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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS2019

Liftoff and Transition Database Generation for Launch Vehicles Using Data-Fusion-Based Modeling

A data fusion technique for merging multiple data sources with differing fidelity and resolution was developed to support the production of aerodynamic line load databases for the Liftoff and Transition (LOT) flight phase of the Space Launch System (SLS). The technique uses a reduced order model based on a high-fidelity line load data set from Computational Fluid Dynamics (CFD) to predict solutions for a much larger solution space. Even higher-fidelity force and moment information (from wind-tunnel tests) is then used to adjust the model. The adjustment uses constrained optimization through the method of Lagrange multipliers in order to minimize the deviation of the line load distribution from the spatially-dense CFD solution, while ensuring that the integrated force and moment values match those observed in physical wind tunnel measurements. Though the wind-tunnel data are operationally-dense (available at many flow conditions), they are spatially coarse (as only the overall forces and moments are available). Conversely, CFD for such complex configurations is expensive, and thus operationally sparse. Data fusion techniques are necessary to make the most efficient use of available information, delivering accurate results within time and resource constraints.

Wignall, T. J.↗
DOE OSTI2022

Formulation of the density eigenvalue problem in neutron transport for relevant engineering applications

A new formulation of the density eigenvalue problem for the neutron transport equation is presented. This new eigenvalue, named ζ eigenvalue can be introduced freely in the transport model, acting on a selected portion of the phase space. Despite its broader applications and its connection with the nature of the transport operator, the ζ eigenvalue has been presented here mainly as a design-oriented technique for the efficient evaluation of the critical concentration for a specific nuclide (or mixture of nuclides). This new eigenvalue is particularly adequate to study the definition of the material composition in the criticality design process of a multiplying system. The method is then applied for the study of classical problems such as the critical moderation ratio and the poison concentration to control the reactor. Some results are presented in one dimensional configuration using the multi- group spherical harmonics approach. This eigenvalue formulation proves to be a convenient and useful way to attain criticality, also for complex, realistic systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1995

Methods for prismatic/tetrahedral grid generation and adaptation

The present work involves generation of hybrid prismatic/tetrahedral grids for complex 3-D geometries including multi-body domains. The prisms cover the region close to each body's surface, while tetrahedra are created elsewhere. Two developments are presented for hybrid grid generation around complex 3-D geometries. The first is a new octree/advancing front type of method for generation of the tetrahedra of the hybrid mesh. The main feature of the present advancing front tetrahedra generator that is different from previous such methods is that it does not require the creation of a background mesh by the user for the determination of the grid-spacing and stretching parameters. These are determined via an automatically generated octree. The second development is a method for treating the narrow gaps in between different bodies in a multiply-connected domain. This method is applied to a two-element wing case. A High Speed Civil Transport (HSCT) type of aircraft geometry is considered. The generated hybrid grid required only 170 K tetrahedra instead of an estimated two million had a tetrahedral mesh been used in the prisms region as well. A solution adaptive scheme for viscous computations on hybrid grids is also presented. A hybrid grid adaptation scheme that employs both h-refinement and redistribution strategies is developed to provide optimum meshes for viscous flow computations. Grid refinement is a dual adaptation scheme that couples 3-D, isotropic division of tetrahedra and 2-D, directional division of prisms.

Kallinderis, Y.↗
NASA NTRS1978

Stochastic inverse problem in the radiation of noise

The reported investigation is concerned with a stochastic inverse radiation problem in a uniform medium. The problem is illustrated with the aid of a simple model consisting of an array of point sources. The entropy functional is chosen to be the structural functional in determining the source distribution. A general theory for the stochastic inverse problem is introduced. It is shown that the general procedure yields the methods of the Lagrangian multiplier, when the structural and residual functionals are specialized. Tihonov's regularization and a method related to generalized or pseudoinverses are also obtained. Examples considered for purposes of illustration are related to a continuous source with the least noise intensity, a continuous source with a potential, and an axisymmetric line source.

Chow, P. L.↗
NASA NTRS1995

Adaptive hybrid prismatic-tetrahedral grids for viscous flows

The paper presents generation of adaptive hybrid prismatic/tetrahedral grids for complex 3-D geometries including multi-body domains. The prisms cover the region close to each body's surface, while tetrahedra are created elsewhere. Two developments are presented for hybrid grid generation around complex 3-D geometries. The first is a new octree/advancing front type of method for generation of the tetrahedra of the hybrid mesh. The main feature of the present advancing front tetrahedra generator that is different from previous such methods is that it does not require the creation of a background mesh by the user for the determination of the grid-spacing and stretching parameters. These are determined via an automatically generated octree. The second development is an Automatic Receding Method (ARM) for treating the narrow gaps in between different bodies in a multiply-connected domain. This method is applied to a two-element wing case. A hybrid grid adaptation scheme that employs both h-refinement and redistribution strategies is developed to provide optimum meshes for viscous flow computations. Grid refinement is a dual adaptation scheme that couples division of tetrahedra, as well as 2-D directional division of prisms.

