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NASA NTRS1992

Two neural network algorithms for designing optimal terminal controllers with open final time

Multilayer neural networks, trained by the backpropagation through time algorithm (BPTT), have been used successfully as state-feedback controllers for nonlinear terminal control problems. Current BPTT techniques, however, are not able to deal systematically with open final-time situations such as minimum-time problems. Two approaches which extend BPTT to open final-time problems are presented. In the first, a neural network learns a mapping from initial-state to time-to-go. In the second, the optimal number of steps for each trial run is found using a line-search. Both methods are derived using Lagrange multiplier techniques. This theoretical framework is used to demonstrate that the derived algorithms are direct extensions of forward/backward sweep methods used in N-stage optimal control. The two algorithms are tested on a Zermelo problem and the resulting trajectories compare favorably to optimal control results.

Plumer, Edward S.↗

DOE OSTI2025

Phase-field model of alloy solidification far from chemical equilibrium at the solid-liquid interface

We further develop a recently introduced phase-field model of far-from-equilibrium alloy solidification under additive manufacturing conditions [K. Ji et al., Phys. Rev. Lett. 130, 026203 (2023)]. This model utilizes enhanced solute diffusivity within the spatially diffuse interface region to quantitatively capture solute trapping with a larger interface width, thereby making simulations on experimentally relevant length and timescales computationally feasible. The main developments presented here include testing the robustness of different variational formulations, extending the model to concentrated alloys by incorporating solid and liquid free energies from thermodynamic databases, as illustrated for hypoeutectic Al-Ag alloys with CALPHAD, extending convergence tests as a function of interface width to 3D, and carrying out simulations in both 2D and 3D to examine existing theories of microstructure development. Our results indicate that the simplest variational formulation that interpolates the bulk free-energy density between its solid and liquid forms is the most robust. Remarkably, for hypoeutectic Al-Ag alloys, this formulation yields a high-velocity nonequilibrium phase diagram that is independent of interface width, thereby demonstrating that the framework of enhanced solute diffusivity can be nontrivially extended to concentrated alloys. Other variational formulations have restricted ranges of materials or processing parameters that can be reliably modeled. We use 2D simulations to construct high-velocity microstructure selection maps for dilute Al-Cu alloys. The results validate the important role of latent heat rejection at the interface and extend the limited predictions of linear stability analysis [A. Karma and A. Sarkissian, Phys. Rev. E 47, 513 (1993)] and sharp-interface 1D simulations to fully nonlinear regimes. Furthermore, 3D simulations, carried out using a computationally tractable axisymmetric cellular/dendritic interface shape, demonstrate a good convergence similar to that observed in 2D as a function of interface width. Full 3D simulations, in turn, reveal that the standard theory of absolute stability is a good predictor of the upper critical velocity beyond which steady-state growth becomes unstable, despite the different morphological manifestations of this instability in 2D and 3D.

36 MATERIALS SCIENCE↗

NASA NTRS1979

Two-dimensional, time-dependent MHD description of interplanetary disturbances Simulation of high speed solar wind interactions

A two-dimensional, time-dependent nonlinear MHD model is used to simulate the general features of multiply-interacting, transient solar wind flows. The major advantage of the two-dimensional model over the one-dimensional one is the proper consideration of azimuthal gradients. In addition, the new model can provide contour maps for disturbed plasma properties in the equatorial plane, thereby enabling one to perform essential tests of the physical assumptions through direct comparison with space probe data.

Wu, S. T.↗

NASA NTRS1985

The Kronecker indices of affine-nonlinear control systems

The Kronecker indices of smooth affine-nonlinear control systems presently defined are noted to determine the collection of controllable linear systems that are obtainable on the basis of local feedback equivalences and state-space reductions. Because attention is given to the invariants of systems under equivalences, and the behavior of these invariants under mappings that arise from state submersions, local representations of systems are used wherever possible to render cases more accessible.

Lewis, J. H.↗

NASA NTRS1994

Fuzzy self-learning control for magnetic servo system

It is known that an effective control system is the key condition for successful implementation of high-performance magnetic servo systems. Major issues to design such control systems are nonlinearity; unmodeled dynamics, such as secondary effects for copper resistance, stray fields, and saturation; and that disturbance rejection for the load effect reacts directly on the servo system without transmission elements. One typical approach to design control systems under these conditions is a special type of nonlinear feedback called gain scheduling. It accommodates linear regulators whose parameters are changed as a function of operating conditions in a preprogrammed way. In this paper, an on-line learning fuzzy control strategy is proposed. To inherit the wealth of linear control design, the relations between linear feedback and fuzzy logic controllers have been established. The exercise of engineering axioms of linear control design is thus transformed into tuning of appropriate fuzzy parameters. Furthermore, fuzzy logic control brings the domain of candidate control laws from linear into nonlinear, and brings new prospects into design of the local controllers. On the other hand, a self-learning scheme is utilized to automatically tune the fuzzy rule base. It is based on network learning infrastructure; statistical approximation to assign credit; animal learning method to update the reinforcement map with a fast learning rate; and temporal difference predictive scheme to optimize the control laws. Different from supervised and statistical unsupervised learning schemes, the proposed method learns on-line from past experience and information from the process and forms a rule base of an FLC system from randomly assigned initial control rules.

