Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linear systems”

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 883 records · Page 49

Low-Friction, Low-Profile, High-Moment Two-Axis Joint

The two-axis joint is a mechanical device that provides two-degrees-of-freedom motion between connected components. A compact, moment-resistant, two-axis joint is used to connect an electromechanical actuator to its driven structural members. Due to the requirements of the overall mechanism, the joint has a low profile to fit within the allowable space, low friction, and high moment-reacting capability. The mechanical arrangement of this joint can withstand high moments when loads are applied. These features allow the joint to be used in tight spaces where a high load capability is required, as well as in applications where penetrating the mounting surface is not an option or where surface mounting is required. The joint consists of one base, one clevis, one cap, two needle bearings, and a circular shim. The base of the joint is the housing (the base and the cap together), and is connected to the grounding structure via fasteners and a bolt pattern. Captive within the housing, between the base and the cap, are the rotating clevis and the needle bearings. The clevis is attached to the mechanical system (linear actuator) via a pin. This pin, and the rotational movement of the clevis with respect to the housing, provides two rotational degrees of freedom. The larger diameter flange of the clevis is sandwiched between a pair of needle bearings, one on each side of the flange. During the assembly of the two-axis joint, the circular shims are used to adjust the amount of preload that is applied to the needle bearings. The above arrangement enables the joint to handle high moments with minimal friction. To achieve the high-moment capability within a low-profile joint, the use of depth of engagement (like that of a conventional rotating shaft) to react moment is replaced with planar engagement parallel to the mounting surface. The needle bearings with the clevis flange provide the surface area to react the clevis loads/moments into the joint housing while providing minimal friction during rotation. The diameter of the flange and the bearings can be increased to react higher loads and still maintain a compact surface mounting capability. This type of joint can be used in a wide variety of mechanisms and mechanical systems. It is especially effective where precise, smooth, continuous motion is required. For example, the joint can be used at the end of a linear actuator that is required to extend and rotate simultaneously. The current design application is for use in a spacecraft docking-system capture mechanism. Other applications might include industrial robotic or assembly line apparatuses, positioning systems, or in the motion-based simulator industry that employs complex, multi-axis manipulators for various types of motions.

Lewis, James L.↗

Parallel interior-point solver for block-structured nonlinear programs on SIMD/GPU architectures

Here, we investigate how to port the standard interior-point method to new exascale architectures for block-structured nonlinear programs with state equations. Computationally, we decompose the interior-point algorithm into two successive operations: the evaluation of the derivatives and the solution of the associated Karush-Kuhn-Tucker (KKT) linear system. Our method accelerates both operations using two levels of parallelism. First, we distribute the computations on multiple processes using coarse parallelism. Second, each process uses SIMD/GPU accelerators locally to accelerate the operations using fine-grained parallelism. The KKT system is reduced by eliminating the inequalities and the state variables from the corresponding equations. We demonstrate our method's capability on the supercomputer Polaris, a testbed for the future exascale Aurora system. Each node is equipped with four GPUs, a setup amenable to our two-level approach. Our experiments on the stochastic optimal power flow problem show that the reduction method is 50x faster than the sparse linear solver HSL MA57 running in serial on the CPU, and 6x faster than Pardiso running in parallel on CPU on the same number of processes.

97 MATHEMATICS AND COMPUTING↗

Two-phase flows within systems with ambient pressure

In systems where the design inlet and outlet pressures are maintained above the thermodynamic critical pressure, it is often assumed that two phase flows within the system cannot occur. Designers rely on this simple rule of thumb to circumvent problems associated with a highly compressible two phase flow occurring within the supercritical pressure system along with the uncertainties in rotordynamics, load capacity, heat transfer, fluid mechanics, and thermophysical property variations. The simple rule of thumb is adequate in many low power designs but is inadequate for high performance turbomachines and linear systems, where two phase regions can exist even though outlet pressure is greater than critical pressure. Rotordynamic-fluid-mechanic restoring forces depend on momentum differences, and those for a two phase zone can differ significantly from those for a single-phase zone. Using the Reynolds equation the angular velocity, eccentricity, geometry, and ambient conditions are varied to determine the point of two phase flow incipience.

