Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linear system”

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 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Biophotonic rogue waves in red blood cell suspensions

Rogue waves are ubiquitous in nature, appearing in a variety of physical systems ranging from acoustics, microwave cavities, optical fibers, and resonators to plasmas, superfluids, and Bose–Einstein condensates. Unlike nonlinear solitary waves, rogue waves are extreme events that can occur even without nonlinearity by, for example, spontaneous synchronization of waves with different spatial frequencies in a linear system. Here, we report the observation of rogue-wave-like events in human red blood cell (RBC) suspensions under weak light illumination, characterized by an abnormal L-shaped probability distribution. Such biophotonic extreme events arise mostly due to the constructive interference of Mie-scattered waves from the suspended RBCs, whose biconcave shape and mutable orientation give rise to a time-dependent random phase modulation to an incident laser beam. We numerically simulate the beam propagation through the colloidal suspensions with added disorder in both spatial and temporal domains to mimic random scattering due to Brownian motion. In addition, at high power levels, nonlinear beam self-focusing is also observed, leading to a dual-exponential probability distribution associated with the formation of multiple soliton-like spots. Such rogue wave events should also exist in environments with cells of other species such as swimming bacteria, and understanding of their underlying physics may lead to unexpected biophotonic applications.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Convergence analysis of Anderson-type acceleration of Richardson's iteration

We consider here Anderson extrapolation to accelerate the (stationary) Richardson iterative method for sparse linear systems. Using an Anderson mixing at periodic intervals, we assess how this benefits convergence to a prescribed accuracy. The method, named alternating Anderson–Richardson, has appealing properties for high-performance computing, such as the potential to reduce communication and storage in comparison to more conventional linear solvers. We establish sufficient conditions for convergence, and we evaluate the performance of this technique in combination with various preconditioners through numerical examples. Furthermore, we propose an augmented version of this technique.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

The effect of amorphous selenium detector thickness on dual-energy digital breast imaging

Purpose: Contrast enhanced (CE) imaging techniques for both planar digital mammography (DM) and three-dimensional (3D) digital breast tomosynthesis (DBT) applications requires x-ray photon energies higher than the k-edge of iodine (33.2 keV). As a result, x-ray tube potentials much higher (>40 kVp) than those typical for screening mammography must be utilized. Amorphous selenium (a-Se) based direct conversion flat-panel imagers (FPI) have been widely used in DM and DBT imaging systems. The a-Se layer is typically 200 μm thick with quantum detective efficiency (QDE) >87% for x-ray energies below 26 keV. However, QDE decreases substantially above this energy. To improve the object detectability of either CE-DM or CE-DBT, it may be advantageous to increase the thickness (d{sub Se}) of the a-Se layer. Increasing the d{sub Se} will improve the detective quantum efficiency (DQE) at the higher energies used in CE imaging. However, because most DBT systems are designed with partially isocentric geometries, where the gantry moves about a stationary detector, the oblique entry of x-rays will introduce additional blur to the system. The present investigation quantifies the effect of a-Se thickness on imaging performance for both CE-DM and CE-DBT, discussing the effects of improving photon absorption and blurring from oblique entry of x-rays. Methods: In this paper, a cascaded linear system model (CLSM) was used to investigate the effect of d{sub Se} on the imaging performance (i.e., MTF, NPS, and DQE) of FPI in CE-DM and CE-DBT. The results from the model are used to calculate the ideal observer signal-to-noise ratio, d′, which is used as a figure-of-merit to determine the total effect of increasing d{sub Se} for CE-DM and CE-DBT. Results: The results of the CLSM show that increasing d{sub Se} causes a substantial increase in QDE at the high energies used in CE-DM. However, at the oblique projection angles used in DBT, the increased length of penetration through a-Se introduces additional image blur. The reduced MTF and DQE at high spatial frequencies lead to reduced two-dimensional d′. These losses in projection image resolution may subsequently result in a decrease in the 3D d′, but the degree of which is largely dependent on the DBT reconstruction algorithm. For a filtered backprojection (FBP) algorithm with spectral apodization and slice-thickness filters, which dominate the blur for reconstructed images at oblique angles, the effect of oblique entry of x-rays on 3D d′ is minimal. Thus, increasing d{sub Se} results in an improvement in d′ for both CE-DM and CE-DBT with typical FBP reconstruction parameters. Conclusions: Increased d{sub Se} improves CE breast imaging performance by increasing QDE of detectors at higher energies, e.g., 49 kVp. Although there is additional blur in the oblique angled projections of a DBT scan, the overall 3D d′ for DBT is not degraded because the dominant source blur at these angles results from the reconstruction filters of the employed FBP algorithm.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Batched Sparse Linear Algebra (Final Report for Subcontract B648960)