Tarn, J. H.↗

DOE OSTI2024

Relating Hydro–Mechanical and Elastodynamic Properties of Dynamically Stressed Tensile–Fractured Rock in Relation to Applied Normal Stress, Fracture Aperture, and Contact Area

We exploit nonlinear elastodynamic properties of fractured rock to probe the micro-scale mechanics of fractures and understand the relation between fluid transport and fracture aperture under dynamic stressing. Experiments were conducted on rough, tensile-fractured Westerly granite subject to triaxial stresses. We measure fracture permeability for steady-state fluid flow with deionized water. Pore pressure oscillations are applied at amplitudes ranging from 0.2 to 1 MPa at 1 Hz frequency. During dynamic stressing we transmit ultrasonic signals through the fracture using an array of piezoelectric transducers (PZTs) to monitor evolution of interface properties. We examine the influence of fracture aperture and contact area by conducting measurements at effective normal stresses of 10–20 MPa. Additionally, the evolution of contact area with stress is characterized using pressure sensitive film. These experiments are conducted separately with the same fracture and map contact area at stresses from 9 to 21 MPa. The measurements are a proxy for “true” contact area for the fracture surface and we relate them to elastic properties using the calculated PZT sensor footprints via numerical modeling of Fresnel zones. We compare the elastodynamic response of the fracture using the stress-induced changes in ultrasonic wave velocities for transmitter-receiver pairs to image spatial variations in contact properties. We show that nonlinear elasticity and permeability enhancement decrease with increasing normal stress. Additionally, post-oscillation wave velocity and permeability exhibit quick recoveries toward pre-oscillation values. Estimates of fracture contact area (global and local) demonstrate that the elastodynamic and permeability responses are dominated by fracture topology.

58 GEOSCIENCES↗

DOE OSTI2022

The nonlinear rheology of complex yield stress foods

Many foods have a yield stress that allows them to retain a desired shape at rest, but transition into a viscous fluid when being served or consumed. The determination of the yield stress of the food dictates how the foods are formed and packaged, how they are served, and how they are perceived when being eaten. Oscillatory shearing provides an ideal test protocol to map the rheology across a range of time and flow strength scales. We couple oscillatory shearing and an iterative recovery procedure to show that the yielding process is a continuous transition for two common yield stress foods. We show that unrecoverable processes from oscillatory tests are equivalent to the steady shear flow behavior. We show that this yielding behavior can be well approximated by a recently published model that treats yield stress materials as continuous viscoelastic fluids with a rate-dependent relaxation time and has parameters that can be obtained from the linear viscoelastic oscillatory frequency sweep and the steady shear flow curve.

Griebler, James J.↗

NASA NTRS2022

Effective Uncertainty Quantification for Multi-Angle Polarimetric Aerosol Remote Sensing Over Ocean

Multi-angle polarimetric (MAP) measurements can enable detailed characterization of aerosol microphysical and optical properties and improve atmospheric correction in ocean color remote sensing. Advanced retrieval algorithms have been developed to obtain multiple geophysical parameters in the atmosphere–ocean system. Theoretical pixel-wise retrieval uncertainties based on error propagation have been used to quantify retrieval performance and determine the quality of data products. However, standard error propagation techniques in high-dimensional retrievals may not always represent true retrieval errors well due to issues such as local minima and the nonlinear dependence of the forward model on the retrieved parameters near the solution. In this work, we analyze these theoretical uncertainty estimates and validate them using a flexible Monte Carlo approach. The Fast Multi-Angular Polarimetric Ocean coLor (FastMAPOL) retrieval algorithm, based on efficient neural network forward models, is used to conduct the retrievals and uncertainty quantification on both synthetic HARP2 (Hyper-Angular Rainbow Polarimeter 2) and AirHARP (airborne version of HARP2) datasets. In addition, for practical application of the uncertainty evaluation technique in operational data processing, we use the automatic differentiation method to calculate derivatives analytically based on the neural network models. Both the speed and accuracy associated with uncertainty quantification for MAP retrievals are addressed in this study. Pixel-wise retrieval uncertainties are further evaluated for the real AirHARP field campaign data. The uncertainty quantification methods and results can be used to evaluate the quality of data products, as well as guide MAP algorithm development for current and future satellite systems such as NASA’s Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission.

