SEARCH · Engineering Papers

Results for “nonlinear function”

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 919 records · Page 51

All sources NASA NTRS DOE OSTI

DOE OSTI2026

An Atom-Precise Approach to Damp First-Order Phase Transitions and Its Implications for Neuromorphic Signal Processing

Neuromorphic computing inspired by mammalian intelligence aims to emulate the nonlinear dynamics of biological neurons and synapses to achieve fast, low-energy, and highly efficient information processing. Brain-inspired computing relies on the design and discovery of materials exhibiting nonlinear current–voltage profiles, frequently underpinned by electronic state transitions, to achieve spiking neurons and dynamically tunable synapses. A signature challenge in the design of artificial neurons is controlling the steepness of first-order transitions in active elements, as abrupt transitions are at risk of driving unstable voltage and temperature oscillations, which result in catastrophic device failure. A critical knowledge gap is the lack of structure–function correlations mapping the composition and atomistic structure of crystalline solids to nonlinear dynamical response characteristics. Here, we address the key question of how modification of atomistic structure correlates with alteration of neuron-like functionality. Constructing oscillator circuits from millimeter-scale single crystals enables high-resolution atomic structure solutions, which we use to demonstrate that the selective positioning of Pb cations modifies charge ordering along a one-dimensional CuxV2O5 framework even at low insertion stoichiometries, thereby providing an atom-precise design parameter for damping first-order transitions. We use temperature-variant X-ray diffraction and X-ray spectroscopy to elucidate the suppression of Cu-ion shuttling based on the precise positioning of Pb ions in seven-coordinated tunnel interstitial sites as the mechanistic basis for transition broadening, thus bridging a critical gap between statistical mechanics and quantum chemical descriptions of phase transitions. Such mechanistic understanding thus paves the way to site-selective modification strategies for modulating the sharpness of first-order transitions, with an exemplary demonstration here in tuning neuronal signal processing.

Crystal structure↗

NASA NTRS1990

Characterization of the Nonlinear Elastic Properties of Graphite/Epoxy Composites Using Ultrasound

The normalized change in ultrasonic "natural" velocity as a function of stress and temperature was measured in a unidirectional laminate of T300/5208 graphite/epoxy composite using a pulsed phase locked loop ultrasonic interferometer. These measurements were used together with the linear (second order) elastic moduli to calculate some of the nonlinear (third order) moduli of this material.

Prosser, William H.↗

NASA NTRS2016

Sensorimotor Results from the Joint NASA and Russian Pilot Field Test

Testing of crew responses following long-duration flights has not previously been possible until a minimum of 24 hours after landing. As a result, it has not been possible to estimate the nonlinear trend of the early (<24 hours) recovery process, nor has it been possible to accurately assess the full impact of the decrements associated with long-duration flight. To overcome these limitations, both the Russian and U.S. programs have implemented testing at the Soyuz landing site. This research effort has been identified as the Field Test (FT). For operational reasons the FT has been divided into two phases: the full FT and a preliminary pilot version (PFT) of the FT that is reduced in both length and scope. The PFT has now been completed with the landing of the crew of International Space Station Increment 42/43 (Soyuz expedition 41S). RESEARCH: The primary goal of this research was to determine functional abilities associated with long-duration space flight crews beginning as soon after landing as possible (< 2 hours) with an additional two follow-up measurement sessions within 24 hours after landing. This study goal has both sensorimotor and cardiovascular elements. The PFT represented a initial evaluation of the feasibility of testing in the field and was comprised of a jointly agreed upon subset of tests drawn from the full FT and relied heavily on Russia's Institute of Biomedical Problems Sensory-Motor and Countermeasures Department for content and implementation. Data from the PFT was collected following several ISS missions. Testing on the U.S. side has included: (1) a sit-to-stand test, (2) recovery from a fall stand test where the crewmember begins in the prone position on the ground and then stands for 3.5 minutes while cardiovascular performance and postural ataxia data are acquired, and (3) a tandem heel-to-toe walk test to determine changes in the central locomotor program. Video, cardiovascular parameters (heart rate and blood pressure), data from body-worn inertial sensors, and severity of postflight motion sickness were collected during each test session. In addition our Russian investigators have made measurements associated with: (a) obstacle avoidance, (b) muscle compliance, (c) postural adjustments to perturbations (pushes) applied to the subject's chest area and (d) center of mass measurements made across most test objectives with insoles inserted into the subjects' shoes. Data from 18 subjects have been obtained for a majority of the PFT objectives. SUMMARY: The increased level of functional deficit observed in the crewmembers tested with the PFT objectives has been typically greater than previously observed when measurements were collected after the 2 hr window. Significant improvement in crew performance was observed within 24 hours, but full recovery appears to require 6 to 16 days. Clearly measureable performance parameters such as ability to perform a seat egress, recovery from a fall or the ability to see clearly when walking, and related physiologic data (orthostatic responses) are required to provide an evidence base for characterizing programmatic risks and the variability among crewmembers for exploration missions where the crew will be unassisted after landing. Overall, these early functional and related physiologic measurements will allow the estimation of nonlinear sensorimotor and cardiovascular recovery trends that have not been previously captured.