This report finalizes design specifications for developing batched kernels for small tensor operations for unassembled matrix-free iterative solvers, batched solvers for partially assembled operators, and batched solvers with support for various sparse formats. The outcome of the project milestones is a set of interfaces to Batched Sparse LA solvers running on hardware accelerators for use in ECP Libraries and Applications. It is part of the development of sparse batched kernels, solvers/preconditioners as well as creating interoperability in xSDK libraries with sparse and dense batched functions to benefit ECP applications. The participants included representatives from ECP libraries (not limited to the xSDK project), applications, and vendors (AMD, Intel, and NVIDIA). Batched sparse linear algebra solvers form the new frontier for algorithmic development and performance engineering. Many applications (ECP and non-ECP alike) require simultaneous solutions of small linear systems of equations that are structurally sparse. To move towards high hardware utilization, it is important to provide these applications with appropriate interfaces to efficient batched sparse solvers running on modern hardware accelerators. We present interface designs in use by HPC software libraries supporting batched sparse linear algebra and the development of sparse batched kernel codes for solvers and preconditioners. We also address the potential interoperability opportunities to keep the software portable between the major hardware accelerators from AMD, Intel, and NVIDIA. The presented interface specifications includes batched band, sparse iterative, and sparse direct solvers. This report summarizes progress in Kokkos Kernels and the xSDK libraries MAGMA, Ginkgo, hypre, SUNDIALS, and SuperLU_dist.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Bilevel parameter optimization for learning nonlocal image denoising models

We propose a bilevel optimization approach for the estimation of parameters in nonlocal image denoising models. The parameters we consider are both the space-dependent fidelity weight and 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 trust-region algorithm in combination with a finite element discretization of the nonlocal denoising models and we introduce a computational strategy for the solution of the resulting dense linear systems. Several experiments illustrate the applicability and effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

SIRTF controller simulation - Instability masked by numerical integration

In the course of a simulation study of a candidate design for the Space Infrared Telescope Facility (SIRTF), an unusual phenomenon was observed. The uncompensated control system was unstable, but a numerical simulation with the fixed-step-size classical fourth-order Runge-Kutta method gave a stable response. This phenomenon is described in the setting in which it occurred. The Runge-Kutta simulation model is analyzed as a discrete linear system and shown to be stable, thus corroborating the numerical results.

Rajan, N.↗
NASA NTRS1991

New bounds on parameter uncertainties for robust stability

The problem of robust stability in linear systems with parametric uncertainties is considered. A method is developed to determine bounds on uncertain parameters in the state-space model of the system, so that stability is preserved. Both continuous- and discrete-time systems are considered. Unlike previous results, the stability bounds are derived in terms of actual parameters instead of their absolute values, and consequently the stable region in the parameter space is not necessarily symmetric with respect to the origin. Furthermore, the uncertain parameters do not have to be linearly independent to each other.

Gao, Zhiqiang↗
NASA NTRS1994

Advanced data assimilation in strongly nonlinear dynamical systems

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Miller, Robert N.↗
NASA NTRS2011

Development and Verification of the Charring, Ablating Thermal Protection Implicit System Simulator

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver (CATPISS) is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method (FEM) with first and second order fully implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton s method, while the linear system is solved via the Generalized Minimum Residual method (GMRES). Verification results from exact solutions and Method of Manufactured Solutions (MMS) are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Amar, Adam J.↗
NASA NTRS2010

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Amar, Adam J.↗
NASA NTRS1992

An analytic formula for H-infinity norm sensitivity with applications to control system design

An analytic formula for the sensitivity of singular value peak variation with respect to parameter variation is derived. As a corollary, the derivative of the H-infinity norm of a stable transfer function with respect to a parameter is presented. It depends on some of the first two derivatives of the transfer function with respect to frequency and the parameter. For cases when the transfer function has a linear system realization whose matrices depend on the parameter, analytic formulas for these first two derivatives are derived, and an efficient algorithm for calculating them is discussed. Examples are given which provide numerical verification of the H-infinity norm sensitivity formula and which demonstrate its utility in designing control systems satisfying H-infinity norm constraints. In the appendix, derivative formulas for singular values are paraphrased.

