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NASA NTRS1994

Multigrid one shot methods for optimal control problems: Infinite dimensional control

The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

Arian, Eyal↗

NASA NTRS2011

Design and Evaluation of the Terminal Area Precision Scheduling and Spacing System

This paper describes the design, development and results from a high fidelity human-in-the-loop simulation of an integrated set of trajectory-based automation tools providing precision scheduling, sequencing and controller merging and spacing functions. These integrated functions are combined into a system called the Terminal Area Precision Scheduling and Spacing (TAPSS) system. It is a strategic and tactical planning tool that provides Traffic Management Coordinators, En Route and Terminal Radar Approach Control air traffic controllers the ability to efficiently optimize the arrival capacity of a demand-impacted airport while simultaneously enabling fuel-efficient descent procedures. The TAPSS system consists of four-dimensional trajectory prediction, arrival runway balancing, aircraft separation constraint-based scheduling, traffic flow visualization and trajectory-based advisories to assist controllers in efficient metering, sequencing and spacing. The TAPSS system was evaluated and compared to today's ATC operation through extensive series of human-in-the-loop simulations for arrival flows into the Los Angeles International Airport. The test conditions included the variation of aircraft demand from a baseline of today's capacity constrained periods through 5%, 10% and 20% increases. Performance data were collected for engineering and human factor analysis and compared with similar operations both with and without the TAPSS system. The engineering data indicate operations with the TAPSS show up to a 10% increase in airport throughput during capacity constrained periods while maintaining fuel-efficient aircraft descent profiles from cruise to landing.

Swenson, Harry N.↗

DOE OSTI2025

Parallel derivative-free optimization for simulation-based design of behind-the-meter energy systems

In this work, the integrated design and dispatch of behind-the-meter or distributed resources (e.g. stationary battery storage and solar PV generation) is considered. A simulation-based framework is employed, generating high-fidelity results with closed-loop predictive control at a fine resolution, at the expense of high computational cost (several minutes to a few hours per design point). To address this challenge, parallel derivative-free design methods are considered. Four methods are compared, including state-of-the-art surrogate-based methods (Radial-Basis Functions and Gaussian processes) and sampling strategies, an evolutionary-based method, and a simple sequential grid refinement method. As a case study, two types of design problem with increasing complexity are considered, namely, the design of behind-the-meter resources (three design variables) and the inclusion of grid capacity (four design variables). The second yields a constrained design problem for which violations can only be determined after solving the computationally expensive simulation. For the three-dimensional case, all methods present a good performance, achieving a solution within 1% of the optimum after the first iteration, with the sequential grid refinement exhibiting the fastest convergence and achieving the best final objective value. This indicates that the parallel evaluation of multiple sampling points may be more important than the choice of method for small decision spaces. For the four-dimensional constrained case, the Genetic Algorithm presents the best tradeoff between performance and computational effort, while the rough objective function terrain generated by constraint violation penalties reduces the performance of surrogate-based methods. Contour plots with flat regions indicate flexibility in the optimal design and highlight the importance of characterizing the solution space.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1972

Aeroelastic optimization of a panel in high Mach number supersonic flow.

Solution for a least-weight skin thickness distribution for a panel with a flutter parameter constraint. This panel weighs less than any similar constant thickness panel, but has the same critical supersonic panel flutter parameter. The panel rests on simple supports and is of sandwich construction. The span to chord ratio is large enough that the inertial, elastic, and aerodynamic behavior is one-dimensional. The Mach number is great enough that the aerodynamic forces acting on the upper panel surface may be accurately described by quasi-steady, linearized, supersonic aerodynamic theory. The final optimum design is obtained from theoretical and numerical methods adapted from optimal control theory. The results of this investigation show that the optimal panel thickness distribution is symmetric about the panel chord midpoint. Compared to a reference panel with constant thickness, optimum panels are found to be nearly 12% lighter.

