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Results for “Penalty method”

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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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

CFD assessment of the pollutant environment from RD-170 propulsion system testing

Computational Fluid Dynamics (CFD) technology has been used to assess the exhaust plume pollutant environment of the RD-170 engine hot-firing on the F1 Test Stand at Marshall Space Flight Center. Researchers know that rocket engine hot-firing has the potential for forming thermal nitric oxides (NO(x)), as well as producing carbon monoxide (CO) when hydrocarbon fuels are used. Because of the complicated physics involved, however, little attempt has been made to predict the pollutant emissions from ground-based engine testing, except for simplified methods which can grossly underpredict and/or overpredict the pollutant formations in a test environment. The objective of this work, therefore, has been to develop a technology using CFD to describe the underlying pollutant emission physics from ground-based rocket engine testing. This resultant technology is based on a three-dimensional (3D), viscous flow, pressure-based CFD formulation, where wet CO and thermal NO finite-rate chemistry mechanisms are solved with a Penalty Function method. A nominal hot-firing of a RD-170 engine on the F1 stand has been computed. Pertinent test stand flow physics such as the multiple-nozzle clustered engine plume interaction, air aspiration from base and aspirator, plume mixing with entrained air that resulted in contaminant dilution and afterburning, counter-afterburning due to flame bucket water-quenching, plume impingement on the flame bucket, and restricted multiple-plume expansion and turning have been captured. The predicted total emission rates compared reasonably well with those of the existing hydrocarbon engine hot-firing test data.

Wang, Ten-See↗
NASA NTRS1999

Structural Optimization for Reliability Using Nonlinear Goal Programming

This report details the development of a reliability based multi-objective design tool for solving structural optimization problems. Based on two different optimization techniques, namely sequential unconstrained minimization and nonlinear goal programming, the developed design method has the capability to take into account the effects of variability on the proposed design through a user specified reliability design criterion. In its sequential unconstrained minimization mode, the developed design tool uses a composite objective function, in conjunction with weight ordered design objectives, in order to take into account conflicting and multiple design criteria. Multiple design criteria of interest including structural weight, load induced stress and deflection, and mechanical reliability. The nonlinear goal programming mode, on the other hand, provides for a design method that eliminates the difficulty of having to define an objective function and constraints, while at the same time has the capability of handling rank ordered design objectives or goals. For simulation purposes the design of a pressure vessel cover plate was undertaken as a test bed for the newly developed design tool. The formulation of this structural optimization problem into sequential unconstrained minimization and goal programming form is presented. The resulting optimization problem was solved using: (i) the linear extended interior penalty function method algorithm; and (ii) Powell's conjugate directions method. Both single and multi-objective numerical test cases are included demonstrating the design tool's capabilities as it applies to this design problem.

El-Sayed, Mohamed E.↗
NASA NTRS1992

Global/local analysis of laminated composite plates using variable kinematic finite elements

A finite element modeling methodology is developed for the hierarchical, global/local analysis of laminated composite plates. The method incorporates a new variable kinematics, displacement-based, finite element that is developed using a multiple assumed displacement field approach. The variable kinematic elements provide a great degree of flexibility in defining the transverse (through thickness) variation of the assumed displacement field. The resulting finite element model permits different subregions of the computational domain to be described by different mathematical models. Enforcing displacement continuity along subregion boundaries requires only the specification of certain homogeneous essential boundary conditions, thus avoiding the inconvenience of multi-point constraints, penalty function methods, or special transition elements.

Robbins, D. H., Jr.↗
DOE OSTI2025

A time-parallel multiple-shooting method for large-scale quantum optimal control

Quantum optimal control plays a crucial role in quantum computing by providing the interface between compiler and hardware. Solving the optimal control problem is particularly challenging for multi-qubit gates, due to the exponential growth in computational complexity with the system's dimensionality and the deterioration of optimization convergence. To ameliorate the computational complexity of time-integration, this paper introduces a multiple-shooting approach in which the time domain is divided into multiple windows and the intermediate states at window boundaries are treated as additional optimization variables. Further, this enables parallel computation of state evolution across time-windows, significantly accelerating objective function and gradient evaluations. Since the initial state matrix in each window is only guaranteed to be unitary upon convergence of the optimization algorithm, the conventional gate trace infidelity is replaced by a generalized infidelity that is convex for non-unitary state matrices. Continuity of the state across window boundaries is enforced by equality constraints. A quadratic penalty optimization method is used to solve the constrained optimal control problem, and an efficient adjoint technique is employed to calculate the gradients in each iteration. We demonstrate the effectiveness of the proposed method through numerical experiments on quantum Fourier transform gates in systems with 2, 3, and 4 qubits, noting a speedup of 80x for evaluating the gradient in the 4-qubit case, highlighting the method's potential for optimizing control pulses in multi-qubit quantum systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation

