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Results for “nonlinear dynamical system”

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 145 records · Page 8

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NASA NTRS1989

A general dynamic model of flexible robot arms for control

Hamilton's principle is used to derive the dynamic model for a large class of flexible robot arms. The resultant dynamic model consists of a system of partial differential-integral equations and the dynamic boundary conditions associated with it. Some properties of the model are observed, and its application to control is discussed. This model represents an infinite-dimensional nonlinear dynamic system and yet can be turned into a finite-dimensional system that could be obtained by modal expansion, if it is desired. This provides more flexibility for control purposes as well as for the analysis of the system.

Ding, X.↗

NASA NTRS1987

High gain feedback and telerobotic tracking

Asymptotically stable linear time invariant systems are capable of tracking arbitrary reference signals with a bounded error proportional to the magnitude of the reference signal (and its derivatives). It is shown that a similar property holds for a general class of nonlinear dynamical systems which includes all robots. As in the linear case, the error bound may be made arbitrarily small by increasing the magnitude of the feedback gains which stabilize the system.

Koditschek, D. E.↗

DOE OSTI2026

A Data-Driven Method for Modeling Creep-Fatigue Stress- Strain Behavior Using Neural ODEs

In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke’s Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model’s accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form.

creep-fatigue↗

NASA NTRS1991

Parameter estimation in space systems using recurrent neural networks

The identification of time-varying parameters encountered in space systems is addressed, using artificial neural systems. A hybrid feedforward/feedback neural network, namely a recurrent multilayer perception, is used as the model structure in the nonlinear system identification. The feedforward portion of the network architecture provides its well-known interpolation property, while through recurrency and cross-talk, the local information feedback enables representation of temporal variations in the system nonlinearities. The standard back-propagation-learning algorithm is modified and it is used for both the off-line and on-line supervised training of the proposed hybrid network. The performance of recurrent multilayer perceptron networks in identifying parameters of nonlinear dynamic systems is investigated by estimating the mass properties of a representative large spacecraft. The changes in the spacecraft inertia are predicted using a trained neural network, during two configurations corresponding to the early and late stages of the spacecraft on-orbit assembly sequence. The proposed on-line mass properties estimation capability offers encouraging results, though, further research is warranted for training and testing the predictive capabilities of these networks beyond nominal spacecraft operations.

Parlos, Alexander G.↗

NASA NTRS2008

Variable-Structure Control of a Model Glider Airplane

A variable-structure control system designed to enable a fuselage-heavy airplane to recover from spin has been demonstrated in a hand-launched, instrumented model glider airplane. Variable-structure control is a high-speed switching feedback control technique that has been developed for control of nonlinear dynamic systems.

Waszak, Martin R.↗

NASA NTRS2007

Development of a Linear Stirling System Model with Varying Heat Inputs

The linear model of the Stirling system developed by NASA Glenn Research Center (GRC) has been extended to include a user-specified heat input. Previously developed linear models were limited to the Stirling convertor and electrical load. They represented the thermodynamic cycle with pressure factors that remained constant. The numerical values of the pressure factors were generated by linearizing GRC's nonlinear System Dynamic Model (SDM) of the convertor at a chosen operating point. The pressure factors were fixed for that operating point, thus, the model lost accuracy if a transition to a different operating point were simulated. Although the previous linear model was used in developing controllers that manipulated current, voltage, and piston position, it could not be used in the development of control algorithms that regulated hot-end temperature. This basic model was extended to include the thermal dynamics associated with a hot-end temperature that varies over time in response to external changes as well as to changes in the Stirling cycle. The linear model described herein includes not only dynamics of the piston, displacer, gas, and electrical circuit, but also the transient effects of the heater head thermal inertia. The linear version algebraically couples two separate linear dynamic models, one model of the Stirling convertor and one model of the thermal system, through the pressure factors. The thermal system model includes heat flow of heat transfer fluid, insulation loss, and temperature drops from the heat source to the Stirling convertor expansion space. The linear model was compared to a nonlinear model, and performance was very similar. The resulting linear model can be implemented in a variety of computing environments, and is suitable for analysis with classical and state space controls analysis techniques.