Weisshaar, T. A.↗

NASA NTRS2003

Robust Airfoil Optimization in High Resolution Design Space

The robust airfoil shape optimization is a direct method for drag reduction over a given range of operating conditions and has three advantages: (1) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (2) it uses a large number of B-spline control points as design variables yet the resulting airfoil shape is fairly smooth, and (3) it allows the user to make a trade-off between the level of optimization and the amount of computing time consumed. The robust optimization method is demonstrated by solving a lift-constrained drag minimization problem for a two-dimensional airfoil in viscous flow with a large number of geometric design variables. Our experience with robust optimization indicates that our strategy produces reasonable airfoil shapes that are similar to the original airfoils, but these new shapes provide drag reduction over the specified range of Mach numbers. We have tested this strategy on a number of advanced airfoil models produced by knowledgeable aerodynamic design team members and found that our strategy produces airfoils better or equal to any designs produced by traditional design methods.

Li, Wu↗

NASA NTRS2009

A Comparison of Risk Sensitive Path Planning Methods for Aircraft Emergency Landing

Determining the best site to land a damaged aircraft presents some interesting challenges for standard path planning techniques. There are multiple possible locations to consider, the space is 3-dimensional with dynamics, the criteria for a good path is determined by overall risk rather than distance or time, and optimization really matters, since an improved path corresponds to greater expected survival rate. We have investigated a number of different path planning methods for solving this problem, including cell decomposition, visibility graphs, probabilistic road maps (PRMs), and local search techniques. In their pure form, none of these techniques have proven to be entirely satisfactory - some are too slow or unpredictable, some produce highly non-optimal paths or do not find certain types of paths, and some do not cope well with the dynamic constraints when controllability is limited. In the end, we are converging towards a hybrid technique that involves seeding a roadmap with a layered visibility graph, using PRM to extend that roadmap, and using local search to further optimize the resulting paths. We describe the techniques we have investigated, report on our experiments with these techniques, and discuss when and why various techniques were unsatisfactory.

Meuleau, Nicolas↗

DOE OSTI2025

Low-dimensional solid-state single-photon emitters

Solid-state single-photon emitters (SPEs) are attracting significant attention as fundamental components in quantum computing, communication, and sensing. Low-dimensional materials-based SPEs (LD-SPEs) have drawn particular interest due to their high photon extraction efficiency, ease of integration with photonic circuits, and strong coupling with external fields. The accessible surfaces of LD materials allow for deterministic control over quantum light emission, while enhanced quantum confinement and light–matter interactions improve photon emissive properties. This perspective examines recent progress in LD-SPEs across four key materials: zero-dimensional (0D) semiconductor quantum dots, one-dimensional (1D) nanotubes, two-dimensional (2D) materials, including hexagonal boron nitride (hBN) and transition metal dichalcogenides (TMDCs). We explore their structural and photophysical properties, along with techniques such as spectral tuning and cavity coupling, which enhance SPE performance. Finally, we address future challenges and suggest strategies for optimizing LD-SPEs for practical quantum applications.

42 ENGINEERING↗

NASA NTRS2011

LES of a Jet Excited by the Localized Arc Filament Plasma Actuators

The fluid dynamics of a high-speed jet are governed by the instability waves that form in the free-shear boundary layer of the jet. Jet excitation manipulates the growth and saturation of particular instability waves to control the unsteady flow structures that characterize the energy cascade in the jet.The results may include jet noise mitigation or a reduction in the infrared signature of the jet. The Localized Arc Filament Plasma Actuators (LAFPA) have demonstrated the ability to excite a high-speed jets in laboratory experiments. Extending and optimizing this excitation technology, however, is a complex process that will require many tests and trials. Computational simulations can play an important role in understanding and optimizing this actuator technology for real-world applications. Previous research has focused on developing a suitable actuator model and coupling it with the appropriate computational fluid dynamics (CFD) methods using two-dimensional spatial flow approximations. This work is now extended to three-dimensions (3-D) in space. The actuator model is adapted to a series of discrete actuators and a 3-D LES simulation of an excited jet is run. The results are used to study the fluid dynamics near the actuator and in the jet plume.

