Search NASA⌕ Search

SEARCH · Search NASA

Results for “objective function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10

An enhanced integrated aerodynamic load/dynamic optimization procedure for helicopter rotor blades

An enhanced integrated aerodynamic load/dynamic optimization procedure is developed to minimize vibratory root shears and moments. The optimization is formulated with 4/rev vertical and 3/rev inplane shears at the blade root as objective functions and constraints, and 4/rev lagging moment. Constraints are also imposed on blade natural frequencies, weight, autorotational inertia, centrifugal stress, and rotor thrust. The 'Global Criteria Approach' is used for formulating the multi-objective optimization. Design variables include spanwise distributions of bending stiffnesses, torsional stiffness, nonstructural mass, chord, radius of gyration, and blade taper ratio. The program CAMRAD is coupled with an optimizer, which consists of the program CONMIN and an approximate analysis, to obtain optimum designs. The optimization procedure is applied to an advanced rotor as a reference design. Optimum blade designs, obtained with and without a constraint on the rotor thrust, are presented and are compared to the reference blade. Substantial reductions are obtained in the vibratory root forces and moments. As a byproduct, improvements are also found in some performance parameters, such as total power required, which were not considered during optimization.

Chattopadhyay, Aditi↗

An enhanced integrated aerodynamic load/dynamic approach to optimum rotor blade design

An enhanced integrated aerodynamic load/dynamic optimization procedure is developed to minimize vibratory root shears and moments. The optimization is formulated with 4/rev vertical and 3/rev inplane shears at the blade root as objective functions and constraints, and 4/rev lagging moment. Constraints are also imposed on blade natural frequencies, weight, autorotational inertia, contrifugal stress, and rotor thrust. The Global Criteria Approach is used for formulating the multi-objective optimization. Design variables include spanwise distributions of bending stiffnesses, torsional stiffness, nonstructural mass, chord, radius of gyration, and blade taper ratio. The program CAMRAD is coupled with an optimizer, which consists of the program CONMIN and an approximate analysis, to obtain optimum designs. The optimization procedure is applied to an advanced rotor as a reference design. Optimum blade designs, obtained with and without a constraint on the rotor thrust, are presented and are compared to the reference blade. Substantial reductions are obtained in the vibratory root forces and moments. As a byproduct, improvements are also found in some performance parameters, such as total power required, which were not considered during optimization.

Chattopadhyay, Aditi↗

Modified Interior Distance Functions (Theory and Methods)

In this paper we introduced and developed the theory of Modified Interior Distance Functions (MIDF's). The MIDF is a Classical Lagrangian (CL) for a constrained optimization problem which is equivalent to the initial one and can be obtained from the latter by monotone transformation both the objective function and constraints. In contrast to the Interior Distance Functions (IDF's), which played a fundamental role in Interior Point Methods (IPM's), the MIDF's are defined on an extended feasible set and along with center, have two extra tools, which control the computational process: the barrier parameter and the vector of Lagrange multipliers. The extra tools allow to attach to the MEDF's very important properties of Augmented Lagrangeans. One can consider the MIDFs as Interior Augmented Lagrangeans. It makes MIDF's similar in spirit to Modified Barrier Functions (MBF's), although there is a fundamental difference between them both in theory and methods. Based on MIDF's theory, Modified Center Methods (MCM's) have been developed and analyzed. The MCM's find an unconstrained minimizer in primal space and update the Lagrange multipliers, while both the center and the barrier parameter can be fixed or updated at each step. The MCM's convergence was investigated, and their rate of convergence was estimated. The extension of the feasible set and the special role of the Lagrange multipliers allow to develop MCM's, which produce, in case of nondegenerate constrained optimization, a primal and dual sequences that converge to the primal-dual solutions with linear rate, even when both the center and the barrier parameter are fixed. Moreover, every Lagrange multipliers update shrinks the distance to the primal dual solution by a factor 0 less than gamma less than 1 which can be made as small as one wants by choosing a fixed interior point as a 'center' and a fixed but large enough barrier parameter. The numericai realization of MCM leads to the Newton MCM (NMCM). The approximation for the primal minimizer one finds by Newton Method followed by the Lagrange multipliers update. Due to the MCM convergence, when both the center and the barrier parameter are fixed, the condition of the MDF Hessism and the neighborhood of the primal ninimizer where Newton method is 'well' defined remains stable. It contributes to both the complexity and the numerical stability of the NMCM.