Regan, Timothy F.↗

NASA NTRS2001

Panel Flutter and Sonic Fatigue Analysis for RLV

A methodology is presented for the flutter analysis of the seal of thermal protection system (TPS) panel of X-33 Advanced Technology Demonstrator test vehicle. The seal is simulated as a two-dimensional cantilevered panel with an elastic stopper, which is modeled as an equivalent spring. This cantilever beam-spring model under the aerodynamic pressure at supersonic speeds turns out to be an impact nonlinear dynamic system. The flutter analysis of the seal is thus carried out using, time domain numerical simulation with a displacement stability criterion. The flutter boundary of the seal is further verified with a family of three traditional and one nontraditional panel flutter models. The frequency domain method that applies eigenanalysis on the traditional panel flutter problem was used. The results showed that the critical dynamic pressure could be more than doubled with properly chosen material for the base stopper. The proposed methodology can be easily extended to three-dimensional panel seals with flow angularity.

Mei, Chuh↗

NASA NTRS1981

Alternatives for jet engine control

Research centered on basic topics in the modeling and feedback control of nonlinear dynamical systems is reported. Of special interest were the following topics: (1) the role of series descriptions, especially insofar as they relate to questions of scheduling, in the control of gas turbine engines; (2) the use of algebraic tensor theory as a technique for parameterizing such descriptions; (3) the relationship between tensor methodology and other parts of the nonlinear literature; (4) the improvement of interactive methods for parameter selection within a tensor viewpoint; and (5) study of feedback gain representation as a counterpart to these modeling and parameterization ideas.

Sain, M. K.↗

NASA NTRS2000

Detection of Extraterrestrial Ecology (Exoecology)

Researchers in the Astrobiology Technology Branch at Ames Research Center have begun investigating alternate concepts for the detection of extraterrestrial life. We suggest searching for extraterrestrial ecology, exoecology, as well as for extraterrestrial biology, exobiology. Ecology describes the interactions of living things with their environment. All ecosystems are highly constrained by their environment and are constrained by well-known system design principles. Ecology could exist wherever there is an energy source and living I things have discovered some means to capture, store, and use the available energy. Terrestrial ecosystems use as energy sources, light, organic molecules, and in thermal vents and elsewhere, simple inorganic molecules. Ecosystem behavior is controlled by matter and energy conservation laws and can be described by linear and nonlinear dynamic systems theory. Typically in an ecosystem different molecules are not in chemical equilibrium and scarce material is conserved, stored, or recycled. Temporal cycles and spatial variations are often observed. These and other -eneral principles of exoecology can help guide the search for extraterrestrial life. The chemical structure observed in terrestrial biology may be highly contingent on evolutionary accidents. Oxygen was not always abundant on Earth. Primitive sulfur bacteria use hydrogen sulfide and sulfur to perform photosynthesis instead of water and oxygen. Astrobiologists have assumed, for the sake of narrowing and focusing our life detection strategies, that extraterrestrial life will have detailed chemical similarities with terrestrial life. Such assumptions appear very reasonable and they allow us to design specific and highly sensitive life detection experiments. But the fewer assumptions we make, the less chance we have of being entirely wrong The best strategy for the detection of extraterrestrial life could be a mixed strategy. We should use detailed assumptions based on terrestrial biology to guide some but not all future searches for alien life. The systems principles of exoecology seem much more fundamental and inescapable than the terrestrial biology analogies of exobiology. We should search for exoecology as well as exobiology.

