SEARCH · Engineering Papers

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18

All sources NASA NTRS DOE OSTI

NASA NTRS1991

Nonlinear dynamics of global atmospheric and Earth-system processes

General Circulation Model (GCM) studies of the atmospheric response to change boundary conditions are discussed. Results are reported on an extensive series of numerical studies based on the National Center for Atmospheric Research (NCAR) Community Climate Model (CCM) general circulation model. In these studies the authors determined the response to systematic changes in atmospheric CO2 ranging from 100 to 1000 ppm; to changes in the prescribed sea surface temperature (SST) in the Gulf of Mexico, such as occurred during the deglaciation phase of the last ice age; to changes in soil moisture over North America; and to changes in sea ice extent in the Southern Hemisphere. Study results show that the response of surface temperature and other variables is nearly logarithmic, with lower levels of CO2 implying greater sensitivity of the atmospheric state to changes in CO2. It was found that the surface temperature of the Gulf of Mexico exerts considerable control over the storm track and behavior of storm systems over the North Atlantic through its influence on evaporation and the source of latent heat. It was found that reductions in soil moisture can play a significant role in amplifying and maintaining North American drought, particularly when a negative soil moisture anomaly prevails late in the spring.

Saltzman, Barry↗

DOE OSTI2023

Multi-level optimization with the koopman operator for data-driven, domain-aware, and dynamic system security

Cyber-Physical Systems (CPSs) like the power grid are critically important but also increasingly vulnerable; ensuring reliable system operation in the face of disruptions is becoming more and more challenging. Multi-Level Optimization (MLO) is a powerful way to model adversarial interactions, which naturally makes it applicable to studying CPS security. However, MLO typically does not address underlying system dynamics, and incorporating nonlinear dynamics is generally infeasible. In this paper, we show how to combine MLO with the Koopman Operator (KO) to remedy this. The KO maps nonlinear dynamics to a lifted space in which those dynamics are linear, thus making it ideal for use with MLO. Moreover, the structure of the KO also provides convenient ways to incorporate domain knowledge into the data-driven process of learning the KO representation of a given system. Here we then demonstrate the use of MLO-KO on a small example problem taken from the power grid domain, discuss the scalability and computational cost of MLO-KO, and identify future research directions for this work.

42 ENGINEERING↗

NASA NTRS2016

Active Control of Solar Array Dynamics During Spacecraft Maneuvers

Recent NASA mission plans require spacecraft to undergo potentially significant maneuvers (or dynamic loading events) with large solar arrays deployed. Therefore there is an increased need to understand and possibly control the nonlinear dynamics in the spacecraft system during such maneuvers. The development of a nonlinear controller is described. The utility of using a nonlinear controller to reduce forces and motion in a solar array wing during a loading event is demonstrated. The result is dramatic reductions in system forces and motion during a 10 second loading event. A motion curve derived from the simulation with the closed loop controller is used to obtain similar benefits with a simpler motion control approach.

nonlinear controls↗

DOE OSTI2020

Probability Density Function Control for Stochastic Nonlinear Systems using Monte Carlo Simulation

This paper presents a fast implementation framework of output probability density function (PDF) control for a class of stochastic nonlinear systems which are subjected to non-Gaussian noises. The statistical properties of the system outputs can be adjusted by shaping the dynamic output probability density function to track the reference stochastic distribution. However, the dynamic probability density function evolution is very difficult to obtain analytically even if the system model and the stochastic distributions of the noises are known. Motivated by Monte Carlo simulation, the dynamic probability density function can be estimated by sampling data which forms the contribution of this paper. In particular, the sampling points are generated following the stochastic distribution of the noise for each instant. These points go through the system would generate the histogram for system outputs, then the dynamic model can be established based on the dynamic histogram which reflects the randomness and the nonlinear dynamics of the investigated system. Based on the established model, the output probability density function tracking can be achieved and the simulation results and discussions show the effectiveness and benefits of the presented framework.

Zhang, Qichun↗

NASA NTRS1999

Wavelet Applications for Flight Flutter Testing

Wavelets present a method for signal processing that may be useful for analyzing responses of dynamical systems. This paper describes several wavelet-based tools that have been developed to improve the efficiency of flight flutter testing. One of the tools uses correlation filtering to identify properties of several modes throughout a flight test for envelope expansion. Another tool uses features in time-frequency representations of responses to characterize nonlinearities in the system dynamics. A third tool uses modulus and phase information from a wavelet transform to estimate modal parameters that can be used to update a linear model and reduce conservatism in robust stability margins.

