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At least 1,585 records · Page 88

System Simulation by Recursive Feedback: Coupling a Set of Stand-Alone Subsystem Simulations

Recursive feedback is defined and discussed as a framework for development of specific algorithms and procedures that propagate the time-domain solution for a dynamical system simulation consisting of multiple numerically coupled, self-contained, stand-alone subsystem simulations. A satellite motion example containing three subsystems (orbit dynamics, attitude dynamics, and aerodynamics) has been defined and constructed using this approach. Conventional solution methods are used in the subsystem simulations. Centralized and distributed versions of coupling structure have been addressed. Numerical results are evaluated by direct comparison with a standard total-system, simultaneous-solution approach.

Nixon, Douglas D.↗

Dynamic probabilistic risk assessment for electric grid cybersecurity

Electric grid cybersecurity risk has become a significant concern of industries and governments. This paper proposes a dynamic probabilistic risk assessment method for electric grid cybersecurity risk analysis. The proposed method helps reduce the reliance on expert judgment, capture a broad range of components and system dynamics, and model the interactions between various contributing entities (e.g., attacker, operator). In addition, the scenarios with multiple events, such as the occurrence of both cyberattacks and failures of physical components, the occurrence of both cyberattacks and operators’ (in)correct reactions, are considered and analyzed. Further, for each cyberattack scenario, Monte Carlo simulations are used to obtain possible sequences of the system's evolution under study and then derive risk estimates. As an application of the proposed method, the risk assessment method serves as the basis of risk-informed defense resource allocation to improve electric grid cybersecurity. The proposed method is verified using the IEEE 14-bus system by evaluating different security resource allocations for selected cyberattack scenarios.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Predicting rare events using neural networks and short-trajectory data

Estimating the likelihood, timing, and nature of events is a major goal of modeling stochastic dynamical systems. When the event is rare in comparison with the timescales of simulation and/or measurement needed to resolve the elemental dynamics, accurate prediction from direct observations becomes challenging. In such cases a more effective approach is to cast statistics of interest as solutions to Feynman-Kac equations (partial differential equations). Here, we develop an approach to solve Feynman-Kac equations by training neural networks on short-trajectory data. Our approach is based on a Markov approximation but otherwise avoids assumptions about the underlying model and dynamics. This makes it applicable to treating complex computational models and observational data. Additionally, we illustrate the advantages of our method using a low-dimensional model that facilitates visualization, and this analysis motivates an adaptive sampling strategy that allows on-the-fly identification of and addition of data to regions important for predicting the statistics of interest. Finally, we demonstrate that we can compute accurate statistics for a 75-dimensional model of sudden stratospheric warming. This system provides a stringent test bed for our method.

97 MATHEMATICS AND COMPUTING↗

Development of a model protection and dynamic response monitoring system for the national transonic facility

A state-of-the-art, computerized mode protection and dynamic response monitoring system has been developed for the NASA Langley Research Center National Transonic Facility (NTF). This report describes the development of the model protection and shutdown system (MPSS). A technical description of the system is given along with discussions on operation and capabilities of the system. Applications of the system to vibration problems are presented to demonstrate the system capabilities, typical applications, versatility, and investment research return derived from the system to date. The system was custom designed for the NTF but can be used at other facilities or for other dynamic measurement/diagnostic applications. Potential commercial uses of the system are described. System capability has been demonstrated for forced response testing and for characterizing and quantifying bias errors for onboard inertial model attitude measurement devices. The system is installed in the NTF control room and has been used successfully for monitoring, recording and analyzing the dynamic response of several model systems tested in the NTF.

Young, Clarence P., Jr.↗

Metabolic multistability and hysteresis in a model aerobe-anaerobe microbiome community

Major changes in the microbiome are associated with health and disease. Some microbiome states persist despite seemingly unfavorable conditions, such as the proliferation of aerobe-anaerobe communities in oxygen-exposed environments in wound infections or small intestinal bacterial overgrowth. Mechanisms underlying transitions into and persistence of these states remain unclear. Using two microbial taxa relevant to the human microbiome, we combine genome-scale mathematical modeling, bioreactor experiments, transcriptomics, and dynamical systems theory to show that multistability and hysteresis (MSH) is a mechanism describing the shift from an aerobe-dominated state to a resilient, paradoxically persistent aerobe-anaerobe state. We examine the impact of changing oxygen and nutrient regimes and identify changes in metabolism and gene expression that lead to MSH and associated multi-stable states. In such systems, conceptual causation-correlation connections break and MSH must be used for analysis. Using MSH to analyze microbiome dynamics will improve our conceptual understanding of stability of microbiome states and transitions between states.

