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All sources NASA NTRS DOE OSTI

DOE OSTI2022

An improved framework for the dynamic likelihood filtering approach to data assimilation

Here, we propose improvements to the Dynamic Likelihood Filter (DLF), a Bayesian data assimilation filtering approach, specifically tailored to wave problems. The DLF approach was developed to address the common challenge in the application of data assimilation to hyperbolic problems in the geosciences and in engineering, where observation systems are sparse in space and time. When these observations have low uncertainties, as compared to model uncertainties, the DLF exploits the inherent nature of information and uncertainties to propagate along characteristics to produce estimates that are phase aware as well as amplitude aware, as would be the case in the traditional data assimilation approach. Along characteristics, the stochastic partial differential equations underlying the linear or nonlinear stochastic dynamics are differential equations. This study focuses on developing the explicit challenges of relating dynamics and uncertainties in the Eulerian and Lagrangian frames via dynamic Gaussian processes. It also implements the approach using the ensemble Kalman filter (EnKF) and compares the DLF approach to the conventional one with respect to wave amplitude and phase estimates in linear and nonlinear wave problems. Numerical comparisons show that the DLF/EnKF outperforms the EnKF estimates, when applied to linear and nonlinear wave problems. This advantage is particularly noticeable when sparse, low uncertainty observations are used.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Effective Action for Relativistic Hydrodynamics from the Crooks Fluctuation Theorem

A new effective theory framework for fluctuating hydrodynamics in the relativistic regime is derived using standard thermodynamical principles and general properties of nonequilibrium stochastic dynamics. For the first time, we establish clear and concise conditions for ensuring that the resulting effective theories are causal, stable, and well-posed within general relativity. Here, these properties are independent of spacetime foliation and are valid in the full nonlinear regime. Out-of-equilibrium fluctuations are constrained by a relativistically covariant version of the Crooks fluctuation theorem, which determines how the entropy production is distributed even when the system is driven by an external force. This leads to an emerging Z 2 symmetry responsible for imposing fluctuation-dissipation relations for n-point correlation functions, which matches the standard constraints for the Schwinger-Keldysh effective action.

Fluctuation theorems↗

NASA NTRS1997

Detection of "noisy" chaos in a time series

Time series from biological system often displays fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". The output from most biological systems is probably the result of both the internal dynamics of the systems, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

Non-NASA Center↗

DOE OSTI2025

Preserving nonlinear constraints in variational flow filtering data assimilation

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems of interest obey nonlinear physical constraints, and the corresponding dynamics is confined to a certain sub-manifold of the state space. Standard data assimilation techniques applied to such systems yield posterior states lying outside the manifold, violating the physical constraints. This work focuses on particle flow filters which use stochastic differential equations to evolve state samples from a prior distribution to samples from an observation-informed posterior distribution. The variational Fokker-Planck (VFP)—a generic particle flow filtering framework—is extended to incorporate non-linear, equality state constraints in the analysis. To this end, two algorithmic approaches that modify the VFP stochastic differential equation are discussed: (i) VFPSTAB, to inexactly preserve constraints with the addition of a stabilizing drift term, and (ii) VFPDAE, to exactly preserve constraints by treating the VFP dynamics as a stochastic differential-algebraic equation (SDAE). Additionally, an implicit-explicit time integrator is developed to evolve the VFPDAE dynamics. The strength of the proposed approach for constraint preservation in data assimilation is demonstrated on three test problems: the double pendulum, Korteweg-de-Vries, and the incompressible Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

Computational technology for flight vehicles; Proceedings of the Symposium, Washington, DC, Nov. 5-7, 1990

Recent advances in computational fluid mechanics are discussed in reviews and reports. Sections are devoted to (1) the modeling of local phenomena and edge effects in solids, (2) stochastic modeling and simulation of fracture toughness, and (3) partitioning strategy and new finite elements. Particular attention is given to global and local finite-element/spectral-boundary-element techniques for failure analysis, simulations of microfracture in metal-matrix composites, fatigue analysis of cracked anisotropic plates under stochastic loading, mathematical modeling for the analysis of nonlinear aircraft dynamics, physical and mathematical modeling of wave propagation in the Ariane 5 VEB structure, partitioning based on symmetry transformations, an FEM approach to adaptive reliability assurance, and time-domain FEMs for the large rotational dynamics of multibody systems.

