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NASA NTRS2017

Fuzzy Logic Controller Stability Analysis Using a Satisfiability Modulo Theories Approach

While many widely accepted methods and techniques exist for validation and verification of traditional controllers, at this time no solutions have been accepted for Fuzzy Logic Controllers (FLCs). Due to the highly nonlinear nature of such systems, and the fact that developing a valid FLC does not require a mathematical model of the system, it is quite difficult to use conventional techniques to prove controller stability. Since safety-critical systems must be tested and verified to work as expected for all possible circumstances, the fact that FLC controllers cannot be tested to achieve such requirements poses limitations on the applications for such technology. Therefore, alternative methods for verification and validation of FLCs needs to be explored. In this study, a novel approach using formal verification methods to ensure the stability of a FLC is proposed. Main research challenges include specification of requirements for a complex system, conversion of a traditional FLC to a piecewise polynomial representation, and using a formal verification tool in a nonlinear solution space. Using the proposed architecture, the Fuzzy Logic Controller was found to always generate negative feedback, but inconclusive for Lyapunov stability.

Fuzzy Logic Controller↗

NASA NTRS1995

Newton-Krylov-Schwarz: An implicit solver for CFD

Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton's method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on aerodynamics applications emphasizing comparisons with a standard defect-correction approach, subdomain preconditioner consistency, subdomain preconditioner quality, and the effect of a coarse grid.

Cai, Xiao-Chuan↗

NASA NTRS2006

NASA Tech Briefs, September 2006

Topics covered include: Improving Thermomechanical Properties of SiC/SiC Composites; Aerogel/Particle Composites for Thermoelectric Devices; Patches for Repairing Ceramics and Ceramic- Matrix Composites; Lower-Conductivity Ceramic Materials for Thermal-Barrier Coatings; An Alternative for Emergency Preemption of Traffic Lights; Vehicle Transponder for Preemption of Traffic Lights; Automated Announcements of Approaching Emergency Vehicles; Intersection Monitor for Traffic-Light-Preemption System; Full-Duplex Digital Communication on a Single Laser Beam; Stabilizing Microwave Frequency of a Photonic Oscillator; Microwave Oscillators Based on Nonlinear WGM Resonators; Pointing Reference Scheme for Free-Space Optical Communications Systems; High-Level Performance Modeling of SAR Systems; Spectral Analysis Tool 6.2 for Windows; Multi-Platform Avionics Simulator; Silicon-Based Optical Modulator with Ferroelectric Layer; Multiplexing Transducers Based on Tunnel-Diode Oscillators; Scheduling with Automated Resolution of Conflicts; Symbolic Constraint Maintenance Grid; Discerning Trends in Performance Across Multiple Events; Magnetic Field Solver; Computing for Aiming a Spaceborne Bistatic- Radar Transmitter; 4-Vinyl-1,3-Dioxolane-2-One as an Additive for Li-Ion Cells; Probabilistic Prediction of Lifetimes of Ceramic Parts; STRANAL-PMC Version 2.0; Micromechanics and Piezo Enhancements of HyperSizer; Single-Phase Rare-Earth Oxide/Aluminum Oxide Glasses; Tilt/Tip/Piston Manipulator with Base-Mounted Actuators; Measurement of Model Noise in a Hard-Wall Wind Tunnel; Loci-STREAM Version 0.9; The Synergistic Engineering Environment; Reconfigurable Software for Controlling Formation Flying; More About the Tetrahedral Unstructured Software System; Computing Flows Using Chimera and Unstructured Grids; Avoiding Obstructions in Aiming a High-Gain Antenna; Analyzing Aeroelastic Stability of a Tilt-Rotor Aircraft; Tracking Positions and Attitudes of Mars Rovers; Stochastic Evolutionary Algorithms for Planning Robot Paths; Compressible Flow Toolbox; Rapid Aeroelastic Analysis of Blade Flutter in Turbomachines; General Flow-Solver Code for Turbomachinery Applications; Code for Multiblock CFD and Heat-Transfer Computations; Rotating-Pump Design Code; Covering a Crucible with Metal Containing Channels; Repairing Fractured Bones by Use of Bioabsorbable Composites; Kalman Filter for Calibrating a Telescope Focal Plane; Electronic Absolute Cartesian Autocollimator; Fiber-Optic Gratings for Lidar Measurements of Water Vapor; Simulating Responses of Gravitational-Wave Instrumentation; SOFTC: A Software Correlator for VLBI; Progress in Computational Simulation of Earthquakes; Database of Properties of Meteors; Computing Spacecraft Solar-Cell Damage by Charged Particles; Thermal Model of a Current-Carrying Wire in a Vacuum; Program for Analyzing Flows in a Complex Network; Program Predicts Performance of Optical Parametric Oscillators; Processing TES Level-1B Data; Automated Camera Calibration; Tracking the Martian CO2 Polar Ice Caps in Infrared Images; Processing TES Level-2 Data; SmaggIce Version 1.8; Solving the Swath Segment Selection Problem; The Spatial Standard Observer; Less-Complex Method of Classifying MPSK; Improvement in Recursive Hierarchical Segmentation of Data; Using Heaps in Recursive Hierarchical Segmentation of Data; Tool for Statistical Analysis and Display of Landing Sites; Automated Assignment of Proposals to Reviewers; Array-Pattern-Match Compiler for Opportunistic Data Analysis; Pre-Processor for Compression of Multispectral Image Data; Compressing Image Data While Limiting the Effects of Data Losses; Flight Operations Analysis Tool; Improvement in Visual Target Tracking for a Mobile Robot; Software for Simulating Air Traffic; Automated Vectorization of Decision-Based Algorithms; Grayscale Optical Correlator Workbench; "One-Stop Shopping" for Ocean Remote-Sensing and Model Data; State Analysis Database Tool; Generating CAHV and CAHVOmages with Shadows in ROAMS; Improving UDP/IP Transmission Without Increasing Congestion; FORTRAN Versions of Reformulated HFGMC Codes; Program for Editing Spacecraft Command Sequences; Flight-Tested Prototype of BEAM Software; Mission Scenario Development Workbench; Marsviewer; Tool for Analysis and Reduction of Scientific Data; ASPEN Version 3.0; Secure Display of Space-Exploration Images; Digital Front End for Wide-Band VLBI Science Receiver; Multifunctional Tanks for Spacecraft; Lightweight, Segmented, Mostly Silicon Telescope Mirror; Assistant for Analyzing Tropical-Rain-Mapping Radar Data; and Anion-Intercalating Cathodes for High-Energy- Density Cells.

