Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “method of multipliers”

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 127 records · Page 7

Acoustoelasticity - General theory, acoustic natural modes and forced response to sinusoidal excitation, including comparisons with experiment

A comprehensive theoretical model has been developed for interior sound fields which are created by flexible wall motion resulting from exterior sound fields. Full coupling between the wall and interior acoustic cavity is permitted. An efficient computational method is used to determine acoustic natural frequencies of multiply connected cavities. Simplified formulae are developed for interior sound levels in terms of cavity, wall and external acoustic field parameters. Comparisons of theory and experiment show generally good agreement.

Dowell, E. H.↗

A robust Feasible Directions algorithm for design synthesis

A nonlinear optimization algorithm is developed which combines the best features of the Method of Feasible Directions and the Generalized Reduced Gradient Method. This algorithm utilizes the direction-finding sub-problem from the Method of Feasible Directions to find a search direction which is equivalent to that of the Generalized Reduced Gradient Method, but does not require the addition of a large number of slack variables associated with inequality constraints. This method provides a core-efficient algorithm for the solution of optimization problems with a large number of inequality constraints. Further optimization efficiency is derived by introducing the concept of infrequent gradient calculations. In addition, it is found that the sensitivity of the optimum design to changes in the problem parameters can be obtained using this method without the need for second derivatives or Lagrange multipliers. A numerical example is given in order to demonstrate the efficiency of the algorithm and the sensitivity analysis.

Vanderplaats, G. N.↗

Airfoil optimization by the one-shot method

An efficient numerical approach for the design of optimal aerodynamic shapes is presented in this paper. The objective of any optimization problem is to find the optimum of a cost function subject to a certain state equation (Governing equation of the flow field) and certain side constraints. As in classical optimal control methods, the present approach introduces a costate variable (Language multiplier) to evaluate the gradient of the cost function. High efficiency in reaching the optimum solution is achieved by using a multigrid technique and updating the shape in a hierarchical manner such that smooth (low-frequency) changes are done separately from high-frequency changes. Thus, the design variables are changed on a grid where their changes produce nonsmooth (high-frequency) perturbations that can be damped efficiently by the multigrid. The cost of solving the optimization problem is approximately two to three times the cost of the equivalent analysis problem.

Kuruvila, G.↗

Radiation safety aspects of commercial high-speed flight transportation

High-speed commercial flight transportation is being studied for intercontinental operations in the 21st century, the projected operational characteristics for these aircraft are examined, the radiation environment as it is now known is presented, and the relevant health issues are discussed. Based on a critical examination of the data, a number of specific issues need to be addressed to ensure an adequate knowledge of the ionizing radiation health risks of these aircraft operations. Large uncertainties in our knowledge of the physical fields for high-energy neutrons and multiply-charged ion components need to be reduced. Improved methods for estimating risks in prenatal exposure need to be developed. A firm basis for solar flare monitoring and forecasting needs to be developed with means of exposure abatement.

Wilson, John W.↗

Parallelization of Finite Element Analysis Codes Using Heterogeneous Distributed Computing

Performance gains in computer design are quickly consumed as users seek to analyze larger problems to a higher degree of accuracy. Innovative computational methods, such as parallel and distributed computing, seek to multiply the power of existing hardware technology to satisfy the computational demands of large applications. In the early stages of this project, experiments were performed using two large, coarse-grained applications, CSTEM and METCAN. These applications were parallelized on an Intel iPSC/860 hypercube. It was found that the overall speedup was very low, due to large, inherently sequential code segments present in the applications. The overall execution time T(sub par), of the application is dependent on these sequential segments. If these segments make up a significant fraction of the overall code, the application will have a poor speedup measure.

Ozguner, Fusun↗

Airfoil Design and Optimization by the One-Shot Method

An efficient numerical approach for the design of optimal aerodynamic shapes is presented in this paper. The objective of any optimization problem is to find the optimum of a cost function subject to a certain state equation (governing equation of the flow field) and certain side constraints. As in classical optimal control methods, the present approach introduces a costate variable (Lagrange multiplier) to evaluate the gradient of the cost function. High efficiency in reaching the optimum solution is achieved by using a multigrid technique and updating the shape in a hierarchical manner such that smooth (low-frequency) changes are done separately from high-frequency changes. Thus, the design variables are changed on a grid where their changes produce nonsmooth (high-frequency) perturbations that can be damped efficiently by the multigrid. The cost of solving the optimization problem is approximately two to three times the cost of the equivalent analysis problem.