Polyak, Roman A.↗

Validation of an Impedance Education Method in Flow

This paper reports results of a research effort to validate a method for educing the normal incidence impedance of a locally reacting liner, located in a grazing incidence, nonprogressive acoustic wave environment with flow. The results presented in this paper test the ability of the method to reproduce the measured normal incidence impedance of a solid steel plate and two soft test liners in a uniform flow. The test liners are known to be locally react- ing and exhibit no measurable amplitude-dependent impedance nonlinearities or flow effects. Baseline impedance spectra for these liners were therefore established from measurements in a conventional normal incidence impedance tube. A key feature of the method is the expansion of the unknown impedance function as a piecewise continuous polynomial with undetermined coefficients. Stewart's adaptation of the Davidon-Fletcher-Powell optimization algorithm is used to educe the normal incidence impedance at each Mach number by optimizing an objective function. The method is shown to reproduce the measured normal incidence impedance spectrum for each of the test liners, thus validating its usefulness for determining the normal incidence impedance of test liners for a broad range of source frequencies and flow Mach numbers. Nomenclature

Watson, Willie R.↗

In-flight demonstration of the Space Station Freedom Health Maintenance Facility fluid therapy system (E300/E05)

The Space Station Freedom (SSF) Health Maintenance Facility (HMF) will provide medical care for crew members for up to 10 days. An integral part of the required medical care consists of providing intravenous infusion of fluids, electrolyte solutions, and nutrients to sustain an ill or injured crew member. In terrestrial health care facilities, intravenous solutions are normally stored in large quantities. However, due to the station's weight and volume constraints, an adequate supply of the required solutions cannot be carried onboard SSF. By formulating medical fluids onboard from concentrates and station water as needed, the Fluid Therapy System (FTS) eliminates weight and volume concerns regarding intravenous fluids. The first full-system demonstration of FTS is continuous microgravity will be conducted in Spacelab-Japan (SL-J). The FTS evaluation consists of two functional objectives and an in-flight demonstration of intravenous administration of fluids. The first is to make and store sterile water and IV solutions onboard the spacecraft. If intravenous fluids are to be produced in SSF, successful sterilization of water and reconstituting of IV solutions must be achieved. The second objective is to repeat the verification of the FTS infusion pump, which had been performed in Spacelab Life Sciences - 1 (SLS-1). during SLS-1, the FTS IV pump was operated in continuous microgravity for the first time. The pump functioned successfully, and valuable knowledge on its performance in continuous microgravity was obtained. Finally, the technique of starting an IF in microgravity will be demonstrated. The IV technique requires modifications in microgravity, such as use of restraints for equipment and crew members involved.

Lloyd, Charles W.↗

Multi-Objective Hybrid Optimal Control for Interplanetary Mission Planning

Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. Because low-thrust trajectory design is tightly coupled with systems design, power and propulsion characteristics must be chosen as well. In addition, a time-history of control variables must be chosen which defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated. The customer who commissions a trajectory design is not usually interested in a point solution, but rather the exploration of the trade space of trajectories between several different objective functions. This can be very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a multi-objective hybrid optimal control problem. The methods is demonstrated on hypothetical mission to the main asteroid belt and to Deimos.

Trajectory Design↗

Multi-Objective Hybrid Optimal Control for Multiple-Flyby Low-Thrust Mission Design

Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. In addition, a time-history of control variables must be chosen that defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated. The customer who commissions a trajectory design is not usually interested in a point solution, but rather the exploration of the trade space of trajectories between several different objective functions. This can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a multi-objective hybrid optimal control problem. The method is demonstrated on a hypothetical mission to the main asteroid belt.

Optimization↗

Multi-Objective Hybrid Optimal Control for Interplanetary Mission Planning

Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. Because low-thrust trajectory design is tightly coupled with systems design, power and propulsion characteristics must be chosen as well. In addition, a time-history of control variables must be chosen which defines the trajectory. There are often may thousands, if not millions, of possible trajectories to be evaluated. The customer who commissions a trajectory design is not usually interested in a point solution, but rather the exploration of the trade space of trajectories between several different objective functions. This can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a multi-objective hybrid optimal control problem. The method is demonstrated on hypothetical mission to the main asteroid belt and to Deimos.

Low Thrust↗

Multi-Objective Hybrid Optimal Control for Multiple-Flyby Interplanetary Mission Design using Chemical Propulsion