Reschke, Millard↗

NASA NTRS1997

Design of Neural Networks for Fast Convergence and Accuracy: Dynamics and Control

A procedure for the design and training of artificial neural networks, used for rapid and efficient controls and dynamics design and analysis for flexible space systems, has been developed. Artificial neural networks are employed, such that once properly trained, they provide a means of evaluating the impact of design changes rapidly. Specifically, two-layer feedforward neural networks are designed to approximate the functional relationship between the component/spacecraft design changes and measures of its performance or nonlinear dynamics of the system/components. A training algorithm, based on statistical sampling theory, is presented, which guarantees that the trained networks provide a designer-specified degree of accuracy in mapping the functional relationship. Within each iteration of this statistical-based algorithm, a sequential design algorithm is used for the design and training of the feedforward network to provide rapid convergence to the network goals. Here, at each sequence a new network is trained to minimize the error of previous network. The proposed method should work for applications wherein an arbitrary large source of training data can be generated. Two numerical examples are performed on a spacecraft application in order to demonstrate the feasibility of the proposed approach.

Maghami, Peiman G.↗

NASA NTRS1985

Nonlinear adhesive behavior effects in a cracked orthotropic sheet stiffened by a semi-infinite orthotropic sheet

The stress-intensity factors are determined for a cracked orthotropic sheet adhesively bonded to an orthotropic stringer where the adhesive layer is modeled with a nonlinear stress-strain curve. By the use of Green's functions and the complex variable theory of orthotropic elasticity, a set of integral equations is obtained. The integral equations are replaced by an equivalent set of algebraic equations, which are solved to obtain the shear stress distribution in the adhesive layer, with which the crack-tip stress-intensity factors are found. When the adhesive was modeled with a nonlinear stress-strain curve, the peak shear stresses in the adhesive were considerably reduced in comparison to the solution for the linear elastic adhesive. This resulted in increases in the stress-intensity factors for the nonlinear adhesive solution compared to the linear adhesive solution. The nonlinear adhesive has no significant effect on the stress-intensity factor unless the near crack tip is beneath the stringer. It is assumed that the adhesive bond remains intact and it is predicted that onset of adhesive failure occurs at decreasing levels of applied stress as the crack propagates beneath the stringer.

Bigelow, C. A.↗

NASA NTRS1986

Nonlinear adhesive behavior effects in a cracked orthotropic sheet stiffened by a semi-infinite orthotropic sheet

Bigelow, C. A.↗

DOE OSTI2023

An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems

We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low accuracy in handling high-dimensional and highly nonlinear problems. EnSF attacks this challenge by exploiting the score-based diffusion model, defined in a pseudo-temporal domain, to characterizing the evolution of the filtering density. EnSF stores the information of the recursively updated filtering density function in the score function, in stead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation that uses mini-batch-based Monte Carlo estimator to directly approximate the score function at any pseudo-spatial-temporal location, which provides sufficient accuracy in solving high-dimensional nonlinear problems as well as saves tremendous amount of time spent on training neural networks. Another essential aspect of EnSF is its analytical update step, gradually incorporating data information into the score function, which is crucial in mitigating the degeneracy issue faced when dealing with very high-dimensional nonlinear filtering problems. High-dimensional Lorenz systems are used to demonstrate the performance of our method. EnSF provides surprisingly impressive performance in reliably tracking extremely high-dimensional Lorenz systems (up to 1,000,000 dimension) with highly nonlinear observation processes, which is a well-known challenging problem for existing filtering methods.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1991

A numerical modeling study of the interaction between the tides and the circulation forced by high-latitude plasma convection

