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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Aerodynamic shape optimization of arbitrary hypersonic vehicles

A new method was developed to optimize, in terms of aerodynamic wave drag minimization, arbitrary (nonaxisymmetric) hypersonic vehicles in modified Newtonian flow, while maintaining the initial volume and length of the vehicle. This new method uses either a surface fitted Fourier series to represent the vehicle's geometry or an independent point motion algorithm. In either case, the coefficients of the Fourier series or the spatial locations of the points defining each cross section were varied and a numerical optimization algorithm based on a quasi-Newton gradient search concept was used to determine the new optimal configuration. Results indicate a significant decrease in aerodynamic wave drag for simple and complex geometries at relatively low CPU costs. In the case of a cone, the results agreed well with known analytical optimum ogive shapes. The procedure is capable of accepting more complex flow field analysis codes.

Dulikravich, George S.↗
NASA NTRS2003

Optimized Shapes of Ocsillating Resonators for Generating High-Amplitude Pressure Waves

It is well known that the resonator geometry strongly influences the resonant frequencies of an acoustical resonator and the generated nonlinear standing pressure waveform. Maximizing the ratio of maximum to minimum gas pressure at an end of an oscillating resonator by optimizing the cavity contour is investigated numerically. A quasi-Newton type scheme is used to find optimized axisymmetric resonator shapes to achieve the maximum pressure compression ratio. The acoustical field is solved using a one-dimensional model, and the resonance frequency shift and hysteresis effects are obtained through an automation scheme based on continuation methods. Results are presented from optimizing cone, horn-cone, and cosine resonator geometries. Significant performance improvement is found in the optimized shapes over others previously published. Different optimized shapes are found when starting with different initial guesses, indicating multiple local extrema. The numerical model is validated by comparing with the experimental results of a horn-cone shaped resonator.

Li, Xiao-Fan↗
NASA NTRS1973

Automated procedure for design of wing structures to satisfy strength and flutter requirements

A pilot computer program was developed for the design of minimum mass wing structures under flutter, strength, and minimum gage constraints. The wing structure is idealized by finite elements, and second-order piston theory aerodynamics is used in the flutter calculation. Mathematical programing methods are used for the optimization. Computation times during the design process are reduced by three techniques. First, iterative analysis methods used to reduce significantly reanalysis times. Second, the number of design variables is kept small by not using a one-to-one correspondence between finite elements and design variables. Third, a technique for using approximate second derivatives with Newton's method for the optimization is incorporated. The program output is compared witH previous published results. It is found that some flutter characteristics, such as the flutter speed, can display discontinous dependence on the design variables (which are the thicknesses of the structural elements). It is concluded that it is undesirable to use such quantities in the formulation of the flutter constraint.

Haftka, R. T.↗
NASA NTRS1999

Approximation of the Newton Step by a Defect Correction Process

In this paper, an optimal control problem governed by a partial differential equation is considered. The Newton step for this system can be computed by solving a coupled system of equations. To do this efficiently with an iterative defect correction process, a modifying operator is introduced into the system. This operator is motivated by local mode analysis. The operator can be used also for preconditioning in Generalized Minimum Residual (GMRES). We give a detailed convergence analysis for the defect correction process and show the derivation of the modifying operator. Numerical tests are done on the small disturbance shape optimization problem in two dimensions for the defect correction process and for GMRES.

