Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “nonlinear modeling”

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.

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

At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method used to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.

42 ENGINEERING↗
DOE OSTI2021

Joint effects of climate, tree size, and year on annual tree growth derived from tree–ring records of ten globally distributed forests

Tree rings provide an invaluable long-term record for understanding how climate and other drivers shape tree growth and forest productivity. However, conventional tree-ring analysis methods were not designed to simultaneously test effects of climate, tree size, and other drivers on individual growth. This has limited the potential to test ecologically relevant hypotheses on tree growth sensitivity to environmental drivers and their interactions with tree size. Here, we develop and apply a new method to simultaneously model nonlinear effects of primary climate drivers, reconstructed tree diameter at breast height (DBH), and calendar year in generalized least squares models that account for the temporal autocorrelation inherent to each individual tree's growth. We analyze data from 3811 trees representing 40 species at 10 globally distributed sites, showing that precipitation, temperature, DBH, and calendar year have additively, and often interactively, influenced annual growth over the past 120 years. Growth responses were predominantly positive to precipitation (usually over ≥3-month seasonal windows) and negative to temperature (usually maximum temperature, over ≤3-month seasonal windows), with concave-down responses in 63% of relationships. Climate sensitivity commonly varied with DBH (45% of cases tested), with larger trees usually more sensitive. Trends in ring width at small DBH were linked to the light environment under which trees established, but basal area or biomass increments consistently reached maxima at intermediate DBH. Accounting for climate and DBH, growth rate declined over time for 92% of species in secondary or disturbed stands, whereas growth trends were mixed in older forests. These trends were largely attributable to stand dynamics as cohorts and stands age, which remain challenging to disentangle from global change drivers. By providing a parsimonious approach for characterizing multiple interacting drivers of tree growth, our method reveals a more complete picture of the factors influencing growth than has previously been possible.

generalized least squares (GLS)↗
NASA NTRS1995

Spurious Numerical Solutions Of Differential Equations

Paper presents detailed study of spurious steady-state numerical solutions of differential equations that contain nonlinear source terms. Main objectives of this study are (1) to investigate how well numerical steady-state solutions of model nonlinear reaction/convection boundary-value problem mimic true steady-state solutions and (2) to relate findings of this investigation to implications for interpretation of numerical results from computational-fluid-dynamics algorithms and computer codes used to simulate reacting flows.

Lafon, A.↗
DOE OSTI2013

Determination of Optimal Operating Schemes for a Multi-Reservoir System Under Environmental Constraints

In strati ed reservoirs, both dam tailwater discharge and thermal plant intake water quality and temperature can be highly dependent on structure depth. A two- dimensional laterally-averaged model allows for better prediction of water quality over time at specfi c depths. Because high- fidelity models are typically too computationally expensive for direct inclusion within optimization algorithms, water quality is incorporated using one dimensional models are simple flow requirements. Water quality predictions can be incorporated within the optimization process through using surrogate modeling methods, in this application artificial neural network (ANN) models. ANNs are flexible machine learning tools for function approximation composed of a structure of neurons assembled within a multi-layer architecture. They are capable of handling large amounts of training data and modeling nonlinear dynamic systems, making ANNs a well-suited method for this application. This report illustrates the development of ANN models to emulate the hydrodynamic and water quality modeling capabilities of the high- fidelity, two-dimensional CE-QUAL-W2 (W2) model, as well as a linked riverine reservoir system optimization process which accounts for energy generation, water balance and hydraulics, and compliance point water quality. A process for hourly hydropower generation planning is demonstrated on a pair of reservoirs linked in series. The two reservoirs are U.S. Army Corps of Engineers projects with hydropower capabilities on the Cumberland River near Nashville, Tennessee, USA.

13 HYDRO ENERGY↗
NASA NTRS2009

Control-Relevant Modeling, Analysis, and Design for Scramjet-Powered Hypersonic Vehicles

Within this paper, control-relevant vehicle design concepts are examined using a widely used 3 DOF (plus flexibility) nonlinear model for the longitudinal dynamics of a generic carrot-shaped scramjet powered hypersonic vehicle. Trade studies associated with vehicle/engine parameters are examined. The impact of parameters on control-relevant static properties (e.g. level-flight trimmable region, trim controls, AOA, thrust margin) and dynamic properties (e.g. instability and right half plane zero associated with flight path angle) are examined. Specific parameters considered include: inlet height, diffuser area ratio, lower forebody compression ramp inclination angle, engine location, center of gravity, and mass. Vehicle optimizations is also examined. Both static and dynamic considerations are addressed. The gap-metric optimized vehicle is obtained to illustrate how this control-centric concept can be used to "reduce" scheduling requirements for the final control system. A classic inner-outer loop control architecture and methodology is used to shed light on how specific vehicle/engine design parameter selections impact control system design. In short, the work represents an important first step toward revealing fundamental tradeoffs and systematically treating control-relevant vehicle design.

