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Results for “Higher-order optimization”

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NASA NTRS1993

Function approximations

A development status evaluation is presented for applications of main approximation concepts in nonlinear programming for structural optimization requiring local, midrange, and global approximations. It is noted that there is not yet a sufficient basis for a comprehensive evaluation of relative effectiveness among approximation concepts. Attention is presently given to the careful selection of intermediate-variable and response quantity, and improvements in the traditional Taylor-series expansion by inclusion of either some higher-order terms or information at various points in the design space.

Barthelemy, J.-F. M.↗

NASA NTRS2005

Cognitive Performance in Operational Environments

Optimal cognition during complex and sustained operations is a critical component for success in current and future military operations. "Cognitive Performance, Judgment, and Decision-making" (CPJD) is a newly organized U.S. Army Medical Research and Materiel Command research program focused on sustaining operational effectiveness of Future Force Warriors by developing paradigms through which militarily-relevant, higher-order cognitive performance, judgment, and decision-making can be assessed and sustained in individuals, small teams, and leaders of network-centric fighting units. CPJD evaluates the impact of stressors intrinsic to military operational environments (e.g., sleep deprivation, workload, fatigue, temperature extremes, altitude, environmental/physiological disruption) on military performance, evaluates noninvasive automated methods for monitoring and predicting cognitive performance, and investigates pharmaceutical strategies (e.g., stimulant countermeasures, hypnotics) to mitigate performance decrements. This manuscript describes the CPJD program, discusses the metrics utilized to relate militarily applied research findings to academic research, and discusses how the simulated combat capabilities of a synthetic battle laboratory may facilitate future cognitive performance research.

Russo, Michael↗

NASA NTRS1995

Adaptive unstructured triangular mesh generation and flow solvers for the Navier-Stokes equations at high Reynolds number

A method for generating high quality unstructured triangular grids for high Reynolds number Navier-Stokes calculations about complex geometries is described. Careful attention is paid in the mesh generation process to resolving efficiently the disparate length scales which arise in these flows. First the surface mesh is constructed in a way which ensures that the geometry is faithfully represented. The volume mesh generation then proceeds in two phases thus allowing the viscous and inviscid regions of the flow to be meshed optimally. A solution-adaptive remeshing procedure which allows the mesh to adapt itself to flow features is also described. The procedure for tracking wakes and refinement criteria appropriate for shock detection are described. Although at present it has only been implemented in two dimensions, the grid generation process has been designed with the extension to three dimensions in mind. An implicit, higher-order, upwind method is also presented for computing compressible turbulent flows on these meshes. Two recently developed one-equation turbulence models have been implemented to simulate the effects of the fluid turbulence. Results for flow about a RAE 2822 airfoil and a Douglas three-element airfoil are presented which clearly show the improved resolution obtainable.

Ashford, Gregory A.↗

NASA NTRS1997

Reduced Navier Stokes Relaxation Procedures for Internal Flows

In spite of significant advancement in the field of high speed computing, flow calculations involving complex geometries and/or flow behavior still require large amounts of CPU time and memory. In order to predict such flows without sacrificing grid convergence and accuracy, adaptive gridding techniques that provide optimal resolution are highly desirable. The present work combines multigrid techniques and domain decomposition concepts to provide local, solution adaptive, grid refinement. Several viscous compressible and incompressible, two and three-dimensional, flows with strong inviscid interaction and/or axial flow reversal, are considered with a segmented multigrid domain decomposition (SMGDD) procedure for which uniform meshes result in each domain. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable non-staggered grid computation. The SMGDD technique presented herein has previously been applied for incompressible two dimensional flows. The present work offers improvement in the gridding strategy, by allowing for disjoint subdomains that provide optimal resolution of disparate flow features. It also extends the SMGDD technique to three dimensional compressible flows. Laminar and turbulent flow in a backward facing step channel is considered; although the procedure is applicable to more severe geometries. The standard K-epsilon model is applied for turbulence closure. For Re greater than 400, differences between two-dimensional theory and experiment are resolved through a three dimensional simulation, which confirms the experimentally observed three dimensionality of the recirculation patterns on the upper and lower surfaces.

