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At least 1,063 records · Page 59

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NASA NTRS1988

An application of eigenspace methods to symmetric flutter suppression

An eigenspace assignment approach to the design of parameter insensitive control laws for linear multivariable systems is presented. The control design scheme utilizes constrained optimization techniques to exploit the flexibility in eigenvector assignments to reduce control system sensitivity to changes in system parameters while maintaining performance requirements; it thus provides a systematic approach for choosing values for eigensystem design variables. The methods involve use of the singular value decomposition to provide an exact description of allowable eigenvectors in terms of a minimum number of design parameters. In a design example, the methods are applied to the problem of symmetric flutter suppression in an aeroelastic vehicle. In this example the flutter mode is sensitive to changes in dynamic pressure and eigenspace methods are used to enhance the performance of a stabilizing minimum energy/linear quadratic regulator controller and associated observer. Numerical results indicate that the methods provide feedback control laws that make the stability of the nominal closed loop systems less sensitive to changes in dynamic pressure, while maintaining acceptable control power and robustness constraints.

Fennell, Robert E.↗

NASA NTRS1983

A function space approach to state and model error estimation for elliptic systems

An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed.

Rodriguez, G.↗

NASA NTRS1983

A function space approach to state and model error estimation for elliptic systems

An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal esimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed. While this paper focuses on theoretical developments, applications arising in the area of large structure static shape determination are contained in a closely related paper (Rodriguez and Scheid, 1982).

Rodriguez, G.↗

DOE OSTI2021

Efficient Trainability of Linear Optical Modules in Quantum Optical Neural Networks

The existence of “barren plateau landscapes” for generic discrete-variable quantum neural networks, which obstructs efficient gradient-based optimization of cost functions defined by global measurements, would be surprising in the case of generic linear optical modules in quantum optical neural networks due to the tunability of the intensity of continuous variable states and the relevant unitary group having exponentially smaller dimension. We demonstrate that coherent light in m modes can be generically compiled efficiently if the total intensity scales sublinearly with m, and extend this result to cost functions based on homodyne, heterodyne, or photon detection measurement statistics, and to noisy cost functions in the presence of attenuation. Here, we further demonstrate efficient trainability of m mode linear optical quantum circuits for variational mean field energy estimation of positive quadratic Hamiltonians for input states that do not have energy exponentially vanishing with m.

47 OTHER INSTRUMENTATION↗

NASA NTRS1988

Active control law synthesis for flexible aircraft

An application of an active control law synthesis procedure is presented, to meet multiple design requirements for a flexible aircraft modeled by a large order state space system. In this synthesis procedure, a linear quadratic Gaussian type cost function is minimized by updating the free parameters of the control law, while satisfying a set of constraints on the design loads, responses and stability margins. Analytical expressions for gradients of the cost function and the constraints, with respect to the control law design variables are used to facilitate rapid numerical convergence. These gradients can also be used for sensitivity study. A stable classical control law as well as an estimator-based full or reduced order control law can be modified, in order to meet individual root-mean-square response limitations as well as minimum singular value restrictions. Both analog and digital control laws can be optimized. Low order, robust control laws were synthesized for flutter suppression of a flexible aircraft.

Mukhopadhyay, V.↗

DOE OSTI2014

Perturbational treatment of spin-orbit coupling for generally applicable high-level multi-reference methods

An efficient perturbational treatment of spin-orbit coupling within the framework of high-level multi-reference techniques has been implemented in the most recent version of the COLUMBUS quantum chemistry package, extending the existing fully variational two-component (2c) multi-reference configuration interaction singles and doubles (MRCISD) method. The proposed scheme follows related implementations of quasi-degenerate perturbation theory (QDPT) model space techniques. Our model space is built either from uncontracted, large-scale scalar relativistic MRCISD wavefunctions or based on the scalar-relativistic solutions of the linear-response-theory-based multi-configurational averaged quadratic coupled cluster method (LRT-MRAQCC). The latter approach allows for a consistent, approximatively size-consistent and size-extensive treatment of spin-orbit coupling. The approach is described in detail and compared to a number of related techniques. The inherent accuracy of the QDPT approach is validated by comparing cuts of the potential energy surfaces of acrolein and its S, Se, and Te analoga with the corresponding data obtained from matching fully variational spin-orbit MRCISD calculations. The conceptual availability of approximate analytic gradients with respect to geometrical displacements is an attractive feature of the 2c-QDPT-MRCISD and 2c-QDPT-LRT-MRAQCC methods for structure optimization and ab inito molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. In conclusion, the approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.