Rodriguez, Armando A.↗
NASA NTRSDate not supplied

Enabling in-time Prognostics with Surrogate Modeling through Physics-enhanced Dynamic Mode Decomposition Method

Computational models provide essential quantitative tools for assessing and predicting the health and performance of physical systems. However, high-fidelity models are rarely used in real-time operations or large optimization loops, due to their time-intensive nature. A common approach to improving computational efficiency of prognosis is to employ surrogate models. Such models can significantly decrease computation time for some accuracy loss. In this context, use of Dynamic Mode Decomposition (DMD) is proposed to generate surrogate models for lithium-ion (Li-ion) battery discharge. DMD has been suggested and used successfully in the area of fluid dynamics for over a decade, but it has not been applied to the PHM domain, where far-ahead prediction of nonlinear behavior is crucial to propagate faults or predict Remaining Useful Life (RUL). For Li-ion battery health management, the standard application of DMD using only the observable quantities of interest was unable to capture the nonlinear discharge of batteries exhibited in lab testing. The Koopman theory, however, provides a mechanism to tradeoff low dimensional nonlinear models with high-dimensional linear ones in a DMD framework, by augmenting nonlinear state variables into the system representation. In this way, DMD allows for configurable simulation accuracy dependent on the dimensionality of the Koopman operator. For battery health management, we augmented the observable variables with the hidden states of a higher-fidelity physics model to build the DMD surrogate. In comparison to a high-fidelity model, the surrogate improved computational efficiency with only a minimal loss of accuracy, and enabled long-term prognostics horizons. A generalized method for this was implemented in the prog models python package.

prognostics and health management↗
DOE OSTI2021

Constrained Block Nonlinear Neural Dynamical Models

Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear dynamical models by embedding local model structure and constraints. The proposed method consists of neural network blocks that represent input, state, and output dynamics with constraints placed on the network weights and system variables. For handling partially observable dynamical systems, we utilize a state observer neural network to estimate the states of the system's latent dynamics. We evaluate the performance of the proposed architecture and training methods on system identification tasks for three nonlinear systems: a continuous stirred tank reactor, a two tank interacting system, and an aerodynamics body. Models optimized with a few thousand system state observations accurately represent system dynamics in open loop simulation over thousands of time steps from a single set of initial conditions. Experimental results demonstrate an order of magnitude reduction in open-loop simulation mean squared error for our constrained, block-structured neural models when compared to traditional unstructured and unconstrained neural network models.

Skomski, Elliott↗
DOE OSTI2017

Plasma turbulence in the equatorial electrojet: A two-dimensional Hamiltonian fluid model

A nonlinear unified fluid model that describes the Equatorial Electrojet, including the Farley-Buneman and gradient-drift plasma instabilities, is defined and shown to be a noncanonical Hamiltonian system. Two geometric constants of motion for the model are obtained and shown to be Casimir invariants. Here, a reformulation of the model shows the roles of the density-gradient scale-length ( L n ) and the cross-field drift-velocity ($υ_E$) in controlling the dynamics of unstable modes in the growing, transition, and saturation phases of a simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2012

Implementation of an Integrated On-Board Aircraft Engine Diagnostic Architecture

An on-board diagnostic architecture for aircraft turbofan engine performance trending, parameter estimation, and gas-path fault detection and isolation has been developed and evaluated in a simulation environment. The architecture incorporates two independent models: a realtime self-tuning performance model providing parameter estimates and a performance baseline model for diagnostic purposes reflecting long-term engine degradation trends. This architecture was evaluated using flight profiles generated from a nonlinear model with realistic fleet engine health degradation distributions and sensor noise. The architecture was found to produce acceptable estimates of engine health and unmeasured parameters, and the integrated diagnostic algorithms were able to perform correct fault isolation in approximately 70 percent of the tested cases

