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At least 1,477 records · Page 82

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NASA NTRS1993

Calculation of optimum airfoils using direct solutions of the Navier-Stokes equations

A method has been developed which calculates the optimum airfoil shape at a specified operating condition. The Reynolds-averaged Navier-Stokes equations with a turbulence model are used as the governing equations for the fluid flow, and are explicitly introduced into the optimization analysis as constraint equations. The locations of all grid points which define the surface of the airfoil are design variables, eliminating the need for shape functions to describe changes in the airfoil geometry. A generalized reduced-gradient method is used to find the optimum airfoil shape. The use of a direct solution technique (Newton's method) to solve the Navier-Stokes equations allows for the efficient solution of the problem. This paper describes the optimization method and presents sample results.

Felker, Fort F.↗

NASA NTRS1983

Flight directors for STOl aircraft

Flight director logic for flight path and airspeed control of a powered-lift STOL aircraft in the approach, transition, and landing configurations are developed. The methods for flight director design are investigated. The first method is based on the Optimal Control Model (OCM) of the pilot. The second method, proposed here, uses a fixed dynamic model of the pilot in a state space formulation similar to that of the OCM, and includes a pilot work-load metric. Several design examples are presented with various aircraft, sensor, and control configurations. These examples show the strong impact of throttle effectiveness on the performance and pilot work-load associated with manual control of powered-lift aircraft during approach. Improved performed and reduced pilot work-load can be achieved by using direct-lift-control to increase throttle effectiveness.

Rabin, U. H.↗

NASA NTRS1987

Dynamics and control of a planar truss actuator

The concept of using an active truss actuator to control the vibration of a flexible (space) structure has been investigated. The actuator with a generic beam continuum cantilevered from it has been modeled using energy methods. A time-invariant optimal state feedback scheme was utilized for the control method. A digital simulation of the system dynamic response demonstrated the good vibration control possibilities for the (planar) truss actuator on a large flexible space structure.

Lovejoy, V. D.↗

NASA NTRS1993

Effect of rotation rate on the forces of a rotating cylinder: Simulation and control

In this paper we present numerical solutions to several optimal control problems for an unsteady viscous flow. The main thrust of this work is devoted to simulation and control of an unsteady flow generated by a circular cylinder undergoing rotary motion. By treating the rotation rate as a control variable, we can formulate two optimal control problems and use a central difference/pseudospectral transform method to numerically compute the optimal control rates. Several types of rotations are considered as potential controls, and we show that a proper synchronization of forcing frequency with the natural vortex shedding frequency can greatly influence the flow. The results here indicate that using moving boundary controls for such systems may provide a feasible mechanism for flow control.

Burns, John A.↗

NASA NTRS1985

Noise constraints effecting optimal propeller designs

A preliminary design tool for advanced propellers was developed combining a fast vortex lattice aerodynamic analysis, a fast subsonic point source noise analysis, and an optimization scheme using a conjugate directions method. Twist, chord and sweep distributions are optimized to simultaneously improve both the aerodynamic performance and the noise observed at a fixed relative position. The optimal noise/performance tradeoffs for straight and advanced concept blades are presented. The techniques used include increasing the blade number, blade sweep, reducing the rotational speed, shifting the spanwise loading and diameter changes.

Miller, C. J.↗

NASA NTRS1985

Noise constraints effecting optimal propeller designs

Miller, C. J.↗

NASA NTRS1988

Optimization of motion control laws for tether crawler or elevator systems

Based on the proposal of a motion control law by Lorenzini (1987), a method is developed for optimizing motion control laws for tether crawler or elevator systems in terms of the performance measures of travel time, the smoothness of acceleration and deceleration, and the maximum values of velocity and acceleration. The Lorenzini motion control law, based on powers of the hyperbolic tangent function, is modified by the addition of a constant-velocity section, and this modified function is then optimized by parameter selections to minimize the peak acceleration value for a selected travel time or to minimize travel time for the selected peak values of velocity and acceleration. It is shown that the addition of a constant-velocity segment permits further optimization of the motion control law performance.

