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NASA NTRS1984

Hurricane Debby - Analysis and numerical forecasts using VAS soundings

The utility of VISSR Atmospheric Sounder (VAS) temperature and moisture soundings in defining the storm and its surroundings at subsynoptic scales has been examined using a numerical analysis and prognosis system. In particular, VAS temperature and moisture soundings and cloud and water vapor motion winds have been used in numerical analysis for three time periods. It is shown that the VAS temperature and moisture data which specify temperature and moisture well in cloud free regions are complemented by cloud and water vapor wind data which provide horizontal gradient information for the cloudy areas. The loss of analysis integrity due to the reduction of VAS data density in the cloudy regions associated with synoptic activity is ameliorated by using cloud and water vapor motion winds. The improvement in numerical forecasts resulting from the addition of these data to the numerical data base is also recorded.

Le Marshall, J. F.↗

NASA NTRS1985

Hurricane Debby - An illustration of the complementary nature of VAS soundings and cloud and water vapor motion winds

The utility of VISSR Atmospheric Sounder (VAS) temperature and moisture soundings and cloud and water vapor motion winds in defining a storm and its surroundings at subsynoptic scales has been examined using a numerical analysis and prognosis system. It is shown that the VAS temperature and moisture data, which specify temperature and moisture well in cloud-free areas, are complemented by cloud and water vapor motion data generated in the cloudy areas. The cloud and water vapor 'winds' provide thermal gradient information for interpolating the soundings across cloudy regions. The loss of analysis integrity due to the reduction of VAS sounding density in the cloudy regions associated with synoptic activity is ameliorated by using cloud and water vapor motion winds. The improvement in numerical forecasts resulting from the addition of these data to the numerical analysis is recorded.

Le Marshall, J. F.↗

NASA NTRS1986

The development of an environmental disturbance model for large space structures after the onset of thermal shock

Expressions for the temperature response across a thin large space structure during and immediately following the onset of thermal shock are obtained as a function of the properties of the material and the solar incidence angle. The thermal gradients induced due to solar radiation heating result in thermal deformation. From the temperature gradient information, expressions are developed for the time history of the thermally induced deflections based on the thermoelastic relationships. The effect of the variation of the solar incidence angle and the variation of the emissivity of the surface is considered. From the deflection time history, a model of the disturbance moments is developed and evaluated for different solar incidence angles.

Hamsath, N.↗

NASA NTRS1985

The assimilation of satellite soundings, winds and satellite products in a mesoscale analysis/forecast system

Investigations in FY-85 were centered on three case study days in 1982. Two of these, March 6 and April 24, were Atmospheric Variability Experiment/Verical Atmospheric Sounder (AVE/VAS) days for which high spatial and temporal resolution RAOB and Vertical Atmospheric Sounder (VAS) data sets were available. The third investigation day, April 26, was a day of interesting severe weather. In the last part of FY-84 and early FY-85 we were able to demonstrate most importantly the complimentary nature of satellite soundings and winds in a forecast/analysis system. In our variational analysis scheme, cloud drift and water vapor winds enter into the height field as gradient information. The cloud drift winds especially, have the character of supplying information in cloudy areas where satellite soundings are not possible. In the April 26 experiments, analyses and forecasts using the combination satellite winds and soundings were superior to those using only soundings. Good consistency was shown between independent satellite forecasts from different initialization times run to the same verification time. A significant accomplishment in FY-85 was expanding experiments on April 26 to include quasi-continuous initialization inserting satellite soundings and winds from several different times into an analysis/forecast. Contrary to the first set of experiments on April 26, here forecast initialization fields were not independent, but contained satellite information from two data times.