Brown, Clifford A.↗

NASA NTRS2013

Progress of a Cross-correlation Based Optical Strain Measurement Technique for Detecting Radial Growth on a Rotating Disk

The Aeronautical Sciences Project under NASAs Fundamental Aeronautics Program is extremely interested in the development of fault detection technologies, such as optical surface measurements in the internal parts of a flow path, for in situ health monitoring of gas turbine engines. In situ health monitoring has the potential to detect flaws, i.e. cracks in key components, such as engine turbine disks, before the flaws lead to catastrophic failure. In the present study, a cross-correlation imaging technique is investigated in a proof-of-concept study as a possible optical technique to measure the radial growth and strain field on an already cracked sub-scale turbine engine disk under loaded conditions in the NASA Glenn Research Centers High Precision Rotordynamics Laboratory. The optical strain measurement technique under investigation offers potential fault detection using an applied background consisting of a high-contrast random speckle pattern and imaging the background under unloaded and loaded conditions with a CCD camera. Spinning the cracked disk at high speeds induces an external load, resulting in a radial growth of the disk of approximately 50.8-m in the flawed region and hence, a localized strain field. When imaging the cracked disk under static conditions, the disk will appear shifted. The resulting background displacements between the two images will then be measured using the two-dimensional cross-correlation algorithms implemented in standard Particle Image Velocimetry (PIV) software to track the disk growth, which facilitates calculation of the localized strain field. In order to develop and validate this optical strain measurement technique an initial proof-of-concept experiment is carried out in a controlled environment. Using PIV optimization principles and guidelines, three potential backgrounds, for future use on the rotating disk, are developed and investigated in the controlled experiment. A range of known shifts are induced on the backgrounds; reference and data images are acquired before and after the induced shift, respectively, and the images are processed using the cross- correlation algorithms in order to determine the background displacements. The effectiveness of each background at resolving the known shift is evaluated and discussed in order to choose to the most suitable background to be implemented onto a rotating disk in the Rotordynamics Lab. Although testing on the rotating disk has not yet been performed, the driving principles behind the development of the present optical technique are based upon critical aspects of the future experiment, such as the amount of expected radial growth, disk analysis, and experimental design and are therefore addressed in the paper.

Clem, Michelle M.↗

NASA NTRS2009

Physical Principle for Generation of Randomness

A physical principle (more precisely, a principle that incorporates mathematical models used in physics) has been conceived as the basis of a method of generating randomness in Monte Carlo simulations. The principle eliminates the need for conventional random-number generators. The Monte Carlo simulation method is among the most powerful computational methods for solving high-dimensional problems in physics, chemistry, economics, and information processing. The Monte Carlo simulation method is especially effective for solving problems in which computational complexity increases exponentially with dimensionality. The main advantage of the Monte Carlo simulation method over other methods is that the demand on computational resources becomes independent of dimensionality. As augmented by the present principle, the Monte Carlo simulation method becomes an even more powerful computational method that is especially useful for solving problems associated with dynamics of fluids, planning, scheduling, and combinatorial optimization. The present principle is based on coupling of dynamical equations with the corresponding Liouville equation. The randomness is generated by non-Lipschitz instability of dynamics triggered and controlled by feedback from the Liouville equation. (In non-Lipschitz dynamics, the derivatives of solutions of the dynamical equations are not required to be bounded.)

