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Results for “nonlinear mappings”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Influence of doping and thickness on domain avalanches in lead zirconate titanate thin films

In undoped lead zirconate titanate films of 1–2 μm thick, domain walls move in clusters with a correlation length of approximately 0.5–2 μm. Band excitation piezoresponse force microscopy mapping of the piezoelectric nonlinearity revealed that niobium (Nb) doping increases the average concentration or mobility of domain walls without changing the cluster area of correlated domain wall motion. In comparison, manganese (Mn) doping reduces the contribution of mobile domain walls to the dielectric and piezoelectric responses without changing the cluster area for correlated motion. In both Nb and Mn doped films, the cluster area increases and the cluster density drops as the film thickness increases from 250 to 1250 nm. This is evident in spatial maps generated from the analysis of irreversible to reversible ratios of the Rayleigh coefficients.

36 MATERIALS SCIENCE↗
NASA NTRS2003

Improved Fine Sun Sensor Field of View Calibration

The fine Sun sensor used on many spacecraft consists of two independent single-axis sensor heads, nominally mounted perpendicularly. These detect the Sun angle over a field of view typically of +32 deg. (There is a trade-off between accuracy and size of the field of view that allows for much latitude in any numbers quoted.) The nonlinear "transfer" function that maps the telemetered counts into observed angles consists of 9 adjustable parameters for each axis (1 8 total). An augmented transfer function has previously been reported that achieves a significant accuracy improvement across the entire field of view. That function expands the parameter set to 12 coefficients per axis (24 total) and includes cross terms combining counts from both axes. To make the best use of the Sun sensor for attitude determination, it must be calibrated after launch. However, the large number of parameters and the nonlinearity of the problem make this a challenging task. The purpose of this paper is to examine ways to improve convergence of the parameter search algorithm. In particular, experience has shown that the problem should be broken down into several steps, solving for a selected subset of the parameters at each step. This approach has now been incorporated as an option in the calibration utility.

Sedlak, J.↗
DOE OSTI2024

Inverse Design of Photonic Surfaces via High throughput Femtosecond Laser Processing and Tandem Neural Networks

Abstract This work demonstrates a method to design photonic surfaces by combining femtosecond laser processing with the inverse design capabilities of tandem neural networks that directly link laser fabrication parameters to their resulting textured substrate optical properties. High throughput fabrication and characterization platforms are developed that generate a dataset comprising 35280 unique microtextured surfaces on stainless steel with corresponding measured spectral emissivities. The trained model utilizes the nonlinear one‐to‐many mapping between spectral emissivity and laser parameters. Consequently, it generates predominantly novel designs, which reproduce the full range of spectral emissivities (average root‐mean‐squared‐error < 2.5%) using only a compact region of laser parameter space 25 times smaller than what is represented in the training data. Finally, the inverse design model is experimentally validated on a thermophotovoltaic emitter design application. By synergizing laser‐matter interactions with neural network capabilities, the approach offers insights into accelerating the discovery of photonic surfaces, advancing energy harvesting technologies.

36 MATERIALS SCIENCE↗
NASA NTRS1984

Nonlinear control of aircraft

Transformations of nonlinear systems were used to design automatic flight controllers for vertical and short takeoff aircraft. Under the assumption that a nonlinear system can be mapped to a controllable linear system, a method using partial differential equations was constructed to approximate transformations in cases where exact ones cannot be found. An application of the design theory to a rotorcraft, the UH-1H helicopter, was presented.

Hunt, L. R.↗
NASA NTRS1986

A procedure for calculating the damping in multi-element space structures

A procedure for analyzing the damping in a multielement space structure connected by joints is described, in which distributed material damping and discrete nonlinear joint properties are incorporated into a linear analysis. The procedure involves four steps: (1) creation of a linear undamped finite element model; (2) experimental measurements of the transient response of a truss member in free fall tests to obtain material damping properties; with these properties incorporated into a linear damped finite element model of the structure; (3) the identification of the nonlinear joint properties using the force-state mapping technique; and (4) linearization of the identified nonlinear components, which are then incorporated into the linear damped model to create the linearized damped finite element model.