Rubin, Stanley G.↗

NASA NTRS2016

Optimizing Power Density and Efficiency of a Double-Halbach Array Permanent-Magnet Ironless Axial-Flux Motor

NASA Glenn Research Center is investigating hybrid electric and turboelectric propulsion concepts for future aircraft to reduce fuel burn, emissions, and noise. Systems studies show that the weight and efficiency of the electric system components need to be improved for this concept to be feasible. This effort aims to identify design parameters that affect power density and efficiency for a double-Halbach array permanent-magnet ironless axial flux motor configuration. These parameters include both geometrical and higher-order parameters, including pole count, rotor speed, current density, and geometries of the magnets, windings, and air gap.

hybrid propulsion↗

NASA NTRS2016

Optimizing Power Density and Efficiency of a Double-Halbach Array Permanent-Magnet Ironless Axial-Flux Motor

electric propulsion↗

DOE OSTI2025

Half-Life and Precision Shape Measurement of the 2⁢𝜈⁢𝛽⁢𝛽 Decay of 130 Te

Here, we present a new measurement of the 2⁢𝜈⁢𝛽⁢𝛽 half-life of 130 Te (𝑇$^{2⁢𝜈}_{1/2}$) using the first complete model of the CUORE data, based on 1038 kg yr of collected exposure. Thanks to optimized data selection, we achieve a factor of two improvement in precision, obtaining 𝑇$^{2⁢𝜈}_{1/2}$ = (9.32⁢$^{+0.05}_{−0.04}$⁢stat⁢ $^{+0.07}_{−0.07}$⁢syst)×10 20 yr. The signal-to-background ratio is increased by 70% compared to our previous results, enabling the first application of the improved 2⁢𝜈⁢𝛽⁢𝛽 formalism to 130 Te . Within this framework, we determine a credibility interval for the effective axial coupling in the nuclear medium as a function of nuclear matrix elements. We also extract values for the higher-order nuclear matrix element ratios: second-to-first and third-to-first. The second-to-first ratio agrees with nuclear model predictions, while the third-to-first ratio deviates from theoretical expectations. These findings provide essential tests of nuclear models and key inputs for future 0⁢𝜈⁢𝛽⁢𝛽 searches.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1999

The Effect of Interface Roughness and Oxide Film Thickness on the Inelastic Response of Thermal Barrier Coatings to Thermal Cycling

The effects of interfacial roughness and oxide film thickness on thermally-induced stresses in plasma-sprayed thermal barrier coatings subjected to thermal cycling are investigated using the recently developed higher-order theory for functionally graded materials. The higher-order theory is shown to be a viable alternative to the finite-element approach, capable of modeling different interfacial roughness architectures in the presence of an aluminum oxide layer and capturing the high stress gradients that occur at the top coat/bond coat interface. The oxide layer thickness is demonstrated to have a substantially greater effect on the evolution of residual stresses than local variations in interfacial roughness. Further, the location of delamination initiation in the top coat is predicted to change with increasing oxide layer thickness. This result can be used to optimize the thickness of a pre-oxidized layer introduced at the top coat/bond coat interface in order to enhance TBC durability as suggested by some researchers. The results of our investigation also support a recently proposed hypothesis regarding delamination initiation and propagation in the presence of an evolving bond coat oxidation, while pointing to the importance of interfacial roughness details and specimen geometry in modeling this phenomenon.

Pindera, Marek-Jerzy↗

DOE OSTI2025

SDA: a symbolic differential algebra package in C++

Truncated Power Series Algebra (TPSA), or Differential Algebra (DA), is a well-established tool in accelerator physics, commonly used for generating high-order maps of dynamic systems, as well as in symplectic tracking, normal form analysis, verified integration, optimization, and fast multipole methods. This package is the first to perform symbolic DA computations, enabling traceability of initial condition contributions and runtime reduction for repeated DA calculations, potentially expanding DA’s applications.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2010

Explanation of Anomalous Behavior Observed in Impedance Eduction Techniques Using Measured Data

