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Computer program using numerical methods that calculates minimum time for space vehicle to meet its mission with optimum trajectory, and can maximize option if burning time is fixed
Hybrid computer Monte Carlo method for optimization of systems containing random parameters
The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.
Methods for optimizing parabolic dish solar collectors and the consequent effects of various optical, thermal, mechanical, and cost variables are examined. The most important performance optimization is adjusting the receiver aperture to maximize collector efficiency. Other parameters that can be adjusted to optimize efficiency include focal length, and, if a heat engine is used, the receiver temperature. The efficiency maxima associated with focal length and receiver temperature are relatively broad; it may, accordingly, be desirable to design somewhat away from the maxima. Performance optimization is sensitive to the slope and specularity errors of the concentrator. Other optical and thermal variables affecting optimization are the reflectance and blocking factor of the concentrator, the absorptance and losses of the receiver, and, if a heat engine is used, the shape of the engine efficiency versus temperature curve. Performance may sometimes be improved by use of an additional optical element (a secondary concentrator) or a receiver window if the errors of the primary concentrator are large or the receiver temperature is high.
The buckling load of laminated plates having midplane symmetry is maximized for a given total thickness. The thicknesses of the layers are taken as the design variables. Buckling analysis is carried out using the finite element method. The optimality equations are solved by a homotopy method which permits tracing optima as a function of total thickness. It is shown that for any design with a given stacking sequence of ply orientations, there exists a design associated with any other stacking sequence which possesses the same bending stiffness matrix and same total thickness. Hence, from the optimum design for a given stacking sequence, one can directly determine the optimum design for any rearrangement of the ply orientations, and the optimum buckling load is independent of the stacking sequence.
We report on several projects in the field of computational astrobiology, which is devoted to advancing our understanding of the origin, evolution and distribution of life in the Universe using theoretical and computational tools. Research projects included modifying existing computer simulation codes to use efficient, multiple time step algorithms, statistical methods for analysis of astrophysical data via optimal partitioning methods, electronic structure calculations on water-nuclei acid complexes, incorporation of structural information into genomic sequence analysis methods and calculations of shock-induced formation of polycylic aromatic hydrocarbon compounds.
This paper investigates a convex optimization based method that can rapidly generate the fuel optimal asteroid powered descent trajectory. The ultimate goal is to autonomously design the optimal powered descent trajectory on-board the spacecraft immediately prior to the descent burn. Compared to a planetary powered landing problem, the major difficulty is the complex gravity field near the surface of an asteroid that cannot be approximated by a constant gravity field. This paper uses relaxation techniques and a successive solution process that seeks the solution to the original nonlinear, nonconvex problem through the solutions to a sequence of convex optimal control problems.
Pressure-based airspeed and altitude measurements for aircraft typically require calibration of the installed system to account for pressure sensing errors such as those due to local flow field effects. In some cases, calibration is used to meet requirements such as those specified in Federal Aviation Regulation Part 25. Several methods are used for in-flight pitot-static calibration including tower fly-by, pacer aircraft, and trailing cone methods. In the 1990 s, the introduction of satellite-based positioning systems to the civilian market enabled new inflight calibration methods based on accurate ground speed measurements provided by Global Positioning Systems (GPS). Use of GPS for airspeed calibration has many advantages such as accuracy, ease of portability (e.g. hand-held) and the flexibility of operating in airspace without the limitations of test range boundaries or ground telemetry support. The current research was motivated by the need for a rapid and statistically accurate method for in-flight calibration of pitot-static systems for remotely piloted, dynamically-scaled research aircraft. Current calibration methods were deemed not practical for this application because of confined test range size and limited flight time available for each sortie. A method was developed that uses high data rate measurements of static and total pressure, and GPSbased ground speed measurements to compute the pressure errors over a range of airspeed. The novel application of this approach is the use of system identification methods that rapidly compute optimal pressure error models with defined confidence intervals in nearreal time. This method has been demonstrated in flight tests and has shown 2- bounds of approximately 0.2 kts with an order of magnitude reduction in test time over other methods. As part of this experiment, a unique database of wind measurements was acquired concurrently with the flight experiments, for the purpose of experimental validation of the optimization method. This paper describes the GPS-based pitot-static calibration method developed for the AirSTAR research test-bed operated as part of the Integrated Resilient Aircraft Controls (IRAC) project in the NASA Aviation Safety Program (AvSP). A description of the method will be provided and results from recent flight tests will be shown to illustrate the performance and advantages of this approach. Discussion of maneuver requirements and data reduction will be included as well as potential applications.
As part of the NASA Aviation Safety Program (AvSP), a novel pitot-static calibration method was developed to allow rapid in-flight calibration for subscale aircraft while flying within confined test areas. This approach uses Global Positioning System (GPS) technology coupled with modern system identification methods that rapidly computes optimal pressure error models over a range of airspeed with defined confidence bounds. This method has been demonstrated in subscale flight tests and has shown small 2- error bounds with significant reduction in test time compared to other methods. The current research was motivated by the desire to further evaluate and develop this method for full-scale aircraft. A goal of this research was to develop an accurate calibration method that enables reductions in test equipment and flight time, thus reducing costs. The approach involved analysis of data acquisition requirements, development of efficient flight patterns, and analysis of pressure error models based on system identification methods. Flight tests were conducted at The University of Tennessee Space Institute (UTSI) utilizing an instrumented Piper Navajo research aircraft. In addition, the UTSI engineering flight simulator was used to investigate test maneuver requirements and handling qualities issues associated with this technique. This paper provides a summary of piloted simulation and flight test results that illustrates the performance and capabilities of the NASA calibration method. Discussion of maneuver requirements and data analysis methods is included as well as recommendations for piloting technique.