Diak, G. R.↗

NASA NTRS1989

Stability robustness improvement of direct eigenspace assignment based feedback systems using singular value sensitivities

A methodology to improve the stability robustness of feedback control systems designed using direct eigenspace assignment techniques is presented. The method consists of considering the sensitivity of the minimum singular value of the return difference transfer matrix at the plant input to small changes in the desired closed-loop eigenvalues and the specified elements of the desired closed-loop eigenvectors. Closed-form expressions for the gradient of the minimum return difference singular value with respect to desired closed-loop eigenvalue and eigenvector parameters are derived. Closed-form expressions for the gradients of the control feedback gains with respect to the specified eigenspace parameters are obtained as an intermediate step. The use of the gradient information to improve the guaranteed gain and phase margins in eigenspace assignment based designs is demonstrated by application to an advanced fighter aircraft.

Garg, Sanjay↗

NASA NTRS1989

Stability robustness improvement of direct eigenspace assignment based feedback systems using singular value sensitivities

Garg, Sanjay↗

NASA NTRS1991

Airfoil optimization with efficient gradient calculations

The viscous airfoil design analysis code XFOIL was extended to allow optimization using conformal mapping coefficients as design variables. The optimization technique used was the Steepest Descent method applied to a Penalty Function. The gradients of the aerodynamic variables with respect to the design variables were cheaply calculated as by-products of XFOIL's integral boundary layer Newton solver. The speed of the optimization process further increased by updating the Newton system boundary layer variables after each optimization step using the available gradient information. Two examples are presented.

Sorensen, Thomas↗

NASA NTRS1992

Observations on computational methodologies for use in large-scale, gradient-based, multidisciplinary design incorporating advanced CFD codes

How a combination of various computational methodologies could reduce the enormous computational costs envisioned in using advanced CFD codes in gradient based optimized multidisciplinary design (MdD) procedures is briefly outlined. Implications of these MdD requirements upon advanced CFD codes are somewhat different than those imposed by a single discipline design. A means for satisfying these MdD requirements for gradient information is presented which appear to permit: (1) some leeway in the CFD solution algorithms which can be used; (2) an extension to 3-D problems; and (3) straightforward use of other computational methodologies. Many of these observations have previously been discussed as possibilities for doing parts of the problem more efficiently; the contribution here is observing how they fit together in a mutually beneficial way.

Newman, P. A.↗

NASA NTRS1992

Polynomial approximation of Poincare maps for Hamiltonian system

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Froeschle, Claude↗

NASA NTRS1993

A solution scheme for the Euler equations based on a multi-dimensional wave model

A scheme for the solution of scalar advection on an unstructured mesh has been developed, tested, and extended to the Euler equations. The scheme preserves a linear function exactly, and yields nearly monotone results. The flux function associated with the Euler scheme is based on a discrete 'wave model' for the system of equations. The wave model decomposes the solution gradient at a location into shear waves, entropy waves and acoustic waves and calculates the speeds, strengths and directions associated with the waves. The approach differs from typical flux-difference splitting schemes in that the waves are not assumed to propagate normal to the faces of the control volumes; directions of propagation of the waves are instead computed from solution-gradient information. Results are shown for three test cases, and two different wave models. The results are compared to those from other approaches, including MUSCL and Galerkin least squares schemes.

Powell, Kenneth G.↗

NASA NTRS1992

Observations on computational methodologies for use in large-scale, gradient-based, multidisciplinary design

Various computational methodologies relevant to large-scale multidisciplinary gradient-based optimization for engineering systems design problems are examined with emphasis on the situation where one or more discipline responses required by the optimized design procedure involve the solution of a system of nonlinear partial differential equations. Such situations occur when advanced CFD codes are applied in a multidisciplinary procedure for optimizing an aerospace vehicle design. A technique for satisfying the multidisciplinary design requirements for gradient information is presented. The technique is shown to permit some leeway in the CFD algorithms which can be used, an expansion to 3D problems, and straightforward use of other computational methodologies.

