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At least 1,063 records · Page 59

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NASA NTRS1975

Design of low-speed airfoils by numerical optimization

A practical procedure for the optimum design of low-speed airfoils is demonstrated. The procedure uses an optimization program based on a gradient algorithm coupled with an aerodynamic analysis program that uses a relaxation solution of the inviscid, full-potential equation. The analysis program is valid for both incompressible and compressible flow, thereby making optimum design of high-speed, shock-free airfoils possible. Results are presented for the following three constrained optimization problems at fixed angle of attack and Mach number: (1) adverse pressure-gradient minimization, (2) pitching-moment minimization; and (3) lift maximization. All three optimization problems were studied with various aerodynamic and geometric constraints.

Hicks, R. M.↗

NASA NTRS1974

On the design of optimal input signals in system identification

The problem of designing optimal inputs in the identification of multi-input multi-output linear systems with unknown time-varying parameters is considered using a Bayesian approach. A sensitivity index gives a measure of performance for the closed-loop system inputs. The computation of the optimal closed-loop mappings is shown to be a nontrivial exercise in stochastic control with no analytic solution, but optimal open-loop and affine laws yield much more tractable problems. For time-invariant systems, the sensitivity index considered is shown to be equivalent to the trace of the (strictly positive definite) information matrix associated with the system. Numerical examples are given. A Kalman filter is used to estimate the parameters. A necessary condition for the Kalman filter not to diverge when applying linear feedback is also given.

Lopez-Toledo, A. A.↗

NASA NTRS1975

Optimal control of multiplicative control systems arising from cancer therapy

This study deals with ways of curtailing the rapid growth of cancer cell populations. The performance functional that measures the size of the population at the terminal time as well as the control effort is devised. With use of the discrete maximum principle, the Hamiltonian for this problem is determined and the condition for optimal solutions are developed. The optimal strategy is shown to be a bang-bang control. It is shown that the optimal control for this problem must be on the vertices of an N-dimensional cube contained in the N-dimensional Euclidean space. An algorithm for obtaining a local minimum of the performance function in an orderly fashion is developed. Application of the algorithm to the design of antitumor drug and X-irradiation schedule is discussed.

Bahrami, K.↗

NASA NTRS1975

A note on optimal filtering in the presence of unknown biases

This note considers some aspects of the optimal filtering problem for linear processes in the presence of unknown biases in the input and the observations. It is proved via duality that the optimal filtering problem in the presence of an input bias is equivalent to a certain optimal regulator problem incorporating integral feedback. The question of observability of the augmented system used in the state and bias estimation is answered by deriving necessary and sufficient conditions when bias is present (1) in the input, (2) in the observations and (3) both in the input and the observations.

Joshi, S. M.↗

NASA NTRS1975

Hybrid computer methods for direct functional optimization

Control and trajectory optimization involves the minimization of a performance index (PI) of integral form where some optimal control law exists in a dynamic system. In this paper, a hybrid minicomputer with an adaptive random-search algorithm implements an iterative search for the optimal control. The search assumes that some initial control is randomly perturbed and a fast analog computer generates respective PI from the analog response of the dynamic system. An improved PI informs the digital computer to utilize the perturbed control as a basis for the next iteration; otherwise a new perturbation replaces the old perturbation in the next iteration. The search terminates when no further improvements occur.

Andrews, M.↗

NASA NTRS1976

Alloy and structural optimization of a directionally solidified lamellar eutectic alloy

Mechanical property characterization tests of a directionally solidified Ni-20 percent Cb-2.5 percent Al-6 percent Cr cellular eutectic turbine blade alloy demonstrated excellent long time creep stability and indicated intermediate temperature transverse tensile ductility and shear strength to be somewhat low for turbine blade applications. Alloy and structural optimization significantly improves these off-axis properties with no loss of longitudinal creep strength or stability. The optimized alloy-structure combination is a carbon modified Ni-20.1 percent Cb-2.5 percent Al-6.0 percent Cr-0.06 percent C composition processed under conditions producing plane front solidification and a fully-lamellar microstructure. With current processing technology, this alloy exhibits a creep-rupture advantage of 39 C over the best available nickel base superalloy, directionally solidified MAR M200+ Hf. While improved by about 20 percent, shear strength of the optimized alloy remains well below typical superalloy values.

