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The study of time-dependent flows generated by surface-tension gradients in thin liquid layers is reported. Numerical techniques for dealing with the complete float-zone process were investigated. In particular, finite element methods with fast iterative procedures, using multipoint constraints and nonlinear optimization were examined.
This paper presents a data analysis technique that has been developed to support a stratospheric ozone measurement and profiling program. The data consist of solar backscattered UV radiation monitored by a spacecraft. The output consists of ozone mixing ratio profiles complete with error bars throughout the atmosphere. The technique is based upon principles of nonlinear optimal estimation. It provides a number of desirable features that have not been available together in any previously constructed technique for the problem. Iteration on both radiation measurements and total ozone measurements is among these features.
A simple, two dimensional, incompressible and inviscid model for the problem posed by a two dimensional wing with a jet issuing from its lower surface is considered and a parametric analysis is carried out to observe how the aerodynamic characteristics depend on the different parameters. The mathematical problem constitutes a boundary value problem where the position of part of the boundary is not known a priori. A nonlinear optimization approach was used to solve the problem, and the analysis reveals interesting characteristics that may help to better understand the physics involved in more complex situations in connection with high lift systems.
A low-cost collision hazard warning system suitable for implementation in both general and commercial aviation is presented. Laser beacon systems are used as sources of accurate relative position information that are not dependent on communication between aircraft or with the ground. The beacon system consists of a rotating low-power laser beacon, detector arrays with special optics for wide angle acceptance and filtering of solar background light, microprocessors for proximity and relative trajectory computation, and pilot displays of potential hazards. The laser beacon system provides direct measurements of relative aircraft positions; using optimal nonlinear estimation theory, the measurements resulting from the current beacon sweep are combined with previous data to provide the best estimate of aircraft proximity, heading, minimium passing distance, and time to closest approach.
A nonlinear optimization algorithm is developed which combines the best features of the Method of Feasible Directions and the Generalized Reduced Gradient Method. This algorithm utilizes the direction-finding sub-problem from the Method of Feasible Directions to find a search direction which is equivalent to that of the Generalized Reduced Gradient Method, but does not require the addition of a large number of slack variables associated with inequality constraints. This method provides a core-efficient algorithm for the solution of optimization problems with a large number of inequality constraints. Further optimization efficiency is derived by introducing the concept of infrequent gradient calculations. In addition, it is found that the sensitivity of the optimum design to changes in the problem parameters can be obtained using this method without the need for second derivatives or Lagrange multipliers. A numerical example is given in order to demonstrate the efficiency of the algorithm and the sensitivity analysis.
Papers prepared for the use of the U.S. delegation to the 1979 World Administrative Radio Conference; papers contributed to the National CCIR study groups on broadcasting satellites and spectrum-orbit utilization; responses to specific requests for technical analyses and evaluations; and papers presented at technical conferences on related topics are presented. Nonlinear optimization methods for finding optimum positions of satellites in the fixed satellite service; the effects of geography on the use of the geostationary orbit; intercontinental orbit sharing; traffic coordination in interfering satellites operating in the fixed satellite service; and domestic fixed and broadcasting satellite systems are covered. A possible channel orbit plan for broadcasting satellite service in the U.S. and Canada; polarization for broadcasting satellite systems; and the communication capacity of the geostationary satellite orbit are also examined.
An important but relatively uninvestigated problem in remote sensing is the inversion of vegetative canopy reflectance models to obtain agrophysical parameters, given measured reflectances. The problem is here formally defined and its solution outlined. Numerical nonlinear optimization techniques are used to implement this inversion to obtain the leaf area index using Suits' canopy reflectance model. The results for a variety of cases indicate that this can be done successfully using infrared reflectances at different views or azimuth angles or a combination thereof. The other parameters of the model must be known, although reasonable measurement errors can be tolerated without seriously degrading the accuracy of the inversion. The application of the technique to ground based remote-sensing experiments is potentially useful, but is limited to the degree to which the canopy reflectance model can accurately predict observed reflectances.