Hendricks, R. C.↗

Structural modeling for control design (articulated multibody component representation)

High gain, high frequency flexible responses in gimbaled multibody systems are discussed. Their origin and physical significance are described in terms of detailed mass and stiffness modeling at actuator/sensor interfaces. Guyan Reduction, Generalized Dynamic Reduction, inadequate mass modeling detail, as well as system mode truncation, are shown to suppress the high gain high frequency response and thereby lose system flexibility important for stability and performance predictions. Model validation by modal survey testing is shown to risk similar loss of accuracy. Difficulties caused by high frequency responses in component mode simulations, such as DISCOS, and also linearized system mode simulations, are described, and approaches for handling these difficulties are discussed.

Haugse, E. D.↗

ETG turbulence in a tokamak pedestal

This paper explores the fundamental characteristics of electron-temperature-gradient (ETG)-driven turbulence in the tokamak pedestal. The extreme gradients in the pedestal produce linear instabilities and nonlinear turbulence that are distinct from the corresponding ETG phenomenology in the core plasma. The linear system exhibits multiple (greater than ten) unstable eigenmodes at each perpendicular wave vector, representing different toroidal and slab branches of the ETG instability. Proper orthogonal decomposition of the nonlinear fluctuations reveals no clear one-to-one correspondence between the linear and nonlinear modes for most wave vectors. Moreover, nonlinear frequencies deviate strongly from those of the linear instabilities, with spectra peaking at positive frequencies, which is opposite the sign of the ETG instability. The picture that emerges is one in which the linear properties are preserved only in a narrow range of k-space. Outside this range, nonlinear processes produce strong deviations from both the linear frequencies and eigenmode structures. This is interpreted in the context of critical balance, which enforces alignment between the parallel scales and fluctuation frequencies. We also investigate the nonlinear saturation processes. We observe a direct energy cascade from the injection scale to smaller scales in both perpendicular directions. However, in the bi-normal direction, there is also nonlocal inverse energy transfer to larger scales. Neither streamers nor zonal flows dominate the saturation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Scalable Reduced‐Order Model for the Steady Navier–Stokes Equations

Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional numerical methods are computationally intractable even for intermediate pilot plant scales. Recently, the component reduced order modeling method has been developed to tackle this challenge by combining projection reduced order modeling and discontinuous Galerkin domain decomposition. However, while many scientific or engineering applications involve nonlinear physics, this method has only been demonstrated for various linear systems. In this work, the component reduced order modeling method is extended to steady Navier–Stokes flow, with application to general nonlinear physics in view. The large‐scale, global domain is decomposed into a combination of small‐scale unit component. Linear subspaces for flow velocity and pressure are identified via proper orthogonal decomposition over sample snapshots collected from each small‐scale unit component. Velocity bases are augmented with a pressure supremizer to satisfy the inf–sup condition for stable pressure prediction. Two different nonlinear reduced order modeling methods are employed and compared for efficient evaluation of nonlinear advection: A third‐order tensor projection operator and the empirical quadrature procedure. The proposed method is demonstrated on the flow over arrays of five different unit objects, achieving a 23‐fold speedup with less than 4% relative error in domains up to 256 times larger than the unit components. Furthermore, a numerical experiment with the pressure supremizer strongly indicates the need for a supremizer for stable pressure prediction. A comparison between the tensorial approach and the empirical quadrature procedure revealed a slight advantage of the empirical quadrature procedure. The framework is compared with an alternating Schwarz‐based reduced‐order approach, demonstrating improved efficiency and robustness for the DG‐based global solver while retaining flexibility for sub‐scale iterative solvers. The method is further extended to a coupled advection–diffusion and Navier–Stokes system, illustrating its applicability to multi‐physics problems and its potential for more general, inter‐coupled nonlinear systems.

42 ENGINEERING↗

Information and display requirements for independent landing monitors

The ways an Independent Landing Monitor (ILM) may be used to complement the automatic landing function were studied. In particular, a systematic procedure was devised to establish the information and display requirements of an ILM during the landing phase of the flight. Functionally, the ILM system is designed to aid the crew in assessing whether the total system (e.g., avionics, aircraft, ground navigation aids, external disturbances) performance is acceptable, and, in case of anomaly, to provide adequate information to the crew to select the least unsafe of the available alternatives. Economically, this concept raises the possibility of reducing the primary autoland system redundancy and associated equipment and maintenance costs. The required level of safety for the overall system would in these cases be maintained by upgrading the backup manual system capability via the ILM. A safety budget analysis was used to establish the reliability requirements for the ILM. These requirements were used as constraints in devising the fault detection scheme. Covariance propagation methods were used with a linearized system model to establish the time required to correct manually perturbed states due to the fault. Time-to-detect and time-to-correct requirements were combined to devise appropriate altitudes and strategies for fault recovery.