Kuruvila, G.↗

Using Generic Data to Establish Dormancy Failure Rates

Many hardware items are dormant prior to being operated. The dormant period might be especially long, for example during missions to the moon or Mars. In missions with long dormant periods the risk incurred during dormancy can exceed the active risk contribution. Probabilistic Risk Assessments (PRAs) need to account for the dormant risk contribution as well as the active contribution. A typical method for calculating a dormant failure rate is to multiply the active failure rate by a constant, the dormancy factor. For example, some practitioners use a heuristic and divide the active failure rate by 30 to obtain an estimate of the dormant failure rate. To obtain a more empirical estimate of the dormancy factor, this paper uses the recently updated database NPRD-2011 [1] to arrive at a set of distributions for the dormancy factor. The resulting dormancy factor distributions are significantly different depending on whether the item is electrical, mechanical, or electro-mechanical. Additionally, this paper will show that using a heuristic constant fails to capture the uncertainty of the possible dormancy factors.

Reistle, Bruce↗

The Failure of Correlation to Describe Out-of-Plane Carbon=Carbon Bending

Carbon-carbon multiply bonded systems are improperly described with standard correlation methods and basis sets. For computations of vibrational modes, the out-of- plane bends can be reported as imaginary at worst or simply too low at best. Utilizing the simplest of aromatic structures (cyclopropenylidene) and various levels of theory, this work diagnoses this known behavior for the first time. A combined 1-particle and n-particle basis set effect conspire to produce these non-physical results. When moving from sp2 to sp3 hybridization in the carbon atoms, the larger number of basis functions overcorrects the energy. This is exacerbated by correlation methods. These allow for occupation of the π and π∗ orbitals in the expanded wave function that combine with the hydrogen s orbitals. As a result, the improperly described space can be further and non-physically stabilized by post-Hartree-Fock correlation. This represents a fundamental problem with at least Hartree-Fock based methods of all flavors in describing carbon. Beyond being a flaw in quantum chemical theory, other repercussions will be present in computations regarding spectroscopy as well as energy and environmental studies where highly-accurate hydrocabon vibrational transitions or thermochemical data are needed.

Fortenberry, Ryan C.↗

An accurate method for evaluating the kernel of the integral equation relating lift to downwash in unsteady potential flow

The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the nonelementary integrals in the kernel by exponential functions and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. The method can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.

Desmarais, R. N.↗

An accurate and efficient method for evaluating the kernel of the integral equation relating pressure to normalwash in unsteady potential flow

This paper describes an accurate economical method for generating approximations to the kernel of the integral equation relating unsteady pressure to normalwash in nonplanar flow. The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the non elementary integrals in the kernel by exponential approximations and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. Coefficients for 8, 12, 24, and 72 term approximations are tabulated in the report. Also, since the method is automated, it can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.

Desmarais, R. N.↗

Reconfigurable Fault Tolerance for FPGAs

The invention allows a field-programmable gate array (FPGA) or similar device to be efficiently reconfigured in whole or in part to provide higher capacity, non-redundant operation. The redundant device consists of functional units such as adders or multipliers, configuration memory for the functional units, a programmable routing method, configuration memory for the routing method, and various other features such as block RAM, I/O (random access memory, input/output) capability, dedicated carry logic, etc. The redundant device has three identical sets of functional units and routing resources and majority voters that correct errors. The configuration memory may or may not be redundant, depending on need. For example, SRAM-based FPGAs will need some type of radiation-tolerant configuration memory, or they will need triple-redundant configuration memory. Flash or anti-fuse devices will generally not need redundant configuration memory. Some means of loading and verifying the configuration memory is also required. These are all components of the pre-existing redundant FPGA. This innovation modifies the voter to accept a MODE input, which specifies whether ordinary voting is to occur, or if redundancy is to be split. Generally, additional routing resources will also be required to pass data between sections of the device created by splitting the redundancy. In redundancy mode, the voters produce an output corresponding to the two inputs that agree, in the usual fashion. In the split mode, the voters select just one input and convey this to the output, ignoring the other inputs. In a dual-redundant system (as opposed to triple-redundant), instead of a voter, there is some means to latch or gate a state update only when both inputs agree. In this case, the invention would require modification of the latch or gate so that it would operate normally in redundant mode, and would separately latch or gate the inputs in non-redundant mode.