Arian, E.↗
NASA NTRS1986

An optimization model for the US Air-Traffic System

A systematic approach for monitoring U.S. air traffic was developed in the context of system-wide planning and control. Towards this end, a network optimization model with nonlinear objectives was chosen as the central element in the planning/control system. The network representation was selected because: (1) it provides a comprehensive structure for depicting essential aspects of the air traffic system, (2) it can be solved efficiently for large scale problems, and (3) the design can be easily communicated to non-technical users through computer graphics. Briefly, the network planning models consider the flow of traffic through a graph as the basic structure. Nodes depict locations and time periods for either individual planes or for aggregated groups of airplanes. Arcs define variables as actual airplanes flying through space or as delays across time periods. As such, a special case of the network can be used to model the so called flow control problem. Due to the large number of interacting variables and the difficulty in subdividing the problem into relatively independent subproblems, an integrated model was designed which will depict the entire high level (above 29000 feet) jet route system for the 48 contiguous states in the U.S. As a first step in demonstrating the concept's feasibility a nonlinear risk/cost model was developed for the Indianapolis Airspace. The nonlinear network program --NLPNETG-- was employed in solving the resulting test cases. This optimization program uses the Truncated-Newton method (quadratic approximation) for determining the search direction at each iteration in the nonlinear algorithm. It was shown that aircraft could be re-routed in an optimal fashion whenever traffic congestion increased beyond an acceptable level, as measured by the nonlinear risk function.

Mulvey, J. M.↗
NASA NTRS2000

Cascade Optimization for Aircraft Engines With Regression and Neural Network Analysis - Approximators

The NASA Engine Performance Program (NEPP) can configure and analyze almost any type of gas turbine engine that can be generated through the interconnection of a set of standard physical components. In addition, the code can optimize engine performance by changing adjustable variables under a set of constraints. However, for engine cycle problems at certain operating points, the NEPP code can encounter difficulties: nonconvergence in the currently implemented Powell's optimization algorithm and deficiencies in the Newton-Raphson solver during engine balancing. A project was undertaken to correct these deficiencies. Nonconvergence was avoided through a cascade optimization strategy, and deficiencies associated with engine balancing were eliminated through neural network and linear regression methods. An approximation-interspersed cascade strategy was used to optimize the engine's operation over its flight envelope. Replacement of Powell's algorithm by the cascade strategy improved the optimization segment of the NEPP code. The performance of the linear regression and neural network methods as alternative engine analyzers was found to be satisfactory. This report considers two examples-a supersonic mixed-flow turbofan engine and a subsonic waverotor-topped engine-to illustrate the results, and it discusses insights gained from the improved version of the NEPP code.

Patnaik, Surya N.↗
NASA NTRS1985

Optimization of Controlled Structures

A formulation is presented for the coupled optimal design of a structural system and its control by defining a composite objective function as a linear combination of two components: a structural objective and a control objective. For the case when the structural objective is a function of the structural design variables only, and when the control objective is represented by the quadratic functional of the response and control energy, one can analytically express the optimal control in terms of any set of admissible structural design variables. The expression for the optimal control is used recursively in an iterative Newton-Raphson search scheme, the goal of which is to determine a corresponding optimal set of structural design variables that minimize the composite objective function. A numerical example is given to illustrate the computational procedure.

Salama, M.↗
NASA NTRS1987

Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing

This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.

Rodriguez, G.↗
NASA NTRS1995

Bicycle ergometer instrumentation to determine muscle and bone forces during exercise