Several enhancements that improve the accuracy and robustness of an impedance eduction technique that use an automatic optimizer are presented. These enhancements are then used to launch an intensive investigation into the cause of anomalous behavior that occurs for a small number of test conditions. This anomalous behavior is investigated for both a hardwall insert and a conventional liner. The primary conclusions of the study are that: (1) for the hard wall insert, the anomalies are due to narrow peaks in the objective function, (2) For the conventional liner, the anomalies are due to the presence of an extremely flat objective function, and (3) the anomalies appear to be triggered by inconsistencies between the duct propagation model and the measured data. At high frequencies, the duct propagation model may need to include the effects of higher-order duct modes, whereas at low frequencies, the effects of the mean boundary layer may have to be included.

Watson, Willie R.↗

NASA NTRS2007

Optimization of Acoustic Pressure Measurements for Impedance Eduction

As noise constraints become increasingly stringent, there is continued emphasis on the development of improved acoustic liner concepts to reduce the amount of fan noise radiated to communities surrounding airports. As a result, multiple analytical prediction tools and experimental rigs have been developed by industry and academia to support liner evaluation. NASA Langley has also placed considerable effort in this area over the last three decades. More recently, a finite element code (Q3D) based on a quasi-3D implementation of the convected Helmholtz equation has been combined with measured data acquired in the Langley Grazing Incidence Tube (GIT) to reduce liner impedance in the presence of grazing flow. A new Curved Duct Test Rig (CDTR) has also been developed to allow evaluation of liners in the presence of grazing flow and controlled, higher-order modes, with straight and curved waveguides. Upgraded versions of each of these two test rigs are expected to begin operation by early 2008. The Grazing Flow Impedance Tube (GFIT) will replace the GIT, and additional capabilities will be incorporated into the CDTR. The current investigation uses the Q3D finite element code to evaluate some of the key capabilities of these two test rigs. First, the Q3D code is used to evaluate the microphone distribution designed for the GFIT. Liners ranging in length from 51 to 610 mm are investigated to determine whether acceptable impedance eduction can be achieved with microphones placed on the wall opposite the liner. This analysis indicates the best results are achieved for liner lengths of at least 203 mm. Next, the effects of moving this GFIT microphone array to the wall adjacent to the liner are evaluated, and acceptable results are achieved if the microphones are placed off the centerline. Finally, the code is used to investigate potential microphone placements in the CDTR rigid wall adjacent to the wall containing an acoustic liner, to determine if sufficient fidelity can be achieved with 32 microphones available for this purpose. Initial results indicate 32 microphones can provide acceptable measurements to support impedance eduction with this test rig.

Jones, M. G.↗

NASA NTRS1996

A New Higher-Order Composite Theory for Analysis and Design of High Speed Tilt-Rotor Blades

A higher-order theory is developed to model composite box beams with arbitrary wall thicknesses. The theory, based on a refined displacement field, represents a three-dimensional model which approximates the elasticity solution. Therefore, the cross-sectional properties are not reduced to one-dimensional beam parameters. Both inplane and out-of-plane warping are automatically included in the formulation. The model accurately captures the transverse shear stresses through the thickness of each wall while satisfying all stress-free boundary conditions. Several numerical results are presented to validate the present theory. The developed theory is then used to model the load carrying member of a tilt-rotor blade which has thick-walled sections. The composite structural analysis is coupled with an aerodynamic analysis to compute the aeroelastic stability of the blade. Finally, a multidisciplinary optimization procedure is developed to improve the aerodynamic, structural and aeroelastic performance of the tilt-rotor aircraft. The Kreisselmeier-Steinhauser function is used to formulate the multiobjective function problem and a hybrid approximate analysis is used to reduce the computational effort. The optimum results are compared with the baseline values and show significant improvements in the overall performance of the tilt-rotor blade.

