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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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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Learning stochastic dynamics with statistics-informed neural network

We introduce a machine-learning framework named statistics-informed neural network (SINN) for learning stochastic dynamics from data. This new architecture was theoretically inspired by a universal approximation theorem for stochastic systems, which we introduce in this paper, and the projection-operator formalism for stochastic modeling. Here, we devise mechanisms for training the neural network model to reproduce the correct statistical behavior of a target stochastic process. Numerical simulation results demonstrate that a well-trained SINN can reliably approximate both Markovian and non-Markovian stochastic dynamics. We demonstrate the applicability of SINN to coarse-graining problems and the modeling of transition dynamics. Furthermore, we show that the obtained reduced-order model can be trained on temporally coarse-grained data and hence is well suited for rare-event simulations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2007

POD Model Reconstruction for Gray-Box Fault Detection

Proper orthogonal decomposition (POD) is the mathematical basis of a method of constructing low-order mathematical models for the "gray-box" fault-detection algorithm that is a component of a diagnostic system known as beacon-based exception analysis for multi-missions (BEAM). POD has been successfully applied in reducing computational complexity by generating simple models that can be used for control and simulation for complex systems such as fluid flows. In the present application to BEAM, POD brings the same benefits to automated diagnosis. BEAM is a method of real-time or offline, automated diagnosis of a complex dynamic system.The gray-box approach makes it possible to utilize incomplete or approximate knowledge of the dynamics of the system that one seeks to diagnose. In the gray-box approach, a deterministic model of the system is used to filter a time series of system sensor data to remove the deterministic components of the time series from further examination. What is left after the filtering operation is a time series of residual quantities that represent the unknown (or at least unmodeled) aspects of the behavior of the system. Stochastic modeling techniques are then applied to the residual time series. The procedure for detecting abnormal behavior of the system then becomes one of looking for statistical differences between the residual time series and the predictions of the stochastic model.

Park, Han↗
NASA NTRS1989

Stochastic Petri net analysis of a replicated file system

A stochastic Petri-net model of a replicated file system is presented for a distributed environment where replicated files reside on different hosts and a voting algorithm is used to maintain consistency. Witnesses, which simply record the status of the file but contain no data, can be used in addition to or in place of files to reduce overhead. A model sufficiently detailed to include file status (current or out-of-date), as well as failure and repair of hosts where copies or witnesses reside, is presented. The number of copies and witnesses is a parameter of the model. Two different majority protocols are examined, one where a majority of all copies and witnesses is necessary to form a quorum, and the other where only a majority of the copies and witnesses on operational hosts is needed. The latter, known as adaptive voting, is shown to increase file availability in most cases.

Bechta Dugan, Joanne↗
NASA NTRS1979

Minimum-variance fixed-form compensation of linear systems

The problem of determining the linear time-invariant compensator of a specified dimension which minimizes the asymptotic expected value of a quadratic form in the state variables of a linear stochastic system of arbitrary order, is considered. It is shown that under appropriate assumptions, the solution of this problem can be interpreted as a minimum-order observer-based or dual observer-based compensator for an optimally aggregated model of the plant.

Johnson, T. L.↗
NASA NTRS1990

Determining structural performance

An overview of the methods and concepts developed to enhance and predict structural dynamic characteristics of advanced aeropropulsion systems is presented. Aeroelasticity, vibration control, dynamic systems, and computational structural methods are four disciplines that make up the structural dynamic effort at LeRC. The aeroelasticity program develops analytical and experimental methods for minimizing flutter and forced vibration of aerospace propulsion systems. Both frequency domain and time domain methods were developed for applications on the turbofan, turbopump, and advanced turboprop. In order to improve life and performance, the vibration control program conceives, analyzes, develops, and demonstrates new methods for controlling vibrations in aerospace systems. Active and passive vibration control is accomplished with electromagnetic dampers, magnetic bearings, and piezoelectric crystals to control rotor vibrations. The dynamic systems program analyzes and verifies the dynamics of interacting systems, as well as develops concepts and methods for high-temperature dynamic seals. Work in this field involves the analysis and parametric identification of large, nonlinear, damped, stochastic systems. The computational structural methods program exploits modern computer science as an aid to the solutions of structural problems.

