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Automated Design Synthesis (ADS) computer program is general-purpose numerical-optimization program for design engineering. Provides wide range of options for solution of constrained and unconstrained function minimization problems. Suitable for such applications as minimum-weight design. Written in FORTRAN 77.
The present work discusses the generation of the cubic-spline interpolator in numerical optimization methods which use a variable-step integrator with step size control based on local relative truncation error. An algorithm for generating the cubic spline with successive over-relaxation is presented which represents an improvement over that given by Ralston and Wilf (1967). Rewriting the code reduces the number of N-vectors from eight to one. The algorithm is formulated in such a way that the solution of the linear system set up yields the first derivatives at the nodal points. This method is as accurate as other schemes but requires the minimum amount of storage.
This paper discusses the development of large scale numerical optimal control algorithms for nonlinear systems and their application to finite element models of structures. This work is based on our expansion of the optimal control algorithm (DDP) in the following steps: improvement of convergence for initial policies in non-convex regions, development of a numerically accurate penalty function method approach for constrained DDP problems, and parallel processing on supercomputers. The expanded constrained DDP algorithm was applied to the control of a four-bay, two dimensional truss with 12 soft members, which generates geometric nonlinearities. Using an explicit finite element model to describe the structural system requires 32 state variables and 10,000 time steps. Our numerical results indicate that for constrained or unconstrained structural problems with nonlinear dynamics, the results obtained by our expanded constrained DDP are significantly better than those obtained using linear-quadratic feedback control.
A numerical procedure for optimizing the design of the circulation control airfoil for use at high subsonic speeds is presented. The procedure consists of an optimization scheme coupled with a viscous potential flow analysis for the blowing jet. The desired airfoil is defined by a combination of three baseline shapes (cambered ellipse and cambered ellipse with drooped and spiraled trailing edges). The coefficients of these shapes are used as design variables in the optimization process. Under the constraints of lift augmentation and lift-to-drag ratios, the airfoil, optimized at free-stream Mach 0.54 and alpha = -2 degrees can be characterized as a cambered ellipse with a drooped trailing edge. Experimental tests support the performance improvement predicted by numerical optimization.
A study was conducted to assess the feasibility of performing computerized wing design by numerical optimization. The design program combined a full potential, inviscid aerodynamics code with a conjugate gradient optimization algorithm. Three design problems were selected to demonstrate the design technique. The first involved modifying the upper surface of the inboard 50% of a swept wing to reduce the shock drag subject to a constraint on wing volume. The second involved modifying the entire upper surface of the same swept wing (except the tip section) to increase the lift-drag ratio subject to constraints on wing volume and lift coefficient. The final problem involved modifying the inboard 50% of a low-speed wing to achieve good stall progression. Results from the three cases indicate that the technique is sufficiently accurate to permit substantial improvement in the design objectives.
The wind tunnel performance of a 10-percent thick helicopter rotor section design by numerical optimization is presented. The model was tested at Mach number from 0.2 to 0.84 with Reynolds number ranging from 1,900,000 at Mach 0.2 to 4,000,000 at Mach numbers above 0.5. The airfoil section exhibited maximum lift coefficients greater than 1.3 at Mach numbers below 0.45 and a drag divergence Mach number of 0.82 for lift coefficients near 0. A moderate 'drag creep' is observed at low lift coefficients for Mach numbers greater than 0.6.
This paper develops a method to tune fuzzy controllers using numerical optimization. The main attribute of this approach is that it allows fuzzy logic controllers to be tuned to achieve global performance requirements. Furthermore, this approach allows design constraints to be implemented during the tuning process. The method tunes the controller by parameterizing the membership functions for error, change-in-error and control output. The resulting parameters form a design vector which is iteratively changed to minimize an objective function. The minimal objective function results in an optimal performance of the system. A spacecraft mounted science instrument line-of-sight pointing control is used to demonstrate results.
Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.
A numerical procedure for optimizing circulation control airfoils, which consists of the coupling of an optimization scheme with a viscous potential flow analysis for blowing jet, is presented. The desired airfoil is defined by a combination of three baseline shapes (cambered ellipse, and cambered ellipse with drooped and spiralled trailing edges). The coefficients of these shapes are used as design variables in the optimization process. Under the constraints of lift augmentation and lift-to-drag ratios, the optimal airfoils are found to lie between those of cambered ellipse and the drooped trailing edge, towards the latter as the angle of attack increases. Results agree qualitatively with available experimental data.
An efficient transonic wing design procedure based upon numerical optimization together with three-dimensional transonic methods has been developed and used to design an advanced transport wing. The method development included an examination of the use of both full potential and extended small disturbance analysis codes and demonstrated that the former formulation was more reliable. In either case, the design procedure is economical and easy to use. Design verification in a unique semi-span test arrangement demonstrated that the design method produced a wing which satisfied the study design requirements. However, aeroelastic deformation of the wing occurred during the wind tunnel test. The computational methods used in the design procedure were employed to assess the effect of the aeroelastic deformation. The paper concludes with an evaluation of the design procedure and recommendation for its improvement.