McCarthy, Thomas Robert↗

NASA NTRS1995

Parametric studies of stitching effectiveness for preventing substructure disbond

A methodology is desired that will allow a designer to select appropriate amounts of through-thickness reinforcement needed to meet design requirements. The goal is to use a relatively simple analysis to minimize the amount of testing that needs to be performed, and to make test results from simple configurations applicable to more general structures. Using this methodology one should be able to optimize the selection of stitching materials, the weight of the yarn, and the stitching density. The analysis approach is to treat substructure disbond as a crack propagation problem. In this approach, the stitches have little influence until a delamination begins to grow. Once the delamination reaches, or extends beyond a stitch, the stitch serves to reduce the strain-energy-release-rate (G) at the crack tip for a given applied load. The reduced G can then be compared to the unstitched materials toughness to predict the load required to further extend the crack. The current model treats the stitch as a simple spring which responds to displacements in the vertical (through-thickness) direction. In concept, this approach is similar to that proposed by other authors. Test results indicate that the model should be refined to include the shearing stiffness of the stitch. The strain-energy-release-rate calculations are performed using a code which uses interconnected higher-order plates to model built-up composite cross-sections. When plates are stacked vertically, the interfacial tractions between the plates can be computed. The plate differential equations are solved in closed-form. The code, called SUBLAM, was developed as part of this section in one dimension. Because of this limitation, rows of stitches are treated as a two-dimensional sheet. The spring stiffness of a row of stitches can be estimated from the stitch material, weight, and density. As a practical and conservative approach, we can assume that the stitch is bonded until a crack passes the stitch location. After the crack passes, it is fully bonded. A series of tests were performed to exercise this methodology and incorporated an attached flange such that the sudden change in thickness initiated a delamination. The analysis was used to estimate the materials' critical G from that of the unstitched specimens. With this data, a prediction was made for the load required to delaminate the stitched specimens. Using the methodology, design charts have been created for simplified geometries. These charts give stitch force, along with G(sub 1) and G(sub 2) as as function of the stitch spring stiffness. Using the charts, it should be possible to determine the stitch spring stiffness and strength required to reduce the G to a desired level. From these parameters, the actual stitching material, weight, and density can be computed.

Flanagan, Gerry↗

NASA NTRS1995

Testing higher-order Lagrangian perturbation theory against numerical simulations. 2: Hierarchical models

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.

Melott, A. L.↗

DOE OSTI2025

Efficient near-field ptychography reconstruction using the Hessian operator

X-ray ptychography is a powerful and robust coherent imaging method providing access to the complex object and probe (illumination). Ptychography reconstruction is typically performed using first-order methods due to their computational efficiency. Higher-order methods, while potentially more accurate, are often prohibitively expensive in terms of computation. In this study, we present a mathematical framework for reconstruction using second-order information derived from an efficient computation of the bilinear Hessian and Hessian operator. The formulation is provided for Gaussian-based models, enabling the simultaneous reconstruction of the object, probe, and object positions. Synthetic data tests, along with experimental near-field ptychography data processing, demonstrate a ten-fold reduction in computation time compared to first-order methods. The derived formulas for computing the Hessians, along with the strategies for incorporating them into optimization schemes, are well-structured and easily adaptable to various ptychography problem formulations.

Carlsson, Marcus [Lund Univ. (Sweden)] (ORCID:0000↗

DOE OSTI2025

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗

NASA NTRS1990

A real-time approximate optimal guidance law for flight in a plane

A real-time guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higher-order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that real-time approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in three-dimensions is made apparent from the solution presented.

Feeley, Timothy S.↗

NASA NTRS1991

The process of control design for the NASA Langley Minimast structure

The design process used to select sensors for feedback and performance weights on the Minimast facility is discussed. Initially, a series of controllers are synthesized using H2 optimal control techniques for the given structural model, a variety of sensor locations and performance criteria to determine the best displacement sensor and/or accelerometers to be used for feedback. Upon selection of the sensors, controllers are formulated to determine the affect of using a reduced-order model of the Minimast structure instead of the higher-order structural analysis model for control design and the relationship between the actuator torque level and the closed-loop performance. Based on this information, controllers are designed using micro-synthesis techniques and implemented on the Minimast structure. Results of the implementation of these controllers on the Minimast experimental facility are presented.

Balas, Gary J.↗