Lind, Rick↗

NASA NTRS1999

Wavelet Applications for Flight Flutter Testing

Lind, Rick↗

NASA NTRS2010

Success Stories in Control: Nonlinear Dynamic Inversion Control

NASA plays an important role in advancing the state of the art in flight control systems. In the case of Nonlinear Dynamic Inversion (NDI) NASA supported initial implementation of the theory in an aircraft and demonstration in a space vehicle. Dr. Dale Enns of Honeywell Aerospace Advanced Technology performed this work in cooperation with NASA and under NASA contract. Honeywell and Lockheed Martin were subsequently contracted by AFRL to create "Design Guidelines for Multivariable Control Theory". This foundational work directly contributed to the advancement of the technology and the credibility of the control law as a design option. As a result Honeywell collaborated with Lockheed Martin to produce a Nonlinear Dynamic Inversion controller for the X-35 and subsequently Lockheed Martin did the same for the production Lockheed Martin F-35 vehicle. The theory behind NDI is to use a systematic generalized approach to controlling a vehicle. Using general aircraft nonlinear equations of motion and onboard aerodynamic, mass properties, and engine models specific to the vehicle, a relationship between control effectors and desired aircraft motion can be formulated. Using this formulation a control combination is used that provides a predictable response to commanded motion. Control loops around this formulation shape the response as desired and provide robustness to modeling errors. Once the control law is designed it can be used on a similar class of vehicle with only an update to the vehicle specific onboard models.

Bosworth, John T.↗

NASA NTRS2001

Nonlinear Dynamics of a Diffusing Interface

Excitation of two miscible-viscous liquids inside a bounded enclosure in a microgravity environment has shown the evolution of quasi-stationary waves of various modes for a range of parameters. We examine computationally the nonlinear dynamics of the system as the interface breakup and bifurcates to resonance structures typified by the Rayleigh-Taylor instability mechanism. Results show that when the mean steady field is much smaller than the amplitude of the sinusoidal excitation, the system behaves linearly, and growth of quasi-stationary waves occurs through the Kelvin-Helmholtz instability mechanism. However, as the amplitude of excitation increases, nonlinearity occurs through subharmonic bifurcation prior to broadband chaos.

Duval, Walter M. B.↗

NASA NTRS1985

A methodology for designing robust multivariable nonlinear feedback control systems

This paper presents an outline of a methodology for the design of nonlinear dynamic compensators for nonlinear multivariable systems with guarantees of closed-loop stability, robustness, and performance. The method is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate nonlinear inverse operator for the plant. A major feature of the method is a unification of both the state-space and Input-Output formulations. The major results of the paper are: (1) Properties of the solution of certain optimal control problems; (2) New results on nonlinear estimation, including a new nonlinear observer with certain guaranteed properties; (3) The Loop Operator Recovery (LOR) procedure, and (4) Inclusion of command-following and disturbance rejection with a goal of a closed-loop stable, robust system.

Grunberg, D. B.↗

DOE OSTI2024

Practical and Optimal Sequential Bayesian Experimental Design for Complex Systems Incorporating Human Experimenter Preferences (Final Scientific/Technical Report)

Experiments are indispensable for developing models of complex systems. Carefully designed experiments can provide substantial savings for these expensive data-acquisition opportunities. However, designs based on heuristics are often suboptimal for systems with multiphysics, nonlinear dynamics, and uncertain and noisy environments. Optimal experimental design, while leveraging predictive models, seeks to systematically quantify and maximize the value of experiments. In this project, we focused on the design of multiple experiments, where current approaches are largely suboptimal: batch-design does not adapt to new data acquired during the experiment campaign (no feedback), and greedy/myopic design ignores future dynamics and consequences (no lookahead). We developed the mathematical framework and computational methods for sequential optimal experimental design (sOED) for complex systems. We enabled tractable model-based sOED in a rigorous manner through novel algorithms based on reinforcement learning, and investigated the effects of human experimenters on the design process. Our methods are fully Bayesian, able to quantify and update uncertainty in a principled manner. The traits aimed by our approach—mathematical rigor and optimality, human effects and uncertainty quantification, computational practicality—are crucial for elevating the standards of artificial intelligence (AI) to support decision-making in scientific domains, and contribute toward trust and realistic adoption of AI in experimental design practice.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Control Design for a Marine Hydrokinetic Cycloturbine Vehicle

Abstract Marine Hydrokinetic (MHK) cycloturbines generate sustainable power by exploiting tidal currents. By powering the turbines and using pitching foils for control, a vehicle comprised of MHK cycloturbines also has the ability to station keep and maneuver. The vehicle consists of four counter-rotating cycloturbines, with hydrofoils oriented perpendicular to the flow in a paddlewheel configuration. Lift and drag generated from these foils sum together to produce thrust. An experimentally tuned simulation model that solves the six-degrees-of-freedom rigid body equations of motion for the MHK vehicle subject to hydrodynamic, hydrostatic, and propulsive forces is used to aid the design of vehicle controllers. Global feedback controllers are initially designed by applying classical control methods to an approximate linear model of the system dynamics. A higher performing nonlinear controller is designed using the nonlinear dynamic inversion (NDI) method. NDI accounts for the nonlinearities of the MHK system and therefore is suitable for a wide range of operating conditions. The response of the classical and NDI controllers to speed, depth, roll, pitch, and yaw commands are evaluated and compared in simulation. The classical controller outperforms the NDI controller for small amplitude maneuvers, although the degradation with NDI is minor. However, in the nonlinear operating regime the NDI controller outperforms the classical controller and the classical controller exhibits instability.