Noor, Ahmed K.↗

NASA NTRS1996

Expendable Launch Vehicle Studies

Analytical support studies of expendable launch vehicles concentrates on the stability of the dynamics during launch especially during or near the region of maximum dynamic pressure. The in-plane linearized dynamic equations of a generic launch vehicle with multiple flexible bending and fuel sloshing modes are developed. The design of a robust LQR controller based on the reduced order system is accomplished using the parameter perturbation technique. The ELV modeling and analysis team has spent the past three years working on the theoretical development and application of sensitivity analysis to solve eigenvalue problems associated with structural dynamics. Specific application areas include stochastic vibrations, viscously damped vibrations and nonlinear dynamics. In stochastic linear vibrations, sensitivity analysis methods have been developed which determined the expectation and variance of the response for given probability density functions of various stochastic parameters. Examples worked include beam vibrations with up to six stochastic parameters; and the eigensensitivity results differ little from those obtained, with much effect, from Monte Carlo techniques. For viscously damped vibrations, eigensensitivity analysis has given excellent results for homogeneous beams, modeled by either quadratic or quartic eigenvalue equations. Specific applications include Kevin and Maxwell-type viscoelastic beams.

Bainum, P. M.↗

DOE OSTI2023

Dynamics of coupled thermoacoustic modes: Noise and frequency spacing effects

Practical combustion systems consist of multiple thermoacoustic modes that are linearly stable or unstable at a wide range of frequencies. When coupled, the modal interactions are a strong function of the frequency spacing between them – having very significant implications on interpretation of linear stability or instability of modes from experimental data. Frequency spacing between the modes particularly influences the stability and existence of potential limit cycle solutions. In this paper, we extend earlier deterministic studies to include the effects of noise, studying how deterministic dynamics change with the addition of noise and the simultaneous impact of frequency spacing (i.e., closely, or widely spaced). Specifically, this paper characterizes three key effects of noise, which are (1) distribution of limit cycle amplitudes (“diffusion”), (2) shift in the average limit cycle amplitudes (“noise induced drift”), and (3) introduction of new bifurcations that are not present in the deterministic system. Key conclusions from this work are that in highly noisy practical environments, a deterministic/ low noise analysis will not be sufficient to explain even critical qualitative features of the system – such as existence of stable limit cycles or their amplitudes. Furthermore, the nature of noise-induced effects on nonlinear modal interactions can be fundamentally different for degenerate, closely spaced, and widely spaced modes.

42 ENGINEERING↗

NASA NTRS1986

Chaos and nonlinear dynamics of single-particle orbits in a magnetotaillike magnetic field

The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.

Chen, J.↗

NASA NTRS1989

Evanescent radiation, quantum mechanics and the Casimir effect

An attempt to bridge the gap between classical and quantum mechanics and to explain the Casimir effect is presented. The general nature of chaotic motion is discussed from two points of view: the first uses catastrophe theory and strange attractors to describe the deterministic view of this motion; the underlying framework for chaos in these classical dynamic systems is their extreme sensitivity to initial conditions. The second interpretation refers to randomness associated with probabilistic dynamics, as for Brownian motion. The present approach to understanding evanescent radiation and its relation to the Casimir effect corresponds to the first interpretation, whereas stochastic electrodynamics corresponds to the second viewpoint. The nonlinear behavior of the electromagnetic field is also studied. This well-understood behavior is utilized to examine the motions of two orbiting charges and shows a closeness between the classical behavior and the quantum uncertainty principle. The evanescent radiation is used to help explain the Casimir effect.

Schatten, Kenneth H.↗

NASA NTRS1982

Methods of sequential estimation for determining initial data in numerical weather prediction

Numerical weather prediction (NWP) is an initial-value problem for a system of nonlinear differential equations, in which initial values are known incompletely and inaccurately. Observational data available at the initial time must therefore be supplemented by data available prior to the initial time, a problem known as meteorological data assimilation. A further complication in NWP is that solutions of the governing equations evolve on two different time scales, a fast one and a slow one, whereas fast scale motions in the atmosphere are not reliably observed. This leads to the so called initialization problem: initial values must be constrained to result in a slowly evolving forecast. The theory of estimation of stochastic dynamic systems provides a natural approach to such problems. For linear stochastic dynamic models, the Kalman-Bucy (KB) sequential filter is the optimal data assimilation method, for linear models, the optimal combined data assimilation-initialization method is a modified version of the KB filter.