Kallinderis, Yannis↗
NASA NTRS1994

Computing Misalignments From Measured Contact Resistances

Misalignments of contacts in integrated circuits computed, and measured contact resistances corrected for effects of misalignments by use of method based on relatively simple mathematical model of measured contact resistance. Flange resistance of aligned contact multiplied by semiempirical factor. Method particularly useful in estimating effects of misalignments on four- and six-terminal (Kelvin-tap) contact-resistance measurements taken with L-shaped test structures.

Lieneweg, Udo↗
DOE OSTI2021

Assessment of DFT methods for the prediction of detachment energies and electronic structures of complex and multiply charged anions

Here, in this work, we assess the ability of different density functional theory methods to reproduce the vertical/adiabatic detachment energies (VDEs/ADEs) of a series of 40 anions, including monoanion versus multiply charged anions (MCAs) and covalent versus noncovalent interaction. The statistical analysis of errors is firstly performed by comparing the theoretical values with the experimental benchmark data obtained from the negative ion photoelectron spectroscopy (NIPES). The proposed optimally tuned range-separated (OTRS) functionals are proved to not only well reproduce the experimental VDEs/ADEs, but also simulate experimental NIPES. The result implies a more serious issue of delocalization error for MCAs and a balanced description of electron-rich/- deficient region of anions is necessary. The radius of the spherically symmetric average electron localization function (ELF) region is demonstrated as a useful descriptor for the characterization of electronic structure of anionic systems and a quasilinear fitting model is proposed to efficiently obtain their OTRS parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

Here we propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing a scalable parameter in each layer (layer-wise) and for every neuron (neuron-wise) separately, and then optimizing it using a variant of stochastic gradient descent algorithm. In order to further increase the training speed, an activation slope-based slope recovery term is added in the loss function, which further accelerates convergence, thereby reducing the training cost. On the theoretical side, we prove that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposed method is not achievable by base methods with any (adaptive) learning rates. We further show that the adaptive activation methods accelerate the convergence by implicitly multiplying conditioning matrices to the gradient of the base method without any explicit computation of the conditioning matrix and the matrix–vector product. The different adaptive activation functions are shown to induce different implicit conditioning matrices. Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2006

Retrieving Storm Electric Fields from Aircraft Field Mill Data: Theory - Part 1

It is shown that the problem of retrieving storm electric fields from an aircraft instrumented with several electric field mill sensors can be expressed in terms of a standard Lagrange multiplier optimization problem. The method naturally removes aircraft charge from the retrieval process without having to use a high voltage stinger and linearly combined mill data values. It allows a variety of user-supplied physical constraints (the so-called side constraints in the theory of Lagrange multipliers) and also helps improve absolute calibration. Additionally, this paper introduces an alternate way of performing the absolute calibration of an aircraft that has some benefits over conventional analyses. It is accomplished by using the time derivatives of mill and pitch data for a pitch down maneuver performed at high (greater than 1 km) altitude. In Part II of this study, the above methods are tested and then applied to complete a full calibration of a Citation aircraft.

Koshak, W. J.↗
NASA NTRS2005

Retrieving Storm Electric Fields From Aircraft Field Mill Data. Part I: Theory

It is shown that the problem of retrieving storm electric fields from an aircraft instrumented with several electric field mill sensors can be expressed in terms of a standard Lagrange multiplier optimization problem. The method naturally removes aircraft charge from the retrieval process without having to use a high voltage stinger and linearly combined mill data values. It also allows a variety of user-supplied physical constraints (the so-called side constraints in the theory of Lagrange multipliers). Additionally, this paper introduces a novel way of performing the absolute calibration of an aircraft that has several benefits over conventional analyses. In the new approach, absolute calibration is completed by inspecting the time derivatives of mill and pitch data for a pitch down maneuver performed at high (greater than 1 km) altitude. In Part II of this study, the above methods are tested and then applied to complete a full calibration of a Citation aircraft.

Koshak, W. J.↗
NASA NTRS1996

Finite Element Analysis of Geodesically Stiffened Cylindrical Composite Shells Using a Layerwise Theory