A spectral, time-varying thermospheric general circulation model has been used to study the nonlinear interaction at high latitudes between the tides propagating into the thermosphere from below and the circulation induced by magnetospheric forcing and in situ solar heating. The model is discrete in the vertical with 27 layers spaced by half a scale height. In the horizontal, the fields are expanded in a series of spherical harmonics using a triangular truncation at wave number 31, equivalent to a homogeneous global resolution with a minimum wavelength of 1270 km. A hypothetical uniform grid point model would require a horizontal spacing of 417 km to describe the same minimum wavelength. In the high-latitude F region the tides affect the dusk vortex of the neutral flow very little, but the dawn vortex is either suppressed or amplified dependent upon the universal time and tidal phase. In the E region neutral flow, both the dusk and dawn vortices are shifted in local time by the tides, again as a function of universal time and tidal phase. At dusk a nonlinear amplification of the sunward winds occurs for certain combinations of parameters, and at dawn the winds may be completely suppressed. Below 120 km altitude the magnetospheric forcing creates a single cyclonic vortex which is also sensitive to the high-latitude tidal structure.

Mikkelsen, I. S.↗

NASA NTRS1987

Ultrasonic characterization of the nonlinear elastic properties of unidirectional graphite/epoxy composites

The theoretical treatment of linear and nonlinear elasticity in a unidirectionally fiber reinforced composite as well as measurements for a unidirectional graphite/epoxy composite (T300/5208) are presented. Linear elastic properties were measured by both ultrasonic and strain gage measurements. The nonlinear properties were determined by measuring changes in ultrasonic natural phase velocity with a pulsed phase locked loop interferometer as a function of stress and temperature. These measurements provide the basis for further investigations into the relationship between nonlinear elastic properties and other important properties such as strength and fiber-matrix interfacial stength in graphite/epoxy composites.

Prosser, William H.↗

NASA NTRS1987

Ultrasonic characterization of the nonlinear elastic properties of unidirectional graphite/epoxy composites

Prosser, William H.↗

NASA NTRS1973

CONMIN: A FORTRAN program for constrained function minimization: User's manual

CONMIN is a FORTRAN program, in subroutine form, for the solution of linear or nonlinear constrained optimization problems. The basic optimization algorithm is the Method of Feasible Directions. The user must provide a main calling program and an external routine to evaluate the objective and constraint functions and to provide gradient information. If analytic gradients of the objective or constraint functions are not available, this information is calculated by finite difference. While the program is intended primarily for efficient solution of constrained problems, unconstrained function minimization problems may also be solved, and the conjugate direction method of Fletcher and Reeves is used for this purpose. This manual describes the use of CONMIN and defines all necessary parameters. Sufficient information is provided so that the program can be used without special knowledge of optimization techniques. Sample problems are included to help the user become familiar with CONMIN and to make the program operational.

Vanderplaats, G. N.↗

NASA NTRS2004

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ortiz, Francisco↗

NASA NTRS1990

Nonlinear analysis of compressively loaded linked-plate structures

A method is presented for the geometrically nonlinear analysis of the equilibrium behavior of a general class of compressively loaded, prismatic, linked-plate structures. The semi-analytical method accounts for geometric shape imperfections, and allows the use of laminated composite plate properties. Buckling eigenfunctions are used as displacement shape functions, and the associated second-order displacement fields are incorporated. The nonlinear plate equilibrium equations are expressed in terms of the assumed displacement form, and the Galerkin method is used to obtain a set of algebraic equations which are nonlinear in the modal amplitudes and the load parameter. Buckling eigensolutions for the class of structures under consideration can be obtained from the VIPASA computer code; thus, subject to some additional restrictions in loading and plate anisotropy, structural configurations which can be analyzed with regard to buckling response by VIPASA can be analyzed with regard to geometrically nonlinear response using the new method.

