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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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14 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Gramian-Based Characterization of Network Vulnerability to Nodal Impulse Inputs: Preprint

Impulsive inputs applied at influential nodes of a network system may result in undesirable behavior and degrade performance. This paper proposes the notion of vulnerability matrix (VM) to characterize the effect of impulse inputs on a network following either discrete-time or continuous-time dynamics. The VM describes the first-order effects of impulse inputs on edge flows and is based on the controllability Gramian. We provide explicit expressions for the elements of the vulnerability matrix for the class of directed line networks in terms of the edge weights. Simulations validate our results and highlight the utility of the proposed metric in capturing the transient effects of nodal impulse inputs on edge flows.

controllability Gramian↗
DOE OSTI2024

Denoising of imaginary time response functions with Hankel projections

Imaginary-time response functions of finite-temperature quantum systems are often obtained with methods that exhibit stochastic or systematic errors. Reducing these errors comes at a large computational cost—in quantum Monte Carlo simulations, the reduction of noise by a factor of two incurs a simulation cost of a factor of four. In this paper, we relate certain imaginary-time response functions to an inner product on the space of linear operators on Fock space. We then show that data with noise typically does not respect the positive definiteness of its associated Gramian. The Gramian has the structure of a Hankel matrix. As a method for denoising noisy data, we introduce an alternating projection algorithm that finds the closest positive definite Hankel matrix consistent with noisy data. We test our methodology at the example of fermion Green's functions for continuous-time quantum Monte Carlo data and show remarkable improvements of the error, reducing noise by a factor of up to 20 in practical examples. We argue that Hankel projections should be used whenever finite-temperature imaginary-time data of response functions with errors is analyzed, be it in the context of quantum Monte Carlo, quantum computing, or in approximate semianalytic methodologies. Published by the American Physical Society 2024

Yu, Yang (ORCID:0000000186178878)↗
DOE OSTI2020

Power System Event Classification and Localization Using a Convolutional Neural Network

Detection and timely identification of power system disturbances are essential for situation awareness and reliable electricity grid operation. Because records of actual events in the system are limited, ensemble simulation-based events are needed to provide adequate data for building event-detection models through deep learning; e.g., a convolutional neural network (CNN). An ensemble numerical simulation-based training data set have been generated through dynamic simulations performed on the Polish system with various types of faults in different locations. Such data augmentation is proven to be able to provide adequate data for deep learning. The synchronous generators’ frequency signals are used and encoded into images for developing and evaluating CNN models for classification of fault types and locations. With a time-domain stacked image set as the benchmark, two different time-series encoding approaches, i.e., wavelet decomposition-based frequency-domain stacking and polar coordinate system-based Gramian Angular Field (GAF) stacking, are also adopted to evaluate and compare the CNN model performance and applicability. The various encoding approaches are suitable for different fault types and spatial zonation. With optimized settings of the developed CNN models, the classification and localization accuracies can go beyond 84 and 91%, respectively.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

On the dual advantage of placing observations through forward sensitivity analysis

The four-dimensional variational data assimilation methodology for assimilating noisy observations into a deterministic model has been the workhorse in forecasting centres for over three decades. While this method provides a computationally efficient framework for dynamic data assimilation, it is largely silent on the important question concerning the minimum number and placement of observations. To answer this question, we demonstrate the dual advantage of placing the observations where the square of the sensitivity of the model solution with respect to the unknown control variables, called forward sensitivities, attains its maximum. By following this approach, we can force the observability Gramian to be of full rank, which in turn guarantees efficient recovery of the optimal values of the control variables, which is the first of the two advantages of this strategy. We further show that the proposed strategy of placing observations has another inherent optimality: the square of the sensitivity of the optimal estimates of the control with respect to the observations (used to obtain these estimates) attains its minimum value, a second advantage that is a direct consequence of the above strategy for placing observations. Our analytical framework and numerical experiments on linear and nonlinear systems confirm the effectiveness of our proposed strategy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Data-driven Resilience Characterization of Control Dynamical Systems

In this paper, we define and quantify resiliency of a power network and propose data-driven algorithms for computing the same for the power grid. To do this, we use the Koopman operator framework to lift the controlled dynamical system to an abstract (possibly higher) dimensional space, where the evolution is linear. The linear system representation allows us to relate small time local controllability and observability of a general nonlinear control system to the controllability and observability of the lifted linear system. Finally, we define the resiliency of the underlying power grid in terms of the controllability and observability gramians of the lifted linear system. We illustrate the proposed approach to compute the resiliency metrics on time-series data obtained from a microgrid.

