Application of numerical optimization techniques to high speed inlet bleed system design
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Hingst, W.↗
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Application of numerical optimization to rotor aerodynamic design
Based on initial results obtained from the performance optimization code, a number of observations can be made regarding the utility of optimization codes in supporting design of rotors for improved performance. (1) The primary objective of improving the productivity and responsiveness of current design methods can be met. (2) The use of optimization allows the designer to consider a wider range of design variables in a greatly compressed time period. (3) Optimization requires the user to carefully define his problem to avoid unproductive use of computer resources. (4) Optimization will increase the burden on the analyst to validate designs and to improve the accuracy of analysis methods. (5) Direct calculation of finite difference derivatives by the optimizer was not prohibitive for this application but was expensive. Approximate analysis in some form would be considered to improve program response time. (6) Program developement is not complete and will continue to evolve to integrate new analysis methods, design problems, and alternate optimizer options.
Pleasants, W. A., III↗
An indirect method for numerical optimization using the Kreisselmeir-Steinhauser function
A technique is described for converting a constrained optimization problem into an unconstrained problem. The technique transforms one of more objective functions into reduced objective functions, which are analogous to goal constraints used in the goal programming method. These reduced objective functions are appended to the set of constraints and an envelope of the entire function set is computed using the Kreisselmeir-Steinhauser function. This envelope function is then searched for an unconstrained minimum. The technique may be categorized as a SUMT algorithm. Advantages of this approach are the use of unconstrained optimization methods to find a constrained minimum without the draw down factor typical of penalty function methods, and that the technique may be started from the feasible or infeasible design space. In multiobjective applications, the approach has the advantage of locating a compromise minimum design without the need to optimize for each individual objective function separately.
Wrenn, Gregory A.↗
Computation of maximum gust loads in nonlinear aircraft using a new method based on the matched filter approach and numerical optimization
Time-correlated gust loads are time histories of two or more load quantities due to the same disturbance time history. Time correlation provides knowledge of the value (magnitude and sign) of one load when another is maximum. At least two analysis methods have been identified that are capable of computing maximized time-correlated gust loads for linear aircraft. Both methods solve for the unit-energy gust profile (gust velocity as a function of time) that produces the maximum load at a given location on a linear airplane. Time-correlated gust loads are obtained by re-applying this gust profile to the airplane and computing multiple simultaneous load responses. Such time histories are physically realizable and may be applied to aircraft structures. Within the past several years there has been much interest in obtaining a practical analysis method which is capable of solving the analogous problem for nonlinear aircraft. Such an analysis method has been the focus of an international committee of gust loads specialists formed by the U.S. Federal Aviation Administration and was the topic of a panel discussion at the Gust and Buffet Loads session at the 1989 SDM Conference in Mobile, Alabama. The kinds of nonlinearities common on modern transport aircraft are indicated. The Statical Discrete Gust method is capable of being, but so far has not been, applied to nonlinear aircraft. To make the method practical for nonlinear applications, a search procedure is essential. Another method is based on Matched Filter Theory and, in its current form, is applicable to linear systems only. The purpose here is to present the status of an attempt to extend the matched filter approach to nonlinear systems. The extension uses Matched Filter Theory as a starting point and then employs a constrained optimization algorithm to attack the nonlinear problem.
Pototzky, Anthony S.↗
Numerical optimization of composite hip endoprostheses under different loading conditions
The optimization of composite hip implants was investigated. Emphasis was placed on the effect of shape and material tailoring of the implant to improve the implant-bone interaction. A variety of loading conditions were investigated to better understand the relationship between loading and optimization outcome. Comparisons of the initial and optimal models with more complex 3D finite element models were performed. The results indicate that design improvements made using this method result in similar improvements in the 3D models. Although the optimization outcomes were significantly affected by the choice of loading conditions, certain trends were observed that were independent of the applied loading.
Blake, T. A.↗
Experimental and Numerical Optimization of a High-Lift System to Improve Low-Speed Performance, Stability, and Control of an Arrow-Wing Supersonic Transport
An investigation was performed to evaluate leading-and trailing-edge flap deflections for optimal aerodynamic performance of a High-Speed Civil Transport concept during takeoff and approach-to-landing conditions. The configuration used for this study was designed by the Douglas Aircraft Company during the 1970's. A 0.1-scale model of this configuration was tested in the Langley 30- by 60-Foot Tunnel with both the original leading-edge flap system and a new leading-edge flap system, which was designed with modem computational flow analysis and optimization tools. Leading-and trailing-edge flap deflections were generated for the original and modified leading-edge flap systems with the computational flow analysis and optimization tools. Although wind tunnel data indicated improvements in aerodynamic performance for the analytically derived flap deflections for both leading-edge flap systems, perturbations of the analytically derived leading-edge flap deflections yielded significant additional improvements in aerodynamic performance. In addition to the aerodynamic performance optimization testing, stability and control data were also obtained. An evaluation of the crosswind landing capability of the aircraft configuration revealed that insufficient lateral control existed as a result of high levels of lateral stability. Deflection of the leading-and trailing-edge flaps improved the crosswind landing capability of the vehicle considerably; however, additional improvements are required.