Giesy, Daniel P.↗
NASA NTRS1998

Predictive Feedback and Feedforward Control for Systems with Unknown Disturbances

Predictive feedback control has been successfully used in the regulation of plate vibrations when no reference signal is available for feedforward control. However, if a reference signal is available it may be used to enhance regulation by incorporating a feedforward path in the feedback controller. Such a controller is known as a hybrid controller. This paper presents the theory and implementation of the hybrid controller for general linear systems, in particular for structural vibration induced by acoustic noise. The generalized predictive control is extended to include a feedforward path in the multi-input multi-output case and implemented on a single-input single-output test plant to achieve plate vibration regulation. There are cases in acoustic-induce vibration where the disturbance signal is not available to be used by the hybrid controller, but a disturbance model is available. In this case the disturbance model may be used in the feedback controller to enhance performance. In practice, however, neither the disturbance signal nor the disturbance model is available. This paper presents the theory of identifying and incorporating the noise model into the feedback controller. Implementations are performed on a test plant and regulation improvements over the case where no noise model is used are demonstrated.

Juang, Jer-Nan↗
NASA NTRS1972

Pilot/vehicle control optimization using averaged operational mode and subsystem relative performance index sensitivities

A method is presented for designing optimal feedback controllers for systems having subsystem sensitivity constraints. Such constraints reflect the presence of subsystem performance indices which are in conflict with the performance index of the overall system. The key to the approach is the use of relative performance index sensitivity (a measure of the deviation of a performance index from its optimum value). The weighted sum of subsystem and/or operational mode relative performance index sensitivies is defined as an overall performance index. A method is developed to handle linear systems with quadratic performance indices and either full or partial state feedback. The usefulness of this method is demonstrated by applying it to the design of a stability augmentation system (SAS) for a VTOL aircraft. A desirable VTOL SAS design is one that produces good VTOL transient response both with and without active pilot control. The system designed using this method is shown to effect a satisfactory compromise solution to this problem.

Leininger, G. G.↗
DOE OSTI2023

The wave energy converter control competition (WECCCOMP): Wave energy control algorithms compared in both simulation and tank testing

The wave energy control competition established a benchmark problem which was offered as an open challenge to the wave energy system control community. The competition had two stages: In the first stage, competitors used a standard wave energy simulation platform (WEC-Sim) to evaluate their controllers while, in the second stage, competitors were invited to test their controllers in a real-time implementation on a prototype system in a wave tank. The performance function used was based on converted energy across a range of standard sea states, but also included aspects related to economic performance, such as peak/average power, peak force, etc. This paper compares simulated and experimental results and, in particular, examines if the results obtained in a linear system simulation are borne out in reality. Overall, within the scope of the device tested, the range of sea states employed, and the performance metric used, the conclusion is that high-performance WEC controllers work well in practice, with good carry-over from simulation to experimentation. However, the availability of a good WEC mathematical model is deemed to be crucial.

16 TIDAL AND WAVE POWER↗
DOE OSTI2013

Tau leaping of stiff stochastic chemical systems via local central limit approximation

Stiffness manifests in stochastic dynamic systems in a more complex manner than in deterministic systems; it is not only important for a time-stepping method to remain stable but it is also important for the method to capture the asymptotic variances accurately. In the context of stochastic chemical systems, time stepping methods are known as tau leaping. Well known existing tau leaping methods have shortcomings in this regard. The implicit tau method is far more stable than the trapezoidal tau method but underestimates the asymptotic variance. On the other hand, the trapezoidal tau method which estimates the asymptotic variance exactly for linear systems suffers from the fact that the transients of the method do not decay fast enough in the context of very stiff systems. We propose a tau leaping method that possesses the same stability properties as the implicit method while it also captures the asymptotic variance with reasonable accuracy at least for the test system S{sub 1}↔S{sub 2}. The proposed method uses a central limit approximation (CLA) locally over the tau leaping interval and is referred to as the LCLA-τ. The CLA predicts the mean and covariance as solutions of certain differential equations (ODEs) and for efficiency we solve these using a single time step of a suitable low order method. We perform a mean/covariance stability analysis of various possible low order schemes to determine the best scheme. Numerical experiments presented show that LCLA-τ performs favorably for stiff systems and that the LCLA-τ is also able to capture bimodal distributions unlike the CLA itself. The proposed LCLA-τ method uses a split implicit step to compute the mean update. We also prove that any tau leaping method employing a split implicit step converges in the fluid limit to the implicit Euler method as applied to the fluid limit differential equation.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1971