Ernst, Michael A.↗
DOE OSTI2023

Vibrational heat-bath configuration interaction with semistochastic perturbation theory using harmonic oscillator or VSCF modals

Vibrational heat-bath configuration interaction (VHCI)—a selected configuration interaction technique for vibrational structure theory—has recently been developed in two independent works [J. H. Fetherolf and T. C. Berkelbach, J. Chem. Phys. 154, 074104 (2021); A. U. Bhatty and K. R. Brorsen, Mol. Phys. 119, e1936250 (2021)], where it was shown to provide accuracy on par with the most accurate vibrational structure methods with a low computational cost. Here, we eliminate the memory bottleneck of the second-order perturbation theory correction using the same (semi)stochastic approach developed previously for electronic structure theory. This allows us to treat, in an unbiased manner, much larger perturbative spaces, which are necessary for high accuracy in large systems. Stochastic errors are easily controlled to be less than 1 cm−1. We also report two other developments: (i) we propose a new heat-bath criterion and an associated exact implicit sorting algorithm for potential energy surfaces expressible as a sum of products of one-dimensional potentials; (ii) we formulate VHCI to use a vibrational self-consistent field (VSCF) reference, as opposed to the harmonic oscillator reference configuration used in previous reports. Our tests are done with quartic and sextic force fields, for which we find that with VSCF, the minor improvements to accuracy are outweighed by the higher computational cost associated the matrix element evaluations. We expect VSCF-based VHCI to be important for more general potential representations, for which the harmonic oscillator basis function integrals are no longer analytic.

Chemistry↗
NASA NTRS1990

Application of stochastic robustness to aircraft control systems

Guaranteeing robustness has long been an important design objective of control system analysis. Stochastic robustness is a simple numerical procedure that can be used to measure and gain insight into robustness properties associated with linear control systems. In the realm of aircraft control systems, problems such as the effects of flight condition perturbations and model-order uncertainties on robustness are easily and effectively analyzed using stochastic robustness. The concept of stochastic robustness is reviewed and examples are presented demonstrating its use in flight control system analysis.

Ryan, Laura E.↗
DOE OSTI2023

Improving Estimation of the Koopman Operator with Kolmogorov–Smirnov Indicator Functions

It has become common to perform kinetic analysis using approximate Koopman operators that transform high-dimensional timeseries of observables into ranked dynamical modes. The key to the practical success of the approach is the identification of a set of observables that form a good basis on which to expand the slow relaxation modes. Good observables are, however, difficult to identify a priori and suboptimal choices can lead to significant underestimations of characteristic time scales. Leveraging the representation of slow dynamics in terms of Hidden Markov Models (HMM), we propose a simple and computationally efficient clustering procedure to infer surrogate observables that form a good basis for slow modes. Here, we apply the approach to an analytically solvable model system as well as on three protein systems of different complexities. We consistently demonstrate that the inferred indicator functions can significantly improve the estimation of the leading eigenvalues of Koopman operators and correctly identify key states and transition time scales of stochastic systems, even when good observables are not known a priori.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2020

Application of Sparse Identification of Nonlinear Dynamics for Physics-Informed Learning

Advances in machine learning and deep neural networks has enabled complex engineering tasks like image recognition, anomaly detection, regression, and multi-objective optimization, to name but a few. The complexity of the algorithm architecture, e.g., the number of hidden layers in a deep neural network, typically grows with the complexity of the problems they are required to solve, leaving little room for interpreting (or explaining) the path that results in a specific solution. This drawback is particularly relevant for autonomous aerospace and aviation systems, where certifications require a complete understanding of the algorithm behavior in all possible scenarios. Including physics knowledge in such data-driven tools may improve the interpretability of the algorithms, thus enhancing model validation against events with low probability but relevant for system certification. Such events include, for example, spacecraft or aircraft sub-system failures, for which data may not be available in the training phase. This paper investigates a recent physics-informed learning algorithm for identification of system dynamics, and shows how the governing equations of a system can be extracted from data using sparse regression. The learned relationships can be utilized as a surrogate model which, unlike typical data-driven surrogate models, relies on the learned underlying dynamics of the system rather than large number of fitting parameters. The work shows that the algorithm can reconstruct the differential equations underlying the observed dynamics using a single trajectory when no uncertainty is involved. However, the training set size must increase when dealing with stochastic systems, e.g., nonlinear dynamics with random initial conditions.