Zak, Michail↗

NASA NTRS2015

A High-Resolution Merged Wind Dataset for DYNAMO: Progress and Future Plans

In order to support research on optimal data assimilation methods for the Cyclone Global Navigation Satellite System (CYGNSS), launching in 2016, work has been ongoing to produce a high‐resolution merged wind dataset for the Dynamics of the Madden Julian Oscillation (DYNAMO) field campaign, which took place during late 2011/early 2012. The winds are produced by assimilating DYNAMO observations into the Weather Research and Forecasting (WRF) three‐dimensional variational (3DVAR) system. Data sources from the DYNAMO campaign include the upper‐air sounding network, radial velocities from the radar network, vector winds from the Advanced Scatterometer (ASCAT) and Oceansat‐2 Scatterometer (OSCAT) satellite instruments, the NOAA High Resolution Doppler Lidar (HRDL), and several others. In order the prep them for 3DVAR, significant additional quality control work is being done for the currently available TOGA and SMART‐R radar datasets, including automatically dealiasing radial velocities and correcting for intermittent TOGA antenna azimuth angle errors. The assimilated winds are being made available as model output fields from WRF on two separate grids with different horizontal resolutions ‐ a 3‐km grid focusing on the main DYNAMO quadrilateral (i.e., Gan Island, the R/V Revelle, the R/V Mirai, and Diego Garcia), and a 1‐km grid focusing on the Revelle. The wind dataset is focused on three separate approximately 2‐week periods during the Madden Julian Oscillation (MJO) onsets that occurred in October, November, and December 2011. Work is ongoing to convert the 10‐m surface winds from these model fields to simulated CYGNSS observations using the CYGNSS End‐To‐End Simulator (E2ES), and these simulated satellite observations are being compared to radar observations of DYNAMO precipitation systems to document the anticipated ability of CYGNSS to provide information on the relationships between surface winds and oceanic precipitation at the mesoscale level. This research will improve our understanding of the future utility of CYGNSS for documenting key MJO processes.

Lang, Timothy J.↗

NASA NTRS2002

Three-Dimensional High-Order Spectral Finite Volume Method for Unstructured Grids

Many areas require a very high-order accurate numerical solution of conservation laws for complex shapes. This paper deals with the extension to three dimensions of the Spectral Finite Volume (SV) method for unstructured grids, which was developed to solve such problems. We first summarize the limitations of traditional methods such as finite-difference, and finite-volume for both structured and unstructured grids. We then describe the basic formulation of the spectral finite volume method. What distinguishes the SV method from conventional high-order finite-volume methods for unstructured triangular or tetrahedral grids is the data reconstruction. Instead of using a large stencil of neighboring cells to perform a high-order reconstruction, the stencil is constructed by partitioning each grid cell, called a spectral volume (SV), into 'structured' sub-cells, called control volumes (CVs). One can show that if all the SV cells are partitioned into polygonal or polyhedral CV sub-cells in a geometrically similar manner, the reconstructions for all the SVs become universal, irrespective of their shapes, sizes, orientations, or locations. It follows that the reconstruction is reduced to a weighted sum of unknowns involving just a few simple adds and multiplies, and those weights are universal and can be pre-determined once for all. The method is thus very efficient, accurate, and yet geometrically flexible. The most critical part of the SV method is the partitioning of the SV into CVs. In this paper we present the partitioning of a tetrahedral SV into polyhedral CVs with one free parameter for polynomial reconstructions up to degree of precision five. (Note that the order of accuracy of the method is one order higher than the reconstruction degree of precision.) The free parameter will be determined by minimizing the Lebesgue constant of the reconstruction matrix or similar criteria to obtain optimized partitions. The details of an efficient, parallelizable code to solve three-dimensional problems for any order of accuracy are then presented. Important aspects of the data structure are discussed. Comparisons with the Discontinuous Galerkin (DG) method are made. Numerical examples for wave propagation problems are presented.