A dynamic force sensing method is proposed for a robot manipulator. A 6-axis wrist force sensor which is commonly used for robot force sensing does not take the direct measurement of the force and moment applied to an end effector externally from the environment of the manipulator, but takes the resultant of the gravity, the inertial force and moment on the end effector, and the external force and moment. The separation of gravitational and inertial force and moment from the measurement of the force sensor is crucial to achieving dynamically accurate force sensing and fast manipulator motion under force feedback control. A mathematical model is derived for the force sensing process and the separation of the force and moment as a nonlinear optimal state estimation problem formulated. Then an approximate solution is given using extended Kalman filtering techniques.
A competition-based connectionist model for solving diagnostic problems is described. The problems considered are computationally difficult in that (1) multiple disorders may occur simultaneously and (2) a global optimum in the space exponential to the total number of possible disorders is sought as a solution. The diagnostic problem is treated as a nonlinear optimization problem, and global optimization criteria are decomposed into local criteria governing node activation updating in the connectionist model. Nodes representing disorders compete with each other to account for each individual manifestation, yet complement each other to account for all manifestations through parallel node interactions. When equilibrium is reached, the network settles into a locally optimal state. Three randomly generated examples of diagnostic problems, each of which has 1024 cases, were tested, and the decomposition plus competition plus resettling approach yielded very high accuracy.
The process of finding the coordinate transformation between a robot and an external sensor system has been addressed. This calibration is equivalent to solving a nonlinear optimization problem for the parameters that characterize the transformation. A two-step procedure is herein proposed for solving the problem. The first step involves finding a nominal solution that is a good approximation of the final solution. A varational problem is then generated to replace the original problem in the next step. With the assumption that the variational parameters are small compared to unity, the problem that can be more readily solved with relatively small computation effort.
The simultaneous design of a structure/active control system is addressed in which the mass of the actuators required to implement the active control is considered. An algorithm for estimating the required actuator mass given the control law and the desired maneuver is presented. A nonlinear optimization algorithm is used to direct the design process. Results are given for the design of a L shaped structure where it is desired to minimize the line of sight pointing error after a worst case slew maneuver.
A new physically based analytical model of the bidirectional reflectance of vegetation canopies is derived. The model expresses the bidirectional reflectance field of a semiinfinite canopy as a combination of functions describing (1) the optical properties of the leaves through their single-scattering albedo and their phase function, (2) the average distribution of leaf orientations, and (3) the architecture of the canopy. The model is validated against laboratory and ground-based measurements in the visible and IR spectral regions, taken over two vegetation covers. The intrinsic optical properties of leaves and the information on the geometrical canopy arrangements in space were obtained using an inversion procedure based on a nonlinear optimization technique. Model predictions of bidirectional reflectances obtained using the inversion procedure compare well with actual observations.
An algorithm for identifying state-space models from frequency response data of linear systems is presented. A matrix-fraction description of the transfer function is employed to curve-fit the frequency response data, using the least-squares method. The parameters of the matrix-fraction representation are then used to construct the Markov parameters of the system. Finally, state-space models are obtained through the Eigensystem Realization Algorithm using Markov parameters. The main advantage of this approach is that the curve-fitting and the Markov parameter construction are linear problems which avoid the difficulties of nonlinear optimization of other approaches. Another advantage is that it avoids windowing distortions associated with other frequency domain methods.
Damping parameters found by solving nonlinear optimization problem. Paper discusses assignment of matrices of damping parameters to mathematical models of vibrations and rotations of interconnected flexible components of large, flexible structure. Such models truncated at component level to reduce amount of computation necessary to simulate dynamics of structure numerically at both component and system levels.
An analytical formulation of optimum rotor interdisciplinary design is presented. A finite-state aeroelastic rotor model, coupling generalized dynamic wake with blade finite elements, is applied to perform the optimum rotor blade design for improved aerodynamic performance and vehicle vibration, while a feasible direction nonlinear optimizer, CONMIN, provides the optimization algorithm. The approach features a systematic rotor aeroelastic model which offers an efficient analytical tool, and retains necessary aerodynamic and blade dynamic building blocks for a sufficient rotor dynamic response analysis. The formulation is well suited for an efficient design sensitivity computation without resorting to finite difference, and thus provides a practical design tool. The results show improved rotor aerodynamic performance and reduced hub vibratory loads for the optimized blade as compared to the advanced rotor of reference design.