Preliminary design of high‐thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys and the bodies at which those flybys are performed. For some missions, such as surveys of small bodies, the mission designer also contributes to target selection. In addition, real‐valued decision variables, such as launch epoch, flight times, maneuver and flyby epochs, and flyby altitudes must be chosen. There are often many thousands of possible trajectories to be evaluated. The customer who commissions a trajectory design is not usually interested in a point solution, but rather the exploration of the trade space of trajectories between several different objective functions. This can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the impulsive mission design problem as a multi‐objective hybrid optimal control problem. The method is demonstrated on several real‐world problems. Two assumptions are frequently made to simplify the modeling of an interplanetary high‐thrust trajectory during the preliminary design phase. The first assumption is that because the available thrust is high, any maneuvers performed by the spacecraft can be modeled as discrete changes in velocity. This assumption removes the need to integrate the equations of motion governing the motion of a spacecraft under thrust and allows the change in velocity to be modeled as an impulse and the expenditure of propellant to be modeled using the time‐independent solution to Tsiolkovsky's rocket equation [1]. The second assumption is that the spacecraft moves primarily under the influence of the central body, i.e. the sun, and all other perturbing forces may be neglected in preliminary design. The path of the spacecraft may then be modeled as a series of conic sections. When a spacecraft performs a close approach to a planet, the central body switches from the sun to that planet and the trajectory is modeled as a hyperbola with respect to the planet. This is known as the method of patched conics. The impulsive and patched‐conic assumptions significantly simplify the preliminary design problem.

Optimization↗

Multi-Objective Hybrid Optimal Control for Interplanetary Mission Planning

Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed and in some cases the final destination. In addition, a time-history of control variables must be chosen which defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated. The customer who commissions a trajectory design is not usually interested in a point solution, but rather the exploration of the trade space of trajectories between several different objective functions. This can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very diserable. This work presents such as an approach by posing the mission design problem as a multi-objective hybrid optimal control problem. The method is demonstrated on a hypothetical mission to the main asteroid belt.

Optimization↗

Solution of nonlinear finite difference ocean models by optimization methods with sensitivity and observational strategy analysis

The paper studies with finite difference nonlinear circulation models the uncertainties in interesting flow properties, such as western boundary current transport, potential and kinetic energy, owing to the uncertainty in the driving surface boundary condition. The procedure is based upon nonlinear optimization methods. The same calculations permit quantitative study of the importance of new information as a function of type, region of measurement and accuracy, providing a method to study various observing strategies. Uncertainty in a model parameter, the bottom friction coefficient, is studied in conjunction with uncertain measurements. The model is free to adjust the bottom friction coefficient such that an objective function is minimized while fitting a set of data to within prescribed bounds. The relative importance of the accuracy of the knowledge about the friction coefficient with respect to various kinds of observations is then quantified, and the possible range of the friction coefficients is calculated.

Schroeter, Jens↗

The Katydid system for compiling KEE applications to Ada

Components of a system known as Katydid are developed in an effort to compile knowledge-based systems developed in a multimechanism integrated environment (KEE) to Ada. The Katydid core is an Ada library supporting KEE object functionality, and the other elements include a rule compiler, a LISP-to-Ada translator, and a knowledge-base dumper. Katydid employs translation mechanisms that convert LISP knowledge structures and rules to Ada and utilizes basic prototypes of a run-time KEE object-structure library module for Ada. Preliminary results include the semiautomatic compilation of portions of a simple expert system to run in an Ada environment with the described algorithms. It is suggested that Ada can be employed for AI programming and implementation, and the Katydid system is being developed to include concurrency and synchronization mechanisms.

Filman, Robert E.↗

Comparison of polynomial approximations and artificial neural nets for response surfaces in engineering optimization

Engineering optimization problems involve minimizing some function subject to constraints. In areas such as aircraft optimization, the constraint equations may be from numerous disciplines such as transfer of information between these disciplines and the optimization algorithm. They are also suited to problems which may require numerous re-optimizations such as in multi-objective function optimization or to problems where the design space contains numerous local minima, thus requiring repeated optimizations from different initial designs. Their use has been limited, however, by the fact that development of response surfaces randomly selected or preselected points in the design space. Thus, they have been thought to be inefficient compared to algorithms to the optimum solution. A development has taken place in the last several years which may effect the desirability of using response surfaces. It may be possible that artificial neural nets are more efficient in developing response surfaces than polynomial approximations which have been used in the past. This development is the concern of the work.

Carpenter, William C.↗

Sonic Boom Prediction and Minimization of the Douglas Reference OPT5 Configuration