Sheffler, K. D.↗

NASA NTRS1975

An algorithm for optimal single linear feature extraction from several Gaussian pattern classes

A computational algorithm is presented for the extraction of an optimal single linear feature from several Gaussian pattern classes. The algorithm minimizes the increase in the probability of misclassification in the transformed (feature) space. Numerical results on the application of this procedure to the remotely sensed data from the Purdue Cl flight line as well as LANDSAT data are presented. It was found that classification using the optimal single linear feature yielded a value for the probability of misclassification on the order of 30% less than that obtained by using the best single untransformed feature. Also, the optimal single linear feature gave performance results comparable to those obtained by using the two features which maximized the average divergence.

Starks, S. A.↗

NASA NTRS1976

A rapid method for optimization of the rocket propulsion system for single-stage-to-orbit vehicles

A rapid analytical method for the optimization of rocket propulsion systems is presented for a vertical take-off, horizontal landing, single-stage-to-orbit launch vehicle. This method utilizes trade-offs between propulsion characteristics affecting flight performance and engine system mass. The performance results from a point-mass trajectory optimization program are combined with a linearized sizing program to establish vehicle sizing trends caused by propulsion system variations. The linearized sizing technique was developed for the class of vehicle systems studied herein. The specific examples treated are the optimization of nozzle expansion ratio and lift-off thrust-to-weight ratio to achieve either minimum gross mass or minimum dry mass. Assumed propulsion system characteristics are high chamber pressure, liquid oxygen and liquid hydrogen propellants, conventional bell nozzles, and the same fixed nozzle expansion ratio for all engines on a vehicle.

Eldred, C. H.↗

NASA NTRS1976

Optimization and design of three-dimensional aerodynamic configurations of arbitrary shape by a vortex lattice method

A new method based on vortex lattice theory has been developed which can be applied to the combined analysis, induced drag optimization, and aerodynamic design of three-dimensional configurations of arbitrary shape. Geometric and aerodynamic constraints can be imposed on both the optimization and the design process. The method is compared with several known analytical solutions and is applied to several different design and optimization problems, including formation flight and wingtip fins for the Boeing KC-135 tanker airplane. Good agreement has been observed between the theoretical predictions and the wind tunnel test results for the KC-135 modification.

Feifel, W. M.↗

NASA NTRS1976

Numerical Airfoil Optimization Using a Reduced Number of Design Coordinates

A method is presented for numerical airfoil optimization whereby a reduced number of design coordinates are used to define the airfoil shape. The approach is to define the airfoil as a linear combination of shapes. These basic shapes may be analytically or numerically defined, allowing the designer to use his insight to propose candidate designs. The design problem becomes one of determining the participation of each such function in defining the optimum airfoil. Examples are presented for two-dimensional airfoil design and are compared with previous results based on a polynomial representation of the airfoil shape. Four existing NACA airfoils are used as basic shapes. Solutions equivalent to previous results are achieved with a factor of more than 3 improvements in efficiency, while superior designs are demonstrated with an efficiency greater than 2 over previous methods. With this shape definition, the optimization process is shown to exploit the simplifying assumptions in the inviscid aerodynamic analysis used here, thus demonstrating the need to use more advanced aerodynamics for airfoil optimization.

Vanderplaats, G. N.↗

NASA NTRS1975

A two-level trajectory decomposition algorithm featuring optimal intermediate target selection

A decomposition algorithm is presented that optimizes complex missions by partitioning the trajectory into natural segments such as ascent or entry. Each segment defines a full-rank targeting subproblem. These are solved sequentially using the Newton-Raphson algorithm. The master problem, representing the complete mission, is to determine subproblem targets and master-problem controls that optimize the mission objective subject to intersegment constraints. The gradient projection algorithm solves this problem using derivatives obtained analytically from finite-difference subproblem sensitivities. Thus, the mission is optimized by coordinating the solution of tractible subproblems. Computational results for a synchronous equatorial mission are included.

Petersen, F. M.↗

NASA NTRS1975

Optimization of duct acoustic liners of finite length

Lining design procedures generally ignore the effects of discontinuous impedance changes on reflection and modal redistribution of incident energy. The present study involves identification of the mechanisms of optimal suppression by segmented liners, including impedance discontinuity effects. The mathematical model involves rectangular ducts in the absence of mean flow. Segmented acoustic fields are represented by duct eigenfunction expansions, and mode matching is used to ensure continuity of the total field. Extensive parameter studies were used to identify attenuation mechanisms and to define preliminary liner configurations. These are used as starting values in conjugate-gradient optimization studies. Optimal segmented liners are presented and it is shown that, if the sound source is sufficiently well-defined, conventional infinite duct optimum attenuation rates can be improved upon by taking advantage of wall impedance discontinuities. Finally, follow-on work which will involve experimental verification and extension to the case with mean flow in the duct is described.

