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At least 109 records · Page 6

Multiple Input Design for Real-Time Parameter Estimation in the Frequency Domain

A method for designing multiple inputs for real-time dynamic system identification in the frequency domain was developed and demonstrated. The designed inputs are mutually orthogonal in both the time and frequency domains, with reduced peak factors to provide good information content for relatively small amplitude excursions. The inputs are designed for selected frequency ranges, and therefore do not require a priori models. The experiment design approach was applied to identify linear dynamic models for the F-15 ACTIVE aircraft, which has multiple control effectors.

Morelli, Eugene↗

Updating the Finite Element Model of the Aerostructures Test Wing using Ground Vibration Test Data

Improved and/or accelerated decision making is a crucial step during flutter certification processes. Unfortunately, most finite element structural dynamics models have uncertainties associated with model validity. Tuning the finite element model using measured data to minimize the model uncertainties is a challenging task in the area of structural dynamics. The model tuning process requires not only satisfactory correlations between analytical and experimental results, but also the retention of the mass and stiffness properties of the structures. Minimizing the difference between analytical and experimental results is a type of optimization problem. By utilizing the multidisciplinary design, analysis, and optimization (MDAO) tool in order to optimize the objective function and constraints; the mass properties, the natural frequencies, and the mode shapes can be matched to the target data to retain the mass matrix orthogonality. This approach has been applied to minimize the model uncertainties for the structural dynamics model of the Aerostructures Test Wing (ATW), which was designed and tested at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center (DFRC) (Edwards, California). This study has shown that natural frequencies and corresponding mode shapes from the updated finite element model have excellent agreement with corresponding measured data.

Lung, Shun-fat↗

Updating the Finite Element Model of the Aerostructures Test Wing Using Ground Vibration Test Data

Improved and/or accelerated decision making is a crucial step during flutter certification processes. Unfortunately, most finite element structural dynamics models have uncertainties associated with model validity. Tuning the finite element model using measured data to minimize the model uncertainties is a challenging task in the area of structural dynamics. The model tuning process requires not only satisfactory correlations between analytical and experimental results, but also the retention of the mass and stiffness properties of the structures. Minimizing the difference between analytical and experimental results is a type of optimization problem. By utilizing the multidisciplinary design, analysis, and optimization (MDAO) tool in order to optimize the objective function and constraints; the mass properties, the natural frequencies, and the mode shapes can be matched to the target data to retain the mass matrix orthogonality. This approach has been applied to minimize the model uncertainties for the structural dynamics model of the aerostructures test wing (ATW), which was designed and tested at the National Aeronautics and Space Administration Dryden Flight Research Center (Edwards, California). This study has shown that natural frequencies and corresponding mode shapes from the updated finite element model have excellent agreement with corresponding measured data.

Lung, Shun-Fat↗

A silicon singlet–triplet qubit driven by spin-valley coupling

Spin–orbit effects, inherent to electrons confined in quantum dots at a silicon heterointerface, provide a means to control electron spin qubits without the added complexity of on-chip, nanofabricated micromagnets or nearby coplanar striplines. Here, we demonstrate a singlet–triplet qubit operating mode that can drive qubit evolution at frequencies in excess of 200 MHz. This approach offers a means to electrically turn on and off fast control, while providing high logic gate orthogonality and long qubit dephasing times. We utilize this operational mode for dynamical decoupling experiments to probe the charge noise power spectrum in a silicon metal-oxide-semiconductor double quantum dot. In addition, we assess qubit frequency drift over longer timescales to capture low-frequency noise. We present the charge noise power spectral density up to 3 MHz, which exhibits a 1/ f α dependence consistent with α ~ 0.7, over 9 orders of magnitude in noise frequency.

97 MATHEMATICS AND COMPUTING↗

Cycle equivalence classes, orthogonal Weingarten calculus, and the mean field theory of memristive systems

Abstract It has been recently noted that for a class of dynamical systems with explicit conservation laws represented via projector operators, the dynamics can be understood in terms of lower dimensional equations. This is the case, for instance, of memristive circuits. Memristive systems are important classes of devices with wide-ranging applications in electronic circuits, artificial neural networks, and memory storage. We show that such mean-field theories can emerge from averages over the group of orthogonal matrices, interpreted as cycle-preserving transformations applied to the projector operator describing Kirchhoff’s laws. Our results provide insights into the fundamental principles underlying the behavior of resistive and memristive circuits and highlight the importance of conservation laws for their mean-field theories. In addition, we argue that our results shed light on the nature of the critical avalanches observed in quasi-two-dimensional nanowires as boundary phenomena.