59 BASIC BIOLOGICAL SCIENCES↗

IDEAS-Watersheds FY21 Annual Report for July 1, 2020-June 30, 2021

Watersheds play a critical role in our water supply infrastructure and require sustainable management in a changing environment. Sustainable management of watershed systems and their interaction with the built environment rely on understanding the hydrologic and biogeochemical processes that control watershed system dynamics and water availability and quality. The overarching objective of the U.S. Department of Energy’s (DOE’s) Environmental System Science (ESS) program is to advance a robust, predictive understanding of how watersheds function and respond to perturbations as integrated hydrobiogeochemical systems. ESS supports a network of watershed testbeds within the United States where national laboratories and university partners work in interdisciplinary teams to advance watershed system science for energy.

54 ENVIRONMENTAL SCIENCES↗

Neural Ordinary Differential Equations for Nonlinear System Identification

Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art nonlinear and classical linear methods. In particular, we present a quantitative study comparing NODE's performance against neural state-space models and classical linear system identification methods and evaluate their inference speed and prediction performance on open-loop errors across eight different dynamical systems. The experiments show that NODEs can consistently improve the prediction accuracy by order of magnitude compared to benchmark methods. Besides improved accuracy, we also observed that NODEs are less sensitive to hyperparameters compared to neural state-space models by paying the cost of increased computation at the inference time.

machine leaning, system identification, physics in↗

HIRM v1.0: a hybrid impulse response model for climate modeling and uncertainty analyses

Simple climate models (SCMs) are frequently used in research and decision-making communities because of their flexibility, tractability, and low computational cost. SCMs can be idealized, flexibly representing major climate dynamics as impulse response functions, or process-based, using explicit equations to model possibly nonlinear climate and Earth system dynamics. Each of these approaches has strengths and limitations. Here we present and test a hybrid impulse response modeling framework (HIRM) that combines the strengths of process-based SCMs in an idealized impulse response model, with HIRM's input derived from the output of a process-based model. This structure enables the model to capture some of the major nonlinear dynamics that occur in complex climate models as greenhouse gas emissions transform to atmospheric concentration to radiative forcing to climate change. As a test, the HIRM framework was configured to emulate the total temperature of the simple climate model Hector 2.0 under the four Representative Concentration Pathways and the temperature response of an abrupt 4 times CO 2 concentration step. HIRM was able to reproduce near-term and long-term Hector global temperature with a high degree of fidelity. Additionally, we conducted two case studies to demonstrate potential applications for this hybrid model: examining the effect of aerosol forcing uncertainty on global temperature and incorporating more process-based representations of black carbon into a SCM. The open-source HIRM framework has a range of applications including complex climate model emulation, uncertainty analyses of radiative forcing, attribution studies, and climate model development.

54 ENVIRONMENTAL SCIENCES↗

REDUCE 2: A computer program for the symbolic reduction of large block diagrams

REDUCE 2 is reported as a FORMAC program which symbolically calculates the transfer function(s) of any linear-block-diagram output variable to any or all input variables. The program requires as input a set of algebraic expressions representing the block diagram, the desired transfer function(s), and a string of variables indicating the desired order of reduction. The solution is presented in the compact form of a set of nested functions (super G's). The program can handle systems as large as 600 equations and is intended as a tool for the analysis of complex control and dynamic systems. A companion FORTRAN program, EVAL 2, which numerically evaluates the solution set to obtain amplitude ratio and phase angle as functions of frequency is also presented.

Lorenzo, C. F.↗

Applications of NASTRAN in Gust Response Analysis at Northrop

A comprehensive gust response analysis was performed on a complete model of an airplane using the NASTRAN aeroelastic package. The analysis investigated random response to atmospheric turbulence and transient response to a discrete gust, including control system dynamics in both cases. It is shown that NASTRAN is an effective tool for aeroelastic analysis and active control system design.

Singh, A. K.↗

A new method of boundary parameter estimation for a two-dimensional diffusion system under noisy observations

The purpose of this paper is to establish a method for identifying unknown parameters involved in the boundary state of a class of diffusion systems under noisy observations. A mathematical model of the system dynamics is given by a two-dimensional diffusion equation. Noisy observations are made by sensors allocated on the system boundary. Starting with the mathematical model mentioned above, an online parameter estimation algorithm is proposed within the framework of the maximum likelihood estimation. Existence of the optimal solution and related necessary conditions are discussed. By solving a local variation of the cost functional with respect to the perturbation of parameters, the estimation mechanism is proposed in a form of recursive computations. Finally, the feasibility of the estimator proposed here is demonstrated through results of digital simulation experiments.