Corbetta, Matteo↗
DOE OSTI2021

Fluctuation–dissipation relation for a quantum Brownian oscillator in a parametrically squeezed thermal field

In this paper we study the nonequilibrium evolution of a quantum Brownian oscillator, modeling the internal degree of freedom of a harmonic atom or an Unruh–DeWitt detector, coupled to a nonequilibrium and nonstationary quantum field bath and inquire whether a fluctuation–dissipation relation (FDR) can exist after/if it approaches equilibration. This is a nontrivial issue because a squeezed field bath cannot reach equilibration and yet, as this work shows, the system oscillator indeed can, which is a necessary condition for FDRs. We discuss three different settings: (A) The bath field essentially remains in a squeezed thermal state throughout, whose squeeze parameter is a mode- and time-independent constant. This situation is often encountered in quantum optics and quantum thermodynamics. (B) The bath field is initially in a thermal state, but is subjected to a parametric process leading to mode- and time-dependent squeezing. This scenario is encountered in cosmology and dynamical Casimir effects. The squeezing in the bath in both types of processes will affect the oscillator’s nonequilibrium evolution. We show that at late times it approaches equilibration and this stationarity condition warrants the existence of a FDR. The trait of squeezing is marked by the oscillator’s effective equilibrium temperature, and the proportionality factor in the FDR is only related to the stationary component of the noise kernel of the bath field. Setting (C) is more subtle: A finite system–bath coupling strength can set the oscillator in a squeezed state even though the bath field is stationary and does not engage in any parametric process. The squeezing of the system in this case is in general time-dependent but becomes constant when the internal dynamics is fully relaxed. We begin with comments on the broad range of physical processes involving squeezed thermal baths and end with some remarks on the significance of FDRs in capturing the essence of quantum backreaction in nonequilibrium and stochastic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Dynamic Probabilistic Safety Assessment Studies for Advanced Reactor Using RAVEN

Probabilistic Safety Assessment (PSA) is used extensively to evaluate the risks associated with complex engineering systems like Nuclear Power Plants (NPPs). Current PSA models are based on the Event-Tree/Fault-Tree (ET/FT) methodology. ET and FT models are static and are based on Boolean logic approaches. In the past, concerns have been raised in the literature regarding the capability of the traditional static modelling approaches to adequately account for the impact of process, hardware, software, firmware and human interactions on the stochastic system behaviour. To overcome the limitations of the traditional approach to PSA, several dynamic PSA methodologies have been proposed. One of the dynamic PSA methodologies used for dynamic evaluations is Dynamic Event Tree (DET) framework which can be used to assess the impact of the parameter variability and scenario dynamics on the PSA model for the initiating event. The DET framework couples the stochastic model (number of component/trains that start on demand, operator action timing, etc.) with a Thermal-Hydraulic (TH) model of the plant. This paper explores the use of DET along with a case study on advanced reactor. The initiating event selected for the study was Class IV power supply failure event. The TH analysis considering uncertainty in various parameters was performed using RELAP5 and Reactor Analysis and Virtual control ENvironment (RAVEN) tool. Based on the uncertainty analysis, it is concluded that the peak clad temperatures (PCT) are within the limits in all the code runs implying a high-degree of safety margin. However, variation in time to reach the PCT was observed among the code runs and the mean time to reach the PCT was found to be around 8590sec (approximately 2.4 hours). Hence, sufficient time margin is available for human intervention and the operator might have a relatively stress-free state during such an accident scenario. Due to the static nature of the traditional PSA models, the safety margin available was lesser, whereas, with the help of dynamic PSA models, one can demonstrate that the actual available safety margin is more in the present case study and is valuable input from the design point of view.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2023

Optimal mitigation and control over power system dynamics for stochastic grid resilience

Optimal mitigation planning for highly disruptive contingencies to a transmission-level power system requires optimization with dynamic power system constraints, due to the key role of dynamics in system stability to major perturbations. We formulate a generalized disjunctive program to determine optimal grid component hardening choices for protecting against major failures, with differential algebraic constraints representing system dynamics (specifically, differential equations representing generator and load behavior and algebraic equations representing instantaneous power balance over the transmission system). We optionally allow stochastic optimal pre-positioning across all considered failure scenarios, and optimal emergency control within each scenario. This novel formulation allows, for the first time, analyzing the resilience interdependencies of mitigation planning, preventive control, and emergency control. Using all three strategies in concert is particularly effective at maintaining robust power system operation under severe contingencies, as we demonstrate on the western system coordinating council 9-bus test system using synthetic multi-device outage scenarios.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2022