Crawley, E. F.↗
NASA NTRS1989

A design philosophy for multi-layer neural networks with applications to robot control

A system is proposed which receives input information from many sensors that may have diverse scaling, dimension, and data representations. The proposed system tolerates sensory information with faults. The proposed self-adaptive processing technique has great promise in integrating the techniques of artificial intelligence and neural networks in an attempt to build a more intelligent computing environment. The proposed architecture can provide a detailed decision tree based on the input information, information stored in a long-term memory, and the adapted rule-based knowledge. A mathematical model for analysis will be obtained to validate the cited hypotheses. An extensive software program will be developed to simulate a typical example of pattern recognition problem. It is shown that the proposed model displays attention, expectation, spatio-temporal, and predictory behavior which are specific to the human brain. The anticipated results of this research project are: (1) creation of a new dynamic neural network structure, and (2) applications to and comparison with conventional multi-layer neural network structures. The anticipated benefits from this research are vast. The model can be used in a neuro-computer architecture as a building block which can perform complicated, nonlinear, time-varying mapping from a multitude of input excitory classes to an output or decision environment. It can be used for coordinating different sensory inputs and past experience of a dynamic system and actuating signals. The commercial applications of this project can be the creation of a special-purpose neuro-computer hardware which can be used in spatio-temporal pattern recognitions in such areas as air defense systems, e.g., target tracking, and recognition. Potential robotics-related applications are trajectory planning, inverse dynamics computations, hierarchical control, task-oriented control, and collision avoidance.

Vadiee, Nader↗
NASA NTRS2004

Putting Priors in Mixture Density Mercer Kernels

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. We describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using predefined kernels. These data adaptive kernels can en- code prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS). The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains template for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic- algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code. The results show that the Mixture Density Mercer-Kernel described here outperforms tree-based classification in distinguishing high-redshift galaxies from low- redshift galaxies by approximately 16% on test data, bagged trees by approximately 7%, and bagged trees built on a much larger sample of data by approximately 2%.

Srivastava, Ashok N.↗
NASA NTRS2005

An Ensemble Approach to Building Mercer Kernels with Prior Information

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly dimensional feature space. we describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using pre-defined kernels. These data adaptive kernels can encode prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. Specifically, we demonstrate the use of the algorithm in situations with extremely small samples of data. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS) and demonstrate the method's superior performance against standard methods. The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains templates for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic-algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code.

Srivastava, Ashok N.↗
NASA NTRS2016

Control Systems with Normalized and Covariance Adaptation by Optimal Control Modification

Disclosed is a novel adaptive control method and system called optimal control modification with normalization and covariance adjustment. The invention addresses specifically to current challenges with adaptive control in these areas: 1) persistent excitation, 2) complex nonlinear input-output mapping, 3) large inputs and persistent learning, and 4) the lack of stability analysis tools for certification. The invention has been subject to many simulations and flight testing. The results substantiate the effectiveness of the invention and demonstrate the technical feasibility for use in modern aircraft flight control systems.

Nguyen, Nhan T.↗
DOE OSTI2020

The extended auxiliary equation mapping method to determine novel exact solitary wave solutions of the nonlinear fractional PDEs

Abstract In this paper, some new nonlinear fractional partial differential equations (PDEs) have been considered.Three models are including the space-time fractional-order Boussinesq equation, space-time (2 + 1)-dimensional breaking soliton equations, and space-time fractional-order SRLW equation describe the behavior of these equations in the diverse applications. Meanwhile, the fractional derivatives in the sense of β -derivative are defined. Some fractional PDEs will convert to the considered ordinary differential equations by the help of transformation of β -derivative. These equations are analyzed utilizing an integration scheme, namely, the extended auxiliary equation mapping method. The different kinds of traveling wave solutions, solitary, topological, dark soliton, periodic, kink, and rational, fall out as a by-product of this scheme. Finally, the existence of the solutions for the constraint conditions is also shown. The outcome indicates that some fractional PDEs are used as a growing finding in the engineering sciences, mathematical physics, and so forth.

Engineering↗
NASA NTRS1991

Non-Gaussian microwave background fluctuations from nonlinear gravitational effects

Whether the statistics of primordial fluctuations for structure formation are Gaussian or otherwise may be determined if the Cosmic Background Explorer (COBE) Satellite makes a detection of the cosmic microwave-background temperature anisotropy delta T(sub CMB)/T(sub CMB). Non-Gaussian fluctuations may be generated in the chaotic inflationary model if two scalar fields interact nonlinearly with gravity. Theoretical contour maps are calculated for the resulting Sachs-Wolfe temperature fluctuations at large angular scales (greater than 3 degrees). In the long-wavelength approximation, one can confidently determine the nonlinear evolution of quantum noise with gravity during the inflationary epoch because: (1) different spatial points are no longer in causal contact; and (2) quantum gravity corrections are typically small-- it is sufficient to model the system using classical random fields. If the potential for two scalar fields V(phi sub 1, phi sub 2) possesses a sharp feature, then non-Gaussian fluctuations may arise. An explicit model is given where cold spots in delta T(sub CMB)/T(sub CMB) maps are suppressed as compared to the Gaussian case. The fluctuations are essentially scale-invariant.