Data-driven model reduction↗

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 NTRS1999

Integration of a Decentralized Linear-Quadratic-Gaussian Control into GSFC's Universal 3-D Autonomous Formation Flying Algorithm

A decentralized control is investigated for applicability to the autonomous formation flying control algorithm developed by GSFC for the New Millenium Program Earth Observer-1 (EO-1) mission. This decentralized framework has the following characteristics: The approach is non-hierarchical, and coordination by a central supervisor is not required; Detected failures degrade the system performance gracefully; Each node in the decentralized network processes only its own measurement data, in parallel with the other nodes; Although the total computational burden over the entire network is greater than it would be for a single, centralized controller, fewer computations are required locally at each node; Requirements for data transmission between nodes are limited to only the dimension of the control vector, at the cost of maintaining a local additional data vector. The data vector compresses all past measurement history from all the nodes into a single vector of the dimension of the state; and The approach is optimal with respect to standard cost functions. The current approach is valid for linear time-invariant systems only. Similar to the GSFC formation flying algorithm, the extension to linear LQG time-varying systems requires that each node propagate its filter covariance forward (navigation) and controller Riccati matrix backward (guidance) at each time step. Extension of the GSFC algorithm to non-linear systems can also be accomplished via linearization about a reference trajectory in the standard fashion, or linearization about the current state estimate as with the extended Kalman filter. To investigate the feasibility of the decentralized integration with the GSFC algorithm, an existing centralized LQG design for a single spacecraft orbit control problem is adapted to the decentralized framework while using the GSFC algorithm's state transition matrices and framework. The existing GSFC design uses both reference trajectories of each spacecraft in formation and by appropriate choice of coordinates and simplified measurement modeling is formulated as a linear time-invariant system. Results for improvements to the GSFC algorithm and a multiple satellite formation will be addressed. The goal of this investigation is to progressively relax the assumptions that result in linear time-invariance, ultimately to the point of linearization of the non-linear dynamics about the current state estimate as in the extended Kalman filter. An assessment will then be made about the feasibility of the decentralized approach to the realistic formation flying application of the EO-1/Landsat 7 formation flying experiment.

Folta, David C.↗

DOE OSTI2019

Parallel accelerated Custom Correlation Coefficient calculations for genomics applications

The massive quantities of genomic data being made available through gene sequencing techniques are enabling breakthroughs in genomic science in many areas such as medical advances in the diagnosis and treatment of diseases. Analyzing this data, however, is a computational challenge insofar as the computational costs of the relevant algorithms can grow with quadratic, cubic or higher complexity—leading to the need for leadership scale computing. In this paper we describe a new approach to calculations of the Custom Correlation Coefficient (CCC) between Single Nucleotide Polymorphisms (SNPs) across a population, suitable for parallel systems equipped with graphics processing units (GPUs) or Intel Xeon Phi processors. We describe the mapping of the algorithms to accelerated processors, techniques used for eliminating redundant calculations due to symmetries, and strategies for efficient mapping of the calculations to many-node parallel systems. Results are presented demonstrating high per-node performance and near-ideal parallel scalability with rates of more than nine quadrillion (9 × 10 15 ) elementwise comparisons achieved per second with the latest optimized code on the ORNL Titan system, this being orders of magnitude faster than rates achieved using other codes and platforms as reported in the literature. Also it is estimated that as many as 90 quadrillion (90 × 10 15 ) comparisons per second may be achievable on the upcoming ORNL Summit system, an additional 10X performance increase. Finally, in a companion paper we describe corresponding techniques applied to calculations of the Proportional Similarity metric for comparative genomics applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Semiglobal Safety-Filtered Extremum Seeking With Unknown CBFs