koopman operator, resilience, control↗
NASA NTRS1977

Imaginary-frequency polarizability and van der Waals force constants of two-electron atoms, with rigorous bounds

Variational functionals of Braunn and Rebane (1972) for the imagery-frequency polarizability (IFP) have been generalized by the method of Gramian inequalities to give rigorous upper and lower bounds, valid even when the true (but unknown) unperturbed wavefunction must be represented by a variational approximation. Using these formulas in conjunction with flexible variational trial functions, tight error bounds are computed for the IFP and the associated two- and three-body van der Waals interaction constants of the ground 1(1S) and metastable 2(1,3S) states of He and Li(+). These bounds generally establish the ground-state properties to within a fraction of a per cent and metastable properties to within a few per cent, permitting a comparative assessment of competing theoretical methods at this level of accuracy. Unlike previous 'error bounds' for these properties, the present results have a completely a priori theoretical character, with no empirical input data.

Glover, R. M.↗
NASA NTRS1992

Dominant modes via model error

Obtaining a reduced model of a stable mechanical system with proportional damping is considered. Such systems can be conveniently represented in modal coordinates. Two popular schemes, the modal cost analysis and the balancing method, offer simple means of identifying dominant modes for retention in the reduced model. The dominance is measured via the modal costs in the case of modal cost analysis and via the singular values of the Gramian-product in the case of balancing. Though these measures do not exactly reflect the more appropriate model error, which is the H2 norm of the output-error between the full and the reduced models, they do lead to simple computations. Normally, the model error is computed after the reduced model is obtained, since it is believed that, in general, the model error cannot be easily computed a priori. The authors point out that the model error can also be calculated a priori, just as easily as the above measures. Hence, the model error itself can be used to determine the dominant modes. Moreover, the simplicity of the computations does not presume any special properties of the system, such as small damping, orthogonal symmetry, etc.

Yousuff, A.↗
NASA NTRS1995

Autonomous control system reconfiguration for spacecraft with non-redundant actuators

The Small Satellite Technology Initiative (SSTI) 'CLARK' spacecraft is required to be single-failure tolerant, i.e., no failure of any single component or subsystem shall result in complete mission loss. Fault tolerance is usually achieved by implementing redundant subsystems. Fault tolerant systems are therefore heavier and cost more to build and launch than non-redundent, non fault-tolerant spacecraft. The SSTI CLARK satellite Attitude Determination and Control System (ADACS) achieves single-fault tolerance without redundancy. The attitude determination system system uses a Kalman Filter which is inherently robust to loss of any single attitude sensor. The attitude control system uses three orthogonal reaction wheels for attitude control and three magnetic dipoles for momentum control. The nominal six-actuator control system functions by projecting the attitude correction torque onto the reaction wheels while a slower momentum management outer loop removes the excess momentum in the direction normal to the local B field. The actuators are not redundant so the nominal control law cannot be implemented in the event of a loss of a single actuator (dipole or reaction wheel). The spacecraft dynamical state (attitude, angular rate, and momentum) is controllable from any five-element subset of the six actuators. With loss of an actuator the instantaneous control authority may not span R(3) but the controllability gramian integral(limits between t,0) Phi(t, tau)B(tau )B(prime)(tau) Phi(prime)(t, tau)d tau retains full rank. Upon detection of an actuator failure the control torque is decomposed onto the remaining active axes. The attitude control torque is effected and the over-orbit momentum is controlled. The resulting control system performance approaches that of the nominal system.

Grossman, Walter↗
NASA NTRS2003

Closed-Loop Performance Measures for Flight Controllers Subject to Neutron-Induced Upsets

It has been observed that atmospheric neutrons can produce single event upsets in digital flight control hardware. The phenomenon has been studied extensively at the chip level, and now system level experiments are underway. In this paper analytical closed-loop performance measures for the tracking error are developed for a plant that is stabilized by a recoverable computer system subject to neutron induced upsets. The underlying model is a Markov jump-linear system with process noise. The steady-state tracking error is expressed in terms of a generalized observability Gramian.