PACE↗

NASA NTRS1972

Numerical calculation of transonic flow about swept wings.

Description of a mixed elliptic-hyperbolic relaxation algorithm which calculates solutions to the three-dimensional, nonlinear transonic small disturbance potential equation for flows about thin swept lifting wings with free-stream Mach number less than 1. The algorithm is designed to treat supercritical flows, including cases with embedded shock waves. Nonrectangular planform shapes, including sweep and taper, are treated by a coordinate transformation which maps the wing planform into a rectangle. Computed results at angles of attack of 0 and 2 deg for a AR = 4, constant chord, 23.75 deg sweptback planform model with a Lockheed C141 airfoil section are compared with data obtained experimentally for both subcritical and supercritical flows. Subcritical results are also compared with those obtained by a subsonic 'panel' method.

Ballhaus, W. F.↗

DOE OSTI2022

Multi-element flow-driven spectral chaos (ME-FSC) method for uncertainty quantification of dynamical systems

The flow-driven spectral chaos (FSC) is a recently developed method for tracking and quantifying uncertainties in the long-time response of stochastic dynamical systems using the spectral approach. The method uses a novel concept called enriched stochastic flow maps as a means to construct an evolving finite-dimensional random function space that is both accurate and computationally efficient in time. In this paper, we present a multi-element version of the FSC method (the ME-FSC method for short) to tackle (mainly) those dynamical systems that are inherently discontinuous over the probability space. In ME-FSC, the random domain is partitioned into several elements, and then the problem is solved separately on each random element using the FSC method. Subsequently, results are aggregated to compute the probability moments of interest using the law of total probability. To demonstrate the effectiveness of the ME-FSC method in dealing with discontinuities and long-time integration of stochastic dynamical systems, four representative numerical examples are presented in this paper, including the Van-der-Pol oscillator problem and the Kraichnan-Orszag three-mode problem. Results show that the ME-FSC method is capable of solving problems that have strong nonlinear dependencies over the probability space, both reliably and at low computational cost.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Suppressing the enhancement of stimulated Raman scattering in inhomogeneous plasmas by tuning the modulation frequency of a broadband laser

The stimulated Raman scattering (SRS) instability can inhibit the performance of laser driven inertial confinement fusion (ICF) implosions by scattering light into unwanted directions or by generating hot electrons that preheat the target fuel. In principle, ICF target designs can avoid parameter regimes conducive to large, linear SRS gains. In practice, kinetic inflation—the nonlinear enhancement of SRS due to electron trapping in the excited plasma wave—makes this difficult. Here we show that laser bandwidth in the form of frequency modulation can either decrease or increase the inflationary SRS (iSRS) threshold in inhomogeneous plasmas depending on the maximum chirp of the laser pulse. The threshold, mapped out by a series of particle-in-cell simulations, exhibits a minimum when the frequency change within the pulse cancels the spatial detuning due to density inhomogeneities along the trajectory of the scattered light. In conclusion, by tuning the pump laser parameters away from this minimum, the iSRS threshold can be larger than at zero bandwidth, providing a path to mitigating kinetic inflation in ignition relevant plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1992

Functional expansion representations of artificial neural networks

In the past few years, significant interest has developed in using artificial neural networks to model and control nonlinear dynamical systems. While there exists many proposed schemes for accomplishing this and a wealth of supporting empirical results, most approaches to date tend to be ad hoc in nature and rely mainly on heuristic justifications. The purpose of this project was to further develop some analytical tools for representing nonlinear discrete-time input-output systems, which when applied to neural networks would give insight on architecture selection, pruning strategies, and learning algorithms. A long term goal is to determine in what sense, if any, a neural network can be used as a universal approximator for nonliner input-output maps with memory (i.e., realized by a dynamical system). This property is well known for the case of static or memoryless input-output maps. The general architecture under consideration in this project was a single-input, single-output recurrent feedforward network.

Gray, W. Steven↗

NASA NTRS1994

Unsupervised texture image segmentation by improved neural network ART2

We here propose a segmentation algorithm of texture image for a computer vision system on a space robot. An improved adaptive resonance theory (ART2) for analog input patterns is adapted to classify the image based on a set of texture image features extracted by a fast spatial gray level dependence method (SGLDM). The nonlinear thresholding functions in input layer of the neural network have been constructed by two parts: firstly, to reduce the effects of image noises on the features, a set of sigmoid functions is chosen depending on the types of the feature; secondly, to enhance the contrast of the features, we adopt fuzzy mapping functions. The cluster number in output layer can be increased by an autogrowing mechanism constantly when a new pattern happens. Experimental results and original or segmented pictures are shown, including the comparison between this approach and K-means algorithm. The system written in C language is performed on a SUN-4/330 sparc-station with an image board IT-150 and a CCD camera.