It is hypothesized that bone loss experienced by astronauts in zero gravity conditions may be curtailed by appropriate exercise. According to Wolf's law, bone regenerates when muscles produce stresses by pulling on the bone during daily activity and/or exercise on Earth. to use this theory to prevent or decrease bone loss, one needs to quantify musculoskeletal loads and relate them to bone density changes. In the context of the space program, it is desirable to determine musculoskeletal loads during exercise (using the bicycle ergometer in this case) so that one may make similar measurements on Earth and in space. In this manner, load measurements on Earth may be used as reference to generate similar loads during exercise in space. The work reported in this document entails a musculoskeletal load measurement system that, when complete, will provide forces at muscle insertion points and other contact points, on bone. This data will be used by Dr. Beth A. Todd, who is also a SSF working with Dr. Shackelford, as input to a finite element model of bone sections to determine stress distributions. A bicycle ergometer has been instrumented to measure parameters needed to determine musculoskeletal forces during exercise. A primary feature of the system is its compactness. It uses small/light sensors without line-of-sight requirements. The system developed includes sensors, signal processing, a data acquisition system, and software to collect the data. The sensors used include optical encoders to measure position and orientation of the pedal (foot), accelerometers to determine kinematic parameters of the shank and thigh, load cells to measure pedal forces on the sagittal plane, and EMG probes to measure muscle activity. The signals are processed using anti-aliasing filters and amplifiers. The sensors' output is digitized using 30 channels of a board mounted inside a 486 class PC. A program sets the data acquisition parameters and collects data during a time period specified by the user. The data is put directly into a file on the hard disk in binary form. The 30 channels are sampled at 200 KHz, and each 30 channel scan is done at a rate of 1000 Hz. The instrumented ergometer has been flown in the KC-135 zero-gravity (zero-g) flight to collect information needed to determine musculoskeletal forces under these conditions. Similar information has been collected in 1-g conditions for comparision with the results from the zero-g case. At this time, the sets of data from both experiments are being processed. An existing methodology will be used to determine the kinematic parameters of the shank and thigh using accelerometer and encoder data. This methodology was developed during the fellow's previous NASA/ASEE fellowship and thanks to a Director's Grant. In the future, a methodology to determine the musculoskeletal forces using Newton's Law of Motion and optimization techniques will be developed to determine forces exerted by particular muscles.

Figueroa, Fernando↗
NASA NTRS2016

Real-Time Adaptive Least-Squares Drag Minimization for Performance Adaptive Aeroelastic Wing

This paper contains a simulation study of a real-time adaptive least-squares drag minimization algorithm for an aeroelastic model of a flexible wing aircraft. The aircraft model is based on the NASA Generic Transport Model (GTM). The wing structures incorporate a novel aerodynamic control surface known as the Variable Camber Continuous Trailing Edge Flap (VCCTEF). The drag minimization algorithm uses the Newton-Raphson method to find the optimal VCCTEF deflections for minimum drag in the context of an altitude-hold flight control mode at cruise conditions. The aerodynamic coefficient parameters used in this optimization method are identified in real-time using Recursive Least Squares (RLS). The results demonstrate the potential of the VCCTEF to improve aerodynamic efficiency for drag minimization for transport aircraft.

Aeroservoelasticity↗
NASA NTRSDate not supplied

Investigation of a Smooth Local Correlation-based Transition Model in a Discrete-Adjoint Aerodynamic Shape Optimization Algorithm

A smooth local correlation-based transition model is fully coupled to a RANS-based Newton-Krylov flow solver and discrete-adjoint gradient-based optimization algorithm. The free-transition optimization framework is evaluated using lift-constrained drag minimizations of airfoils at design conditions ranging from light to single-aisle aircraft and an infinite swept wing at design conditions representative of a transonic strut-braced wing aircraft. The impact of the streamwise grid resolution on the ability of the optimization algorithm to delay boundary-layer transition is investigated, with the results demonstrating that streamwise grid resolution requirements increase as the transition length decreases with increasing Reynolds number. The optimization problem at the light aircraft design conditions is demonstrated to be multi-modal, with the optimization algorithm producing two distinct designs: one with a thin, reflexed trailing edge and steep pressure recovery regions, the other with increased aft loading, with the latter design outperforming the former. A drag minimization of an airfoil at transonic design conditions demonstrates that the optimization algorithm successfully trades a decrease in viscous drag by delaying boundary-layer transition with an increase in wave drag, while the drag minimization of an infinite swept wing demonstrates the capability of the optimizational gorithm to delay both Tollmien-Schlichting and stationary crossflow instabilities.