Source record↗

DOE OSTI2022

A modified model parametrization algorithm for solving a special type of heat and mass transfer systems

A new method for solving nonlinear heat and mass transfer design tasks was considered. Systems using the Number of Transfer Units (NTU) method are a special type of mathematical model of heat and mass exchangers. It was observed, that the NTU models in a form of differential-algebraic equations (DAEs) cannot be directly solved with higher values of NTU. The requirements for consistent initial conditions, as well as numerical limitations of DAEs solvers, result, that the solution to the considered design problems that cannot be obtained by a classical direct shooting procedure. To overcome the presented difficulties, the αDAE model optimization algorithm was adjusted for solving NTU-based models. The new approach consists of 3 main steps: 1) task discretization by a multiple-shooting approach, 2) design an appropriate function $f_{NTU}$(α) to effectively influence the variability of the state variables described by dynamical relations, 3) the iterative numerical optimization algorithm for the new parametrized system. Moreover, computations can be performed by a chosen numerical optimization approach, which can be communicated with an available outer procedure for solving differential-algebraic equations. The presented algorithm was implemented and applied to solve the design task with the NTU model of a counter-flow exchanger. Here, the new approach was used to modify the system dynamics to influence the difficulty of the considered problem. Finally, the presented method enabled failure-free numerical computations for the higher values of the NTU parameter.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1992

The natural flow wing-design concept

A wing-design study was conducted on a 65 degree swept leading-edge delta wing in which the wing geometry was modified to take advantage of the naturally occurring flow that forms over a slender wing in a supersonic flow field. Three-dimensional nonlinear analysis methods were used in the study which was divided into three parts: preliminary design, initial design, and final design. In the preliminary design, the wing planform, the design conditions, and the near-conical wing-design concept were derived, and a baseline standard wing (conventional airfoil distribution) and a baseline near-conical wing were chosen. During the initial analysis, a full-potential flow solver was employed to determine the aerodynamic characteristics of the baseline standard delta wing and to investigate modifications to the airfoil thickness, leading-edge radius, airfoil maximum-thickness position, and wing upper to lower surface asymmetry on the baseline near-conical wing. The final design employed an Euler solver to analyze the best wing configurations found in the initial design and to extend the study of wing asymmetry to develop a more refined wing. Benefits resulting from each modification are discussed, and a final 'natural flow' wing geometry was designed that provides an improvement in aerodynamic performance compared with that of a baseline conventional uncambered wing, linear-theory cambered wing, and near-conical wing.

