Search NASA⌕ Search

SEARCH · Search NASA

Results for “Discrete 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Fast Assessment of Metal Performance through Dislocation Physics and Machine Learning

The microstructure of metals is key to their mechanical properties. The types, density, composition and morphology of crystal defects all have pronounced impact on the properties. Changes to the microstructure occurring during processing and use can be very striking. The emerging technology additive manufacturing (AM) has the potential to improve performance by allowing optimized designs, but the process and environments can lead to unusual microscale features whose properties must be understood and characterized to enable higher technological readiness levels and application. Experimentally, an extensive evaluation of mechanical properties of 3D printed metals is a challenge, and anomalous effects related to the AM process add complexity. We present a new machine learning (ML) model predicting mechanical response based on dislocation mediated plasticity simulations. A large set of 3D discrete dislocation dynamics simulations with wide ranges of loading conditions is transformed to preprocessed data ready for training with the ML model. The trained model can predict the mechanical response of Mo30W for a given microstructure evolution, providing key information essential for optimization of AM processing.

Jaehyun Cho↗
NASA NTRSDate not supplied

Fast Assessment of Metal Performance through Dislocation Physics and Machine Learning

The microstructure of metals is key to their mechanical properties. The types, density, composition and morphology of crystal defects all have pronounced impact on the properties. Changes to the microstructure occurring during processing and use can be very striking. The emerging technology additive manufacturing (AM) has the potential to improve performance by allowing optimized designs, but the process and environments can lead to unusual microscale features whose properties must be understood and characterized to enable higher technological readiness levels and application. Experimentally, an extensive evaluation of mechanical properties of 3D printed metals is a challenge, and anomalous effects related to the AM process add complexity. We present a new machine learning (ML) model predicting mechanical response based on dislocation mediated plasticity simulations. A large set of 3D discrete dislocation dynamics simulations with wide ranges of loading conditions is transformed to preprocessed data ready for training with the ML model. The trained model can predict the mechanical response of Mo30W for a given microstructure evolution, providing key information essential for optimization of AM processing.

Jaehyun Cho↗
DOE OSTI2025

An Adaptive Newton-Based Free-Boundary Grad–Shafranov Solver

Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for the poloidal magnetic flux, commonly known as the Grad–Shafranov equation. It is challenging to develop a scalable and accurate free-boundary Grad–Shafranov solver, since it is a fully nonlinear optimization problem that simultaneously solves for the magnetic field coil current outside the plasma to control the plasma shape. In this work, we develop a Newton-based free-boundary Grad–Shafranov solver using adaptive finite elements and preconditioning strategies. The free-boundary interaction leads to the evaluation of a domain-dependent nonlinear form of which its contribution to the Jacobian matrix is achieved through shape calculus. The optimization problem aims to minimize the distance between the plasma boundary and specified control points while satisfying two nontrivial constraints, which correspond to the nonlinear finite element discretization of the Grad–Shafranov equation and a constraint on the total plasma current involving a nonlocal coupling term. The linear system is solved by a block factorization, and AMG is called for subblock elliptic operators. The unique contributions of this work include the treatment of a global constraint, preconditioning strategies, nonlocal reformulation, and the implementation of adaptive finite elements. Furthermore, it is found that the resulting Newton solver is robust, successfully reducing the nonlinear residual to 1e-6 and lower in a small handful of iterations while addressing the challenging case to find a Taylor state equilibrium where conventional Picard-based solvers fail to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2013

Real-Time Minimization of Tracking Error for Aircraft Systems

This technology presents a novel, stable, discrete-time adaptive law for flight control in a Direct adaptive control (DAC) framework. Where errors are not present, the original control design has been tuned for optimal performance. Adaptive control works towards achieving nominal performance whenever the design has modeling uncertainties/errors or when the vehicle suffers substantial flight configuration change. The baseline controller uses dynamic inversion with proportional-integral augmentation. On-line adaptation of this control law is achieved by providing a parameterized augmentation signal to a dynamic inversion block. The parameters of this augmentation signal are updated to achieve the nominal desired error dynamics. If the system senses that at least one aircraft component is experiencing an excursion and the return of this component value toward its reference value is not proceeding according to the expected controller characteristics, then the neural network (NN) modeling of aircraft operation may be changed.