Layerwise finite element analyses of geodesically stiffened cylindrical shells are presented. The layerwise laminate theory of Reddy (LWTR) is developed and adapted to circular cylindrical shells. The Ritz variational method is used to develop an analytical approach for studying the buckling of simply supported geodesically stiffened shells with discrete stiffeners. This method utilizes a Lagrange multiplier technique to attach the stiffeners to the shell. The development of the layerwise shells couples a one-dimensional finite element through the thickness with a Navier solution that satisfies the boundary conditions. The buckling results from the Ritz discrete analytical method are compared with smeared buckling results and with NASA Testbed finite element results. The development of layerwise shell and beam finite elements is presented and these elements are used to perform the displacement field, stress, and first-ply failure analyses. The layerwise shell elements are used to model the shell skin and the layerwise beam elements are used to model the stiffeners. This arrangement allows the beam stiffeners to be assembled directly into the global stiffness matrix. A series of analytical studies are made to compare the response of geodesically stiffened shells as a function of loading, shell geometry, shell radii, shell laminate thickness, stiffener height, and geometric nonlinearity. Comparisons of the structural response of geodesically stiffened shells, axial and ring stiffened shells, and unstiffened shells are provided. In addition, interlaminar stress results near the stiffener intersection are presented. First-ply failure analyses for geodesically stiffened shells utilizing the Tsai-Wu failure criterion are presented for a few selected cases.

Gerhard, Craig Steven↗
NASA NTRS1974

Operations on power series and higher derivatives of functions

Equations are derived for the general terms of the series obtained when certain operations are carried out on one or several given series. Explicit and recurrence relations are given for the literal groups which are common to the given series. A general method is shown to obtain the multipliers which depend on the operation being performed, and the method is illustrated for several examples.

Chang, F.-C.↗
NASA NTRS1993

Merits and limitations of optimality criteria method for structural optimization

The merits and limitations of the optimality criteria (OC) method for the minimum weight design of structures subjected to multiple load conditions under stress, displacement, and frequency constraints were investigated by examining several numerical examples. The examples were solved utilizing the Optimality Criteria Design Code that was developed for this purpose at NASA Lewis Research Center. This OC code incorporates OC methods available in the literature with generalizations for stress constraints, fully utilized design concepts, and hybrid methods that combine both techniques. Salient features of the code include multiple choices for Lagrange multiplier and design variable update methods, design strategies for several constraint types, variable linking, displacement and integrated force method analyzers, and analytical and numerical sensitivities. The performance of the OC method, on the basis of the examples solved, was found to be satisfactory for problems with few active constraints or with small numbers of design variables. For problems with large numbers of behavior constraints and design variables, the OC method appears to follow a subset of active constraints that can result in a heavier design. The computational efficiency of OC methods appears to be similar to some mathematical programming techniques.

Patnaik, Surya N.↗
NASA NTRS1992

A robust direct-integration method for rotorcraft maneuver and periodic response

The Newmark-Beta method and the Newton-Raphson iteration scheme are combined to develop a direct-integration method for evaluating the maneuver and periodic-response expressions for rotorcraft. The method requires the generation of Jacobians and includes higher derivatives in the formulation of the geometric stiffness matrix to enhance the convergence of the system. The method leads to effective convergence with nonlinear structural dynamics and aerodynamic terms. Singularities in the matrices can be addressed with the method as they arise from a Lagrange multiplier approach for coupling equations with nonlinear constraints. The method is also shown to be general enough to handle singularities from quasisteady control-system models. The method is shown to be more general and robust than the similar 2GCHAS method for analyzing rotorcraft dynamics.

Panda, Brahmananda↗
NASA NTRS1992

Two neural network algorithms for designing optimal terminal controllers with open final time

Multilayer neural networks, trained by the backpropagation through time algorithm (BPTT), have been used successfully as state-feedback controllers for nonlinear terminal control problems. Current BPTT techniques, however, are not able to deal systematically with open final-time situations such as minimum-time problems. Two approaches which extend BPTT to open final-time problems are presented. In the first, a neural network learns a mapping from initial-state to time-to-go. In the second, the optimal number of steps for each trial run is found using a line-search. Both methods are derived using Lagrange multiplier techniques. This theoretical framework is used to demonstrate that the derived algorithms are direct extensions of forward/backward sweep methods used in N-stage optimal control. The two algorithms are tested on a Zermelo problem and the resulting trajectories compare favorably to optimal control results.

Plumer, Edward S.↗
DOE OSTI2023

Efficient Network Partitioning: Application for Decentralized State Estimation in Power Distribution Grids

Increase in the proliferation of distributed energy resources require real-time situational awareness for efficient grid operations. State estimation plays an important role for the real-time control and management of the power grid. As the sensing infrastructure grows, aggregating and handling high volumes of data at a centralized location is extremely difficult. To address this challenge, this paper first proposes a novel and efficient hier-archical spectral clustering-based network partitioning algorithm followed by a decentralized compressive sensing (DCS)-based state estimation. The applicability of the proposed network partitioning algorithm is tested on an IEEE 123-bus network, an IEEE 8,500-node system, and a 6,000+ node distribution network. The results shows that the proposed approach efficiently divides the network into multiple sub-networks with the minimum number of edge connections among the neighbors. Then, we perform DCS-based state estimation on the 6,000+ node distribution network after dividing the network into 18 optimal partitions. Simulation results show that the DCS-based state estimation recovers the system states with high accuracy and low complexity.

alternating direction method of multipliers↗