Salopek, D. S.↗
DOE OSTI2026

Extremized nonlinear and linearized responses in soft metamaterials enabled by gradient-based design and grayscale digital light processing

In this study, we develop a gradient-based design approach that exploits grayscale digital light processing (DLP) 3D printing for extremizing the nonlinear and linearized response of soft metamaterials — materials that harness engineered geometric instabilities to undergo large and programmable changes in configuration. Grayscale DLP approaches modulate local mechanical properties at the pixel scale by tuning the light intensity within a single grayscale image, unlocking an exceptionally large design space. To effectively navigate this space, we develop smooth mappings between local light intensity values and global quantities of interest that characterize the behavior of soft metamaterials. Enabling these smooth mappings are robust and differentiable nonlinear finite element simulations powered by a trust region solver. A PDE-constrained optimization problem is then solved to invert these mappings and produce light intensity distributions that endow the printed part with varying stiffness and flexibility in distinctive regions. It is shown that optimizing the distribution of soft and stiff phases throughout a metamaterial structure results in markedly different buckling and self-contact configurations to drive extremized nonlinear compression and linearized vibration responses. Optimized light intensity distributions are translated to grayscale images and directly used to print soft metamaterial samples, showing remarkable agreement between the buckling and self-contact response in simulated and measured deformed configurations.

Additive manufacturing↗
DOE OSTI2022

Manifold Learning-Based Polynomial Chaos Expansions for High-Dimensional Surrogate Models

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data representing quantities of interest of the computational or analytical model. For this purpose, we employ Grassmannian diffusion maps, a two-step nonlinear dimension reduction technique which allows us to reduce the dimensionality of the data and identify meaningful geometric descriptions in a parsimonious and inexpensive manner. Polynomial chaos expansion is then used to construct a mapping between the stochastic input parameters and the diffusion coordinates of the reduced space. An adaptive clustering technique is proposed to identify an optimal number of clusters of points in the latent space. The similarity of points allows us to construct a number of geometric harmonic emulators which are finally utilized as a set of inexpensive pretrained models to perform an inverse map of realizations of latent features to the ambient space and thus perform accurate out-of-sample predictions. Thus, the proposed method acts as an encoder-decoder system which is able to automatically handle very high-dimensional data while simultaneously operating successfully in the small-data regime. The method is demonstrated on two benchmark problems and on a system of advection-diffusion-reaction equations which model a first-order chemical reaction between two species. In all test cases, the proposed method is able to achieve highly accurate approximations which ultimately lead to the significant acceleration of UQ tasks.

42 ENGINEERING↗
NASA NTRS1984

Application of nonlinear transformations to automatic flight control

The theory of transformations of nonlinear systems to linear ones is applied to the design of an automatic flight controller for the UH-1H helicopter. The helicopter mathematical model is described and it is shown to satisfy the necessary and sufficient conditions for transformability. The mapping is constructed, taking the nonlinear model to canonical form. The performance of the automatic control system in a detailed simulation on the flight computer is summarized.

Meyer, G.↗
DOE OSTI2026

MAPS: the MFEM Anisotropic Plasma Solver

Simulating magnetically confined fusion plasmas presents a uniquely challenging problem due to the nonlinear anisotropic heat conduction. We introduce the MAPS (MFEM Anisotropic Plasma Solver) tool, which uses a high-order finite element method to compute transport solutions on unstructured meshes. We show results for a set of three 2-D verification tests, two of which demonstrate the expected convergence properties for various mesh resolutions and polynomial degrees. We then discuss the convergence rate for the third test.

Barnett, Rhea [ORNL] (ORCID:0000000317527979)↗
NASA NTRS1991

Communications and control for electric power systems

The first section of the report describes the AbNET system, a hardware and software communications system designed for distribution automation (it can also find application in substation monitoring and control). The topology of the power system fixes the topology of the communications network, which can therefore be expected to include a larger number of branch points, tap points, and interconnections. These features make this communications network unlike any other. The network operating software has to solve the problem of communicating to all the nodes of a very complex network in as reliable a way as possible even if the network is damaged, and it has to do so with minimum transmission delays and at minimum cost. The design of the operating protocols is described within the framework of the seven-layer Open System Interconnection hierarchy of the International Standards Organization. Section 2 of the report describes the development and testing of a high voltage sensor based on an electro-optic polymer. The theory of operation is reviewed. Bulk fabrication of the polymer is discussed, as well as results of testing of the electro-optic coefficient of the material. Fabrication of a complete prototype sensor suitable for use in the range 1-20 kV is described. The electro-optic polymer is shown to be an important material for fiber optic sensing applications. Appendix A is theoretical support for this work. The third section of the report presents the application of an artificial neural network, Kohonen's self-organizing feature map, for the classification of power system states. This classifier maps vectors of an N-dimensional space to a 2-dimensional neural net in a nonlinear way preserving the topological order of the input vectors. These mappings are studied using a nonlinear power system model.

Kirkham, H.↗