Garud, Sumedha↗
NASA NTRSDate not supplied

Dynamic Spectrum Allocation in Urban Air Transportation System via Deep Reinforcement Learning

The emerging concepts of Urban Air Mobility (UAM) and Advanced Air Mobility (AAM) open a new paradigm for urban air transportation. A big challenge is that these new aerial vehicles will quickly saturate the already crowded aviation spectrum, which is an essential resource to ensure reliable communications for safe operations. In this paper, we consider an air transportation system where multiple aerial vehicles are operated to transport passengers or cargo from different sources to destinations along their pre-defined paths. During the flight, the minimum communication Quality of Service (QoS) requirement must be achieved to ensure flight safety. Our objective is to minimize the average mission completion time by jointly optimizing the velocity selection and spectrum allocation for all aerial vehicles. We formulate the optimization problem as a multi-stage Markov Decision Process (MDP) where the optimization variables are coupled together. A multi-agent Deep Reinforcement Learning (DRL) based solution is proposed where Value Decomposition Networks (VDN) algorithm is utilized to take discrete actions. Additionally, we propose a heuristic greedy algorithm as a baseline solution. Simulation results show that our learning based solution outperforms the heuristic greedy algorithm and another Orthogonal Multiple Access (OMA) solution in minimizing the mission completion time.

Ruixuan Han↗
NASA NTRSDate not supplied

Dynamic Spectrum Allocation in Urban Air Transportation System via Deep Reinforcement Learning

The emerging concepts of Urban Air Mobility (UAM) and Advanced Air Mobility (AAM) open a new paradigm for urban air transportation. A big challenge is that these new aerial vehicles will quickly saturate the already crowded aviation spectrum, which is an essential resource to ensure reliable communications for safe operations. In this paper, we consider an air transportation system where multiple aerial vehicles are operated to transport passengers or cargo from different sources to destinations along their pre-defined paths. During the flight, the minimum communication Quality of Service (QoS) requirement must be achieved to ensure flight safety. Our objective is to minimize the average mission completion time by jointly optimizing the velocity selection and spectrum allocation for all aerial vehicles. We formulate the optimization problem as a multi-stage Markov Decision Process (MDP) where the optimization variables are coupled together. A multi-agent Deep Reinforcement Learning (DRL) based solution is proposed where Value Decomposition Networks (VDN) algorithm is utilized to take discrete actions. Additionally, we propose a heuristic greedy algorithm as a baseline solution. Simulation results show that our learning based solution outperforms the heuristic greedy algorithm and another Orthogonal Multiple Access (OMA) solution in minimizing the mission completion time.

Ruixuan Han↗
DOE OSTI2024

Thermal Management of Discretized Heaters Using CuW Microchannel Heat Sinks and FC3283

Single-phase cooling using microchannel heat sinks (MCHS) has become a popular approach for overcoming the thermal challenges associated with high-powered microelectronic devices. Thermal management is one of the largest barriers to higher power densities in electronics and frequently limits overall device performance. The implementation of forced convective cooling via single-phase liquid cooling in MCHS reduces the thermal resistance resulting in lower device temperatures at high-power conditions, which can decrease the package size and extend the lifespan of devices. The goal of the work described in this article was to investigate practical cooling solutions for laser diode bars. This study examined the effectiveness of a copper tungsten (CuW) microchannel heat sink paired with a dielectric coolant (FC3283) for dissipating both discrete and uniform heat fluxes up to 600 W/cm2 across a 0.25-cm2 surface area through a numerical and experimental study. CuW was chosen as the MCHS material because it is thermal expansion matched to GaAs, which is a common laser diode substrate. FC3283 serves as a dielectric coolant that is compatible with power electronics cooling. The microchannels utilized in this work were approximately $365$ $μ$ m deep and $100$ $μ$ m wide resulting in a hydraulic diameter of $160$ $μ$ m. The study investigated the cooling performance across a variety of applied power loads and flow rates to determine optimal effectiveness. The resulting thermal resistance ranged from 0.15 cm2 K/W at the highest flow rate to 0.26 cm2 K/W at the lowest flow rate. Further, the resulting thermal performance from this study demonstrates the importance of considering discrete heat sources separately from uniform heat sources and proved that the unique combination of CuW microchannels with FC3283 can be a promising cooling option toward future advancements of laser diode bars and other high-power microelectronics.

