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Results for “Higher-order optimization”

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.

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99 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Insights from high-fidelity modeling of industrial rotary bell atomization

The global automotive industry sprayed over 2.6 billion liters of paint in 2018, much of which through electrostatic rotary bell atomization, a highly complex process involving the fluid mechanics of rapidly rotating thin films tearing apart into micrometer-thin filaments and droplets. Coating operations account for 65% of the energy usage in a typical automotive assembly plant, representing 10,000s of gigawatt-hours each year in the United States alone. Optimization of these processes would allow for improved robustness, reduced material waste, increased throughput, and significantly reduced energy usage. Here, we introduce a high-fidelity mathematical and algorithmic framework to analyze rotary bell atomization dynamics at industrially relevant conditions. Our approach couples laboratory experiment with the development of robust non-Newtonian fluid models; devises high-order accurate numerical methods to compute the coupled bell, paint, and gas dynamics; and efficiently exploits high-performance supercomputing architectures. These advances have yielded insight into key dynamics, including i) parametric trends in film, sheeting, and filament characteristics as a function of fluid rheology, delivery rates, and bell speed; ii) the impact of nonuniform film thicknesses on atomization performance; and iii) an understanding of spray composition via primary and secondary atomization. These findings result in coating design principles that are poised to improve energy- and cost-efficiency in a wide array of industrial and manufacturing settings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Nuclear charge densities in spherical and deformed nuclei: Toward precise calculations of charge radii

Precise measurements of atomic transitions affected by electron-nucleus hyperfine interactions offer sensitivity to explore basic properties of the atomic nucleus and study fundamental symmetries, including the search for new physics beyond the standard model of particle physics. Specifically, such measurements, augmented by atomic and nuclear calculations, will enable extraction of the higher-order radial moments of the charge-density distribution in spherical and deformed nuclei. The new data impose higher precision requirements on a theoretical description. The nuclear charge density is composed of the proton point distribution folded with the nucleonic charge distributions. The latter induce subtle relativistic corrections due to the coupling of nucleon magnetic moments with the nuclear spin-orbit density. Additional corrections come from the effect of center-of-mass projection. We assess the precision of nuclear charge density calculations by studying the behavior of relativistic and center-of-mass motion corrections to the second and fourth charge radial moments. Special attention has been paid to the magnetic spin-orbit density associated with the local variations of the spin-orbit current. The calculations for semimagic and open-shell nuclei are performed in the framework of self-consistent mean-field theory using quantified energy density functionals and density-dependent pairing forces. We used the general expression for the spin-orbit form factor that is valid for spherical and deformed nuclei. We studied the impact of various correction terms on the charge radii, fourth radial moments, diffraction radii, and surface thickness of spherical and deformed nuclei. The spin-orbit corrections to charge radial moments and surface thickness show strong shell fluctuations which can make an appreciable effect when aiming at high-precision predictions of isotopic shifts. The inclusion of relativistic and center-of-mass corrections impacts the quality of energy density functionals optimized to charge radii data. To establish reliable constraints on the existence of new forces from isotope shift measurements, precise calculations of nuclear charge densities of deformed nuclei are needed. The proper inclusion of the spin-orbit charge density and other correction terms is essential when aiming at extraction of subtle effects which become particularly visible in isotopic trends. It is also important when developing high-quality nuclear energy density functionals optimized using heterogeneous datasets involving absolute charge radii, differential charge radii, and charge form factor properties deduced from electron-scattering data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Higher-order correlations between different moments of two flow amplitudes in Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV

The correlations between different moments of two flow amplitudes, extracted with the recently developed asymmetric cumulants, are measured in Pb-Pb collisions at $\sqrt {s_{NN}}$ = 5.02 TeV recorded by the ALICE detector at the CERN Large Hadron Collider. The magnitudes of the measured observables show a dependence on the different moments as well as on the collision centrality, indicating the presence of nonlinear response in all even moments up to the eighth. Furthermore, the higher-order asymmetric cumulants show different signatures than the symmetric and lower-order asymmetric cumulants. Comparisons with state-of-the-art event generators using two different parametrizations obtained from Bayesian optimization show differences between data and simulations in many of the studied observables, indicating a need for further tuning of the models behind those event generators. These results provide new and independent constraints on the initial conditions and transport properties of the system created in heavy-ion collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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.↗
NASA NTRS1993