Stoll, Frederick↗

NASA NTRS1993

FD-TD modeling of 2-D dielectric waveguides for propagation and scattering of femtosecond optical solitons

Experimentalists have produced all-optical switches capable of 100-fs responses. To adequately model such switches, nonlinear effects in optical materials (both instantaneous and dispersive) must be included. In principle, the behavior of electromagnetic fields in nonlinear dielectrics can be determined by solving Maxwell's equations subject to the assumption that the electric polarization has a nonlinear relation to the electric field. However, until our previous work, the resulting nonlinear Maxwell's equations have not been solved directly. Rather, approximations have been made that result in a class of generalized nonlinear Schrodinger equations (GNLSE) that solve only for the envelope of the optical pulses. In this paper, we present first-time calculations from the vector nonlinear Maxwell's equations of femtosecond soliton propagation and scattering, including carrier waves, in two-dimensional systems of dielectric waveguides exhibiting the Kerr and Raman quantum effects. We use the finite-difference time-domain (FD-TD) method in an extension of our 1-D work. There, in a fundamental innovation, we treated the linear and nonlinear convolutions for the electric polarization as new dependent variables. By differentiating these convolutions in the time domain, we derived an equivalent system of coupled, nonlinear second-order ODE's. These equations together with Maxwell's equations form the system that is solved to determine the electromagnetic fields in inhomogeneous nonlinear dispersive media. Backstorage in time is limited to only that needed by the time-integration algorithm for the ODE's, rather than that needed to store the time-history of the kernel functions of the convolutions (1000-10,000 time steps). Thus, a 2-D nonlinear optics model from Maxwell's equations is now feasible.

Joseph, Rose↗

NASA NTRS1976

Extended Lyapunov stability criterion using a nonlinear algebraic relation with application to adaptive control

A new nonlinear stability criterion is developed by use of a class of Lyapunov functionals for model-reference adaptive systems (MRAS). Results are compared with traditional results, and a comparative design technique is used to illustrate its function in improving the transient response of an MRAS controller. For a particular system structure and class of input signals, the new stability criterion is shown to include traditional sufficiency stability conditions as a special case. An example is cited to illustrate the use of the nonlinear criterion and its definite advantages in helping improve the adaptive error transient response of a system. Analysis of results is effected by use of a linearization technique on the resulting adaptive equations.

Colburn, B. K.↗

DOE OSTI2024

Linear-frequency conversion with time-varying metasurfaces

Frequency conversion is a hallmark of nonlinearity. The spectral manifestations, emergent within a system, can typically be attributed to a marked nonlinearity within the material properties, complex geometric configurations, and/or the unique functional form of interactions taking place in the constitutive subsystems. These phenomena, irrespective of their origins, have been harnessed and exploited in applications ranging from the generation of entangled photons, a cornerstone in quantum technologies, to nanomechanical frequency mixing, advancing subsurface scanning probe microscopy. Here, we propose a frequency conversion mechanism based on time-varying metasurfaces, an emerging frontier in metamaterial research. We show how temporal properties of metasurfaces can effectively emulate a nonlinear medium, thereby facilitating frequency conversion. The proposed material configuration has the potential not only to advance integrated photonics and quantum optics, but also to create opportunities in quantum sensing, quantum materials, and crucially quantum communications. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1999

Structural Reliability Analysis and Optimization: Use of Approximations

This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different approximations including the higher-order reliability methods (HORM) for representing the failure surface. This report is divided into several parts to emphasize different segments of the structural reliability analysis and design. Broadly, it consists of mathematical foundations, methods and applications. Chapter I discusses the fundamental definitions of the probability theory, which are mostly available in standard text books. Probability density function descriptions relevant to this work are addressed. In Chapter 2, the concept and utility of function approximation are discussed for a general application in engineering analysis. Various forms of function representations and the latest developments in nonlinear adaptive approximations are presented with comparison studies. Research work accomplished in reliability analysis is presented in Chapter 3. First, the definition of safety index and most probable point of failure are introduced. Efficient ways of computing the safety index with a fewer number of iterations is emphasized. In chapter 4, the probability of failure prediction is presented using first-order, second-order and higher-order methods. System reliability methods are discussed in chapter 5. Chapter 6 presents optimization techniques for the modification and redistribution of structural sizes for improving the structural reliability. The report also contains several appendices on probability parameters.

Grandhi, Ramana V.↗

DOE OSTI2021

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN with a single hidden layer can accurately approximate any nonlinear continuous operator. This universal approximation theorem of operators is suggestive of the structure and potential of deep neural networks (DNNs) in learning continuous operators or complex systems from streams of scattered data. Here, in this work, we thus extend this theorem to DNNs. We design a new network with small generalization error, the deep operator network (DeepONet), which consists of a DNN for encoding the discrete input function space (branch net) and another DNN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. We study different formulations of the input function space and its effect on the generalization error for 16 different diverse applications.

97 MATHEMATICS AND COMPUTING↗