We introduce a safe extremum-seeking (Safe ES) algorithm which achieves the minimization of an unknown objective function while ensuring that an unknown, yet measured, control barrier function (CBF) remains above an arbitrarily small negative value for all time. In other words, “practical safety” is maintained during the entire period of convergence to the constrained extremum. Our design is based on quadratic program (QP) CBF style filters for safety, which is applied in an average and estimated sense. Using nonsmooth analysis tools, we guarantee semiglobal practical asymptotic (SPA) stability of the global constrained optimum, practical convergence to the safe set if starting in a condition violating the CBF, and practical safety for all time—semiglobally—if starting in safe set. The safety result of the paper is analogous with modern notions of SPA stability, guaranteeing that, for any small violation of safety, there exist design coefficients which guarantee that such a small violation is not exceeded. The paper outlines a set of sufficient conditions on the barrier and objective functions, and by way of a Lyapunov argument, we demonstrate that nonconvex constrained optimization problems can be solved. We present these results in the setting of a static map and a dynamical system. A simulation example illustrates the results.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1997

Hypersonic Vehicle Trajectory Optimization and Control

Two classes of neural networks have been developed for the study of hypersonic vehicle trajectory optimization and control. The first one is called an 'adaptive critic'. The uniqueness and main features of this approach are that: (1) they need no external training; (2) they allow variability of initial conditions; and (3) they can serve as feedback control. This is used to solve a 'free final time' two-point boundary value problem that maximizes the mass at the rocket burn-out while satisfying the pre-specified burn-out conditions in velocity, flightpath angle, and altitude. The second neural network is a recurrent network. An interesting feature of this network formulation is that when its inputs are the coefficients of the dynamics and control matrices, the network outputs are the Kalman sequences (with a quadratic cost function); the same network is also used for identifying the coefficients of the dynamics and control matrices. Consequently, we can use it to control a system whose parameters are uncertain. Numerical results are presented which illustrate the potential of these methods.

Balakrishnan, S. N.↗

DOE OSTI2018

An efficient algorithm for solving the generalized trust region subproblem

In this paper, we consider the interval bounded generalized trust region subproblem (GTRS) which is the problem of minimizing a general quadratic function subject to an upper and lower bounded general quadratic constraint. Under the assumption that two matrices from the objective and the constraint functions can be simultaneously diagonalizable via congruence, a diagonalization-based algorithm is introduced to solve it by showing that GTRS is indeed equivalent to a linearly constrained convex univariate problem. Some numerical experiments are given to show the effectiveness of the proposed method and to compare it with the extended Rendl–Wolkowicz algorithm due to Pong and Wolkowicz.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

WE-G-204-03: Photon-Counting Hexagonal Pixel Array CdTe Detector: Optimal Resampling to Square Pixels

Purpose: Detectors with hexagonal pixels require resampling to square pixels for distortion-free display of acquired images. In this work, the presampling modulation transfer function (MTF) of a hexagonal pixel array photon-counting CdTe detector for region-of-interest fluoroscopy was measured and the optimal square pixel size for resampling was determined. Methods: A 0.65mm thick CdTe Schottky sensor capable of concurrently acquiring up to 3 energy-windowed images was operated in a single energy-window mode to include ≥10 KeV photons. The detector had hexagonal pixels with apothem of 30 microns resulting in pixel spacing of 60 and 51.96 microns along the two orthogonal directions. Images of a tungsten edge test device acquired under IEC RQA5 conditions were double Hough transformed to identify the edge and numerically differentiated. The presampling MTF was determined from the finely sampled line spread function that accounted for the hexagonal sampling. The optimal square pixel size was determined in two ways; the square pixel size for which the aperture function evaluated at the Nyquist frequencies along the two orthogonal directions matched that from the hexagonal pixel aperture functions, and the square pixel size for which the mean absolute difference between the square and hexagonal aperture functions was minimized over all frequencies up to the Nyquist limit. Results: Evaluation of the aperture functions over the entire frequency range resulted in square pixel size of 53 microns with less than 2% difference from the hexagonal pixel. Evaluation of the aperture functions at Nyquist frequencies alone resulted in 54 microns square pixels. For the photon-counting CdTe detector and after resampling to 53 microns square pixels using quadratic interpolation, the presampling MTF at Nyquist frequency of 9.434 cycles/mm along the two directions were 0.501 and 0.507. Conclusion: Hexagonal pixel array photon-counting CdTe detector after resampling to square pixels provides high-resolution imaging suitable for fluoroscopy.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS2014

Conceptual Design Optimization of an Augmented Stability Aircraft Incorporating Dynamic Response and Actuator Constraints