Armstrong, Jeffrey B.↗
DOE OSTI2014

A HYBRID MODE MODEL OF THE BLAZHKO EFFECT, SHOWN TO ACCURATELY FIT KEPLER DATA FOR RR Lyr

The waveform for Blazhko stars can be substantially different during the ascending and descending parts of the Blazhko cycle. A hybrid model, consisting of two component oscillators of the same frequency, is proposed as a means to fit the data over the entire cycle. One component exhibits a sawtooth-like velocity waveform while the other is nearly sinusoidal. One method of generating such a hybrid is presented: a nonlinear model is developed for the first overtone mode, which, if excited to large amplitude, is found to drop strongly in frequency and become highly non-sinusoidal. If the frequency drops sufficiently to become equal to the fundamental frequency, the two can become phase locked and form the desired hybrid. A relationship is assumed between the hybrid mode velocity and the observed light curve, which is approximated as a power series. An accurate fit of the hybrid model is made to actual Kepler data for RR Lyr. The sinusoidal component may tend to stabilize the period of the hybrid which is found in real Blazhko data to be extremely stable. It is proposed that the variations in amplitude and phase might result from a nonlinear interaction with a third mode, possibly a nonradial mode at 3/2 the fundamental frequency. The hybrid model also applies to non-Blazhko RRab stars and provides an explanation for the light curve bump. A method to estimate the surface gravity is also proposed.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1973

The muscle spindle as a feedback element in muscle control

The muscle spindle, the feedback element in the myotatic (stretch) reflex, is a major contributor to muscular control. Therefore, an accurate description of behavior of the muscle spindle during active contraction of the muscle, as well as during passive stretch, is essential to the understanding of muscle control. Animal experiments were performed in order to obtain the data necessary to model the muscle spindle. Spectral density functions were used to identify a linear approximation of the two types of nerve endings from the spindle. A model reference adaptive control system was used on a hybrid computer to optimize the anatomically defined lumped parameter estimate of the spindle. The derived nonlinear model accurately predicts the behavior of the muscle spindle both during active discharge and during its silent period. This model is used to determine the mechanism employed to control muscle movement.

Andrews, L. T.↗
DOE OSTI2023

Linearization errors in discrete goal-oriented error estimation

This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete, adjoint-based approach for error estimation is considered. The traditional method to derive an error estimate in this context requires linearizing both the nonlinear variational form and the nonlinear functional of interest which introduces linearization errors into the error estimate. In this paper, we investigate these linearization errors. In particular, we develop a novel discrete goal-oriented error estimate that accounts for traditionally neglected nonlinear terms at the expense of greater computational cost. We demonstrate how this error estimate can be used to drive mesh adaptivity. Here, we show that accounting for linearization errors in the error estimate can improve its effectivity for several nonlinear model problems and quantities of interest. We also demonstrate that an adaptive strategy based on the newly proposed estimate can lead to more accurate approximations of the nonlinear functional with fewer degrees of freedom when compared to uniform refinement and traditional adjoint-based approaches.

42 ENGINEERING↗
DOE OSTI2021

Estimating and Forecasting Time-Varying Groundwater Recharge in Fractured Rock: A State-Space Formulation with Preferential and Diffuse Flow to the Water Table

Rapid infiltration following precipitation may result in groundwater contamination from surface contaminants or pathogens. In fractured rock, contaminants can migrate rapidly to points of groundwater withdrawals. In contrast to the temporal availability of groundwater quality chemical indicators, meteorological and groundwater level observations are available in real-time to estimate time-varying recharge, which can act as a surrogate to identify periods of rapid infiltration that may indicate contamination susceptibility. Estimating recharge using methods, such as base-flow recession, unsaturated infiltration models, or Water-Table Fluctuations (WTF), cannot capitalize on currently available technologies and telecommunication infrastructure to conduct real-time recharge estimation at scales relevant to characterizing rapid infiltration. We present a linear, physics-based State-Space (SS) model of one-dimensional infiltration to estimate recharge, which includes preferential and diffuse-flow to the water table. The model can take advantage of real-time data for water-table altitude, precipitation, and evapotranspiration. Model parameters are calibrated over an observation period, and the Kalman Filter (KF) is subsequently applied to continuously update the observed (water-table altitude) and unobserved (groundwater recharge) system states and predict future states as new data become available. The SS/KF algorithm is demonstrated at the Masser Groundwater Recharge Site in Pennsylvania, USA and comparisons are made with recharge estimates from WTF methods. Model results indicate that the frequency of observations (daily versus sub-daily) dictates the allocation between preferential and diffuse flow. Additionally, because infiltration processes encompass many nonlinearities, model parameters estimated from observation periods need to be updated at least seasonally to account for changing recharge conditions.

groundwater, Recharge, infiltration, recursive est↗
DOE OSTI2015

Nonlinear study of an ion-channel guiding free-electron laser

A nonlinear model and simulations of the output power of an ion-channel guiding free-electron laser (FEL) are presented in this paper. Results show that the nonlinear output power of an ion-channel guiding FEL is comparable to that of an axial guide magnetic field FEL. Compared to an axial guide magnetic field FEL, an ion-channel guiding FEL substantially weakens the negative effect of the electron-beam energy spread on the output power due to its advantageous focusing mechanism on the electron motion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1991