Hahne, David E.↗
Numerical Optimization of the Thermal Field in Bridgman Detached Growth
The global modeling of the thermal field in two vertical Bridgman-like crystal growth configurations, has been performed to get optimal thermal conditions for a successful detached growth of Ge and CdTe crystals. These computations are performed using the CrysMAS code and expand upon our previous analysis [1] that propose a new mechanism involving the thermal field and meniscus position to explain stable conditions for dewetted Bridgman growth. The analysis of the vertical Bridgman configuration with two heaters, used by Palosz et al. for the detached growth of Ge, shows, consistent with their results, that the large wetting angle of germanium on boron nitride surfaces was an important factor to promote a successful detached growth. Our computations predict that by initiating growth much higher into the hot zone of the furnace, the thermal conditions will be favorable for continued detachment even for systems that did not exhibit high contact angles. The computations performed for a vertical gradient freeze configuration with three heaters representative of that used for the detached growth of CdTe, show favorable thermal conditions for dewetting during the entirely growth run described. Improved thermal conditions are also predicted for coated silica crucibles when the solid-liquid interface advances higher into the hot zone during the solidification process. The second set of experiments on CdTe growth described elsewhere has shown the reattachment of the crystal to the crucible after few centimeters of dewetted growth. The thermal modeling of this configuration shows a second solidification front appearing at the top of the sample and approaching the middle line across the third heater. In these conditions, the crystal grows detached from the bottom, but will be attached to the crucible in the upper part because of the solidification without gap in this region. The solidification with two interfaces can be avoided when the top of the sample is positioned below the middle position of the third furnace.
Stelian, C.↗
HabEx: Numerically Optimized Coronagraph Designs for the Imaging HabEx Mission
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Riggs, A.J. Eldorado↗
Numerically Optimized Coronagraph Designs for the Habitable Exoplanet Imaging Mission (HabEx) Concept
The primary science goal of the Habitable Exoplanet Imaging Mission (HabEx), one of four candidate flagship missions under investigation, is to image and spectrally characterize Earth-like exoplanets. It is well known that pupil obscurations degrade coronagraphic performance and complicate coronagraph design, so HabEx is planned to have an off-axis, unobscured primary mirror. We utilize the circular symmetry of the aperture to investigate 1D-radial coronagraph optimization methods that are prohibitively time-consuming or intractable in 2D, such as diffractive pupil remapping and concurrent, multi-plane optimization. We also directly constrain sensitivities to dynamic, low-order Zernike aberrations, which are separable in polar coordinates and can thus be propagated as 1D-radial integrals. The mask technologies in our designs claim heritage from the extensive modeling and testbed experiments performed by the Wide-Field Infrared Survey Telescope (WFIRST) Coronagraph Instrument (CGI) project. In this paper, we detail our optimization methods and outline future work to complete our design survey.
Balasubramaian, Kunjithapatham↗
Automated tuning of airframe vibration by structural optimization
Numerical optimization techniques are used to modify the dynamic response at a specified point(s) of a helicopter airframe structure due to a steady state narrow band excitation. Calculation of steady state vibration amplitude is reduced to the solution of linear equations with complex coefficients. The sensitivity of the dynamic amplitudes with respect to the structural parameter perturbations can be computed with the same technique as the one used in the static displacement sensitivity without requiring eigenvector sensitivity. Approximate models for critical structural responses are created based on the sensitivity data to reduce the amount of computational effort and to enable the design of structures of practical scale and complexity. This approach is general in that it accommodates static, dynamic, and frequency constraints simultaneously as long as their computational models are available. It can be used in optimizing mass distribution as well as stiffness modifications of practical structures.
Miura, H.↗
On domains of convergence in optimization problems
Numerical optimization algorithms require the knowledge of an initial set of design variables. Starting from an initial design x(sup 0), improved solutions are obtained by updating the design iteratively in a way prescribed by the particular algorithm used. If the algorithm is successful, convergence is achieved to a local optimal solution. Let A denote the iterative procedure that characterizes a typical optimization algorithm, applied to the problem: Find x belonging to R(sup n) that maximizes f(x) subject to x belonging to Omega contained in R(sup n). We are interested in problems with several local maxima (x(sub j))(sup *), j=1, ..., m, in the feasible design space Omega. In general, convergence of the algorithm A to a specific solution (x(sub j))(sup *) is determined by the choice of initial design x(sup 0). The domain of convergence D(sub j) of A associated with a local maximum (x(sub j))(sup *) is a subset of initial designs x(sup 0) in Omega such that the sequence (x(sup k)), k=0,1,2,... defined by x(sup k+1) = A(x(sup k)), k=0,1,... converges to (x(sub j))(sup *). The set D(sub j) is also called the basin of attraction of (x(sub j))(sup *). Cayley first proposed the problem of finding the basin of attraction for Newton's method in 1897. It has been shown that the basin of attraction for Newton's method exhibits chaotic behavior in problems with polynomial objective. This implies that there may be regions in the feasible design space where arbitrarily close starting points will converge to different local optimal solutions. Furthermore, the boundaries of the domains of convergence may have a very complex, even fractal structure. In this paper we show that even simple structural optimization problems solved using standard gradient based (first order) algorithms exhibit similar features.