Combining Simulation and Optimization to Derive Operating Policies for a Concentrating Solar Power Plant

Optimizing short-term decisions over a rolling horizon and/or using deterministic penalties to capture system stochasticity can lead to myopic policies that fail to consider unplanned events and their long-term adverse effects. We present a methodology that integrates an off-line optimization model with a simulation procedure to determine the profitability of different operating strategies; specifically, the latter is used to generate additional constraints for the former when failures occur according to system component operating lifetimes that (i) are subject to exogenous uncertainty, and (ii) may degrade more quickly under specific operating conditions. We use the feedback provided by the simulation model in a parametric analysis to obtain penalties that can be used in short-term operations scheduling to maximize the long-term revenues obtained by the optimization model. We apply this research to a concentrating solar power plant; our results show that the methodology can be used to choose an operating policy that balances maximizing profit while accounting for maintenance costs. Integrating the optimization model with a simulation procedure reveals that aggressive prices for cycling yield about 55% fewer startups and 30% fewer failures compared to using a more typical start-up operating strategy, and can save hundreds of thousands to millions of dollars in repair costs over the lifetime of the plant.

concentrating solar power↗
DOE OSTI2020

Deep learning for characterizing the self-assembly of three-dimensional colloidal systems

Creating a systematic framework to characterize the structural states of colloidal self-assembly systems is crucial for unraveling the fundamental understanding of these systems’ stochastic and non-linear behavior. The most accurate characterization methods create high-dimensional neighborhood graphs that may not provide useful information about structures unless these are well-defined reference crystalline structures. Dimensionality reduction methods are thus required to translate the neighborhood graphs into a low-dimensional space that can be easily interpreted and used to characterize non-reference structures. We investigate a framework for colloidal system state characterization that employs deep learning methods to reduce the dimensionality of neighborhood graphs. The framework next uses agglomerative hierarchical clustering techniques to partition the low-dimensional space and assign physically meaningful classifications to the resulting partitions. In this work, we first demonstrate the proposed colloidal self-assembly state characterization framework on a three-dimensional in silico system of 500 multi-flavored colloids that self-assemble under isothermal conditions. We next investigate the generalizability of the characterization framework by applying the framework to several independent self-assembly trajectories, including a three-dimensional in silico system of 2052 colloidal particles that undergo evaporation-induced self-assembly.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold

This paper introduces a surrogate modeling scheme based on Grassmannian manifold learning to be used for cost-efficient predictions of high-dimensional stochastic systems. The method exploits subspace-structured features of each solution by projecting it onto a Grassmann manifold. This point-wise linear dimensionality reduction harnesses the structural information to assess the similarity between solutions at different points in the input parameter space. The method utilizes a solution clustering approach in order to identify regions of the parameter space over which solutions are sufficiently similarly such that they can be interpolated on the Grassmannian. In this clustering, the reduced-order solutions are partitioned into disjoint clusters on the Grassmann manifold using the eigen-structure of properly defined Grassmannian kernels and, the Karcher mean of each cluster is estimated. Then, the points in each cluster are projected onto the tangent space with origin at the corresponding Karcher mean using the exponential mapping. For each cluster, a Gaussian process regression model is trained that maps the input parameters of the system to the reduced solution points of the corresponding cluster projected onto the tangent space. Using this Gaussian process model, the full-field solution can be efficiently predicted at any new point in the parameter space. In certain cases, the solution clusters will span disjoint regions of the parameter space. In such cases, for each of the solution clusters we utilize a second, density-based spatial clustering to group their corresponding input parameter points in the Euclidean space. The proposed method is applied to two numerical examples. Here, the first is a nonlinear stochastic ordinary differential equation with uncertain initial conditions where the surrogate is used to predict the time history solution. The second involves modeling of plastic deformation in a model amorphous solid using the Shear Transformation Zone theory of plasticity, where the proposed surrogate is used to predict the full strain field of a material specimen under large shear strains.

42 ENGINEERING↗