An approach to simultaneous control of trajectory and interaction forces in dual-arm configurations

An approach to the control of constrained dynamic systems such as multiple arm systems, multifingered grippers, and walking vehicles is described. The basic philosophy is to utilize a minimal set of inputs to control the trajectory and the surplus input to control the constraint or interaction forces and moments in the closed chain. A dynamic control model for the closed chain is derived that is suitable for designing a controller in which the trajectory and the interaction forces and moments are explicitly controlled. Nonlinear feedback techniques derived from differential geometry are then applied to linearize and decouple the nonlinear model. These ideas are illustrated through a planar example in which two arms are used for cooperative manipulation. Results from a simulation are used to illustrate the efficacy of the method.

Yun, Xiaoping↗
DOE OSTI2021

Estimating viscoelastic compliance of desiccating cementitious materials using drying prism tests

Highlights: • Determining relative humidity and degree of reaction of desiccating cementitious materials via an integrated method • Extracting moisture diffusion coefficient of cement mortar using the mass loss data of the prism specimens • Estimating uniaxial viscoelastic compliance of cement mortar using the shrinkage strain data of the prism specimens An integrated modeling approach to determining internal relative humidity and degree of reaction of desiccating cementitious materials has been developed. By simultaneously accounting for both self-desiccation and external drying, the model is capable of predicting the evolution of material properties of desiccating cementitious materials. Using the mass loss data of the prism specimens, the moisture diffusion coefficient of a nonlinear model for cement mortar was determined. Additionally, a previous poroviscoelastic shrinkage model was modified and extended. Through comparison of predicted and measured axial strain of the prism specimens, the viscoelastic compliance of cement mortar was extracted. The present work revealed that it is possible to use a simple drying prism test to fit the moisture diffusion coefficient and creep compliance of cementitious materials, though the comparison of the extracted viscoelastic compliance with measured compliance was only reasonable if the outer layer of the drying mortar was presumed to have microcracking.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Decomposition of Nonlinear Dynamical Systems Using Koopman Gramians

In this paper we propose a new Koopman operator approach for nonlinear model decomposition using Koopman gramians. We introduce Koopman operators and discuss the notion of a input-Koopman operator. We show how input-Koopman operators can be used to cast a nonlinear system into the classical state-space form, as well as conditions under which input and state observable functions are well separated. We extend an existing method of dynamic mode decomposition for learning Koopman operators from data known as deep dynamic mode decomposition, for systems with control or disturbances. We illustrate the accuracy of the method on learning an input-state separable Koopman operator for an example system, even when the underlying system exhibits mixed state-input terms. Finally, we introduce a nonlinear decomposition algorithm, based on Koopman gramians, that maximizes internal subsystem observability and disturbance rejection from unwanted noise in other subsystems. To relieve the NP-hardness of the decomposition problem, we derive a relaxation based on Koopman gramians and multi-way partitioning. We illustrate our algorithm on a swing dynamics model for a IEEE 39 bus and discuss our findings.

Learning, Control, Distributed Control, koopman op↗
DOE OSTI2024

Domain-decomposition nonlinear manifold reduced order model

This software combines nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD) techniques. NM-ROMs, which utilize a shallow, sparse autoencoder trained with full order model (FOM) snapshot data, approximate the FOM state on a nonlinear manifold. These models offer advantages over linear-subspace ROMs (LS-ROMs) particularly in scenarios with slowly decaying Kolmogorov n-width. However, the training of NM-ROMs involves a number of parameters that scale with the size of the FOM, and storing high-dimensional FOM snapshots can significantly increase the cost of ROM training for extreme-scale problems. To mitigate these costs, the software employs DD to partition the FOM into smaller subdomains, computes NM-ROMs for each, and then integrates these to form a global NM-ROM. This strategy offers multiple benefits: it enables parallel training of subdomain NM-ROMs, reduces the number of parameters needed, decreases the dimensional requirements of subdomain FOM training data, and allows for customization to the unique characteristics of each FOM subdomain. The use of a shallow, sparse autoencoder architecture in each subdomain NM-ROM facilitates the application of hyper-reduction (HR), simplifying the nonlinear complexities and enhancing computational speed. This software marks the inaugural application of NM-ROM combined with HR to a DD problem. It features an algebraic DD reformulation of the FOM, training of NM-ROMs with HR for each subdomain, and employs a sequential quadratic programming (SQP) solver for the evaluation of the coupled global NMROM. The effectiveness of the DD NM-ROM with HR is numerically demonstrated on the 2D steady-state Burgers' equation, showing an order of magnitude improvement in accuracy over the DD LS-ROM with HR.

Diaz, AlejandroN↗