Wang, Zhiling↗

NASA NTRS1982

Kerr Reservoir LANDSAT experiment analysis for March 1981

LANDSAT radiance data were used in an experiment conducted on the waters of Kerr Reservoir to determine if reliable algorithms could be developed that relate water quality parameters to remotely sensed data. A mix of different types of algorithms using the LANDSAT bands was generated to provide a thorough understanding of the relationships among the data involved. Except for secchi depth, the study demonstrated that for the ranges measured, the algorithms that satisfactorily represented the data encompass a mix of linear and nonlinear forms using only one LANDSAT band. Ratioing techniques did not improve the results since the initial design of the experiment minimized the errors against which this procedure is effective. Good correlations were found for total suspended solids, iron, turbidity, and secchi depth. Marginal correlations were discovered for nitrate and tannin + lignin. Quantification maps of Kerr Reservoir are presented for many of the water quality parameters using the developed algorithms.

Lecroy, S. R.↗

NASA NTRS1985

Numerical solution of Euler's equation by perturbed functionals

A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

Dey, S. K.↗

NASA NTRS2018

The Ozone Mapping and Profiler Suite (OMPS) Limb Profiler (LP) Version 1 Aerosol Extinction Retrieval Algorithm: Theoretical Basis

The theoretical basis of the Ozone Mapping and Profiler Suite (OMPS) Limb Profiler (LP) Version 1 aerosol extinction retrieval algorithm is presented. The algorithm uses an assumed bimodal lognormal aerosol size distribution to retrieve aerosol extinction profiles at 675 nm from OMPS LP radiance measurements. A first-guess aerosol extinction profile is updated by iteration using the Chahine nonlinear relaxation method, based on comparisons between the measured radiance profile at 675 nm and the radiance profile calculated by the Gauss Seidel limb-scattering (GSLS) radiative transfer model for a spherical-shell atmosphere. This algorithm is discussed in the context of previous limb-scattering aerosol extinction retrieval algorithms, and the most significant error sources are enumerated. The retrieval algorithm is limited primarily by uncertainty about the aerosol phase function. Horizontal variations in aerosol extinction, which violate the spherical-shell atmosphere assumed in the version 1 algorithm, may also limit the quality of the retrieved aerosol extinction profiles significantly.

Loughman, Robert↗

DOE OSTI2022

Unraveling the Correlation between Raman and Photoluminescence in Monolayer MoS 2 through Machine‐Learning Models

Abstract 2D transition metal dichalcogenides (TMDCs) with intense and tunable photoluminescence (PL) have opened up new opportunities for optoelectronic and photonic applications such as light‐emitting diodes, photodetectors, and single‐photon emitters. Among the standard characterization tools for 2D materials, Raman spectroscopy stands out as a fast and non‐destructive technique capable of probing material's crystallinity and perturbations such as doping and strain. However, a comprehensive understanding of the correlation between photoluminescence and Raman spectra in monolayer MoS 2 remains elusive due to its highly nonlinear nature. Here, the connections between PL signatures and Raman modes are systematically explored, providing comprehensive insights into the physical mechanisms correlating PL and Raman features. This study's analysis further disentangles the strain and doping contributions from the Raman spectra through machine‐learning models. First, a dense convolutional network (DenseNet) to predict PL maps by spatial Raman maps is deployed. Moreover, a gradient boosted trees model (XGBoost) with Shapley additive explanation (SHAP) to bridge the impact of individual Raman features in PL features is applied. Last, a support vector machine (SVM) to project PL features on Raman frequencies is adopted. This work may serve as a methodology for applying machine learning to characterizations of 2D materials.

Lu, Ang‐Yu↗

DOE OSTI2021

MOSAIC: An Effective FFT-based Numerical Method to Assess Aging Properties of Concrete

As the nuclear fleet in the United States ages and subsequent license renewal applications grow, the prediction of concrete durability at extended operation becomes more important. To address this issue, a Fast-Fourier Transform (FFT) method is utilized to simulate aging-related degradation of concrete within the Microstructure Oriented Scientific Analysis of Irradiated Concrete (MOSAIC) software. MOSAIC utilizes compositional phase maps to simulate damage from radiation-induced volumetric expansion (RIVE), applied force, creep, and thermal expansion. This compositional detail allows each mineral in the microstructure to be assigned specific material properties, allowing the simulation to be as accurate and representative as possible. The principal goal of MOSAIC is to simulate the effects of nonlinear aging mechanisms occurring in nuclear concrete on the macroscopic mechanical properties, using only the aggregate microstructure compositional information as a starting point. Here, several realistic example simulations are shown to demonstrate the utility and uniqueness of the MOSAIC software.

36 MATERIALS SCIENCE↗