Diaz, Alejandro R.↗
The computer for design and optimization
Computerized design using numerical optimization techniques is discussed and guidelines for writing analysis computer codes that can be readily coupled to optimization codes are presented. The following numerical optimization techniques are examined: random search, sequential unconstrained minimization, direct constrained optimization, and one-dimensional search. A number of design applications are considered including high speed airfoil lift maximization, the preliminary design of a wing, design of a planar tower for optimal geometry, and the conceptual design of a tactical fighter aircraft.
Vanderplaats, G. N.↗
Aerodynamic shape optimization using control theory
Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.
Reuther, James↗
Multiple burn fuel-optimal orbit transfers: Numerical trajectory computation and neighboring optimal feedback guidance
This report describes current work in the numerical computation of multiple burn, fuel-optimal orbit transfers and presents an analysis of the second variation for extremal multiple burn orbital transfers as well as a discussion of a guidance scheme which may be implemented for such transfers. The discussion of numerical computation focuses on the use of multivariate interpolation to aid the computation in the numerical optimization. The second variation analysis includes the development of the conditions for the examination of both fixed and free final time transfers. Evaluations for fixed final time are presented for extremal one, two, and three burn solutions of the first variation. The free final time problem is considered for an extremal two burn solution. In addition, corresponding changes of the second variation formulation over thrust arcs and coast arcs are included. The guidance scheme discussed is an implicit scheme which implements a neighboring optimal feedback guidance strategy to calculate both thrust direction and thrust on-off times.
Chuang, C.-H.↗
Supersonic transport grid generation, validation, and optimization
The ever present demand for reduced flight times has renewed interest in High Speed Civil Transports (HSCT). The need for an HSCT becomes especially apparent when the long distance, over-sea, high growth Pacific rim routes are considered. Crucial to any successful HSCT design are minimal environmental impact and economic viability. Vital is the transport's aerodynamic efficiency, ultimately effecting both the environmental impact and the operating cost. Optimization, including numerical optimization, coupled with the use of computational fluid dynamics (CFD) technology, has and will offer a significant improvement beyond traditional methods.
Aaronson, Philip G.↗
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.↗
Analysis of a theoretically optimized transonic airfoil
Numerical optimization was used in conjunction with an inviscid, full potential equation, transonic flow analysis computer code to design an upper surface contour for a conventional airfoil to improve its supercritical performance. The modified airfoil was tested in a compressible flow wind tunnel. The modified airfoil's performance was evaluated by comparison with test data for the baseline airfoil and for an airfoil developed by optimization of leading edge of the baseline airfoil. While the leading edge modification performed as expected, the upper surface re-design did not produce all of the expected performance improvements. Theoretical solutions computed using a full potential, transonic airfoil code corrected for viscosity were compared to experimental data for the baseline airfoil and the upper surface modification. These correlations showed that the theory predicted the aerodynamics of the baseline airfoil fairly well, but failed to accurately compute drag characteristics for the upper surface modification.
Lores, M. E.↗
Trajectory optimization for an asymmetric launch vehicle
A numerical optimization technique is used to fully automate the trajectory design process for an symmetric configuration of the proposed Advanced Launch System (ALS). The objective of the ALS trajectory design process is the maximization of the vehicle mass when it reaches the desired orbit. The trajectories used were based on a simple shape that could be described by a small set of parameters. The use of a simple trajectory model can significantly reduce the computation time required for trajectory optimization. A predictive simulation was developed to determine the on-orbit mass given an initial vehicle state, wind information, and a set of trajectory parameters. This simulation utilizes an idealized control system to speed computation by increasing the integration time step. The conjugate gradient method is used for the numerical optimization of on-orbit mass. The method requires only the evaluation of the on-orbit mass function using the predictive simulation, and the gradient of the on-orbit mass function with respect to the trajectory parameters. The gradient is approximated with finite differencing. Prelaunch trajectory designs were carried out using the optimization procedure. The predictive simulation is used in flight to redesign the trajectory to account for trajectory deviations produced by off-nominal conditions, e.g., stronger than expected head winds.
Sullivan, Jeanne Marie↗