Karmarker, J. S.↗

Decoupling control of a long flexible beam in orbit

The paper presents a method of control for large flexible systems using state variable feedback, with a long flexible beam given as an example. These feedback gains are selected: (1) based on the decoupling of the original coordinates and to obtain proper damping and (2) by applying the linear regulator problem to the individual modal coordinates separately. It is shown that the linear control law thus obtained are then evaluated by numerical integration of the non-linear system equations. Also included are results showing the effects (control spillover) on the uncontrolled modes when the number of controllers is less than the number of modes, and the effects of inaccurate knowledge of the control influence coefficients which lead to errors in the calculated feedback gains.

Reddy, A. S. S. R.↗

Accelerated convergence of structured banded systems using constrained corrections

An efficient iterative method for solving a structured banded system of equations is described. The method was developed for a full potential flow program and uses a basic interation step, a dynamic relation step, and a multigrid concept of constraining iterative corrections. The solution of a large linear system of equations is examined. Efficient iterative methods have become attractive for large problems. In the nonlinear cases, these iterations may be effectively merged to improve convergence rates.

Kneile, K.↗

Force Model for Control of Tendon Driven Hands

Knowing the tendon forces generated for a given task such as grasping via a model, an artificial hand can be controlled. A two-dimensional force model for the index finger was developed. This system is assumed to be in static equilibrium, therefore, the equations of equilibrium were applied at each joint. Constraint equations describing the tendon branch connectivity were used. Gaussian elimination was used to solve for the unknowns of the Linear system. Results from initial work on estimating tendon forces in post-operative hands during active motion therapy were discussed. The results are important for understanding the effects of hand position on tendon tension, elastic effects on tendon tension, and overall functional anatomy of the hand.

Pena, Edward↗

Aerodynamic Shape Sensitivity Analysis and Design Optimization of Complex Configurations Using Unstructured Grids

A three-dimensional unstructured grid approach to aerodynamic shape sensitivity analysis and design optimization has been developed and is extended to model geometrically complex configurations. The advantage of unstructured grids (when compared with a structured-grid approach) is their inherent ability to discretize irregularly shaped domains with greater efficiency and less effort. Hence, this approach is ideally suited for geometrically complex configurations of practical interest. In this work the nonlinear Euler equations are solved using an upwind, cell-centered, finite-volume scheme. The discrete, linearized systems which result from this scheme are solved iteratively by a preconditioned conjugate-gradient-like algorithm known as GMRES for the two-dimensional geometry and a Gauss-Seidel algorithm for the three-dimensional; similar procedures are used to solve the accompanying linear aerodynamic sensitivity equations in incremental iterative form. As shown, this particular form of the sensitivity equation makes large-scale gradient-based aerodynamic optimization possible by taking advantage of memory efficient methods to construct exact Jacobian matrix-vector products. Simple parameterization techniques are utilized for demonstrative purposes. Once the surface has been deformed, the unstructured grid is adapted by considering the mesh as a system of interconnected springs. Grid sensitivities are obtained by differentiating the surface parameterization and the grid adaptation algorithms with ADIFOR (which is an advanced automatic-differentiation software tool). To demonstrate the ability of this procedure to analyze and design complex configurations of practical interest, the sensitivity analysis and shape optimization has been performed for a two-dimensional high-lift multielement airfoil and for a three-dimensional Boeing 747-200 aircraft.

Taylor, Arthur C., III↗

Bounds of linear time‐varying systems with applications to quantify model gap of synchronous generators

Abstract Linear time‐varying (LTV) systems play a key role in many engineering problems, for example, trajectory sensitivity analysis of power systems. Because LTV systems do not generally have closed‐form solutions, estimates of their bounds are crucial to their analysis. In this paper, bounds for LTV systems with known inputs and unknown but bounded inputs are obtained via Grönwall's inequality. The estimated bounds are then used to quantify the gap between synchronous generators and their models in different scenarios through simulation.