Jones, Harry↗

DOE OSTI2026

Semi-Analytical Hierarchical Bayesian Inference of Nonlinear Model Structure in Stochastic Dynamics: Applied to Compartmental Models of Infectious Diseases

A Bayesian computational framework for parsimonious inference in stochastic nonlinear dynamical systems is presented. This framework enables the concurrent estimation of system states, time-varying parameters, time-invariant parameters, and the optimal sparsity structure of the model parameters. Because differential equation-based models are often simplified mechanistic or phenomenological representations, robust inference from noisy measurement data requires explicit treatment of model error and uncertainty. Model error and time-varying parameters can be represented as random processes, enabling inference while making minimal assumptions about the underlying sources of discrepancy and variability. Adopting stochastic differential equation representations affords the model significant flexibility, but can also render it susceptible to overfitting during statistical inversion, where the inferred model may track noise rather than the underlying signal. To alleviate the effects of overfitting and to enable the discovery of the optimal sparse representation of the time-invariant parameters, a Bayesian sparse learning algorithm is embedded within the framework. This sparse learning framework adopts an approximate hierarchical Bayesian setting defined by a series of semi-analytical expressions. The model structure inference framework is validated using a stochastic compartmental model for tracking and forecasting active cases of an infectious disease. Compartmental models describe population-level infectious disease dynamics through interactions among population fractions grouped by disease state. Mathematically, such models consist of a system of coupled ordinary differential equations. This example adopts an expressive compartmental model that includes multiple possible interactions between disease states, motivated by early uncertainty surrounding COVID-19 reinfection dynamics and their implications for long-term epidemic forecasting. The sparse learning exercise permits the inference of a priori unknown epidemiological dynamics from simulated public health data, discovering the nested compartmental model that optimizes the trade-off between average data-fit and model complexity. It is shown that inducing sparsity among the model parameters eliminates redundant interactions between compartments, equivalently revealing the optimal coupling structure between differential equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Encoding nonlinear and unsteady aerodynamics of limit cycle oscillations using nonlinear sparse Bayesian learning

This article investigates the applicability of a recently proposed, nonlinear sparse Bayesian learning (NSBL) algorithm to identify and estimate the complex aerodynamics of limit cycle oscillations. NSBL provides a semi-analytical framework for determining the data-optimal sparse model nested within a (potentially) over-parameterized model. This is particularly relevant to nonlinear dynamical systems where modelling approaches involve the use of physics-based and data-driven components. In such cases, the data-driven components, where analytical descriptions of the physical processes are not readily available, are often prone to overfitting, meaning that the empirical aspects of these models will often involve the calibration of an unnecessarily large number of parameters. While an overparameterized model may fit the observed data well, such models may be inadequate for making predictions in regimes that are different from those wherein the data were recorded. In view of this, it is desirable to not only calibrate the model parameters, but also identify the optimal compromise between data fit and model complexity. In this article, we exhibit the optimal model discovery for an aeroelastic system wherein the structural dynamics are well-known and described by a differential equation model, coupled with a semi-empirical aerodynamic model for laminar separation flutter, resulting in low-amplitude limit cycle oscillations (LCO). To illustrate the performance of the algorithm, in this article, we use synthetic data and demonstrate the ability of the algorithm to correctly rediscover the optimal model and model parameters, given a known data-generating model. The synthetic data are generated from a forward simulation of a known differential equation model with parameters selected so as to mimic the dynamics observed in wind-tunnel experiments. Subsequently, we demonstrate the performance of the algorithm for model selection using noisy LCO data from wind tunnel experiments. As there is no ground truth available for the experimental data case, we provide a comparison between NSBL and Bayesian model selection to validate the results, and demonstrate the use of NSBL as an efficient alternative to traditional methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

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↗

DOE OSTI2021

A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physics-informed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers' equations. A speedup of up to 2.6 for 1D Burgers' and a speedup of 11.7 for 2D Burgers' equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique. Lastly, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation

Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a low-dimensional emulation framework for systems that may be intrinsically high-dimensional. This is accomplished by utilizing a construction algorithm that is purely data-driven. It is no surprise, therefore, that the algorithmic advances of machine learning have led to non-intrusive ROMs with greater accuracy and computational gains. However, in bypassing the utilization of an equation-based evolution, it is often seen that the interpretability of the ROM framework suffers. This becomes more problematic when black-box deep learning methods are used which are notorious for lacking robustness outside the physical regime of the observed data. In this article, we propose the use of a novel latent-space interpolation algorithm based on Gaussian process regression. Notably, this reduced-order evolution of the system is parameterized by control parameters to allow for interpolation in space. The use of this procedure also allows for a continuous interpretation of time which allows for temporal interpolation. The latter aspect provides information, with quantified uncertainty, about full-state evolution at a finer resolution than that utilized for training the ROMs. This research assesses the viability of this algorithm for an advection-dominated system given by the inviscid shallow water equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Posterior comparison of model dynamics in several hybrid turbulence model forms