We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between neighboring elements. The resulting bilinear form, and a Schur complement (reduced) version of it, are utilized in a number of auxiliary space preconditioners for the original conforming finite element discretization problem. Furthermore, these preconditioners are analyzed on the fine scale, and their performance is illustrated on model second order scalar elliptic problems discretized with high order elements.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

Optimal rocket thrust profile shaping using third degree spline function interpolation

Optimal solid-rocket thrust profiles for the parallel-burn, solid-rocket-assisted space shuttle are investigated. Solid-rocket thrust profiles are simulated by using third-degree spline functions, with the values of the thrust ordinates defined as parameters. The profiles are optimized parametrically, using the Davidon-Fletcher-Powell penalty function method, by minimizing propellant weight subject to state and control inequality constraints and to terminal boundary conditions. This study shows that optimizing a control variable parametrically by using third-degree spline function interpolation allows the control to be shaped so that inequality constraints are strictly adhered to and all corners are eliminated. The absence of corners, which is realistic in nature, makes this method attractive from the viewpoint of solid rocket grain design.

Johnson, I. L.↗
NASA NTRS1983

Coolant passage heat transfer with rotation. A progress report on the computational aspects

Turbine airfoils are subjected to increasingly higher heat loads which escalate the cooling requirements in order to satisfy life goals for the component materials. If turbine efficiency is to be maintained, however, cooling requirements should be as low as possible. To keep the quantity of cooling air bounded, a more efficient internal cooling scheme must be developed. One approach is to employ airfoils with multipass cooling passages that contain devices to augment internal heat transfer while limiting pressure drop. Design experience with multipass cooling passage airfoils has shown that a surplus of cooling air must be provided as a margin of safety. This increased cooling air leads to a performance penalty. Reliable methods for predicting the internal thermal and aerodynamic performance of multipass cooling passage airfoils would reduce or eliminate the need for the safety margin of surplus cooling air. The objective of the program is to develop and verify improved analytical methods that will form the basis for design technology which will result in efficient turbine components with improved durability without sacrificing performance. The objective will be met by: (1) establishing a comprehensive experimental data base that can form the basis of an empirical design system; (2) developing computational fluid dynamic techniques; and (3) analyzing the information in the data base with both phenomenological modeling and mathematical modeling to derive a suitable design and analysis procedure.

Aceto, L. D.↗
NASA NTRS1990

Large scale nonlinear numerical optimal control for finite element models of flexible structures

This paper discusses the development of large scale numerical optimal control algorithms for nonlinear systems and their application to finite element models of structures. This work is based on our expansion of the optimal control algorithm (DDP) in the following steps: improvement of convergence for initial policies in non-convex regions, development of a numerically accurate penalty function method approach for constrained DDP problems, and parallel processing on supercomputers. The expanded constrained DDP algorithm was applied to the control of a four-bay, two dimensional truss with 12 soft members, which generates geometric nonlinearities. Using an explicit finite element model to describe the structural system requires 32 state variables and 10,000 time steps. Our numerical results indicate that for constrained or unconstrained structural problems with nonlinear dynamics, the results obtained by our expanded constrained DDP are significantly better than those obtained using linear-quadratic feedback control.