Sunahara, Y.↗

A method of boundary parameter estimation for a two-dimensional diffusion system under noisy observations

The purpose of this paper is to establish a method for identifying unknown parameters involved in the boundary state of a class of diffusion systems under noisy observations. A mathematical model of the system dynamics is given by a two-dimensional diffusion equation. Noisy observations are made by sensors allocated on the system boundary. Starting with the mathematical model mentioned above, an online parameter estimation algorithm is proposed within the framework of the maximum likelihood estimation. Existence of the optimal solution and related necessary conditions are discussed. By solving a local variation of the cost functional with respect to the perturbation of parameters, the estimation mechanism is proposed in a form of recursive computations. Finally, the feasibility of the estimator proposed here is demonstrated through results of digital simulation experiments.

Sunahara, Y.↗

Postinstability Models in Dynamics

This paper is devoted to the concept of instability in dynamical systems with the main emphasis on orbital, Hadamard, and Reynolds instabilities. It demonstrates that the requirement about differentiability in dynamics in some cases is not consistent with the physical nature of motions, and may lead to unrealistic solutions. Special attention is paid to the fact that instability is not an invariant of motion: it depends upon frames of reference, the metric of configuration space, and classes of functions selected for mathematical models of physical phenomena. This leads to the possibility of elimination of certain types of instabilities (in particular, those which lead to chaos and turbulence) by enlarging the class of functions using the Reynolds-type transformation in combination with the stabilization principle: the additional terms (the so-called Reynolds stresses) are found from the conditions that they suppress the original instability. Based upon these ideas, a new approach to chaos and turbulence as well as a new mathematical formalism for nonlinear dynamics are discussed.

Zak, Michail↗

System Identification and POD Method Applied to Unsteady Aerodynamics

The representation of unsteady aerodynamic flow fields in terms of global aerodynamic modes has proven to be a useful method for reducing the size of the aerodynamic model over those representations that use local variables at discrete grid points in the flow field. Eigenmodes and Proper Orthogonal Decomposition (POD) modes have been used for this purpose with good effect. This suggests that system identification models may also be used to represent the aerodynamic flow field. Implicit in the use of a systems identification technique is the notion that a relative small state space model can be useful in describing a dynamical system. The POD model is first used to show that indeed a reduced order model can be obtained from a much larger numerical aerodynamical model (the vortex lattice method is used for illustrative purposes) and the results from the POD and the system identification methods are then compared. For the example considered, the two methods are shown to give comparable results in terms of accuracy and reduced model size. The advantages and limitations of each approach are briefly discussed. Both appear promising and complementary in their characteristics.

Tang, Deman↗

A robust model predictive control algorithm for uncertain nonlinear systems that guarantees resolvability

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees resolvability. With resolvability, initial feasibility of the finite-horizon optimal control problem implies future feasibility in a receding-horizon framework. The control consists of two components; (i) feed-forward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives and derivatives in polytopes. An illustrative numerical example is also provided.

feed - forward↗

Small Body GN&C Research Report: A Robust Model Predictive Control Algorithm with Guaranteed Resolvability

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees the resolvability of the associated finite-horizon optimal control problem in a receding-horizon implementation. The control consists of two components; (i) feedforward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives, and derivatives in polytopes. An illustrative numerical example is also provided.

model predictive control algorithm (MPC)↗

The formulation of simulation models of aeronautical systems

Recent developments in formula-manipulation compilers have led to a significant reduction in the time spent in formulating models of complex multi-degrees-of-freedom dynamical systems. MACSYMA, a computer system that can be used to perform symbolic manipulations in an interactive mode, is applied to the problem of formulating models of aeronautical systems for simulation studies. An example demonstrates that once the procedure is established, the formulation and modification of the models can be reduced to a series of routine computer operations.

Howard, J. C.↗

Research developing closed loop roll control for magnetic balance systems

Computer inputs were interfaced to the magnetic balance outputs to provide computer position control and data acquisition. The use of parameter identification of a means of determining dynamic characteristics was investigated. The thyraton and motor generator power supplies for the pitch and yaw degrees of freedom were repaired. Topics covered include: choice of a method for handling dynamic system data; applications to the magnetic balance; the computer interface; and wind tunnel tests, results, and error analysis.

Covert, E. E.↗