An optimal active noise controller is formulated and analyzed for three different active noise control problems. The first problem formulated is the active control of enclosed or partially enclosed harmonic sound fields where the noise source strengths and enclosure boundary description are known. The enclosure boundary is described by either pressure, velocity, or impedance boundary conditions. The second problem formulated is the active control of the free field power radiated from a distributed noise source with a known time harmonic surface velocity. The third problem formulated is the active control of enclosed or partially enclosed harmonic sound field where the noise source strengths of enclosure boundary description may not be known. All three formulations are derived using an indirect boundary element technique. Formulation and verification of an indirect boundary element method is presented. The active noise controller formulations for enclosures are capable of analyzing systems with generalized enclosure shapes, point noise sources, and/or locally reacting impedance boundary conditions. For each formulation, representative results of optimal active noise controller case studies are presented, and some general conclusions are drawn.
A control-system design method, quadratic optimal cooperative control synthesis (CCS), is applied to the design of a stability and control augmentation system (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design method, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and linear quadratic regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.
The invention is an apparatus and method of biofeedback training for attaining a physiological state optimally consistent with the successful performance of a task, wherein the probability of successfully completing the task is made is inversely proportional to a physiological difference value, computed as the absolute value of the difference between at least one physiological signal optimally consistent with the successful performance of the task and at least one corresponding measured physiological signal of a trainee performing the task. The probability of successfully completing the task is made inversely proportional to the physiological difference value by making one or more measurable physical attributes of the environment in which the task is performed, and upon which completion of the task depends, vary in inverse proportion to the physiological difference value.
The fundamental methods are described for the general spacecraft trajectory design and optimization software system called Copernicus. The methods rely on a unified framework that is used to model, design, and optimize spacecraft trajectories that may operate in complex gravitational force fields, use multiple propulsion systems, and involve multiple spacecraft. The trajectory model, with its associated equations of motion and maneuver models, are discussed.
We present robust trajectory optimization techniques using a sweeping gradient method for ordinary differential equations with events (SGM) and linear covariance analysis (LinCov). SGM is a method for computing the gradient of trajectory analyses defined by performance indices over initial value problems with events with respect to static parameters. LinCov is an analytic technique for predicting stochastic behavior of dynamical systems. By combining SGM and LinCov, it is possible use efficient, off-the-shelf, gradient-based optimizers to solve robust optimal trajectory design problems. We describe the individual methods and some details on how they can be combined. Then we apply the combined techniques to a variety of orbital trajectory design problems to demonstrate its use, including minimum fuel transfer and mid-course correction burn scheduling.
Recursive method for the optimal smoothing of data has numerical superiority and is more easily understood in terms of physical reasoning than earlier methods. Using a Kalman filter, the smoothing technique, applied to a nonlinear parameter identification problem, is useful in those situations where linearization about a reference solution is valid.
A control-system design method, Quadratic Optimal Cooperative Control Synthesis (CCS), is applied to the design of a Stability and Control Augmentation Systems (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design model, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing Vertol CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and Linear Quadratic Regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.
A method of shaping diffraction-grating grooves to optimize the spectral efficiency, spectral range, and image quality of a spectral imaging instrument is under development. The method is based on the use of an advanced design algorithm to determine the possibly complex shape of grooves needed to obtain a desired efficiency-versus-wavelength response (see figure). Then electron- beam fabrication techniques are used to realize the required groove shape. The method could be used, for example, to make the spectral efficiency of the grating in a given wavelength range proportional to the inverse of the spectral efficiency of a photodetector array so that the overall spectral efficiency of the combination of the grating and the photodetector array would be flat. The method has thus far been applied to one-dimensional gratings only, but in principle, it is also applicable to two-dimensional gratings. The algorithm involves calculations in the spatial-frequency domain. The spatial-frequency spectrum of a grating is represented as a diffraction-order spectral-peak-width function multiplied by an efficiency function for a single grating groove. This representation affords computational efficiency and accuracy by making it possible to consider only the response from one grating groove (one period of the grating), instead of from the whole grating area, in determining the response from the entire grating. This combination of efficiency and accuracy is crucial for future extensions of the algorithm to two-dimensional designs and to designs in which polarization must also be taken into account. The algorithm begins with the definition of target values of relative efficiency that represent the desired spectral response of the grating in certain spectral frequencies calculated from the diffraction order and wavelength. The grating period is divided into a number of cells - typically, 100. The phase contribution from each cell is determined from the phase of the incident electromagnetic wave and the height of the grating surface in the cell. The total contribution from all cells to each target value is then calculated. Then a method known to specialists as the optimum-rotation-angle method is used to adjust the height of each cell so that the total response from all cells is optimized. The computation is iterative and continues until the desired response is obtained. In the event that the desired response is unphysical, the algorithm nevertheless strives to generate a grating-grove profile for which the response approximates the desired one as closely as possible.
General formulae for mapping optimization problems into systems of ordinary differential equations associated with artificial neural networks are presented. A comparison is made to optimization using gradient-search methods. The performance measure is the settling time from an initial state to a target state. A simple analytical example illustrates a situation where dynamical systems representing artificial neural network methods would settle faster than those representing gradient-search. Settling time was investigated for a more complicated optimization problem using computer simulations. The problem was a simplified version of a problem in medical imaging: determining loci of cerebral activity from electromagnetic measurements at the scalp. The simulations showed that gradient based systems typically settled 50 to 100 times faster than systems based on current neural network optimization methods.