Gray, W. Steven↗
NASA NTRS2015

Coupled Inertial Navigation and Flush Air Data Sensing Algorithm for Atmosphere Estimation

This paper describes an algorithm for atmospheric state estimation that is based on a coupling between inertial navigation and flush air data sensing pressure measurements. In this approach, the full navigation state is used in the atmospheric estimation algorithm along with the pressure measurements and a model of the surface pressure distribution to directly estimate atmospheric winds and density using a nonlinear weighted least-squares algorithm. The approach uses a high fidelity model of atmosphere stored in table-look-up form, along with simplified models of that are propagated along the trajectory within the algorithm to provide prior estimates and covariances to aid the air data state solution. Thus, the method is essentially a reduced-order Kalman filter in which the inertial states are taken from the navigation solution and atmospheric states are estimated in the filter. The algorithm is applied to data from the Mars Science Laboratory entry, descent, and landing from August 2012. Reasonable estimates of the atmosphere and winds are produced by the algorithm. The observability of winds along the trajectory are examined using an index based on the discrete-time observability Gramian and the pressure measurement sensitivity matrix. The results indicate that bank reversals are responsible for adding information content to the system. The algorithm is then applied to the design of the pressure measurement system for the Mars 2020 mission. The pressure port layout is optimized to maximize the observability of atmospheric states along the trajectory. Linear covariance analysis is performed to assess estimator performance for a given pressure measurement uncertainty. The results indicate that the new tightly-coupled estimator can produce enhanced estimates of atmospheric states when compared with existing algorithms.

Karlgaard, Christopher D.↗
NASA NTRS2016

Coupled Inertial Navigation and Flush Air Data Sensing Algorithm for Atmosphere Estimation

This paper describes an algorithm for atmospheric state estimation based on a coupling between inertial navigation and flush air data-sensing pressure measurements. The navigation state is used in the atmospheric estimation algorithm along with the pressure measurements and a model of the surface pressure distribution to estimate the atmosphere using a nonlinear weighted least-squares algorithm. The approach uses a high-fidelity model of atmosphere stored in table-lookup form, along with simplified models propagated along the trajectory within the algorithm to aid the solution. Thus, the method is a reduced-order Kalman filter in which the inertial states are taken from the navigation solution and atmospheric states are estimated in the filter. The algorithm is applied to data from the Mars Science Laboratory entry, descent, and landing from August 2012. Reasonable estimates of the atmosphere are produced by the algorithm. The observability of winds along the trajectory are examined using an index based on the observability Gramian and the pressure measurement sensitivity matrix. The results indicate that bank reversals are responsible for adding information content. The algorithm is applied to the design of the pressure measurement system for the Mars 2020 mission. A linear covariance analysis is performed to assess estimator performance. The results indicate that the new estimator produces more precise estimates of atmospheric states than existing algorithms.

Karlgaard, Christopher D.↗
DOE OSTI2023

A greedy Galerkin method to efficiently select sensors for linear dynamical systems

A key challenge in inverse problems is the selection of sensors to gather the most effective data. In this paper, we consider the problem of inferring the initial condition to a linear dynamical system and develop an efficient control-theoretical approach for greedily selecting sensors. Our method employs a Galerkin projection to reduce the size of the inverse problem, resulting in a computationally efficient algorithm for sensor selection. As a byproduct of our algorithm, we obtain a preconditioner for the inverse problem that enables the rapid recovery of the initial condition. Here, we analyze the theoretical performance of our greedy sensor selection algorithm as well as the performance of the associated preconditioner. Finally, we verify our theoretical results on various inverse problems involving partial differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Multistage Stabilized Continuation for Indirect Optimal Control of Three-Dimensional Hypersonic Trajectories

This work presents the development of a multistaged stabilized continuation for the three-dimensional unpowered hypersonic trajectory planning problem using indirect optimal control methods. The stabilized continuation method is noniterative and guaranteed to terminate within a finite number of floating point operations, thereby making it well suited for onboard autonomous implementations. Here, we present a multistage formulation of the stabilized continuation scheme that involves starting with a “loose” integration tolerance during the first stage and ramping up toward a “strict” integration tolerance through subsequent stages. An important benefit of this approach is that even when the solution to the underlying optimal control problem is numerically unstable, such as with the hypersonic vehicle footprint generation problem, the stabilized continuation algorithm is shown to be successful in finding a solution while providing some additional insights into the underlying cause of the numerical instability.

33 ADVANCED PROPULSION SYSTEMS↗