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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

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↗
NASA NTRS1985

Vector Lyapunov Functions for Stochastic Interconnected Systems

Theoretical paper presents set of sufficient conditions for asymptotic and exponential stability with probability 1 for class of stochastic interconnected systems. Theory applicable to complicated, large-scale mechanical or electrical systems, and, for several design problems, it reduces computational difficulty by relating stability criteria to fundamental structural features of system.

Boussalis, D.↗
NASA NTRS1992

A stochastic approach to robust broadband structural control

Viewgraphs on a stochastic approach to robust broadband structural control are presented. Topics covered include: travelling wave model; dereverberated mobility model; computation of dereverberated mobility; power flow; impedance matching; stochastic systems; control problem; control of stochastic systems; using cost functional; Bernoulli-Euler beam example; compensator design; 'power' dual variables; dereverberation of complex structure; and dereverberated transfer function.

Macmartin, Douglas G.↗
DOE OSTI2021

Flow-driven spectral chaos (FSC) method for long-time integration of second-order stochastic dynamical systems

For decades, uncertainty quantification techniques based on the spectral approach have been demonstrated to be computationally more efficient than the Monte Carlo method for a wide variety of problems, particularly when the dimensionality of the probability space is relatively low. The time-dependent generalized polynomial chaos (TD-gPC) is one such technique that uses an evolving orthogonal basis to better represent the stochastic part of the solution space in time. Here in this paper, we present a new numerical method that uses the concept of enriched stochastic flow maps to track the evolution of the stochastic part of the solution space in time. The computational cost of this proposed flow-driven stochastic chaos (FSC) method is an order of magnitude lower than TD-gPC for comparable solution accuracy. This gain in computational cost is realized because, unlike most existing methods, the number of basis vectors required to track the stochastic part of the solution space does not depend upon the dimensionality of the probability space. Four representative numerical examples are presented to demonstrate the performance of the FSC method for long-time integration of second-order stochastic dynamical systems in the context of stochastic dynamics of structures.

FSC↗
DOE OSTI2021

Fault isolation and fault-tolerant control for Takagi-Sugeno fuzzy time-varying delay stochastic distribution systems

A fault isolation, estimation, and fault-tolerant control (FTC) scheme for nonlinear time-varying delay stochastic distribution control systems was presented in this paper. The Takagi-Sugeno fuzzy model was adopted to approach the nonlinear dynamics of time-varying delay systems. According to the output equivalence principle and Laplace transformation, an augmented state vector was given to solve the time-varying delay problem. When multiple actuator faults and interference occur simultaneously, fault detection, isolation and fault estimation was designed to obtained the fault information. To decouple faults and obtain the value and location information of the fault, the system was separated into two parts through the designed multiple conversion matrices, in which one subsystem was only affected by one actuator fault. This has simplified the design of fault isolation and estimation. A adaptive observer for fault estimation was given. Then, fault information such as the time, location, and size was determined. The observer gain matrices were calculated using linear matrix inequality (LMI). When a fault was detected and diagnosed, a FTC algorithm was devised using the proportional-integral control scheme to compensate the fault as much as possible. It has been shown that even if multiple faults actuator occurred simultaneously, the FTC controller still ensured the output probability density function of the system traced the desired probability density function when a fault occurred. Finally, the expected results were obtained through the simulation example, which confirmed the effectiveness of the method.

42 ENGINEERING↗
DOE OSTI2021

Survey on stochastic distribution systems: A full probability density function control theory with potential applications

Complex systems seen either in general engineering practice or economics are subjected to ever increased uncertainties that are mostly represented as random variables or parameters, and the characteristics of random variables are represented by their probability density functions (PDFs). Controlling their PDFs means to shape their stochastic distributions and in general it would provide a full treatment for system analysis and operational control and optimization. This leads to the development of stochastic distribution control (SDC) systems theory in the past decades, where the original aim of the controller design is to realize a shape control of the distributions of certain random variables in their PDFs sense for some engineering processes. Indeed, once the PDFs of these random variables or parameters are used to describe their distribution characters, the control task is to obtain control signals so that the output PDFs of stochastic systems are made to follow their target PDFs. The subject of SDC was initially originated for non-Gaussian stochastic control systems design but has found a wide spectrum of applications in general systems in terms of data-driven modeling, analysis, signal processing (filtering), data mining via multivariable statistics, decision-making (optimization) for systems subjected to uncertainties and even in economics. In this context, SDC constitutes an effective primer tool for complex system analysis, control and operational optimizations. In this review paper, a detailed survey of the developments on the research of SDC systems will be made together with their wide spectrum applications and future perspectives.

42 ENGINEERING↗
DOE OSTI2020

Assessment of wind power scenario creation methods for stochastic power systems operations

Probabilistic scenarios of renewable energy production, such as wind, have been gaining popularity for use in stochastic variants of power systems operations scheduling problems, allowing for optimal decision-making under uncertainty. The quality of the scenarios has a direct impact on the value of the resulting decisions, but until now, methods for creating scenarios have not been compared under realistic operational conditions. Here, we compare the quality of scenario sets created using three different methods, based on a simulated re-enactment of stochastic day-ahead unit commitment and subsequent dispatch for a realistic test system. We create scenarios using a dataset of forecasted and actual wind power values, scaled to evaluate the effects of increasing wind penetration levels. We show that the choice of scenario set can significantly impact system operating cost, renewable energy use, and the ability of the system to meet demand. This result has implications for the ability of system operators to efficiently integrate renewable production into their day-ahead planning, highlighting the need for the use of performance-based assessments for scenario evaluation.