42 ENGINEERING↗
DOE OSTI2024

Asynchronous GPU-based DEM solver embedded in commercial CFD software with polyhedral mesh support

A novel graphical processing unit-based discrete element method solver is introduced to improve stability, performance, and provide seamless integration into commercial or open-source computational fluid dynamics software. A key innovation is eliminating a need for network communication between solvers, which was previously required for cross-platform coupling. This is accomplished by a direct coupling method that employs dynamic-linked libraries. Furthermore, the solver optimizes memory usage by streamlining the particle-cell search algorithm by eliminating the cells' searching grid. This ensures the solver is compatible with a wide range of mesh types, providing high geometric flexibility. The approach simplifies the simulation process by directly incorporating computational fluid dynamics mesh information into the discrete element method solver. The performance analysis indicates about sixteen times boost in computational speed compared to benchmark central processing unit-based solvers. Finally, the solver's compatibility with polyhedral meshes, a vital advantage for complex geometries, is tested against a referenced study regarding the simulation of an immersed-tube fluidized bed.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Stochastic average model methods

We consider the solution of finite-sum minimization problems, such as those appearing in nonlinear least-squares or general empirical risk minimization problems. We are motivated by problems in which the summand functions are computationally expensive and evaluating all summands on every iteration of an optimization method may be undesirable. Here we present the idea of stochastic average model (SAM) methods, inspired by stochastic average gradient methods. SAM methods sample component functions on each iteration of a trust-region method according to a discrete probability distribution on component functions; the distribution is designed to minimize an upper bound on the variance of the resulting stochastic model. We present promising numerical results concerning an implemented variant extending the derivative-free model-based trust-region solver POUNDERS, which we name SAM-POUNDERS.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1978

Discrete-time pilot model

Pilot behavior is considered as a discrete-time process where the decision making has a sequential nature. This model differs from both the quasilinear model which follows from classical control theory and from the optimal control model which considers the human operator as a Kalman estimator-predictor. An additional factor considered is that the pilot's objective may not be adequately formulated as a quadratic cost functional to be minimized, but rather as a more fuzzy measure of the closeness with which the aircraft follows a reference trajectory. All model parameters, in the digital program simulating the pilot's behavior, were successfully compared in terms of standard-deviation and performance with those of professional pilots in IFR configuration. The first practical application of the model was in the study of its performance degradation when the aircraft model static margin decreases.

Cavalli, D.↗
NASA NTRS1985

A new approach to approximating the linear quadratic optimal control law for hereditary systems with control delays

A factorization approach is presented for deriving approximations to the optimal feedback gain for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the feedback kernels.

Milman, M. H.↗
NASA NTRS1987

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

Milman, Mark H.↗
NASA NTRS1988

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary schemes. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

Milman, Mark H.↗
NASA NTRS1991

Vision-based optimal obstacle-avoidance guidance for rotorcraft

An optimal guidance scheme for vision-based obstacle avoidance is developed. The proposed approach is useful for automating low-altitude rotorcraft flight. It explicitly accounts for the discrete nature of range information available from vision-based sensors and uses a linear combination of flight time, square of the vehicle acceleration and the square of the distance to various sensed obstacles as the performance index. A sixth-order, three-degree-of-freedom nonlinear point-mass vehicle model is included in the analysis. Numerical results using a sample image sequence is given.