Newman, P. A.↗

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↗

NASA NTRS1995

New approaches to optimization in aerospace conceptual design

Aerospace design can be viewed as an optimization process, but conceptual studies are rarely performed using formal search algorithms. Three issues that restrict the success of automatic search are identified in this work. New approaches are introduced to address the integration of analyses and optimizers, to avoid the need for accurate gradient information and a smooth search space (required for calculus-based optimization), and to remove the restrictions imposed by fixed complexity problem formulations. (1) Optimization should be performed in a flexible environment. A quasi-procedural architecture is used to conveniently link analysis modules and automatically coordinate their execution. It efficiently controls a large-scale design tasks. (2) Genetic algorithms provide a search method for discontinuous or noisy domains. The utility of genetic optimization is demonstrated here, but parameter encodings and constraint-handling schemes must be carefully chosen to avoid premature convergence to suboptimal designs. The relationship between genetic and calculus-based methods is explored. (3) A variable-complexity genetic algorithm is created to permit flexible parameterization, so that the level of description can change during optimization. This new optimizer automatically discovers novel designs in structural and aerodynamic tasks.

Gage, Peter J.↗

NASA NTRS1995

Pseudo-time methods for constrained optimization problems governed by PDE

In this paper we present a novel method for solving optimization problems governed by partial differential equations. Existing methods are gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurfaces while improving the residuals of the design equations per each iteration. In contrast, the method presented here march on the design hypersurface and at each iteration improve the residuals of the state and costate equations. The new method is usually much less expensive per iteration step since, in most problems of practical interest, the design equation involves much less unknowns that that of either the state or costate equations. Convergence is shown using energy estimates for the evolution equations governing the iterative process. Numerical tests show that the new method allows the solution of the optimization problem in a cost of solving the analysis problems just a few times, independent of the number of design parameters. The method can be applied using single grid iterations as well as with multigrid solvers.

Taasan, Shlomo↗

NASA NTRS1994

Control theory based airfoil design for potential flow and a finite volume discretization

This paper describes the implementation of optimization techniques based on control theory for airfoil design. In previous studies it was shown that control theory could be used to devise an effective optimization procedure for two-dimensional profiles in which the shape is determined by a conformal transformation from a unit circle, and the control is the mapping function. The goal of our present work is to develop a method which does not depend on conformal mapping, so that it can be extended to treat three-dimensional problems. Therefore, we have developed a method which can address arbitrary geometric shapes through the use of a finite volume method to discretize the potential flow equation. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented, where both target speed distributions and minimum drag are used as objective functions.

Reuther, J.↗

NASA NTRS1996

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↗

NASA NTRS1996

Aerodynamic Shape Optimization of Supersonic Aircraft Configurations via an Adjoint Formulation on Parallel Computers

This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations. In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that this basic methodology could be ported to distributed memory parallel computing architectures. In this paper, our concern will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.

Reuther, James↗

NASA NTRS1994

System Sensitivity Analysis Applied to the Conceptual Design of a Dual-Fuel Rocket SSTO

This paper reports the results of initial efforts to apply the System Sensitivity Analysis (SSA) optimization method to the conceptual design of a single-stage-to-orbit (SSTO) launch vehicle. SSA is an efficient, calculus-based MDO technique for generating sensitivity derivatives in a highly multidisciplinary design environment. The method has been successfully applied to conceptual aircraft design and has been proven to have advantages over traditional direct optimization methods. The method is applied to the optimization of an advanced, piloted SSTO design similar to vehicles currently being analyzed by NASA as possible replacements for the Space Shuttle. Powered by a derivative of the Russian RD-701 rocket engine, the vehicle employs a combination of hydrocarbon, hydrogen, and oxygen propellants. Three primary disciplines are included in the design - propulsion, performance, and weights & sizing. A complete, converged vehicle analysis depends on the use of three standalone conceptual analysis computer codes. Efforts to minimize vehicle dry (empty) weight are reported in this paper. The problem consists of six system-level design variables and one system-level constraint. Using SSA in a 'manual' fashion to generate gradient information, six system-level iterations were performed from each of two different starting points. The results showed a good pattern of convergence for both starting points. A discussion of the advantages and disadvantages of the method, possible areas of improvement, and future work is included.

Olds, John R.↗