Swenson, Frank R.↗

NASA NTRS2016

Strain-Based Damage Determination Using Finite Element Analysis for Structural Health Management

A damage determination method is presented that relies on in-service strain sensor measurements. The method employs a gradient-based optimization procedure combined with the finite element method for solution to the forward problem. It is demonstrated that strains, measured at a limited number of sensors, can be used to accurately determine the location, size, and orientation of damage. Numerical examples are presented to demonstrate the general procedure. This work is motivated by the need to provide structural health management systems with a real-time damage characterization. The damage cases investigated herein are characteristic of point-source damage, which can attain critical size during flight. The procedure described can be used to provide prognosis tools with the current damage configuration.

Hochhalter, Jacob D.↗

NASA NTRS1982

Effect of processing on Polymer/Composite structure and properties

Advances in the vitality and economic health of the field of polymer forecasting are discussed. A consistent and rational point of view which considers processing as a participant in the underlying triad of relationships which comprise materials science and engineering is outlined. This triad includes processing as it influences material structure, and ultimately properties. Methods in processing structure properties, polymer science and engineering, polymer chemistry and synthesis, structure and modification and optimization through processing, and methods of melt flow modeling in processing structure property relations of polymer were developed. Mechanical properties of composites are considered, and biomedical materials research to include polymer processing effects are studied. An analysis of the design technology of advances graphite/epoxy composites is also reported.

Source record↗

NASA NTRS1990

Iterative computation of the optimal H(infinity) norm by using two-Riccati-equation method

The two-Riccati-equation method solution to a standard H(infinity) control problem can be used to characterize all possible stabilizing optimal or suboptimal H(infinity) controllers if the optimal or suboptimal H(infinity) norm is available in the literature. An iterative algorithm for computing the optimal H(infinity) norm is proposed. The algorithm employs fixed-point, double secant and bisection to guarantee a super linear convergence.

Chang, B. C.↗

NASA NTRS1965

Application of a finite-difference newton- raphson algorithm to problems of low-thrust trajectory optimization.

Low thrust trajectory optimization, using Newton- Raphson method to solve nonlinear two-point boundary value problem

BOUNDARY VALUE↗

NASA NTRS2000

Cascade Optimization Strategy with Neural Network and Regression Approximations Demonstrated on a Preliminary Aircraft Engine Design

A preliminary aircraft engine design methodology is being developed that utilizes a cascade optimization strategy together with neural network and regression approximation methods. The cascade strategy employs different optimization algorithms in a specified sequence. The neural network and regression methods are used to approximate solutions obtained from the NASA Engine Performance Program (NEPP), which implements engine thermodynamic cycle and performance analysis models. The new methodology is proving to be more robust and computationally efficient than the conventional optimization approach of using a single optimization algorithm with direct reanalysis. The methodology has been demonstrated on a preliminary design problem for a novel subsonic turbofan engine concept that incorporates a wave rotor as a cycle-topping device. Computations of maximum thrust were obtained for a specific design point in the engine mission profile. The results (depicted in the figure) show a significant improvement in the maximum thrust obtained using the new methodology in comparison to benchmark solutions obtained using NEPP in a manual design mode.