Hybrid turbulence models that can accurately reproduce unsteady three-dimensional flow physics across the entire range of grid scales and turbulence dynamics from Reynolds-averaged Navier–Stokes (RANS), through large-eddy simulation (LES), down to direct numerical simulations (DNS) are of increasing interest to the turbulence modeling community. However, despite decades of research and development, the basic tasks of eliminating poor-performing hybrid RANS-LES models and accelerating adoption of superior models through well-designed validation and verification have yet to occur. As a step in this direction, in this work we evaluate thirteen different hybrid RANS-LES models via systematic grid refinement of decaying homogeneous isotropic turbulence. We further derive a novel mathematical framework for assessing the energy partitioning dynamics of each Hybrid RANS-LES model, wherein model-to-model variations in energy partitioning can be interpreted as different feedback mechanisms operating on a low-dimensional nonlinear dynamical system. We found that model forms similar to the flow simulation methodology—also often termed very-large eddy simulation—are dynamically inconsistent with DNS at all resolutions. Additionally, we found a strong dynamical similarity in the feedback mechanisms of all models related to detached eddy simulation and partially averaged Navier–Stokes that is inherent to their general model forms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Inference of neutrino flavor evolution through data assimilation and neural differential equations

The evolution of neutrino flavor in dense environments such as core-collapse supernovae and binary compact object mergers constitutes an important and unsolved problem. Its solution has potential implications for the dynamics and heavy-element nucleosynthesis in these environments. In this paper, we build upon recent work to explore inference-based techniques for the estimation of model parameters and neutrino flavor evolution histories. Here, we combine data assimilation, ordinary differential equation solvers, and neural networks to craft an inference approach tailored for nonlinear dynamical systems. Using this architecture, and a simple two-neutrino-beam, two-flavor model, we compare the performances of nine different optimization algorithms and expand upon previous assessments of the efficacy of inference for tackling problems in flavor evolution. We find that employing this new architecture, together with evolutionary optimization algorithms, accurately captures flavor histories in the small-scale model and allows us to quickly explore both model parameters and initial flavor content. In future work we plan to extend these inference techniques to large numbers of neutrinos.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Generation of arbitrary probability distributions from chaotic dynamics

A framework is developed to derive nonlinear dynamical systems that chaotically generate arbitrary multivariate probability distributions with smooth, deterministic trajectories. Herein, the ideas are used to extend the Nosé-Hoover thermostat methodology to three-dimensional cases where the momentum distribution is nonisotropic and/or non-Gaussian. Toy models that generate several well-known distributions in physics are given as pedagogical examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

A Model-Free Voltage Control Approach to Mitigate Motor Stalling and FIDVR for Smart Grids

Electric power networks are large and highly nonlinear dynamical systems that present unique challenges to control design. Though there is a large number of dynamic models for power system stability and control, many models are only useful with right assumptions and wrong for other tasks. Moreover, the dynamic behavior of the grid is increasingly complex under the banner of smart grids. These lead to the difficulty of developing appropriate dynamic modeling, and thus an efficient control strategy. To avoid such modeling challenges, here we present a novel dynamic voltage control strategy based on a model-free control (MFC) approach, requiring no modeling procedure. In particular, it focuses on fault-induced delayed voltage recovery (FIDVR) events, which require complex and accurate dynamic load models to replicate such events. This work utilizes MFC as an online controller to achieve the desired voltage stability under the FIDVR event. The proposed MFC strategy allows simple implementation and low computational cost for efficient mitigation of FIDVR. For benchmarking, a reasonably accurate dynamic performance model is explored. Simulation results with the IEEE 57 bus test network demonstrate the enhanced dynamic voltage profile for load buses having induction motors with the support of reactive power resources.

24 POWER TRANSMISSION AND DISTRIBUTION↗