Conventional CFD methods and grids do not yield adequate resolution of the complex shock flow pattern generated by a real aircraft geometry. As a result, a unique grid topology and supersonic flow solver was developed at Northrop Grumman based on the characteristic behavior of supersonic wave patterns emanating from the aircraft. Using this approach, it was possible to compute flow fields with adequate resolution several body lengths below the aircraft. In this region, three-dimensional effects are diminished and conventional two-dimensional modified linear theory (MLT) can be applied to estimate ground pressure signatures or sonic booms. To accommodate real aircraft geometries and alleviate the burdensome grid generation task, an implicit marching multi-block, multi-grid finite-volume Euler code was developed as the basis for the sonic boom prediction methodology. The Thomas two-dimensional extrapolation method is built into the Euler code so that ground signatures can be obtained quickly and efficiently with minimum computational effort suitable to the aircraft design environment. The loudness levels of these signatures can then be determined using a NASA generated noise code. Since the Euler code is a three-dimensional flow field solver, the complete circumferential region below the aircraft is computed. The extrapolation of all this field data from a cylinder of constant radius leads to the definition of the entire boom corridor occurring directly below and off to the side of the aircraft's flight path yielding an estimate for the entire noise "annoyance" corridor in miles as well as its magnitude. An automated multidisciplinary sonic boom design optimization software system was developed during the latter part of HSR Phase 1. Using this system, it was found that sonic boom signatures could be reduced through optimization of a variety of geometric aircraft parameters. This system uses a gradient based nonlinear optimizer as the driver in conjunction with a computationally efficient Euler CFD solver (NIIM3DSB) for computing the three-dimensional near-field characteristics of the aircraft. The intent of the design system is to identify and optimize geometric design variables that have a beneficial impact on the ground sonic boom. The system uses a simple wave drag data format to specify the aircraft geometry. The geometry is internally enhanced and analytic methods are used to generate marching grids suitable for the multi-block Euler solver. The Thomas extrapolation method is integrated into this system, and hence, the aircraft's centerline ground sonic boom signature is also automatically computed for a specified cruise altitude and yields the parameters necessary to evaluate the design function. The entire design system has been automated since the gradient based optimization software requires many flow analyses in order to obtain the required sensitivity derivatives for each design variable in order to converge on an optimal solution. Hence, once the problem is defined which includes defining the objective function and geometric and aerodynamic constraints, the system will automatically regenerate the perturbed geometry, the necessary grids, the Euler solution, and finally the ground sonic boom signature at the request of the optimizer.

Siclari, Michael J.↗

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Nemec, Marian↗

Impact of Gender on Pharmocokinetics of Intranasal Scopolamine

Introduction: An intranasal gel dosage formulation of scopolamine (INSCOP) was developed for the treatment of Space Motion Sickness (SMS), which is commonly experienced by astronauts during space missions. The bioavailability and pharmacokinetics (PK) were evaluated under IND guidelines. Since information is lacking on the effect of gender on the PK of Scopolamine, we examined gender differences in PK parameters of INSCOP at three dose levels of 0.1, 0.2 and 0.4 mg. Methods: Plasma scopolamine concentrations as a function of time data were collected from twelve normal healthy human subjects (6 male/6 female) who participated in a fully randomized double blind crossover study. The PK parameters were derived using WinNonlin. Covariate analysis of PK profiles was performed using NONMEN and statistically compared using a likelihood ratio test on the difference of objective function value (OFV). Statistical significance for covariate analysis was set at P<0.05(ΔOFV=3.84). Results: No significant difference in PK parameters between male and female subjects was observed with 0.1 and 0.2 mg doses. However, CL and Vd were significantly different between male and female subjects at the 0.4 mg dose. Results from population covariate modeling analysis indicate that a onecompartment PK model with first-order elimination rate offers best fit for describing INSCOP concentration-time profiles. The inclusion of sex as a covariate enhanced the model fitting (ΔOFV=-4.1) owing to the genderdependent CL and Vd differences after the 0.4 mg dose. Conclusion: Statistical modeling of scopolamine concentration-time data suggests gender-dependent pharmacokinetics of scopolamine at the high dose level of 0.4 mg. Clearance of the parent compound was significantly faster and the volume of distribution was significantly higher in males than in females, As a result, including gender as a covariate to the pharmacokinetic model of scopolamine offers the best fit for PK modeling of the drug at dose of 0.4 mg or higher.

Putcha, L.↗

Imparting Desired Attributes by Optimization in Structural Design

Commonly available optimization methods typically produce a single optimal design as a Constrained minimum of a particular objective function. However, in engineering design practice it is quite often important to explore as much of the design space as possible with respect to many attributes to find out what behaviors are possible and not possible within the initially adopted design concept. The paper shows that the very simple method of the sum of objectives is useful for such exploration. By geometrical argument it is demonstrated that if every weighting coefficient is allowed to change its magnitude and its sign then the method returns a set of designs that are all feasible, diverse in their attributes, and include the Pareto and non-Pareto solutions, at least for convex cases. Numerical examples in the paper include a case of an aircraft wing structural box with thousands of degrees of freedom and constraints, and over 100 design variables, whose attributes are structural mass, volume, displacement, and frequency. The method is inherently suitable for parallel, coarse-grained implementation that enables exploration of the design space in the elapsed time of a single structural optimization.

Sobieszczanski-Sobieski, Jaroslaw↗

Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

Tiffany, Sherwood H.↗