Planning for manipulation in complex environments often requires reasoning about the geometric and mechanical constraints which are posed by the task. In planning assembly operations, the automatic generation of operations sequences depends on the geometric feasibility of paths which permit parts to be joined into subassemblies. Feasible locations and collision-free paths must be present for part motions, robot and grasping motions, and fixtures. This paper describes an approach to reasoning about the feasibility of straight-line paths among three-dimensional polyhedral parts using an algebra of polyhedral cones. A second method recasts the feasibility conditions as constraints in a nonlinear optimization framework. Both algorithms have been implemented and results are presented.
The problem of mapping a dynamically consistent hydrographic field and associated absolute geostrophic flow in the eastern North Atlantic between 24 deg and 36 deg N is related directly to the solution of the so-called thermocline equations. A nonlinear optimization problem involving Needler's P equation is solved to find the hydrography and resulting flow that minimizes the vertical mixing above about 1500 m in the ocean and is simultaneously consistent with the observations. A sharp minimum (at least in some dimensions) is found, apparently corresponding to a solution nearly conserving potential vorticity and with vertical eddy coefficient less than about 10(exp -5) sq m/s. Estimates of `residual' quantities such as eddy coefficients are extremely sensitive to slight modifications to the observed fields. Boundary conditions, vertical velocities, etc., are a product of the optimization and produce estimates differing quantitatively from prior ones relying directly upon observed hydrography. The results are generally insensitive to particular elements of the solution methodology, but many questions remain concerning the extent to which different synoptic sections can be asserted to represent the same ocean. The method can be regarded as a practical generalization of the beta spiral and geostrophic balance inverses for the estimate of absolute geostrophic flows. Numerous improvements to the methodology used in this preliminary attempt are possible.
Variation in canopy structure and biochemistry induces a concomitant variation in the top-of-canopy spectral reflectance of a vegetation type. Hence, the use of a single endmember spectrum to track the fractional abundance of a given vegetation cover in a hyperspectral image may result in fractions with considerable error. One solution to the problem of endmember variability is to increase the number of endmembers used in a spectral mixture analysis of the image. For example, there could be several tree endmembers in the analysis because of differences in leaf area index (LAI) and multiple scatterings between leaves and stems. However, it is often difficult in terms of computer or human interaction time to select more than six or seven endmembers and any non-removable noise, as well as the number of uncorrelated bands in the image, limits the number of endmembers that can be discriminated. Moreover, as endmembers proliferate, their interpretation becomes increasingly difficult and often applications simply need the aerial fractions of a few land cover components which comprise most of the scene. In order to incorporate endmember variability into spectral mixture analysis, we propose representing a landscape component type not with one endmember spectrum but with a set or bundle of spectra, each of which is feasible as the spectrum of an instance of the component (e.g., in the case of a tree component, each spectrum could reasonably be the spectral reflectance of a tree canopy). These endmember bundles can be used with nonlinear optimization algorithms to find upper and lower bounds on endmember fractions. This approach to endmember variability naturally evolved from previous work in deriving endmembers from the data itself by fitting a triangle, tetrahedron or, more generally, a simplex to the data cloud reduced in dimension by a principal component analysis. Conceptually, endmember variability could make it difficult to find a simplex that both surrounds the data cloud and has vertices that are realistic endmember spectra with reflectances between 0 and 1. In this paper, we create endmember bundles and bounding fraction images for an AVIRIS subscene simulated with a plant canopy radiative transfer model. The simulated subscene is spatially patterned after a subscene from the AVIRIS image acquired August, 1993 over La Copita, Texas. In addition, for comparison, we performed a traditional unmixing with image endmembers.