Beckemeyer, R. J.↗

NASA NTRS1976

A multilevel optimization of large-scale dynamic systems

A multilevel feedback control scheme is proposed for optimization of large-scale systems composed of a number of (not necessarily weakly coupled) subsystems. Local controllers are used to optimize each subsystem, ignoring the interconnections. Then, a global controller may be applied to minimize the effect of interconnections and improve the performance of the overall system. At the cost of suboptimal performance, this optimization strategy ensures invariance of suboptimality and stability of the systems under structural perturbations whereby subsystems are disconnected and again connected during operation.

Siljak, D. D.↗

NASA NTRS1976

Weight comparisons of optimized stiffened, unstiffened, and sandwich cylindrical shells made from composite or aluminum materials

This work presents optimum designs for unstiffened, hat stringer-stiffened and honeycomb sandwich cylinders under axial compression. Optimization results for graphite-epoxy cylinders show about a 50 percent weight savings over corresponding optimized aluminum cylinders for a wide loading range. The inclusion of minimum gage considerations results in a significant weight penalty, especially for a lightly loaded cylinder. Effects of employing a smeared stiffener buckling theory in the optimization program are investigated through comparison of results obtained from a more accurate branched shell buckling computer code. It was found that the stiffener cross-sectional deformations, which are usually ignored in smeared stiffener theory, result in about a 30 percent lower buckling load for the graphite-epoxy hat stiffened cylinder.

Agarwal, B. L.↗

NASA NTRS1976

Disjoint design spaces in the optimization of harmonically excited structures

The paper deals with a method of optimizing harmonically or dynamically excited structures which removes the frequency constraint (that specifies that the structure's first natural frequency of vibration must be greater than the excitation frequency), replaces the displacement constraint by an inequality constraint on the allowable stress and applies finite element approximations to the continuous one-dimensional structures. When the problem is posed in this manner, the feasible design space is disconnected or 'disjoint'. An attempt is made to explain this disjointness by studying the optimal design of a thin-walled cantilevered rod subjected to steady, simple harmonic torsional excitation. The finite element method is applied to the optimization of a harmonically excited structure with an arbitrary number of design variables, with the disjointness of the design space, a complicating factor.

Johnson, E. H.↗

NASA NTRS1976

Theoretical optimization and parametric study of n-on-p Al/x/Ga/1-x/As-GaAs graded band-gap solar cell

A comprehensive theoretical model of the graded band-gap Al(x)Ga(1-x)As-GaAs solar cell is used to optimize the n-on-p cell. The model includes power losses due to surface, bulk, and junction minority-carrier recombination, series resistance, and photon reflection from an SiO antireflection coating of optimum thickness. The optimized cell has a junction depth/graded band-gap layer thickness of 1.0 micron, respective donor and acceptor concentrations of 4 x 10 to the 17th power and 2 x 10 to the 17th power per cu cm, and a surface AlAs mode fraction of x = 0.35. The optimized graded band-gap cell has an air-mass-zero efficiency of 17.7% (not corrected for a 13% front surface contact area) and is shown to be less sensitive than a similar n-on-p GaAs cell to material degradation in the form of decreased minority-carrier diffusion lengths and increased surface-recombination velocity

Hutchby, J. A.↗

NASA NTRS1976

An algorithm for the weighting matrices in the sampled-data optimal linear regulator problem

The sampled-data optimal linear regulator problem provides a means whereby a control designer can use an understanding of continuous optimal regulator design to produce a digital state variable feedback control law which satisfies continuous system performance specifications. A basic difficulty in applying the sampled-data regulator theory is the requirement that certain digital performance index weighting matrices, expressed as complicated functions of system matrices, be computed. Infinite series representations are presented for the weighting matrices of the time-invariant version of the optimal linear sampled-data regulator problem. Error bounds are given for estimating the effect of truncating the series expressions after a finite number of terms, and a method is described for their computer implementation. A numerical example is given to illustrate the results.

Armstrong, E. S.↗

NASA NTRS1976

On the optimal minimum order observer-based compensator and the limited state variable feedback controller

Four design problems are considered: two on the optimal minimum order observer-based compensator design and two on the optimal limited state variable feedback controller. The problem of designing an optimal discrete time linear time-invariant observer-based compensator for the regulation of an n dimensional linear discrete time time-invariant plant with m independent outputs is considered. This is a stochastic design problem to the extent that the initial plant state is assumed to be a random vector with known first and second order statistics. The compensator parameters are obtained by minimizing the expectation, with respect to the initial conditions, of the standard cost, quadratic in the state and control vectors with the inclusion of cross terms.

Llorens-Ortiz, B.↗