42 ENGINEERING↗

Algebraic Multigrid with Filtering: An Efficient Preconditioner for Interior Point Methods in Large-Scale Contact Mechanics Optimization

Large-scale contact mechanics simulations are crucial in many engineering fields such as structural design and manufacturing. In the frictionless case, contact can be modeled by minimizing an energy functional; however, these problems are often nonlinear, nonconvex, and increasingly difficult to solve as mesh resolution increases. In this work, we employ a Newton-based interior-point (IP) filter line-search method, an effective approach for large-scale constrained optimization. While this method converges rapidly, each iteration requires solving a large saddle-point linear system that becomes ill-conditioned as the optimization process converges, largely due to IP treatment of the contact constraints. Such ill-conditioning can hinder solver scalability and increase iteration counts with mesh refinement. Here, to address this, we introduce a novel preconditioner, algebraic multigrid with filtering (AMGF), tailored to the Schur complement of the saddle-point system. Building on the classical AMG solver, commonly used for elasticity, we augment it with a specialized subspace correction that filters near null space components introduced by contact interface constraints. Through theoretical analysis and numerical experiments on a range of linear and nonlinear contact problems, we demonstrate that the proposed solver achieves mesh independent convergence and maintains robustness against the ill-conditioning that notoriously plagues IP methods. These results indicate that AMGF makes contact mechanics simulations more tractable and broadens the applicability of Newton-based IP methods in challenging engineering scenarios. More broadly, AMGF is well suited for problems, optimization or otherwise, where solver performance is limited by a low-dimensional subspace, such as those arising from localized constraints, interface conditions, or model heterogeneities. This makes the method widely applicable beyond contact mechanics and constrained optimization.

Mathematics and Computing↗

Simplified methods for interpreting the effect of transfer-function zeros on the transient response of aircraft

Two simple methods are outlined for evaluating the effect of transfer-function zeros on the system time response. The pole effects can also be evaluated. These methods are useful for simplified analysis or creating design criteria in terms of desirable regions of pole-zero locations. The type of transfer function studied is limited to those linear systems. Corresponding to ordinary longitudinal or lateral aircraft transfer functions, the denominator polynomial is of fourth order and the numerator of third order at most. With the longitudinal motion of the aircraft as an example, the methods are used in the evaluation of optimal regulator control with respect to a particular performance index structure.

Onken, R.↗

Relative control effectiveness technique with application to airplane control coordination

A method to select optimal combinations of the control variables of a linear system is reported. The combinations are chosen so that the control channels have their principal influences on selected fundamental modes of the system. A series of algebraic maximization problems is used to maximize the effects of the control channels on selected modes while simultaneously minimizing the effects on the remaining modes. The method is applied to the lateral and directional control of a linearized airplane model having ailerons, a rudder, and differential tail surfaces. Integration of these control eliminates oscillations present in the roll rate for a step lateral-control input and improves the sideslip response with reduced rolling motions for a step directional-control input. Inclusion of thrust-vectoring engine nozzles improves the roll rate capability of the airplane.

Lallman, F. J.↗

Bilevel Parameter Optimization for Nonlocal Image Denoising Models

We propose a bilevel optimization approach for the determination of parameters in nonlocal image denoising. We consider both spatial weights in front of the fidelity term, as well as weights within the kernel of the nonlocal operator. In both cases we investigate the differentiability of the solution operator in function spaces and derive a first order optimality system that characterizes local minima. For the numerical solution of the problems, we propose a second-order optimization algorithm in combination with a finite element discretization of the nonlocal denoising models and a computational strategy for the solution of the resulting dense linear systems. Several experiments are run in order to show the suitability of our approach.

97 MATHEMATICS AND COMPUTING↗

Practical Implementation of GPU-based Computing at the Grid Edge for Resilience Scenarios

This paper presents a practical implementation of GPU-accelerated computing at the grid edge to enhance power system resilience through next-generation smart meters. Advanced Metering Infrastructure (AMI) systems rely predominantly on centralized processing architectures, which limit real-time response capabilities during grid disturbances. This work proposes the integration of GPU-enabled computational platforms directly within smart meter to enable local execution support for power system analytics, fault detection algorithms, and optimization routines. The proposed framework uses the Julia programming language to leverage highperformance parallel computing capabilities while maintaining code portability and development efficiency. We use two experimental scenarios to benchmark the computational feasibility of this approach: sparse linear system solutions representative of power flow analyses, and multi-stage production cost simulations incorporating unit commitment and economic dispatch operations. Results demonstrate that computationally intensive power system algorithms, such as those supporting resilience scenario calculations, can be effectively executed at the distribution edge using commercially available embedded GPU hardware. Keywords—GPU acceleration, edge computing, smart meters, grid resilience, AMI, resilience.

De Souza, Reubun [School of Electrical Engineering↗