Liu, Yen↗

NASA NTRS2018

Bistable Collapsible Tubular Mast Booms

A promising candidate for deployable composite structures is the two-shelled Collapsible Tubular Mast (CTM) boom, which is to be employed on future solar sail and interplanetary small satellite platforms by the National Aeronautics and Space Administration (NASA). This is due to its two omega-shaped shells forming a closed-section which yields large stiffnesses that allowed for high dimensional stability. An inextensional analytical model describing the bending deformation mechanics of CTM booms was used to determine how design variables induce bistability, or the existence of two strain energy wells. Bistable booms were favorable due to low strain energy requirements for the coiled state and had more controllable deployment when compared to monostable booms. The effects of varying lamina material, laminate layup, and shell arc geometries between different inner and outer shell segments on the second strain energy well and stiffness properties were determined for cross-sections formed by circular segments. The full design space for two-shelled composite CTM booms was explored to evaluate the validity of the simple analytical model developed. Optimal CTM boom designs were manufactured and experimentally characterized for comparisons against model results. The model under-predicted the second stable coiled diameter of the complete two-shelled booms by 27-33% and as low as 3-8% for the individual shells wrapped alone.

Fernandez, Juan M.↗

DOE OSTI2025

A hybrid surrogate modeling framework for the Digital Twin of a Fluoride-salt-cooled High-temperature Reactor (FHR)

While nuclear energy is a non-greenhouse-gas emitting energy source, expensive operational costs due to the high-level of safety requirements decreases their competitiveness in the sustainable energy market. Advanced reactor concepts paired with Digital Twins aim to increase the commercialization gains of nuclear energy by reducing operational costs, increasing reactor reliability and enhancing power generation. To support Digital Twin tasks such as real-time autonomous control, proactive maintenance monitoring or optimizing power demand operations, a fast and accurate virtual representation of the Nuclear Power Plant (NPP) is required. The computational cost of high-fidelity, physics-based models are unsuitable for real-time analysis or scalability. Here, in this work, a hybrid surrogate modeling framework is developed fora Fluoride-salt-cooled High-temperature Reactor (FHR) that leverages physics-inspired models for key reactor components and uses data-driven methods for rapid system state space prediction. The Xenon reactivity feedback model is integrated to inform the surrogate model about the reactor core and the homologous pump theory model is the basis for representing pump degradation. Using a detailed, two dimensional thermal hydraulics model to generate data on the FHR, we train a network of Vectorized Autoregressive Moving-Average with eXogenous input (VARMAX) models to predict the remaining state values. The result is a surrogate model that provides a detailed reactor state representation of 41 system states and a pump degradation analysis. The framework is applied to Load Follows profiles, yielding high accuracy and a speedup that is more than 4000x faster compared to the higher- fidelity thermal hydraulics model, enabling real-time operational intelligence and applications in long horizon predictions. While the surrogate model framework is demonstrated for the particular case of FHR, the hybrid physical/data-driven modeling approach including the network of surrogates and the underlying modularity has the potential to be applied to other physical asset systems.

Digital Twins↗

DOE OSTI2025

Control of core–shell nanoparticles properties through plasma synthesis: a computational study

The improved properties of core–shell nanoparticles (CSNPs) over homogeneous nanoparticles (NPs) have expanded and diversified the applications of these nanomaterials. However, controlling the properties of CSNPs can be a challenging task. Low temperature plasmas have proven to be an effective method of producing NPs with uniform size and morphology, and high yield. That said, NP transport and growth dynamics are sensitive to LTP properties. We report on a computational investigation of the evolution of Ge–Si CSNP properties as a function of operating conditions through the modeling of a flowing, two-zone inductively coupled plasma (ICP) reactor. Ar/GeH 4 and Ar/SiH 4 gas mixtures were supplied to separate plasma zones at a pressure of 1 Torr to promote growth of Ge cores and Si shells. The negatively charged CSNPs are trapped electrostatically in the vicinity of the antennas where the plasma is generated and where the majority of particle growth occurs. Particles that grow to a critical size are then de-trapped by fluid drag due to neutral gas flow. A two-dimensional hybrid plasma model coupled with a three-dimensional kinetic NP transport model were utilized to resolve plasma chemistry and NP growth processes that take place on distinct timescales. The trends in CSNP properties and trapping mechanisms associated with flow rate, applied ICP power and inlet precursor fraction are discussed. While the spatial distribution of plasma produced radical species can have significant impact on the NP growth process, the NP transport dynamics are what ultimately dictates the growth environment that is unique to each particle and so determines their final dimension and composition. The key to optimizing reactor conditions involves controlling the spatial density of growth species and plasma profile as a means to tailor particle trapping dynamics suitable to produce CSNPs for a specific application.

