are compared by using both to minimize the chi-squared statistic. In addition, Cash's C statistic is applied, with Powell's method, and it is shown that the C statistic produces better fits in the low-count regime than chi-squared.
Most finite element packages provide means to generate meshes automatically. However, the user is usually confronted with the problem of not knowing whether the mesh generated is appropriate for the problem at hand. Since the accuracy of the finite element results is mesh dependent, mesh selection forms a very important step in the analysis. Indeed, in accurate analyses, meshes need to be refined or rezoned until the solution converges to a value so that the error is below a predetermined tolerance. A-posteriori methods use error indicators, developed by using the theory of interpolation and approximation theory, for mesh refinements. Some use other criterions, such as strain energy density variation and stress contours for example, to obtain near optimal meshes. Although these methods are adaptive, they are expensive. Alternatively, a priori methods, until now available, use geometrical parameters, for example, element aspect ratio. Therefore, they are not adaptive by nature. An adaptive a-priori method is developed. The criterion is that the minimization of the trace of the stiffness matrix with respect to the nodal coordinates, leads to a minimization of the potential energy, and as a consequence provide a good starting mesh. In a few examples the method is shown to provide the optimal mesh. The method is also shown to be relatively simple and amenable to development of computer algorithms. When the procedure is used in conjunction with a-posteriori methods of grid refinement, it is shown that fewer refinement iterations and fewer degrees of freedom are required for convergence as opposed to when the procedure is not used. The mesh obtained is shown to have uniform distribution of stiffness among the nodes and elements which, as a consequence, leads to uniform error distribution. Thus the mesh obtained meets the optimality criterion of uniform error distribution.
Inaccuracies in the length of members and the diameters of joints of large space structures may produce unacceptable levels of surface distortion and internal forces. Here, two discrete optimization problems are formulated, one to minimize surface distortion (DSQRMS) and the other to minimize internal forces (FSQRMS). Both of these problems are based on the influence matrices generated by a small-deformation linear analysis. Good solutions are obtained for DSQRMS and FSQRMS through the use of a simulated annealing heuristic.
Recent research has shown an artificial neural network (ANN) to be capable of pattern recognition and the classification of image data. This paper examines the potential for the application of neural network computing to satellite image processing. A second objective is to provide a preliminary comparison and ANN classification. An artificial neural network can be trained to do land-cover classification of satellite imagery using selected sites representative of each class in a manner similar to conventional supervised classification. One of the major problems associated with recognition and classifications of pattern from remotely sensed data is the time and cost of developing a set of training sites. This reseach compares the use of an ANN back propagation classification procedure with a conventional supervised maximum likelihood classification procedure using a minimal training set. When using a minimal training set, the neural network is able to provide a land-cover classification superior to the classification derived from the conventional classification procedure. This research is the foundation for developing application parameters for further prototyping of software and hardware implementations for artificial neural networks in satellite image and geographic information processing.
A method is developed for the minimization of gear tooth surface deviations between theoretical and real surfaces for the improvement of precision of surface manufacture. Coordinate measurement machinery is used to determine a grid of surface coordinates. Theoretical calculations are made for the grid points. A least-square method is used to minimize the deviations between real and theoretical surfaces by altering the manufacturing machine-tool settings. An example is given for a hypoid gear.