97 MATHEMATICS AND COMPUTING↗

Bayesian inference of structured latent spaces from neural population activity with the orthogonal stochastic linear mixing model

The brain produces diverse functions, from perceiving sounds to producing arm reaches, through the collective activity of populations of many neurons. Determining if and how the features of these exogenous variables (e.g., sound frequency, reach angle) are reflected in population neural activity is important for understanding how the brain operates. Often, high-dimensional neural population activity is confined to low-dimensional latent spaces. However, many current methods fail to extract latent spaces that are clearly structured by exogenous variables. This has contributed to a debate about whether or not brains should be thought of as dynamical systems or representational systems. Here, we developed a new latent process Bayesian regression framework, the orthogonal stochastic linear mixing model (OSLMM) which introduces an orthogonality constraint amongst time-varying mixture coefficients, and provide Markov chain Monte Carlo inference procedures. We demonstrate superior performance of OSLMM on latent trajectory recovery in synthetic experiments and show superior computational efficiency and prediction performance on several real-world benchmark data sets. We primarily focus on demonstrating the utility of OSLMM in two neural data sets: μ ECoG recordings from rat auditory cortex during presentation of pure tones and multi-single unit recordings form monkey motor cortex during complex arm reaching. We show that OSLMM achieves superior or comparable predictive accuracy of neural data and decoding of external variables (e.g., reach velocity). Most importantly, in both experimental contexts, we demonstrate that OSLMM latent trajectories directly reflect features of the sounds and reaches, demonstrating that neural dynamics are structured by neural representations. Together, these results demonstrate that OSLMM will be useful for the analysis of diverse, large-scale biological time-series datasets.

59 BASIC BIOLOGICAL SCIENCES↗

Algorithm for Stabilizing a POD-Based Dynamical System

This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors.

Kalb, Virginia L.↗

DE-1 measurements of AKR wave directions

In addition to its wave rotation sense, the direction of auroral kilometric radiation (AKR) can also be measured with the plasma wave instrument on Dynamics Explorer 1, from the relative phase of the signals received by its orthogonal electric dipole antennas. By this method, which differs in principle from the previous spin-null method for measuring wave directions, it has been found possible to pinpoint the AKR source by triangulation, using measurements from different points along the DE-1 orbit. The resulting apparent source, in one instance, seemed to occupy a well-defined auroral-zone invariant magnetic latitude and showed the expected increase of altitude with decreasing frequency. An analysis of the method also confirmed the validity of the previous rotation sense measurements.

Calvert, W.↗

Flexible spacecraft maneuver - Inverse attitude control and modal stabilization

A control law is presented for three-axis rotational maneuvers of a spacecraft (orbiter)-beam-tip body (antenna or a reflector) configuration based on nonlinear inversion and modal velocity feedback. Using invertibility and functional reproducibility results, a decoupling attitude control law is presented such that, in the closed-loop system, the attitude angles of the spacecraft are independently controlled using the control moments acting on the space vehicle. This controller asymptotically decouples the flexible dynamics from the rigid one and also allows the decomposition of the elastic dynamics into two subsystems representing the transverse deflections of the beam in two orthogonal planes. These low-order subsystems are used for derivation of a modal velocity feedback stabilizer using the force and moment actuators at the end body. Simulation results are presented to show that, in the closed-loop system, attitude control and elastic mode stabilization are accomplished in spite of the parameter uncertainty and disturbance torque input in the system.