Hopkins, Dale A.↗

NASA NTRS1986

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.↗

NASA NTRS2010

Tuning Parameters in Heuristics by Using Design of Experiments Methods

With the growing complexity of today's large scale problems, it has become more difficult to find optimal solutions by using exact mathematical methods. The need to find near-optimal solutions in an acceptable time frame requires heuristic approaches. In many cases, however, most heuristics have several parameters that need to be "tuned" before they can reach good results. The problem then turns into "finding best parameter setting" for the heuristics to solve the problems efficiently and timely. One-Factor-At-a-Time (OFAT) approach for parameter tuning neglects the interactions between parameters. Design of Experiments (DOE) tools can be instead employed to tune the parameters more effectively. In this paper, we seek the best parameter setting for a Genetic Algorithm (GA) to solve the single machine total weighted tardiness problem in which n jobs must be scheduled on a single machine without preemption, and the objective is to minimize the total weighted tardiness. Benchmark instances for the problem are available in the literature. To fine tune the GA parameters in the most efficient way, we compare multiple DOE models including 2-level (2k ) full factorial design, orthogonal array design, central composite design, D-optimal design and signal-to-noise (SIN) ratios. In each DOE method, a mathematical model is created using regression analysis, and solved to obtain the best parameter setting. After verification runs using the tuned parameter setting, the preliminary results for optimal solutions of multiple instances were found efficiently.

Arin, Arif↗

NASA NTRS1993

Structural design utilizing updated, approximate sensitivity derivatives

A method to improve the computational efficiency of structural optimization algorithms is investigated. In this method, the calculations of 'exact' sensitivity derivatives of constraint functions are performed only at selected iterations during the optimization process. The sensitivity derivatives utilized within other iterations are approximate derivatives which are calculated using an inexpensive derivative update formula. Optimization results are presented for an analytic optimization problem (i.e., one having simple polynomial expressions for the objective and constraint functions) and for two structural optimization problems. The structural optimization results indicate that up to a factor of three improvement in computation time is possible when using the updated sensitivity derivatives.

Scotti, Stephen J.↗

NASA NTRS2020

Squash-Box Feasibility Driven Differential Dynamic Programming

Recently, Differential Dynamic Programming (DDP) and other similar algorithms have become the solvers of choice when performing non-linear Model Predictive Control (nMPC) with modern robotic devices. The reason is that they have a lower computational cost per iteration when compared with off-the-shelf Non-Linear Programming (NLP) solvers, which enables its online operation. However, they cannot handle constraints, and are known to have poor convergence capabilities. In this paper, we propose a method to solve the optimal control problem with control bounds through a squashing function (i.e., a sigmoid, which is bounded by construction). It has been shown that a naive use of squashing functions damage the convergence rate. To tackle this, we first propose to add a quadratic barrier that avoids the difficulty of the plateau produced by the sigmoid. Second, we add an outer loop that adapts both the sigmoid and the barrier; it makes the optimal control problem with the squashing function converge to the original control-bounded problem. To validate our method, we present simulation results for different types of platforms including a multi-rotor, a biped, a quadruped and a humanoid robot.

Navarro, Angel Santamaria↗

NASA NTRS1994

Theory and computation of optimal low- and medium-thrust transfers

This report presents two numerical methods considered for the computation of fuel-optimal, low-thrust orbit transfers in large numbers of burns. The origins of these methods are observations made with the extremal solutions of transfers in small numbers of burns; there seems to exist a trend such that the longer the time allowed to perform an optimal transfer the less fuel that is used. These longer transfers are obviously of interest since they require a motor of low thrust; however, we also find a trend that the longer the time allowed to perform the optimal transfer the more burns are required to satisfy optimality. Unfortunately, this usually increases the difficulty of computation. Both of the methods described use small-numbered burn solutions to determine solutions in large numbers of burns. One method is a homotopy method that corrects for problems that arise when a solution requires a new burn or coast arc for optimality. The other method is to simply patch together long transfers from smaller ones. An orbit correction problem is solved to develop this method. This method may also lead to a good guidance law for transfer orbits with long transfer times.

Chuang, C.-H.↗

NASA NTRS1994

Control theory based airfoil design using the Euler equations

This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using the potential flow equation with either a conformal mapping or a general coordinate system. The goal of our present work is to extend the development to treat the Euler equations in two-dimensions by procedures that can readily be generalized to treat complex shapes in three-dimensions. Therefore, we have developed methods which can address airfoil design through either an analytic mapping or an arbitrary grid perturbation method applied to a finite volume discretization of the Euler equations. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented for both the inverse problem and drag minimization problem.

Jameson, Antony↗