36 MATERIALS SCIENCE↗

NASA NTRS2017

Coilgun Acceleration Model Containing Interactions Between Multiple Coils

Electromagnetic (EM) accelerators have the potential to fill a performance range not currently being met by conventional chemical and electric propulsion systems by providing a specific impulse of 600-1000 seconds and a thrust-to-power ratio greater than 200 mN/kW. A propulsion system based on EM acceleration of small projectiles has the traditional advantages of using a pulsed system, including precise control over a range of thrust and power levels as well as rapid response and repetition rates. Furthermore, EM accelerators have lower power requirements than conventional electric propulsion systems since no plasma creation is necessary. A coilgun is a specific type of EM device where a high-current pulse through a coil of wire interacts with a conductive projectile via an induced magnetic field to accelerate the projectile. There are no physical or electrical connections to the projectile, which leads to less system degradation and a longer life expectancy. Multi-staging a coilgun by adding multiple turns on a single coil or on the projectile increases the inductance, thus permitting acceleration of the projectile to higher velocities. Previously, a simplified problem of modeling an inductively-coupled, single-coil coilgun using a circuit-based analysis coupled to the one-dimensional momentum equation through Lenz's law was solved; however, the analysis was only conducted on uncoupled coils. The problem is significantly more complicated when multiple, independently-powered coils simultaneously operate and interact with each other and the projectile through induced magnetic fields. This paper presents a multi-coil model developed with the magnetostatic finite element solver QuickField. In the model, mutual inductance values between pairs of conductors were found by first computing the magnetic field energy for different cases where individual coils or multiple coils carry current, then integrating over the entire finite element domain for each case, and finally using the definition of inductive energy storage to solve for the self and mutual inductance. The electric circuit model is coupled to the projectile through Lenz's law, with the coils coupled through mutual inductance but able to be independently triggered at different times to optimize the acceleration profile. This initial model to predict the behavior of a projectile's acceleration through a coupled, multi-coil coilgun increases the potential of building a highly efficient coilgun thruster with key advantages over other EM thruster systems, thus making it a promising candidate for satellite main propulsion or attitude control thrusters.

Liu, Connie↗

NASA NTRS1990

A decentralized linear quadratic control design method for flexible structures

A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass and stiffness properties.

Su, Tzu-Jeng↗

DOE OSTI2026

Robust direct laser acceleration of electrons with flying-focus laser pulses

Direct laser acceleration (DLA) offers a compact source of high-charge, energetic electrons for generating secondary radiation or neutrons. While DLA in high-density plasma optimizes the energy transfer from a laser pulse to electrons, it exacerbates nonlinear propagation effects, such as filamentation, that can disrupt the acceleration process. Here, we show that superluminal flying-focus pulses (FFPs) mitigate nonlinear propagation, thereby enhancing the number of high-energy electrons and resulting x-ray yield. Three-dimensional particle-in-cell simulations show that, compared to a Gaussian pulse of equal energy (1 J) and intensity (2 × 10 20 W/cm 2 ), an FFP produces 80 × more electrons above 100 MeV, increases the electron cutoff energy by 20%, triples the high-energy x-ray yield, and improves x-ray collimation. These results illustrate the ability of spatiotemporally structured laser pulses to provide additional control in the highly nonlinear, relativistic regime of laser-plasma interactions.

Laser-produced plasmas↗