Cohn, S. E.↗

DOE OSTI2025

Neural operators for stochastic modeling of nonlinear structural system response to natural hazards

Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on the utilization of deep neural networks to learn operators capable of mapping infinite-dimensional function spaces. Here, in this work, we employ two state-of-the-art neural operators, the deep operator network (DeepONet) and the Fourier neural operator (FNO) for the prediction of the nonlinear time history response of structural systems exposed to natural hazards, such as earthquakes and windstorms. Specifically, we propose two architectures, a self-adaptive FNO and a fast Fourier transform-based DeepONet (DeepFNOnet), where we employ a FNO beyond the DeepONet to learn the discrepancy between the ground truth and the solution predicted by the DeepONet. To demonstrate the efficiency and applicability of the architectures, two problems are considered. In the first, we use the proposed model to predict the seismic nonlinear dynamic response of a six-story shear building subject to stochastic ground motions. In the second problem, we employ the operators to predict the wind-induced nonlinear dynamic response of a high-rise building while explicitly accounting for the stochastic nature of the wind excitation. In both cases, the trained metamodels achieve high accuracy while being orders of magnitude faster than their corresponding high-fidelity models.

DeepONet↗

DOE OSTI2022

Learning Stochastic Parametric Differentiable Predictive Control Policies

We present a scalable unsupervised learning-based method for obtaining explicit control policies for model predictive control problems for stochastic linear systems with additive uncertainties subject to nonlinear chance constraints. We call the proposed method stochastic parametric differentiable predictive control (SP-DPC), which extends the recently proposed deterministic DPC policy optimization algorithm. We formulate the SP-DPC as a deterministic approximation to the stochastic parametric constrained optimal control problem via independent sampling of the problem's parameters and uncertainties. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. In particular, the computed expectation of the problem's value function is backpropagated through the finite-time closed-loop system rollouts parametrized by a known nominal system dynamics model and neural control policy. We also provide theoretical probabilistic guarantees on closed-loop stability and chance constraints satisfaction for systems controlled by learned neural policies. We demonstrate the computational efficiency and scalability of the proposed policy optimization algorithm in three numerical examples, including systems with a large number of states or subject to nonlinear constraints.

Drgona, Jan↗

NASA NTRS2002

Interannual Variability of Martian Global Dust Storms: Simulations with a Low-Order Model of the General Circulation

We present simulations of the interannual variability of martian global dust storms (GDSs) with a simplified low-order model (LOM) of the general circulation. The simplified model allows one to conduct computationally fast long-term simulations of the martian climate system. The LOM is constructed by Galerkin projection of a 2D (zonally averaged) general circulation model (GCM) onto a truncated set of basis functions. The resulting LOM consists of 12 coupled nonlinear ordinary differential equations describing atmospheric dynamics and dust transport within the Hadley cell. The forcing of the model is described by simplified physics based on Newtonian cooling and Rayleigh friction. The atmosphere and surface are coupled: atmospheric heating depends on the dustiness of the atmosphere, and the surface dust source depends on the strength of the atmospheric winds. Parameters of the model are tuned to fit the output of the NASA AMES GCM and the fit is generally very good. Interannual variability of GDSs is possible in the IBM, but only when stochastic forcing is added to the model. The stochastic forcing could be provided by transient weather systems or some surface process such as redistribution of the sand particles in storm generating zones on the surface. The results are sensitive to the value of the saltation threshold, which hints at a possible feedback between saltation threshold and dust storm activity. According to this hypothesis, erodable material builds up its a result of a local process, whose effect is to lower the saltation threshold until a GDS occurs. The saltation threshold adjusts its value so that dust storms are barely able to occur.

Pankine, A. A.↗

DOE OSTI2023

Incorporation of market signals for the optimal design of post combustion carbon capture systems

Recent studies have shown that fossil generators equipped with post-combustion carbon capture (PCC) systems are needed to reduce the cost of deep decarbonization. Such generators need to be flexible and responsive to grid conditions, particularly in a high variable renewable energy (VRE) environment. In this work, we evaluate the net present value (NPV) of retrofitting an existing natural gas combined cycle (NGCC) unit with a flexible PCC system while incorporating market signals from a high VRE grid. We use our industrial partner’s NGCC configuration as representative of existing NGCC units and Svante’s rapid-temperature swing adsorption (TSA) for PCC. Because of its ability to rapidly startup/shutdown and ramp-up/ramp-down, the chosen capture technology is very attractive for load-following operations. For a given set of market signals, we formulate a two-stage stochastic multi-period optimization problem, under the price-taker assumption, to simultaneously optimize the design of the capture system and operation of the entire plant. Rigorous models for the NGCC unit, PCC system, and compression system are developed using commercial process simulators and validated with either plant or vendor data. For computational tractability, we develop surrogate/reduced-order models for use in the optimization problem. The surrogate model for the NGCC plant is constructed by linearizing the rigorous dynamic model at 75% load, while data-driven nonlinear surrogate models for the capture and compression systems are constructed using simulation data from the rigorous models. The optimization problem, formulated as a mixed integer bilinear program, is implemented in the IDAES® integrated platform and solved to global optimality using Gurobi 9.5. Using this formulation, we determine the profitability of retrofitting an existing NGCC unit with the chosen capture system for multiple regions in the U.S. under two scenarios with different carbon prices. Importantly, the results show that the optimal decision strongly depends on the region and on the carbon price, thereby demonstrating the importance of the inclusion of market signals in the design process.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