Automation & Control Systems↗

DOE OSTI2020

Data-Driven Approach for Uncertainty Propagation and Reachability Analysis in Dynamical Systems

In this paper, we propose a data-driven approach for uncertainty propagation and reachability analysis in a dynamical system. The proposed approach relies on the linear lifting of a nonlinear system using linear Perron-Frobenius (P-F) and Koopman operators. Here, the uncertainty can be characterized in terms of the moments of a probability density function. We demonstrate how the P-F and Koopman operators are used for propagating the moments. Time-series data is used for the finite-dimensional approximation of the linear operators, thereby enabling data-driven approach for moment propagation. Simulation results are presented to demonstrate the effectiveness of the proposed method.

42 ENGINEERING↗

NASA NTRS1975

Stochastic control system parameter identifiability

The parameter identification problem of general discrete time, nonlinear, multiple input/multiple output dynamic systems with Gaussian white distributed measurement errors is considered. The knowledge of the system parameterization was assumed to be known. Concepts of local parameter identifiability and local constrained maximum likelihood parameter identifiability were established. A set of sufficient conditions for the existence of a region of parameter identifiability was derived. A computation procedure employing interval arithmetic was provided for finding the regions of parameter identifiability. If the vector of the true parameters is locally constrained maximum likelihood (CML) identifiable, then with probability one, the vector of true parameters is a unique maximal point of the maximum likelihood function in the region of parameter identifiability and the constrained maximum likelihood estimation sequence will converge to the vector of true parameters.

Lee, C. H.↗

NASA NTRS2021

A Learn-to-Fly Approach for Adaptively Tuning Flight Control Systems

A method is presented for adaptively tuning feedback control gains in a flight control system to achieve desired closed-loop performance. The method combines efficient aircraft parameter estimation, for identifying closed-loop dynamics models, with online nonlinear optimization, for sequentially perturbing and updating control gains to improve performance. Access to flight measurements and the control gains is required, but no prior information about the aircraft dynamics or the flight control architecture is needed. After the procedure, the optimized control gains (with uncertainties), the open-loop dynamics model, and the closed-loop dynamics model are available. The method is demonstrated for tuning a longitudinal stability augmentation system using a realistic nonlinear flight dynamics simulation of a subscale airplane. Convergence was attained using five maneuvers that spanned approximately one minute of flight test time. Although shown for a relatively simple case, the method is general and can be applied to other aircraft, axes of motion, performance metrics, and control system designs.

Adaptive tuning↗

NASA NTRS1991

A hierarchy for modeling high speed propulsion systems

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery, such as inlets, ramjets, and scramjets. The discussion is separated into four areas: (1) computational fluid dynamics models for the entire nonlinear system or high order nonlinear models; (2) high order linearized models derived from fundamental physics; (3) low order linear models obtained from the other high order models; and (4) low order nonlinear models (order here refers to the number of dynamic states). Included in the discussion are any special considerations based on the relevant control system designs. The methods discussed are for the quasi-one-dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, including moving normal shocks, hammershocks, simple subsonic combustion via heat addition, temperature dependent gases, detonations, and thermal choking. The report also contains a comprehensive list of papers and theses generated by this grant.

Hartley, Tom T.↗

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 NTRS1994

Nonlinear structural response using adaptive dynamic relaxation on a massively-parallel-processing system

A parallel adaptive dynamic relaxation (ADR) algorithm has been developed for nonlinear structural analysis. This algorithm has minimal memory requirements, is easily parallelizable and scalable to many processors, and is generally very reliable and efficient for highly nonlinear problems. Performance evaluations on single-processor computers have shown that the ADR algorithm is reliable and highly vectorizable, and that it is competitive with direct solution methods for the highly nonlinear problems considered. The present algorithm is implemented on the 512-processor Intel Touchstone DELTA system at Caltech, and it is designed to minimize the extent and frequency of interprocessor communication. The algorithm has been used to solve for the nonlinear static response of two and three dimensional hyperelastic systems involving contact. Impressive relative speedups have been achieved and demonstrate the high scalability of the ADR algorithm. For the class of problems addressed, the ADR algorithm represents a very promising approach for parallel-vector processing.

Oakley, David R.↗

NASA NTRS1992

Driven and unloading aspects of magnetospheric substorms

Issues concerning the 'driven' versus 'unloading' nature of substorms are presented. The original concepts attendant to this debate are presented and substorms are concluded to inextricably combine aspects that are driven with aspects that represent a loading-unloading system. For isolated substorms, the magnetosphere-ionosphere system is shown to exhibit a bimodal response to solar wind changes. A 20 min response characteristic is associated with the driven aspect of substorms, while a 1 hr response time is associated with unloading. It is found that for strong solar wind input conditions, the magnetospheric response becomes more nearly unimodal. This is interpreted in terms of a nonlinear dynamical evolution of the system. Simple analog models are described which capture the essence of the nonlinear magnetospheric behavior. These models exhibit chaotic transitions for strong driving conditions: this may explain the observed behavior of the magnetosphere during strong geomagnetic activity.

Baker, D. N.↗