Approximate optimal guidance for the advanced launch system

A real-time guidance scheme for the problem of maximizing the payload into orbit subject to the equations of motion for a rocket over a spherical, non-rotating earth is presented. An approximate optimal launch guidance law is developed based upon an asymptotic expansion of the Hamilton - Jacobi - Bellman or dynamic programming equation. The expansion is performed in terms of a small parameter, which is used to separate the dynamics of the problem into primary and perturbation dynamics. For the zeroth-order problem the small parameter is set to zero and a closed-form solution to the zeroth-order expansion term of Hamilton - Jacobi - Bellman equation is obtained. Higher-order terms of the expansion include the effects of the neglected perturbation dynamics. These higher-order terms are determined from the solution of first-order linear partial differential equations requiring only the evaluation of quadratures. This technique is preferred as a real-time, on-line guidance scheme to alternative numerical iterative optimization schemes because of the unreliable convergence properties of these iterative guidance schemes and because the quadratures needed for the approximate optimal guidance law can be performed rapidly and by parallel processing. Even if the approximate solution is not nearly optimal, when using this technique the zeroth-order solution always provides a path which satisfies the terminal constraints. Results for two-degree-of-freedom simulations are presented for the simplified problem of flight in the equatorial plane and compared to the guidance scheme generated by the shooting method which is an iterative second-order technique.

Feeley, T. S.↗
NASA NTRS2018

Real-Time Adaptive Drag Minimization Wind Tunnel Investigation of a Flexible Wing with Variable Camber Continuous Trailing Edge Flap System

This paper reports the results of a recently completed real-time adaptive drag minimization wind tunnel investigation of a highly flexible wing wind tunnel model equipped with the Variable Camber Continuous Trailing Flap (VCCTEF) technology at the University of Washington Aeronautical Laboratory (UWAL). The wind tunnel investigation is funded by NASA SBIR Phase II contract with Scientific Systems Company, Inc. (SSCI) and University of Washington (UW) as a subcontractor. The wind tunnel model is a sub-scale Common Research Model (CRM) wing constructed of foam core and fiberglass skin and is aeroelastically scaled to achieve a wing tip deflection of 10% of the wing semi-span which represents a typical wing tip deflection for a modern transport such as Boeing 787. The jig-shape twist of the CRM wing is optimized using a CART3D aero-structural model to achieve the minimum induced drag for the design cruise lift coefficient of 0.5. The wing is equipped with two chord wise cambered segments for each of the six span wise flap sections for a total of 12 individual flap segments that comprise the VCCTEF system. Each of the 12 flap segments is actively controlled by an electric servo-actuator. The real-time adaptive drag optimization strategy includes an on-board aerodynamic model identification, a model excitation, and a real-time drag optimization. The on-board aerodynamic model is constructed parametrically as a function of the angle of attack and flap positions to model the lift and drag coefficients of the wing. The lift coefficient models include a linear model and a second-order model. The drag coefficient models include a quadratic model and a higher-order up to 6th-order model to accurately model the drag coefficient at high angles of attack. The onboard aerodynamic model identification includes a recursive least-squares (RLS) algorithm and a batch least-squares (BLS) algorithm designed to estimate the model parameters. The model excitation method is designed to sample the input set that comprises the angle of attack and the flap positions. Three model excitation methods are developed: random excitation method, sweep method, and iterative angle-of-attack seeking method. The real-time drag optimization includes a generic algorithm developed by SSCI and several optimization methods developed by NASA which include a second-order gradient Newton-Raphson optimization method, an iterative gradient optimization method, a pseudo-inverse optimization method, an analytical optimization method, and an iterative refinement optimization method. The first wind tunnel test entry took place in September 2017. This test revealed major hardware issues and required further redesign of the flap servo mechanisms. The second test entry took place in April 2018. However, the test was not successful due to the issues with the onboard aerodynamic model identification RLS algorithm which incorrectly identified model parameters. This test also provides an experimental comparison study between the VCCTEF and a variable camber discrete trailing edge flap (VCDTEF) without the elastomer transition mechanisms. The experimental result confirms the benefit of the VCCTEF which produces lower drag by 5% than the VCDTEF. The third and final test entry took place in June 2018 after the issues with the RLS algorithm have been identified and corrected. Additional improvements were implemented. These include the BLS algorithm, the iterative angle-of-attack seeking method, the iterative gradient optimization method, and the pseudo-inverse optimization method. The test objectives were successfully demonstrated as the real-time drag optimization identifies several optimal solutions at off-design lift coefficients. The iterative gradient optimization method is found to achieve up to 4.7% drag reduction for the off-design lift coefficient of 0.7. The pseudo-inverse optimization method which does not require the drag coefficient model is found to be quite effective in reducing drag. Up to 9.4% drag reduction for the off-design lift coefficient of 0.7 is achieved with the pseudo-inverse optimization method. The wind tunnel investigation demonstrates the potential of real-time drag optimization technology. Several new capabilities are developed that could enable future adaptive wing technologies for flexible wings equipped with drag control devices such as the VCCTEF.

Drag Optimization↗