State estimation with small nonlinearities

A variety of techniques is available for estimating the states of nonlinear dynamic systems from noisy data. The differences among several of these procedures in the presence of small dynamic and observational nonlinearities are investigated. Four discrete estimation algorithms are analyzed. The first is a strictly least square estimator, while the others are recursive algorithms similar to the Kalman filter used for estimating the states of linear systems. A group of analytic expressions is developed for the mean and covariance of the error in each of these estimators so that they may be compared without lengthy Monte Carlo simulations. The covariance expressions show that, to first order, all the estimators have the same covariance. Expressions for the means show that each estimator has a different bias. Several examples are carried out demonstrating that the relative magnitudes of the bias errors in the various estimators can be a strong function of such parameters as initial covariances and number of data points. Under some circumstances, more complicated algorithms can have larger biases than smaller ones.

Conrad, B.↗
NASA NTRS2001

Integrated Modeling for the Next Generation Space Telescope "Yardstick" Concept

The so-called NASA "Yardstick" design concept for the Next Generation Space Telescope presents unique challenges for systems-level analysis. Simulations that integrate controls, optics, thermal, and structural models are required to evaluate baseline performance, study design sensitivities, and perform design optimization. An integrated modeling approach was chosen using a combination of commercial off-the-shelf and "in-house" developed codes. The resulting capability provides a foundation for linear and non-linear analysis, using both the time and frequency-domain methods. It readily allows various combinations of design parameters and environmental loads to be evaluated directly in terms of key science-related metrics, in this case the scalar RMS (root mean square) line-of-sight and RMS wavefront errors. This presentation first addresses the development of the component, or discipline, models for the Yardstick design. It will then proceed to present the integration of the component models, using linear-systems approaches, in order to support two of the most critical baseline performance analyses: jitter and thermal-elastic stability of the optical telescope assembly (OTA). The results of the jitter analysis indicate that disturbances from the reaction wheels coupled with the lightly-damped and highly-flexible structure present significant challenges to the baseline line-of-sight control architecture. Vibration isolation will be required to meet jitter error requirements. The results of the thermal-elastic analysis indicate that the mirror segment displacements due to ground-to-orbit cool-down of the telescope are within the expected capture range of the segment rigid-body control actuators. This means we will be able to align and phase the primary mirror. However, the results for the analysis of the thermal transient response following an attitude maneuver (slew) show that this telescope design is not sufficiently stable, passively, to meet the wavefront error requirements. Structural re-design is one possibility; alternatively, active thermal control of the OTA may be considered. The Yardstick integrated models were successfully used to demonstrate the feasibility of two thermal control strategies.

Mosier, Gary E.↗
DOE OSTI2013

Fundamental radiological and geometric performance of two types of proton beam modulated discrete scanning systems

Purpose: The purpose of this investigation was to compare and contrast the measured fundamental properties of two new types of modulated proton scanning systems. This provides a basis for clinical expectations based on the scanned beam quality and a benchmark for computational models. Because the relatively small beam and fast scanning gave challenges to the characterization, a secondary purpose was to develop and apply new approaches where necessary to do so.Methods: The following performances of the proton scanning systems were investigated: beamlet alignment, static in-air beamlet size and shape, scanned in-air penumbra, scanned fluence map accuracy, geometric alignment of scanning system to isocenter, maximum field size, lateral and longitudinal field uniformity of a 1 l cubic uniform field, output stability over time, gantry angle invariance, monitoring system linearity, and reproducibility. A range of detectors was used: film, ionization chambers, lateral multielement and longitudinal multilayer ionization chambers, and a scintillation screen combined with a digital video camera. Characterization of the scanned fluence maps was performed with a software analysis tool.Results: The resulting measurements and analysis indicated that the two types of delivery systems performed within specification for those aspects investigated. The significant differences were observed between the two types of scanning systems where one type exhibits a smaller spot size and associated penumbra than the other. The differential is minimum at maximum energy and increases inversely with decreasing energy. Additionally, the large spot system showed an increase in dose precision to a static target with layer rescanning whereas the small spot system did not.Conclusions: The measured results from the two types of modulated scanning types of system were consistent with their designs under the conditions tested. The most significant difference between the types of system was their proton spot size and associated resolution, factors of magnetic optics, and vacuum length. The need and benefit of mutielement detectors and high-resolution sensors was also shown. The use of a fluence map analytical software tool was particularly effective in characterizing the dynamic proton energy-layer scanning.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