Wood, Richard M.↗

DOE OSTI2024

Recent Advances of PyROS: A Pyomo Solver for Nonconvex Two-Stage Robust Optimization in Process Systems Engineering

The document presents recent algorithmic and implementation advances of the two-stage robust optimization (RO) solver PyROS, and a benchmarking study which demonstrates the utility of PyROS for two-stage RO problems. The advances include extensions of the scope of PyROS to models with uncertain variable bounds, improvements to the initializations of the subproblems used by the underlying cutting set algorithm, and extensions of the uncertainty set interfaces. The benchmarking study is performed on a library of over 8,500 instances, with variations in the nonlinearities, degree-of-freedom partitioning, uncertainty sets, and polynomial decision rule approximations. An amine-based CO2 capture case study is presented to demonstrate the utility of PyROS for large-scale process models. Overall, the results highlight the effectiveness of PyROS for obtaining robust solutions to optimization problems with uncertain equality constraints.

Sherman, Jason↗

NASA NTRSDate not supplied

Assessment of Edge-Based Viscous Method for Corner-Flow Solutions on Graphics Processing Units

A highly efficient, edge-based viscous (EBV) discretization method has been recently implemented in a practical, unstructured-grid, node-centered, finite-volume flow solver and evaluated for Reynolds-averaged Navier-Stokes (RANS) formulations. In comparison to a well-established cell-based viscous (CBV) method, the EBV method has demonstrated multifold acceleration of all viscous-kernel computations on general unstructured mixed-element grids. The viscous kernels include evaluation of viscous fluxes, diffusion terms in turbulence models, and the corresponding Jacobian terms. In this paper, an EBV implementation of a nonlinear extension of the Spalart-Allmaras turbulence model, SA-neg-QCR2000, is presented and verified. The SA-neg-QCR2000 model is used for simulating turbulent corner flows. Previously reported EBV computations have been conducted on traditional computing architectures based on central processing units (CPU). This paper assesses benefits of the EBV method on modern high-performance computing architectures based on graphics processing units (GPU). The GPU implementations of the CBV and EBV methods are verified by comparing solutions and iterative convergence with those observed in CPU computations on the same grids. A comprehensive assessment of the EBV speedup on CPU and GPU architectures is presented for established benchmark corner flows, namely, a supersonic flow through a long square duct and a subsonic flow around a NASA juncture flow model.

CFD↗

NASA NTRSDate not supplied

Assessment of Edge-Based Viscous Method for Corner-Flow Solutions on Graphics Processing Units

CFD↗

DOE OSTI2023

Recent Advances in PyROS: The Pyomo Solver for Two-Stage Nonconvex Robust Optimization

The slides present recent algorithmic and implementation advances of the two-stage robust optimization (RO) solver PyROS, and a benchmarking study which demonstrates the utility of PyROS for two-stage RO problems. The advances include extensions of the scope of PyROS to models with uncertain variable bounds, improvements to the initializations of the subproblems used by the underlying cutting set algorithm, and extensions of the uncertainty set interfaces. The benchmarking study is performed on a library of over 8,500 instances, with variations in the nonlinearities, degree-of-freedom partitioning, uncertainty sets, and polynomial decision rule approximations. Overall, the results highlight the effectiveness of PyROS for obtaining robust solutions to optimization problems with uncertain equality constraints.

Sherman, Jason↗

DOE OSTI2023

Recent Advances in PyROS: The Pyomo Solver for Two-Stage Nonconvex Robust Optimization

Sherman, Jason↗

DOE OSTI2022

Ponderomotive force driven density modifications parallel to B on the LAPD

The ponderomotive force has previously been identified as a possible driver of observed density modifications close to radio frequency actuators during operation. This nonlinear force redistributes density in regions of gradients in the magnitude of an oscillating electric field and describes the influence of the fast time scale RF wave dynamics on slow time scale plasma transport. Depletion of the saturation current (a proxy for the density) measured at the Large Plasma Device (LAPD) was 30–35% during ion cyclotron range of frequencies operation. A coupled 1D plasma transport and cold plasma frequency domain wave solver was developed to self-consistently describe ponderomotive effects and was used to compare with results obtained from the LAPD experiment. The scaled current density driver for the wave model yielded an RF B field in close agreement with two components of the experimental data. However, the 1D parallel model did not accurately reproduce the amplitude or spatial distribution observed in experimental measurements of By. Within the limitations of the 1D model, initial simulation results showed that the ponderomotive force depleted up to 8% for high power (1 MW) and around 1% for the experimental power of 120 kW. This could suggest that the ponderomotive force is not the main driver of density modification for the LAPD experiments presented in this paper. Higher fidelity tools of at least 2D will be required to give a more realistic description of the RF E fields and the effect of the ponderomotive force on the LAPD.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1998