Singh, Sahjendra N.↗

Three axis rotational maneuver and vibration stabilization of elastic spacecraft

A control law for three-axis rotational maneuvers of a spacecraft beam-tip body configuration based on non-linear inversion and modal velocity feedback is presented. A decoupling attitude control law is presented such that in the closed-loop system the attitude angles of the spacecraft are independently controlled, using the control moments acting on the space vehicle. This controller asymptotically decouples the flexible dynamics from the rigid one and also allows the decomposition of the elastic dynamics into two subsystems representing the transverse deflections of the beam in two orthogonal planes. These low-order subsystems are used for the derivation of a modal velocity feedback stabilizer using the force and moment actuators at the end body. Simulation results are presented to show the capability of the controller.

Singh, Sahjendra N.↗

Geosat crossover analysis in the tropical Pacific. II - Verification analysis of altimetric sea level maps with expendable bathythermograph and island sea level data

Altimetric sea level time series for the tropical Pacific have been generated from the Geosat crossover differences during the classified era of the Geosat mission from April 1985 to September 1986. These are compared with the expendable bathythermograph (XBT)-derived dynamic height and island sea level observations, yielding good agreement. A complex empirical orthogonal function analysis is also applied to the altimetric and XBT results. The analysis demonstrates the dominance of the annual signal in this relatively short time series and the westward propagation of major features away from the equator.

Tai, Chang-Kou↗

Studies in turbulence

Various papers on turbulence are presented. Individual topics addressed include: modeling the dissipation rate in rotating turbulent flows, mapping closures for turbulent mixing and reaction, understanding turbulence in vortex dynamics, models for the structure and dynamics of near-wall turbulence, complexity of turbulence near a wall, proper orthogonal decomposition, propagating structures in wall-bounded turbulence flows. Also discussed are: constitutive relation in compressible turbulence, compressible turbulence and shock waves, direct simulation of compressible turbulence in a shear flow, structural genesis in wall-bounded turbulence flows, vortex lattice structure of turbulent shear slows, etiology of shear layer vortices, trilinear coordinates in fluid mechanics.

Gatski, Thomas B.↗

Real-Time Estimation of Bare-Airframe Frequency Responses from Closed-Loop Data and Multisine Inputs

A method is presented for computing frequency responses of multiple-input multiple-output bare-airframe dynamics from flight test data containing feedback control and/or mixing of control effectors. Orthogonal phase-optimized multisines are used to simultaneously excite each input with unique harmonic frequencies, at which frequency responses are computed as ratios of output-to-input Fourier transform data. The confounding effects of feedback and mixing for frequency response estimation are resolved by interpolating the frequency responses among all the harmonic frequencies. The method can be run in batch for post-flight analysis, or in real time as the aircraft is flying. The effectiveness of the method was verified using closed-loop simulations of the subscale NASA T-2 generic transport airplane. The method was also demonstrated using flight test data from the X-56A MUTT aeroelastic airplane, which was flown with feedback control and mixing.

Jared A Grauer↗

Modal dynamics of wind turbine wake meandering from lidar observations

Horizontal scans from nacelle-mounted lidars provide time series measurements of wind turbine wakes across diverse atmospheric conditions, enabling analysis of coherent turbulent structures that influence wake meandering through proper orthogonal decomposition (POD). While low-order modes capture the most energetic turbulent structures, our analysis reveals that they do not necessarily dominate wake meandering dynamics. We evaluate more than 16,000 combinatorial reconstructions of the flow field for each inflow case, demonstrating that mode relevance depends on mode symmetry, turbulent kinetic energy content, and inflow characteristics. Cases with low turbulence intensity and large integral timescales show stronger correlations between POD modes and wake meandering, whereas higher turbulence conditions (turbulence intensity > 7%) are less effectively described by reduced-order models. However, the qualitative similarity of POD modes across varied atmospheric conditions suggests the potential existence of a semi-universal basis for representing wind turbine wakes, with implications for improving engineering wake models.

