Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “interior methods”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

The expanded LaGrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrainted optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗
NASA NTRS1988

The expanded Lagrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrained optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗
NASA NTRS1998

Application of the Spectral Element Method to Interior Noise Problems

The primary effort of this research project was focused the development of analytical methods for the accurate prediction of structural acoustic noise and response. Of particular interest was the development of curved frame and shell spectral elements for the efficient computational of structural response and of schemes to match this to the surrounding fluid.

Doyle, James F.↗
NASA NTRS1994

An optimization program based on the method of feasible directions: Theory and users guide

The theory and user instructions for an optimization code based on the method of feasible directions are presented. The code was written for wide distribution and ease of attachment to other simulation software. Although the theory of the method of feasible direction was developed in the 1960's, many considerations are involved in its actual implementation as a computer code. Included in the code are a number of features to improve robustness in optimization. The search direction is obtained by solving a quadratic program using an interior method based on Karmarkar's algorithm. The theory is discussed, focusing on the important and often overlooked role played by the various parameters guiding the iterations within the program. Also discussed is a robust approach for handling infeasible starting points. The code was validated by solving a variety of structural optimization test problems that have known solutions obtained by other optimization codes. It has been observed that this code is accurate and robust: it has solved a variety of problems from different starting points. However, the code is inefficient in that it takes considerable CPU time as compared with certain other available codes. Further work is required to improve its efficiency while retaining its robustness.

Ashok D. Belegundu↗
NASA NTRS2011

Observational Effects of Magnetism in O Stars: Surface Nitrogen Abundances

Aims. We investigate the surface nitrogen content of the six magnetic O stars known to date as well as of the early B-type star Tau Sco.. We compare these abundances to predictions of evolutionary models to isolate the effects of magnetic field on the transport of elements in stellar interiors. Methods. We conduct a quantitative spectroscopic analysis of the ample stars with state-of-the-art atmosphere models. We rely on high signal-to-noise ratio, high resolution optical spectra obtained with ESPADONS at CFHT and NARVAL at TBL. Atmosphere models and synthetic spectra are computed with the code CMFGEN. Values of N/H together with their uncertainties are determined and compared to predictions of evolutionary models. Results. We find that the magnetic stars can be divided into two groups: one with stars displaying no N enrichment (one object); and one with stars most likely showing extra N enrichment (5 objects). For one star (Ori C) no robust conclusion can be drawn due to its young age. The star with no N enrichment is the one with the weakest magnetic field, possibly of dynamo origin. It might be a star having experienced strong magnetic braking under the condition of solid body rotation, but its rotational velocity is still relatively large. The five stars with high N content were probably slow rotators on the zero age main sequence, but they have surface N/H typical of normal O stars, indicating that the presence of a (probably fossil) magnetic field leads to extra enrichment. These stars may have a strong differential rotation inducing shear mixing. Our results shOuld be viewed as a basis on which new theoretical simulations can rely to better understand the effect of magnetism on the evolution of massive stars.

Martins, F.↗
NASA NTRS1999

A Method to Solve Interior and Exterior Camera Calibration Parameters for Image Resection

An iterative method is presented to solve the internal and external camera calibration parameters, given model target points and their images from one or more camera locations. The direct linear transform formulation was used to obtain a guess for the iterative method, and herein lies one of the strengths of the present method. In all test cases, the method converged to the correct solution. In general, an overdetermined system of nonlinear equations is solved in the least-squares sense. The iterative method presented is based on Newton-Raphson for solving systems of nonlinear algebraic equations. The Jacobian is analytically derived and the pseudo-inverse of the Jacobian is obtained by singular value decomposition.

Samtaney, Ravi↗
NASA NTRS1984

Evaluation of ride quality prediction methods for helicopter interior noise and vibration environments

The results of a simulator study conducted to compare and validate various ride quality prediction methods for use in assessing passenger/crew ride comfort within helicopters are presented. Included are results quantifying 35 helicopter pilots discomfort responses to helicopter interior noise and vibration typical of routine flights, assessment of various ride quality metrics including the NASA ride comfort model, and examination of possible criteria approaches. Results of the study indicated that crew discomfort results from a complex interaction between vibration and interior noise. Overall measures such as weighted or unweighted root-mean-square acceleration level and A-weighted noise level were not good predictors of discomfort. Accurate prediction required a metric incorporating the interactive effects of both noise and vibration. The best metric for predicting crew comfort to the combined noise and vibration environment was the NASA discomfort index.

Leatherwood, J. D.↗
NASA NTRS1978

Development of fire test methods for airplane interior materials

Fire tests were conducted in a 737 airplane fuselage at NASA-JSC to characterize jet fuel fires in open steel pans (simulating post-crash fire sources and a ruptured airplane fuselage) and to characterize fires in some common combustibles (simulating in-flight fire sources). Design post-crash and in-flight fire source selections were based on these data. Large panels of airplane interior materials were exposed to closely-controlled large scale heating simulations of the two design fire sources in a Boeing fire test facility utilizing a surplused 707 fuselage section. Small samples of the same airplane materials were tested by several laboratory fire test methods. Large scale and laboratory scale data were examined for correlative factors. Published data for dangerous hazard levels in a fire environment were used as the basis for developing a method to select the most desirable material where trade-offs in heat, smoke and gaseous toxicant evolution must be considered.