Menon, P. K. A.↗
NASA NTRS1991

A parallel trajectory optimization tool for aerospace plane guidance

A parallel trajectory optimization algorithm is being developed. One possible mission is to provide real-time, on-line guidance for the National Aerospace Plane. The algorithm solves a discrete-time problem via the augmented Lagrangian nonlinear programming algorithm. The algorithm exploits the dynamic programming structure of the problem to achieve parallelism in calculating cost functions, gradients, constraints, Jacobians, Hessian approximations, search directions, and merit functions. Special additions to the augmented Lagrangian algorithm achieve robust convergence, achieve (almost) superlinear local convergence, and deal with constraint curvature efficiency. The algorithm can handle control and state inequality constraints such as angle-of-attack and dynamic pressure constraints. Portions of the algorithm have been tested. The nonlinear programming core algorithm performs well on a variety of static test problems and on an orbit transfer problem. The parallel search direction algorithm can reduce wall clock time by a factor of 10 for this part of the computation task.

Psiaki, Mark L.↗
DOE OSTI2024

The Monolithic Heat Pipe Microreactor Reference Plant Model

This work introduces a reference plant model for a generic monolithic heat-pipe-cooled microreactor. The model will serve as a springboard to develop future evaluation models in the licensing process of similar microreactor designs at the U.S. Nuclear Regulatory Commission. This model has been developed with the Comprehensive Reactor Analysis Bundle and its specifications are based on open literature publications for the eVinci TM design. BlueCRAB is the U.S. Nu- clear Regulatory Commission non-light-water reactor analysis system based on the Multiphysics Object-Oriented Simulation Environment framework, which can couple the Griffin, BISON, and Sockeye applications to resolve the various physics that are essential for the safety analysis of this type of reactor system. The core specifications includes tristructural isotropic fuel, graphite monolith, graphite reflectors, and drums composed of graphite and B 4 C. No moderator or burnable poison pins are used in the design. The fuel enrichment is reduced to control excess reactivity in the core. This core design is not optimized and only serves for testing purposes, since the primary objective of this work is to exercise the multiphysics coupling for this type of reactor system. A three dimensional (3D) core heterogeneous Griffin discrete ordinates (SN) transport model allows the precise calculation of the flux distribution and pin powers. Griffin transfers the power density distribution and obtains a temperature distribution to and from BISON. The BISON model com- putes the 3D core temperature distribution and is coupled to 876 Sockeye subapplications running a heat pipe model. This 3D conduction model is coupled to the various heat pipes via heat flux boundary conditions. The model includes a small gap between the heat pipe and the monolith. Convective heat transfer boundaries with either ambient temperature or condenser temperature as heat sinks are imposed at the model boundaries. The 2D Sockeye heat pipe model uses a vapor- only methodology, which provides the needed resolution for transient calculations and allows the determination of various heat pipe limits. This approach is superior to the superconductor model traditionally used in steady-state calculations. BlueCRAB computes steady-state power and temperature distributions that serve as the initial condition for a loss-of-heat-sink transient simulation. The steady-state results show significant peaking due to the position of the control drum, but this is a characteristic of the particular design used, which is not optimized at this stage. The transient results show the reactor power slowly stabilizing towards a 3% power level after the partial loss of secondary heat removal. Several recriticalities are observed due to cooling through the secondary system but the reactor is self-stabilizing and behaves as expected.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Data-driven reduced-order models for port-Hamiltonian systems with operator inference

Hamiltonian operator inference has been developed in Sharma et al. (2022) to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method constructs a low-dimensional model using only data and knowledge of the functional form of the Hamiltonian. The resulting ROMs preserve the intrinsic structure of the system, ensuring that the mechanical and physical properties of the system are maintained. In this work, we extend this approach to port-Hamiltonian systems, which generalize Hamiltonian systems by including energy dissipation, external input, and output. Based on snapshots of the system’s state and output, together with the information about the functional form of the Hamiltonian, reduced operators are inferred through optimization and are then used to construct data-driven ROMs. To further alleviate the complexity of evaluating nonlinear terms in the ROMs, a hyper-reduction method via discrete empirical interpolation is applied. Accordingly, we derive error estimates for the ROM approximations of the state and output. Lastly, we demonstrate the structure preservation, as well as the accuracy of the proposed port-Hamiltonian operator inference framework, through numerical experiments on a linear mass–spring-damper problem and a nonlinear Toda lattice problem.

97 MATHEMATICS AND COMPUTING↗