17 WIND ENERGY↗

Flow-driven spectral chaos (FSC) method for simulating long-time dynamics of arbitrary-order non-linear stochastic dynamical systems

Uncertainty quantification techniques such as the time-dependent generalized polynomial chaos (TD-gPC) use an adaptive orthogonal basis to better represent the stochastic part of the solution space (aka random function space) in time. However, because the random function space is constructed using tensor products, TD-gPC-based methods are known to suffer from the curse of dimensionality. Here, we introduce a new numerical method called the flow-driven spectral chaos (FSC) which overcomes this curse of dimensionality at the random-function-space level. The proposed method is not only computationally more efficient than existing TD-gPC-based methods but is also far more accurate. The FSC method uses the concept of enriched stochastic flow maps to track the evolution of a finite-dimensional random function space efficiently in time. To transfer the probability information from one random function space to another, two approaches are developed and studied herein. In the first approach, the probability information is transferred in the mean-square sense, whereas in the second approach the transfer is done exactly using a new theorem that was developed for this purpose. The FSC method can quantify uncertainties with high fidelity, especially for the long-time response of stochastic dynamical systems governed by ODEs of arbitrary order. Six representative numerical examples, including a nonlinear problem (the Van-der-Pol oscillator), are presented to demonstrate the performance of the FSC method and corroborate the claims of its superior numerical properties. Finally, a parametric, high-dimensional stochastic problem is used to demonstrate that when the FSC method is used in conjunction with Monte Carlo integration, the curse of dimensionality can be overcome altogether.

(nonlinear) stochastic dynamical systems↗

The ionospheric signatures of flux transfer events and solar wind dynamic pressure changes

Recent observations of vortical flow patterns in the dayside auroral ionosphere are discussed in terms of two alternative mechanisms: (1) the time-dependent magnetic reconnection in 'flux transfer events' (FTEs); and (2) the action of solar wind dynamic pressure changes at the magnetopause. It is argued that the ionospheric flow signature of an FTE should be a twin vortex, with the mean flow velocity in the central region of the pattern being equal to the velocity of the pattern as a whole. On the other hand, the pulse of enhanced or reduced dynamic pressure is also expected to produce a twin vortex, but with the central plasma flow being generally different in speed from (and almost orthogonal to) the motion of the whole pattern. It is found that, while none of the events discussed here are consistent with the theories of the effects of the dynamic pressure changes, all are well explained in terms of the ionospheric signatures of FTEs.

Lockwood, M.↗

Data-driven recovery of hidden physics in reduced order modeling of fluid flows

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on using first principles to model the known physics in conjunction with utilizing the data-driven machine learning tools to model the remaining residual that is hidden in data. This framework employs proper orthogonal decomposition as a compression tool to construct orthonormal bases and Galerkin projection (GP) as a model to build the dynamical core of the system. Our proposed methodology hence compensates structural or epistemic uncertainties in models and utilizes the observed data snapshots to compute true modal coefficients spanned by these bases. The GP model is then corrected at every time step with a data-driven rectification using a long short-term memory (LSTM) neural network architecture to incorporate hidden physics. A Grassmannian manifold approach is also adopted for interpolating basis functions to unseen parametric conditions. The control parameter governing the system's behavior is thus implicitly considered through true modal coefficients as input features to the LSTM network. The effectiveness of the HAM approach is then discussed through illustrative examples that are generated synthetically to take hidden physics into account. Furthermore, our approach thus provides insights addressing a fundamental limitation of the physics-based models when the governing equations are incomplete to represent underlying physical processes.

42 ENGINEERING↗

LaSDI: Parametric Latent Space Dynamics Identification

Enabling fast and accurate physical simulations with data has become an important area of computational physics to aid in inverse problems, design-optimization, uncertainty quantification, and other various decision-making applications. This paper presents a data-driven framework for parametric latent space dynamics identification procedure that enables fast and accurate simulations. The parametric model is achieved by building a set of local latent space model and designing an interaction among them. An individual local latent space dynamics model achieves accurate solution in a trust region. By letting the set of trust region to cover the whole parameter space, our model shows an increase in accuracy with an increase in training data. Herein we introduce two different types of interaction mechanisms, i.e., point-wise and region-based approach. Both linear and nonlinear data compression techniques are used. We illustrate the framework of Latent Space Dynamics Identification (LaSDI) enable a fast and accurate solution process on various partial differential equations, i.e., Burgers’ equations, radial advection problem, and nonlinear heat conduction problem, achieving 0 (100)x speed-up and 0 (1)% relative error with respect to the corresponding full order models.

97 MATHEMATICS AND COMPUTING↗