Shuler, Robert, Jr.↗

Evolutionary Based Techniques for Fault Tolerant Field Programmable Gate Arrays

The use of SRAM-based Field Programmable Gate Arrays (FPGAs) is becoming more and more prevalent in space applications. Commercial-grade FPGAs are potentially susceptible to permanently debilitating Single-Event Latchups (SELs). Repair methods based on Evolutionary Algorithms may be applied to FPGA circuits to enable successful fault recovery. This paper presents the experimental results of applying such methods to repair four commonly used circuits (quadrature decoder, 3-by-3-bit multiplier, 3-by-3-bit adder, 440-7 decoder) into which a number of simulated faults have been introduced. The results suggest that evolutionary repair techniques can improve the process of fault recovery when used instead of or as a supplement to Triple Modular Redundancy (TMR), which is currently the predominant method for mitigating FPGA faults.

Larchev, Gregory V.↗

Structural Deterministic Safety Factors Selection Criteria and Verification

Though current deterministic safety factors are arbitrarily and unaccountably specified, its ratio is rooted in resistive and applied stress probability distributions. This study approached the deterministic method from a probabilistic concept leading to a more systematic and coherent philosophy and criterion for designing more uniform and reliable high-performance structures. The deterministic method was noted to consist of three safety factors: a standard deviation multiplier of the applied stress distribution; a K-factor for the A- or B-basis material ultimate stress; and the conventional safety factor to ensure that the applied stress does not operate in the inelastic zone of metallic materials. The conventional safety factor is specifically defined as the ratio of ultimate-to-yield stresses. A deterministic safety index of the combined safety factors was derived from which the corresponding reliability proved the deterministic method is not reliability sensitive. The bases for selecting safety factors are presented and verification requirements are discussed. The suggested deterministic approach is applicable to all NASA, DOD, and commercial high-performance structures under static stresses.

Verderaime, V.↗

A hybrid perturbation Galerkin technique with applications to slender body theory

A two step hybrid perturbation-Galerkin method to solve a variety of applied mathematics problems which involve a small parameter is presented. The method consists of: (1) the use of a regular or singular perturbation method to determine the asymptotic expansion of the solution in terms of the small parameter; (2) construction of an approximate solution in the form of a sum of the perturbation coefficient functions multiplied by (unknown) amplitudes (gauge functions); and (3) the use of the classical Bubnov-Galerkin method to determine these amplitudes. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is applied to some singular perturbation problems in slender body theory. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the degree of applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗

A hybrid perturbation Galerkin technique with applications to slender body theory

A two-step hybrid perturbation-Galerkin method to solve a variety of applied mathematics problems which involve a small parameter is presented. The method consists of: (1) the use of a regular or singular perturbation method to determine the asymptotic expansion of the solution in terms of the small parameter; (2) construction of an approximate solution in the form of a sum of the perturbation coefficient functions multiplied by (unknown) amplitudes (gauge functions); and (3) the use of the classical Bubnov-Galerkin method to determine these amplitudes. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is applied to some singular perturbation problems in slender body theory. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the degree of applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗

Investigations with satellite data. 2: Temperature retrievals

A method for retrieving atmospheric temperatures in a severe storm situation was investigated. Retrieval was accomplished through the aid of satellite radiance measurements and nearby radiosondes. A set of coefficients was derived which when multiplied by the measured radiances, yielded smaller temperature retrieval errors than the minimum-information retrieval method.

Fritz, S.↗

Optimization for minimum sensitivity to uncertain parameters

A procedure to design a structure for minimum sensitivity to uncertainties in problem parameters is described. The approach is to minimize directly the sensitivity derivatives of the optimum design with respect to fixed design parameters using a nested optimization procedure. The procedure is demonstrated for the design of a bimetallic beam for minimum weight with insensitivity to uncertainties in structural properties. The beam is modeled with finite elements based on two dimensional beam analysis. A sequential quadratic programming procedure used as the optimizer supplies the Lagrange multipliers that are used to calculate the optimum sensitivity derivatives. The method was perceived to be successful from comparisons of the optimization results with parametric studies.

Pritchard, Jocelyn I.↗

Telemetry Ranging - Concept Paper Summary

Background - Previous CCSDS meetings: Spring 2015: Telemetry ranging technique was described; Fall 2015: A comparison to GMSK (Gaussian Minimum Shift Keying) plus PN (Pseudo-random Noise) ranging was made. -How telemetry ranging works: The spacecraft tracks the phase of the uplink PN ranging signal; Receive-time of downlink telemetry frame provides timing information; No downlink ranging signal is used. - This presentation: Summarizes the telemetry ranging concept paper. - Purpose: The purpose of the concept paper is to propose that the RFM (Radio Frequency Multiplier) Working Group consider telemetry ranging for inclusion as a recommended method for two-way ranging in the 401.0-B Blue Book.

Hamkins, Jon↗