Shoemaker, Christine A.↗
NASA NTRS2000

Design of the Active Elevon Rotor for Low Vibration

Helicopter fuselages vibrate more than desired, and traditional solutions have limited effectiveness and can impose an appreciable weight penalty. Alternative methods of combating high vibration, including Higher Harmonic Control (HHC) via harmonic swashplate motion and Individual Blade Control (IBC) via active pitch links, have been studied for several decades. HHC via an on-blade control surface was tested in 1977 on a full scale rotor using a secondary active swashplate and a mechanical control system. Recent smart material advances have prompted new research into the use of on-blade control concepts. Recent analytical studies have indicated that the use of on-blade control surfaces produces vibration reduction comparable to swashplate-based HHC but for less power. Furthermore, smart materials (such as piezoceramics) have been shown to provide sufficient control authority for preliminary rotor experiments. These experiments were initially performed at small scale for reduced tip speeds. More recent experiments have been conducted at or near full tip speeds, and a full-scale active rotor is under development by Boeing with Eurocopter et al. pursuing a similarly advanced full-scale implementation. The US Army Aeroflightdynamics Directorate has undertaken a new research program called the Active Elevon Rotor (AER) Focus Demo. This program includes the design, fabrication, and wind. tunnel testing of a four-bladed, 12.96 ft diameter rotor with one or two on-blade elevons per blade. The rotor, which will be Mach scaled, will use 2-5/rev elevon motion for closed-loop control and :will be tested in late 2001. The primary goal of the AER Focus Demo is the reduction of vibratory hub loads by 80% and the reduction of vibratory blade structural loads. A secondary goal is the reduction of rotor power. The third priority is the measurement and possible reduction of Blade Vortex Interaction (BVI) noise. The present study is focused on elevon effectiveness, that is, the elevon's ability to reduce all six components of the nonrotating 4/rev hub loads. Some design parameters have been kept fixed in this study, while others have been varied to determine their influence - on elevon effectiveness. The fixed parameters include all blade structural properties except for torsion stiffness; the varied parameters include torsion stiffness, elevon aerodynamic location, and the number and individual authority of elevon aerodynamic surfaces. This paper describes the preliminary design process being used for the AER, and describes and quantifies the emerging active rotor characteristics.

Fulton, Mark V.↗
NASA NTRSDate not supplied

Low-cost Quantification of Fluid Flow Parameter Sensitivity using Reduced-order Modeling

Uncertainty quantification of computational fluid dynamics (CFD) simulations is a complicated procedure which still relies in many cases on engineering judgment and factors of safety. This is in part because the computational cost of measuring the simulation's sensitivity to all meaningful parameters (e.g., body surface roughness) and hyperparameters (e.g., subiteration convergence criterion) is intractable for even a single simulation. Reduced-order modeling dramatically lowers this computational cost of simulating fluid flows, but usually only where similar data is already available. In this work, fluid reduced-order models are utilized to quantify a flow's sensitivity to certain physical parameters for the purposes of improved uncertainty quantification. Characteristic observability and sensitivity are both explored. The resulting sensitivity quantifications enable more informed CFD frameworks and more rigorous uncertainty bounds on the resulting data.

uncertainty quantification↗
NASA NTRSDate not supplied

Low-cost Quantification of Fluid Flow Parameter Sensitivity using Reduced-order Modeling

Uncertainty quantification of computational fluid dynamics (CFD) simulations is a complicated procedure which still relies in many cases on engineering judgment and factors of safety. This is in part because the computational cost of measuring the simulation's sensitivity to all meaningful parameters (e.g., body surface roughness) and hyperparameters (e.g., subiteration convergence criterion) is intractable for even a single simulation. Reduced-order modeling dramatically lowers this computational cost of simulating fluid flows, but usually only where similar data is already available. In this work, fluid reduced-order models are utilized to quantify a flow's sensitivity to certain physical parameters for the purposes of improved uncertainty quantification. Characteristic observability and sensitivity are both explored. The resulting sensitivity quantifications enable more informed CFD frameworks and more rigorous uncertainty bounds on the resulting data.

uncertainty quantification↗
NASA NTRS1996

Implementation of Hybrid V-Cycle Multilevel Methods for Mixed Finite Element Systems with Penalty

The goal of this paper is the implementation of hybrid V-cycle hierarchical multilevel methods for the indefinite discrete systems which arise when a mixed finite element approximation is used to solve elliptic boundary value problems. By introducing a penalty parameter, the perturbed indefinite system can be reduced to a symmetric positive definite system containing the small penalty parameter for the velocity unknown alone. We stabilize the hierarchical spatial decomposition approach proposed by Cai, Goldstein, and Pasciak for the reduced system. We demonstrate that the relative condition number of the preconditioner is bounded uniformly with respect to the penalty parameter, the number of levels and possible jumps of the coefficients as long as they occur only across the edges of the coarsest elements.

Lai, Chen-Yao G.↗
NASA NTRS1984

A strongly implicit procedure for the compressible Navier-Stokes equations

The strongly implicit procedure of Stone is used to obtain numerical solutions of the compressible Navier-Stokes equations in conservative form. In contrast to the spatially split Douglas-Gunn type methods, the method is shown to be numerically stable for the three-dimensional wave equation. The method is applied to a variety of external and internal two-dimensional flow problems involving shock wave boundary-layer interaction for both laminar and turbulent flows. The results are in good agreement with other methods and/or experiments. The storage penalty associated with the method is discussed and a simple, yet effective, means of minimizing the problem is presented.