Tustin, E. A.↗
NASA NTRS2003

Inexpensive Method for Coating the Interior of Silica Growth Ampoules with Pyrolytic Boron Nitride

An inexpensive method was developed for coating the interior of silica ampoules with hexagonal boron nitride. An aqueous solution of boric acid was used to coat the ampoule prior to drying in a vacuum at 200 C. This coating was converted to transparent boron nitride by heating in ammonia at 1000 C. Coated ampoules were used to achieve detached solidification of indium antimonide on earth.

Wang, Jianbin↗
NASA NTRS1995

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.↗
NASA NTRS1997

Modeling of Structural-Acoustic Interaction Using Coupled FE/BE Method and Control of Interior Acoustic Pressure Using Piezoelectric Actuators

A coupled finite element (FE) and boundary element (BE) approach is presented to model full coupled structural/acoustic/piezoelectric systems. The dual reciprocity boundary element method is used so that the natural frequencies and mode shapes of the coupled system can be obtained, and to extend this approach to time dependent problems. The boundary element method is applied to interior acoustic domains, and the results are very accurate when compared with limited exact solutions. Structural-acoustic problems are then analyzed with the coupled finite element/boundary element method, where the finite element method models the structural domain and the boundary element method models the acoustic domain. Results for a system consisting of an isotropic panel and a cubic cavity are in good agreement with exact solutions and experiment data. The response of a composite panel backed cavity is then obtained. The results show that the mass and stiffness of piezoelectric layers have to be considered. The coupled finite element and boundary element equations are transformed into modal coordinates, which is more convenient for transient excitation. Several transient problems are solved based on this formulation. Two control designs, a linear quadratic regulator (LQR) and a feedforward controller, are applied to reduce the acoustic pressure inside the cavity based on the equations in modal coordinates. The results indicate that both controllers can reduce the interior acoustic pressure and the plate deflection.

Mei, Chuh↗
NASA NTRS2018

Optimal Control Prediction Method for Control Allocation

This paper proposes a novel prediction method for online optimal control allocation that extends the volume of moments achievable with the Moore-Penrose generalized inverse to the entire Attainable Moment Set. This method formulates the control allocation problem using selected basis vectors and associated gains which reduces the optimization problem dimensions and provides physical insight into the resulting optimal solutions. The proposed algorithm finds the entire family of unique optimal control solutions along the desired moment vector from the origin to the boundary of the Attainable Moment Set. Numerical results for the Moore-Penrose prediction method show that the unique minimal controls obtained yield the desired moment with near machine precision accuracy while maintaining control effectors within specified position limits. This method has been fully validated against the unique solution obtained on the boundary of the Attainable Moment Set using the Durham Direct Allocation method. Minimal control solutions obtained for moments in the interior of the Attainable Moment Set, similarly yield the desired moment to near machine precision while providing control solutions that are smaller (i.e. 2-norm) than solutions found with traditional control allocation algorithms (e.g. interior point methods) applied to the minimal control problem. Numerical simulations using a Matlab® autocoded executable (MEX) for the representative real world problem of 3-moments with 20 individual control effectors and prescribed control position limits show a mean computation speed of approximately 125 Hz which is sufficient to enable real-time flight allocation.

Acheson, Michael J.↗
NASA NTRS1935

The initial torsional stiffness of shells with interior webs

A method of calculating the stresses and torsional stiffness of thin shells with interior webs is summarized. Comparisons between experimental and calculated results are given for 3 duralumin beams, 5 stainless steel beams and 2 duralumin wings. It is concluded that if the theoretical stiffness is multiplied by a correction factor of 0.9, experimental values may be expected to check calculated values within about 10 percent.

Kuhn, Paul↗
NASA NTRS1974

The computation of steady nozzle flow by a time-dependent method

The steady flow in two-dimensional and axisymmetric nozzles was computed using a time-dependent method. In this method the interior mesh points were computed using the MacCormack finite-difference scheme, while a characteristic scheme was used to calculate the boundary mesh points. No explicit artificial viscosity term was included. The fluid was assumed to be a perfect gas. This method was used to compute the flow in a 45 deg - 15 deg conical, converging-diverging nozzle, a 15 deg conical, converging nozzle, and a 10 deg conical, plug nozzle. Good agreement between the numerical solution and experimental data was found. In contrast to previous time-dependent methods, the computational times were less than one minute on a CDC 6600 computer.

Cline, M. C.↗
NASA NTRS1993

Reliability based structural optimization - A simplified safety index approach

A probabilistic optimal design methodology for complex structures modelled with finite element methods is presented. The main emphasis is on developing probabilistic analysis tools suitable for optimization. An advanced second-moment method is employed to evaluate the failure probability of the performance function. The safety indices are interpolated using the information at mean and most probable failure point. The minimum weight design with an improved safety index limit is achieved by using the extended interior penalty method of optimization. Numerical examples covering beam and plate structures are presented to illustrate the design approach. The results obtained by using the proposed approach are compared with those obtained by using the existing probabilistic optimization techniques.

Reddy, Mahidhar V.↗