17 WIND ENERGY↗
DOE OSTI2020

Fault diagnosis and fault tolerant control for T-S fuzzy stochastic distribution systems subject to sensor and actuator faults

The problem of fault diagnosis (FD) and fault tolerant control (FTC) for a class of Takagi-Sugeno (T-S) fuzzy stochastic distribution control (SDC) systems subject to sensor and actuator faults is discussed in this paper. First, fuzzy logic models are used to approximate the output probability density function (PDF). Next, an adaptive augmented state/fault diagnosis observer is proposed to estimate the system state, sensor and the actuator faults simultaneously. New expected weights based on the sensor fault estimation information and a PI-type fuzzy feedback fault tolerant (FT) controller are designed to compensate the effect of sensor fault and actuator fault simultaneously. When the sensor fault occurs, the expected objective is redesigned to compensate the sensor fault. Meanwhile, the PI controller can compensate the effect of actuator fault, and the output PDF of the system can still track the desired PDF after the fault occurs. Finally, an example of quality distribution control in chemical reaction process is given to confirm the effectiveness of the algorithm.

42 ENGINEERING↗
NASA NTRS1985

Evaluation of performance characteristics for a space antenna system subjected to stochastic disturbances

Control system synthesis for a large space antenna system is investigated based on stochastic linear optimal control techniques and the minimization of a quadratic Gaussian performance index. Parametric studies indicate that suitable combinations of plant and sensor noise characteristics, and state weighting matrices, can be found to meet the mission RMS pointing requirements. Using a combination of the Kalman filter and linear feedback, an optimal control law for the finite element model of the Hoop/Column structural system without damping is obtained. Removing the hoop-mounted actuator resulted in an increase in the RMS errors, an increased control effort, and an increase in the least damped modal time constant. Removing the hoop-mounted sensor resulted in an RMS error increase and estimator performance degradation, with less system RMS performance degradation than noted for removal of the hoop-mounted actuator.

Ananthakrishnan, S.↗
NASA NTRS1980

Optimal regulation in systems with stochastic time sampling

An optimal control theory that accounts for stochastic variable time sampling in a distributed microprocessor based flight control system is presented. The theory is developed by using a linear process model for the airplane dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved for the control law that minimizes the expected value of a quadratic cost function. The optimal cost obtained with a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained with a known and uniform information update interval.

Montgomery, R. C.↗
DOE OSTI2024

Decision-making based on Markov decision process in integrated artificial reasoning framework—Part I: Theory

This paper presents a decision-making framework based on an integrated artificial reasoning framework and Markov decision process (MDP). The integrated artificial reasoning framework provides a physics-based approach that converts system information into state transition models, and the analysis result will be represented by the transition probabilities that can be used with an MDP to find a traceable and explainable optimal pathway. A dynamic Bayesian network (DBN) is well suited for representing the structure of an MDP. The causality information among process variables (or among subsystems) is mathematically represented in a DBN by the conditional probabilities of the node’s states provided different probabilities of the parent node’s states. To define node states in a physically understandable manner, we used multilevel flow modeling (MFM). An MFM follows the fundamental energy and mass conservation laws and supports the selection of process variables that represent the system of interest so that causal relations among process variables are properly captured. An MFM-based DBN supports developing state transition models in an MDP to capture the effect of process variables of system having physical relations. The operators of the target system can capture stochastic system dynamics as multiple subsystem state transitions based on their physical relations and uncertainties coming from component degradation or random failures. We analyzed a simplified exemplary system to illustrate an optimal operational policy using the suggested approach.

Markov decision process↗
DOE OSTI2024

A Pseudoreversible Normalizing Flow for Stochastic Dynamical Systems with Various Initial Distributions

Here, we present a pseudoreversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with various initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDEs, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE’s final state without simulating trajectories. The existing normalizing flow model for SDEs depends on the initial distribution, meaning the model needs to be retrained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. Additionally, we propose to use a pseudoreversible network architecture to define the normalizing flow model, which has sufficient expressive power and training efficiency for a variety of SDEs in science and engineering, e.g., in particle physics. We provide a rigorous convergence analysis of the pseudoreversible normalizing flow model to the target probability density function in the Kullback–Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Robust Statistical Approach for Determination of Graphite Nitridation Using Bayesian Model Comparison

A better estimation of surface reaction efficiency of semiconductor-grade graphite with atomic nitrogen, as well as the calibration error are calculated using Bayesian updating based on experimental data. Compared with a conventional deterministic model, the stochastic model approach is a powerful tool in the sense that the model is capable of taking into account underlying error correlations among the data quantities. In this paper, we investigate four different stochastic models (called “stochastic system model classes” herein) corresponding to different descriptions of modeling and measurement error structures, given one deterministic physical model. These stochastic system model classes differ in the covariance matrix structure that is used in the uncertainty model to represent uncertainties associated with the physical model and experimental measurements. For each model class, Bayesian inference is used to estimate the posterior probabilities of the physical model parameters as well as of the stochastic model parameters. Model comparison and selection are then applied based on two measures including Bayesian evidence and Bayesian information criterion, as well as the deviance information criterion. Both measures suggest the stochastic model class, which considers that a correlation between errors in two data quantities among different data points is the most plausible. With the stochastic model class, the range of uncertainty in surface reaction efficiency is estimated to be about two orders of magnitude at [Formula: see text].

Engineering↗
NASA NTRS1975

Design of optimal partial state feedback controllers for linear systems in stochastic environments

The problem of obtaining an optimal control law, which is constrained to be a feedback of the available measurements, is considered for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise. Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite duration cases. The feedback gain matrices are constrained to be constant for the infinite duration cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. Computational aspects are discussed via application to two continuous time processes, including a helicopter/slung load system subjected to measurement noise and random wind gust input.

Joshi, S. M.↗