The aerodynamic design procedure for a new blade tip suitable for operation at transonic speeds is illustrated. For the first time, 3 dimensional numerical optimization was applied to rotor tip design, using the recent derivative of the ROT22 code, program R22OPT. Program R22OPT utilized an efficient quasi-Newton optimization algorithm. Multiple design objectives were specified. The delocalization of the shock wave was to be eliminated in forward flight for an advance ratio of 0.41 and a tip Mach number of 0.92 at psi = 90 deg. Simultaneously, it was sought to reduce torque requirements while maintaining effective restoring pitching moments. Only the outer 10 percent of the blade span was modified; the blade area was not to be reduced by more than 3 percent. The goal was to combine the advantages of both sweptback and sweptforward blade tips. A planform that featured inboard sweepback was combined with a sweptforward tip and a taper ratio of 0.5. Initially, the ROT22 code was used to find by trial and error a planform geometry which met the design goals. This configuration had an inboard section with a leading edge sweep of 20 deg and a tip section swept forward at 25 deg; in addition, the airfoils were modified.
A computer program developed for the automated design of low speed airfoils utilizes a generalized Joukowski method for aerodynamic analysis coupled with a conjugate gradient, penalty function, numerical optimization algorithm to give an efficient calculation technique for use with minicomputers. The program designs airfoils with a prescribed pressure distribution as well as those which minimize or maximize some aerodynamic force coefficient. At present the method is restricted to inviscid, incompressible flow. A typical design problem will execute in 4.5 hr on an HP 9830 minicomputer.
Engineering design optimization often gives rise to problems in which expensive objective functions are minimized by derivative-free methods. We propose a method for solving such problems that synthesizes ideas from the numerical optimization and computer experiment literatures. Our approach relies on kriging known function values to construct a sequence of surrogate models of the objective function that are used to guide a grid search for a minimizer. Results from numerical experiments on a standard test problem are presented.
An important problem in space flight is the calculation of trajectories for nonthrusting vehicles between fixed points in a given time. A new procedure based on Hamilton's principle for solving such two-point boundary-value problems is presented. It employs numerical optimization methods to perform the extremization required by Hamilton's principle. This procedure is applied to the calculation of an Earth-Moon trajectory. The results show that the initial guesses required to obtain an iteration procedure which converges are not critical and that convergence can be obtained to any predetermined degree of accuracy.
A family of optimized hypersonic waveriders is generated and studied wherein detailed viscous effects are included within the optimization process itself. This is in contrast to previous optimized waverider work, wherein purely inviscid flow is used to obtain the waverider shapes. For the present waveriders, the undersurface is a streamsurface of an inviscid conical flowfield, the upper surface is a streamsurface of the inviscid flow over a tapered cylinder (calculated by the axisymmetric method of characteristics), and the viscous effects are treated by integral solutions of the boundary layer equations. Transition from laminar to turbulent flow is included within the viscous calculations. The optimization is carried out using a nonlinear simplex method. The resulting family of viscous hypersonic waveriders yields predicted high values of lift/drag, high enough to break the L/D barrier based on experience with other hypersonic configurations. Moreover, the numerical optimization process for the viscous waveriders results in distinctly different shapes compared to previous work with inviscid-designed waveriders. Also, the fine details of the viscous solution, such as how the shear stress is distributed over the surface, and the location of transition, are crucial to the details of the resulting waverider geometry. Finally, the moment coefficient variations and heat transfer distributions associated with the viscous optimized waveriders are studied.
A survey of applications of mathematical programming methods is used to improve the design of helicopters and their components. Applications of multivariable search techniques in the finite dimensional space are considered. Five categories of helicopter design problems are considered: (1) conceptual and preliminary design, (2) rotor-system design, (3) airframe structures design, (4) control system design, and (5) flight trajectory planning. Key technical progress in numerical optimization methods relevant to rotorcraft applications are summarized.
A survey of applications of mathematical programming methods is used to improve the design of helicopters and their components. Applications of multivariable search techniques in the finite dimensional space are considered. Five categories of helicopter design problems are considered: (1) conceptual and preliminary design, (2) rotor-system design, (3) airframe structures design, (4) control system design, and (5) flight trajectory planning. Key technical progress in numerical optimization methods relevant to rotorcraft applications are summarized.
A survey of applications of mathematical programming methods is used to improve the design of helicopters and their components. Applications of multivariable search techniques in the finite dimensional space are considered. Five categories of helicopter design problems are considered: (1) conceptual and preliminary design, (2) rotor-system design, (3) airframe structures design, (4) control system design, and (5) flight trajectory planning. Key technical progress in numerical optimization methods relevant to rotorcraft applications are summarized.