Insights into ENSO Diversity from an Intermediate Coupled Model. Part II: Role of Nonlinear Dynamics and Stochastic Forcing

Abstract In this study, we investigate how a single leading linear El Niño–Southern Oscillation (ENSO) mode, as studied in Part I, leads to the irregular coexistence of central Pacific (CP) and eastern Pacific (EP) ENSO, a phenomenon known as ENSO spatiotemporal diversity. This diversity is fundamentally generated by deterministic nonlinear pathways to chaos via the period-doubling route and, more prevailingly, the subharmonic resonance route with the presence of a seasonally varying basic state. When residing in the weakly nonlinear regime, the coupled system sustains a weak periodic oscillation with a mixed CP/EP pattern as captured by the linear ENSO mode. With a stronger nonlinearity effect, the ENSO behavior experiences a period-doubling bifurcation. The single ENSO orbit splits into coexisting CP-like and EP-like ENSO orbits. A sequence of period-doubling bifurcation results in an aperiodic oscillation featuring irregular CP and EP ENSO occurrences. The overlapping of subharmonic resonances between ENSO and the seasonal cycle allows this ENSO irregularity and diversity to be more readily excited. In the strongly nonlinear regime, the coupled system is dominated by regular EP ENSO. The deterministic ENSO spatiotemporal diversity is thus confined to a relatively narrow range corresponding to a moderately unstable ENSO mode. Stochastic forcing broadens this range and allows ENSO diversity to occur when the ENSO mode is weakly subcritical. A close relationship among a weakened mean zonal temperature gradient, stronger ENSO activity, and more (fewer) occurrences of EP (CP) ENSO is noted, indicating that ENSO–mean state interaction may yield ENSO regime modulations on the multidecadal time scale.

Geng, Licheng↗

NASA NTRS1976

Linear and nonlinear analysis of orbital telescope/space shuttle dynamics and control

Work completed on the design and study of an annular suspension and pointing (ASP) system for the space shuttle was presented. This system makes use of a magnetically suspended vernier pointing assembly. The following objectives were pursued in this study: (1) development of a detailed mathematical model of the Space Shuttle/ASP system, (2) design of control laws in order to obtain the desired pointing performance, and (3) prediction of the statistical pointing accuracies in the presence of stochastic disturbances such as crew-motion, and sensor and actuator noise. The first two of these objectives are documented in this report.

Roberts, A. S., Jr.↗

NASA NTRS1985

Probabilistic Structural Analysis Theory Development

The objective of the Probabilistic Structural Analysis Methods (PSAM) project is to develop analysis techniques and computer programs for predicting the probabilistic response of critical structural components for current and future space propulsion systems. This technology will play a central role in establishing system performance and durability. The first year's technical activity is concentrating on probabilistic finite element formulation strategy and code development. Work is also in progress to survey critical materials and space shuttle mian engine components. The probabilistic finite element computer program NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) is being developed. The final probabilistic code will have, in the general case, the capability of performing nonlinear dynamic of stochastic structures. It is the goal of the approximate methods effort to increase problem solving efficiency relative to finite element methods by using energy methods to generate trial solutions which satisfy the structural boundary conditions. These approximate methods will be less computer intensive relative to the finite element approach.

Burnside, O. H.↗

NASA NTRS1987

A combined stochastic feedforward and feedback control design methodology with application to autoland design

A combined stochastic feedforward and feedback control design methodology was developed. The objective of the feedforward control law is to track the commanded trajectory, whereas the feedback control law tries to maintain the plant state near the desired trajectory in the presence of disturbances and uncertainties about the plant. The feedforward control law design is formulated as a stochastic optimization problem and is embedded into the stochastic output feedback problem where the plant contains unstable and uncontrollable modes. An algorithm to compute the optimal feedforward is developed. In this approach, the use of error integral feedback, dynamic compensation, control rate command structures are an integral part of the methodology. An incremental implementation is recommended. Results on the eigenvalues of the implemented versus designed control laws are presented. The stochastic feedforward/feedback control methodology is used to design a digital automatic landing system for the ATOPS Research Vehicle, a Boeing 737-100 aircraft. The system control modes include localizer and glideslope capture and track, and flare to touchdown. Results of a detailed nonlinear simulation of the digital control laws, actuator systems, and aircraft aerodynamics are presented.

Halyo, Nesim↗