Real Gas Computation Using an Energy Relaxation Method and High-Order WENO Schemes

In this paper, we use a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition into two parts: one part is associated with a simpler pressure law and the other part (the nonlinear deviation) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the first part. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Montarnal, Philippe↗

NASA NTRS1998

HPCC Methodologies for Structural Design and Analysis on Parallel and Distributed Computing Platforms

In this grant, we have proposed a three-year research effort focused on developing High Performance Computation and Communication (HPCC) methodologies for structural analysis on parallel processors and clusters of workstations, with emphasis on reducing the structural design cycle time. Besides consolidating and further improving the FETI solver technology to address plate and shell structures, we have proposed to tackle the following design related issues: (a) parallel coupling and assembly of independently designed and analyzed three-dimensional substructures with non-matching interfaces, (b) fast and smart parallel re-analysis of a given structure after it has undergone design modifications, (c) parallel evaluation of sensitivity operators (derivatives) for design optimization, and (d) fast parallel analysis of mildly nonlinear structures. While our proposal was accepted, support was provided only for one year.

Farhat, Charbel↗

NASA NTRS2001

Multigrid approaches to non-linear diffusion problems on unstructured meshes

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Mavriplis, Dimitri J.↗

DOE OSTI2024

Convergence Analysis for an Online Data-Driven Feedback Control Algorithm

This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system’s state via indirect observations, alongside an efficient stochastic maximum principle-type optimal control solver. By integrating weak convergence techniques for the particle filter with convergence analysis for the stochastic maximum principle control solver, we derive a weak convergence result for the optimization procedure in search of optimal data-driven feedback control. Numerical experiments are performed to validate the theoretical findings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

An optimization-based approach to tailor the mechanical response of soft metamaterials undergoing rate-dependent instabilities

An optimization-based design framework is proposed to tune the response of soft metamaterials involving both geometric instabilities and nonlinear viscoelastic material behavior. Designing the response of soft metamaterials to harness instabilities and undergo large, tailored configuration changes will enable advancements in soft robotics, shock and vibration mitigation, and flexible electronics. In line with the metamaterial concept, the response of these materials is governed to a large extent by the geometric and topological makeup of their small-scale features. However, the link between structure and response is less intuitive for soft metamaterials due to their reliance upon highly nonlinear responses triggered by geometric instabilities. This is further complicated by the effects of viscoelastic relaxation, which recent studies have shown to alter the emergence of instabilities in non-intuitive ways. Here, these effects are accounted for in our framework to achieve various design objectives, including tailored force–displacement response and maximized energy absorption from both geometric and material effects. To fully automate this process, it is essential to have a completely robust equation solver for forward problems involving instabilities and viscoelastic relaxation. We achieve this by casting the search for stable mechanical equilibrium — i.e. the forward problem — as a minimization problem and utilize a trust region algorithm to robustly handle instabilities and follow energetically-favorable equilibrium paths through critical points.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Accelerating the solution of the S N equations with highly anisotropic scattering using the Fokker-Planck approximation

The discrete ordinates method can model forward-peaked transport problems accurately. However, convergence of discrete ordinates solution can become arbitrarily slow upon use of standard iterative procedures like source iteration. Standard zeroth and first moment-based acceleration methods like nonlinear diffusion acceleration and diffusion synthetic acceleration are ineffective in accelerating such problems because these methods do not correct higher order Legendre-moments of angular flux. In this paper, we explore the idea of using the Fokker-Planck approximation as a preconditioner to accelerate the convergence of solution of forward-peaked transport problems. Finally, we observe that such preconditioning can successfully reduce the iteration count by up to four orders of magnitude, and solver runtime by up to three orders of magnitude when compared to diffusion synthetic acceleration.

42 ENGINEERING↗

DOE OSTI2022

HyKKT: a hybrid direct-iterative method for solving KKT linear systems

Here, we propose a solution strategy for the large indefinite linear systems arising in interior methods for nonlinear optimization. The method is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for sparse indefinite systems is the LBLT factorization where L is a lower triangular matrix and B is 1×1 or 2×2 block diagonal. However, this requires pivoting, which substantially increases communication cost and degrades performance on GPUs. Our approach solves a large indefinite system by solving multiple smaller positive definite systems, using an iterative solver on the Schur complement and an inner direct solve (via Cholesky factorization) within each iteration. Cholesky is stable without pivoting, thereby reducing communication and allowing reuse of the symbolic factorization. We demonstrate the practicality of our approach on large optimal power flow problems and show that it can efficiently utilize GPUs and outperform LBL T factorization of the full system.

97 MATHEMATICS AND COMPUTING↗