Empirical sizing guidelines such as tail volume coefficients have long been used in the early aircraft design phases for sizing stabilizers, resulting in conservatively stable aircraft. While successful, this results in increased empty weight, reduced performance, and greater procurement and operational cost relative to an aircraft with optimally sized surfaces. Including flight dynamics in the conceptual design process allows the design to move away from empirical methods while implementing modern control techniques. A challenge of flight dynamics and control is the numerous design variables, which are changing fluidly throughout the conceptual design process, required to evaluate the system response to some disturbance. This research focuses on addressing that challenge not by implementing higher order tools, such as computational fluid dynamics, but instead by linking the lower order tools typically used within the conceptual design process so each discipline feeds into the other. In thisresearch, flight dynamics and control was incorporated into the conceptual design process along with the traditional disciplines of vehicle sizing, weight estimation, aerodynamics, and performance. For the controller, a linear quadratic regulator structure with constant gains has been specified to reduce the user input. Coupling all the disciplines in the conceptual design phase allows the aircraft designer to explore larger design spaces where stabilizers are sized according to dynamic response constraints rather than historical static margin and volume coefficient guidelines.

Welstead, Jason↗

NASA NTRS1986

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.↗

DOE OSTI2015

Designing a mixture experiment when the components are subject to a nonlinear multiple-component constraint

This article presents a case study of developing an experimental design for a constrained mixture experiment when the experimental region is defined by single-component constraints (SCCs), linear multiple-component constraints (MCCs), and a nonlinear MCC. Traditional methods and software for designing constrained mixture experiments with SCCs and linear MCCs are not directly applicable because of the nonlinear MCC. A modification of existing methodology to account for the nonlinear MCC was developed and is described in this article. The case study involves a 15-component nuclear waste glass example in which SO3 is one of the components. SO3 has a solubility limit in glass that depends on the composition of the balance of the glass. A goal was to design the experiment so that SO3 would not exceed its predicted solubility limit for any of the experimental glasses. The SO3 solubility limit had previously been modeled by a partial quadratic mixture (PQM) model expressed in the relative proportions of the 14 other components. The PQM model was used to construct a nonlinear MCC in terms of all 15 components. In addition, there were SCCs and linear MCCs. This article discusses the waste glass example and how a layered design was generated to (i) account for the SCCs, linear MCCs, and nonlinear MCC and (ii) meet the goals of the study.

Low-activity waste↗

DOE OSTI2013

Viscoelastic Properties, Ionic Conductivity, and Materials Design Considerations for Poly(styrene-b-ethylene oxide-b-styrene)-Based Ion Gel Electrolytes

The viscoelastic properties and ionic conductivity of ion gels based on the self-assembly of a poly(styrene-b-ethylene oxide-b-styrene) (SOS) triblock copolymer (M{sub n,S} = 3 kDa, M{sub n,O} = 35 kDa) in the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide ([EMI][TFSA]) were investigated over the composition range of 10-50 wt % SOS and the temperature range of 25-160 C. The poly(styrene) (PS) end-blocks associate into micelles, whereas the poly(ethylene oxide) (PEO) midblocks are well-solvated by this ionic liquid. The ion gel with 10 wt % SOS melts at 54 C, with the longest relaxation time exhibiting a similar temperature dependence to that of the viscosity of bulk PS. However, the actual values of the gel relaxation time are more than 4 orders of magnitude larger than the relaxation time of bulk PS. This is attributed to the thermodynamic penalty of pulling PS end-blocks through the PEO/[EMI][TFSA] matrix. Ion gels with 20-50 wt % SOS do not melt and show two plateaus in the storage modulus over the temperature and frequency ranges measured. The one at higher frequencies is that of an entangled network of PEO strands with PS cross-links; the modulus displays a quadratic dependence on polymer weight fraction and agrees with the prediction of linear viscoelastic theory assuming half of the PEO chains are elastically effective. The frequency that separates the two plateaus, {omega}{sub c}, reflects the time scale of PS end-block pull-out. The other plateau at lower frequencies is that of a congested micelle solution with PS cores and PEO coronas, which has a power law dependence on domain spacing similar to diblock melts. The ionic conductivity of the ion gels is compared to PEO homopolymer solutions at similar polymer concentrations; the conductivity is reduced by a factor of 2.1 or less, decreases with increasing PS volume fraction, and follows predictions based on a simple obstruction model. Our collective results allow the formulation of basic design considerations for optimizing the mechanical properties, thermal stability, and ionic conductivity of these gels.

36 MATERIALS SCIENCE↗