AATT↗
NASA NTRS2003

Nonlinear Resonant Oscillations of Gas in Optimized Acoustical Resonators and the Effect of Central Blockage

Optimizing resonator shapes for maximizing the ratio of maximum to minimum gas pressure at an end of the resonator is investigated numerically. It is well known that the resonant frequencies and the nonlinear standing waveform in an acoustical resonator strongly depend on the resonator geometry. A quasi-Newton type scheme was used to find optimized axisymmetric resonator shapes achieving the maximum pressure compression ratio with an acceleration of constant amplitude. The acoustical field was solved using a one-dimensional model, and the resonance frequency shift and hysteresis effects were obtained through an automation scheme based on continuation method. Results are presented for optimizing three types of geometry: a cone, a horn-cone and a half cosine-shape. For each type, different optimized shapes were found when starting with different initial guesses. Further, the one-dimensional model was modified to study the effect of an axisymmetric central blockage on the nonlinear standing wave.

Li, Xiaofan↗
NASA NTRS2003

Nonlinear Resonant Oscillations of Gas in Optimized Acoustical Resonators and the Effect of Central Blockage

Optimizing resonator shapes for maximizing the ratio of maximum to minimum gas pressure at an end of the resonator is investigated numerically. It is well known that the resonant frequencies and the nonlinear standing waveform in an acoustical resonator strongly depend on the resonator geometry. A quasi-Newton type scheme was used to find optimized axisymmetric resonator shapes achieving the maximum pressure compression ratio with an acceleration of constant amplitude. The acoustical field was solved using a one-dimensional model, and the resonance frequency shift and hysteresis effects were obtained through an automation scheme based on continuation method. Results are presented for optimizing three types of geometry: a cone, a horn-cone and a half cosine- shape. For each type, different optimized shapes were found when starting with different initial guesses. Further, the one-dimensional model was modified to study the effect of an axisymmetric central blockage on the nonlinear standing wave.

Li, Xiao-Fan↗
NASA NTRS1989

Design of optimally normal minimum gain controllers by continuation method

A measure of the departure from normality is investigated for system robustness. An attractive feature of the normality index is its simplicity for pole placement designs. To allow a tradeoff between system robustness and control effort, a cost function consisting of the sum of a norm of weighted gain matrix and a normality index is minimized. First- and second-order necessary conditions for the constrained optimization problem are derived and solved by a Newton-Raphson algorithm imbedded into a one-parameter family of neighboring zero problems. The method presented allows the direct computation of optimal gains in terms of robustness and control effort for pole placement problems.

Lim, K. B.↗
NASA NTRS2000

Development of a Composite Tailoring Procedure for Airplane Wings

The quest for finding optimum solutions to engineering problems has existed for a long time. In modern times, the development of optimization as a branch of applied mathematics is regarded to have originated in the works of Newton, Bernoulli and Euler. Venkayya has presented a historical perspective on optimization in [1]. The term 'optimization' is defined by Ashley [2] as a procedure "...which attempts to choose the variables in a design process so as formally to achieve the best value of some performance index while not violating any of the associated conditions or constraints". Ashley presented an extensive review of practical applications of optimization in the aeronautical field till about 1980 [2]. It was noted that there existed an enormous amount of published literature in the field of optimization, but its practical applications in industry were very limited. Over the past 15 years, though, optimization has been widely applied to address practical problems in aerospace design [3-5]. The design of high performance aerospace systems is a complex task. It involves the integration of several disciplines such as aerodynamics, structural analysis, dynamics, and aeroelasticity. The problem involves multiple objectives and constraints pertaining to the design criteria associated with each of these disciplines. Many important trade-offs exist between the parameters involved which are used to define the different disciplines. Therefore, the development of multidisciplinary design optimization (MDO) techniques, in which different disciplines and design parameters are coupled into a closed loop numerical procedure, seems appropriate to address such a complex problem. The importance of MDO in successful design of aerospace systems has been long recognized. Recent developments in this field have been surveyed by Sobieszczanski-Sobieski and Haftka [6].

Chattopadhyay, Aditi↗