Walters, R. W.↗
DOE OSTI2024

Robust and Simple ADMM Penalty Parameter Selection

We present a new method for online selection of the penalty parameter for the alternating direction method of multipliers (ADMM) algorithm. ADMM is a widely used method for solving a range of optimization problems, including those that arise in signal and image processing. In its standard form, ADMM includes a scalar hyperparameter, known as the penalty parameter, which usually has to be tuned to achieve satisfactory empirical convergence. In this work, we develop a framework for analyzing the ADMM algorithm applied to a quadratic problem as an affine fixed point iteration. Using this framework, we develop a new method for automatically tuning the penalty parameter by detecting when it has become too large or small. We analyze this and several other methods with respect to their theoretical properties, i.e., robustness to problem transformations, and empirical performance on several optimization problems. Our proposed algorithm is based on a theoretical framework with clear, explicit assumptions and approximations, is theoretically covariant/invariant to problem transformations, is simple to implement, and exhibits competitive empirical performance.

42 ENGINEERING↗
NASA NTRS1996

Using Statistical Penalties In The Tsai-Wu Failure Criterion

Improved methods of applying statistical penalties when using Tsai-Wu failure criterion lead to more accurate predictions of failures of composite-material structural components under stress, and provide better safety factors for designing such components. Intended to ensure proper use of statistical penalties with respect to failure hypersurface.

Richardson, D. E.↗
NASA NTRS2001

Robust Strategy for Rocket Engine Health Monitoring

Monitoring the health of rocket engine systems is essentially a two-phase process. The acquisition phase involves sensing physical conditions at selected locations, converting physical inputs to electrical signals, conditioning the signals as appropriate to establish scale or filter interference, and recording results in a form that is easy to interpret. The inference phase involves analysis of results from the acquisition phase, comparison of analysis results to established health measures, and assessment of health indications. A variety of analytical tools may be employed in the inference phase of health monitoring. These tools can be separated into three broad categories: statistical, rule based, and model based. Statistical methods can provide excellent comparative measures of engine operating health. They require well-characterized data from an ensemble of "typical" engines, or "golden" data from a specific test assumed to define the operating norm in order to establish reliable comparative measures. Statistical methods are generally suitable for real-time health monitoring because they do not deal with the physical complexities of engine operation. The utility of statistical methods in rocket engine health monitoring is hindered by practical limits on the quantity and quality of available data. This is due to the difficulty and high cost of data acquisition, the limited number of available test engines, and the problem of simulating flight conditions in ground test facilities. In addition, statistical methods incur a penalty for disregarding flow complexity and are therefore limited in their ability to define performance shift causality. Rule based methods infer the health state of the engine system based on comparison of individual measurements or combinations of measurements with defined health norms or rules. This does not mean that rule based methods are necessarily simple. Although binary yes-no health assessment can sometimes be established by relatively simple rules, the causality assignment needed for refined health monitoring often requires an exceptionally complex rule base involving complicated logical maps. Structuring the rule system to be clear and unambiguous can be difficult, and the expert input required to maintain a large logic network and associated rule base can be prohibitive.

Santi, L. Michael↗
DOE OSTI2022

A Reinforcement Learning Approach to Parameter Selection for Distributed Optimal Power Flow

With the increasing penetration of distributed energy resources, distributed optimization algorithms have attracted significant attention for power systems applications due to their potential for superior scalability, privacy, and robustness to a single point-of-failure. The Alternating Direction Method of Multipliers (ADMM) is a popular distributed optimization algorithm; however, its convergence performance is highly dependent on the selection of penalty parameters, which are usually chosen heuristically. In this work, we use reinforcement learning (RL) to develop an adaptive penalty parameter selection policy for alternating current optimal power flow (ACOPF) problem solved via ADMM with the goal of minimizing the number of iterations until convergence. We train our RL policy using deep Q-learning and show that this policy can result in significantly accelerated convergence (up to a 59% reduction in the number of iterations compared to existing, curvatureinformed penalty parameter selection methods). Furthermore, we show that our RL policy demonstrates promise for generalizability, performing well under unseen loading schemes as well as under unseen losses of lines and generators (up to a 50% reduction in iterations). This work thus provides a proof-of-concept for using RL for parameter selection in ADMM for power systems applications.

alternating current optimal power flow↗