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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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2021

Multi-Pass Sequential Mini-Batch Stochastic Gradient Descent Algorithms for Noise Covariance Estimation in Adaptive Kalman Filtering

Estimation of unknown noise covariances in a Kalman filter is a problem of significant practical interest in a wide array of applications. Although this problem has a long history, reliable algorithms for their estimation were scant, and necessary and sufficient conditions for identifiability of the covariances were in dispute until recently. Necessary and sufficient conditions for covariance estimation and a batch estimation algorithm were presented in our previous study. This paper presents stochastic gradient descent algorithms for noise covariance estimation in adaptive Kalman filters that are an order of magnitude faster than the batch method for similar or better root mean square error. More significantly, these algorithms are applicable to non-stationary systems where the noise covariances can occasionally jump up or down by an unknown magnitude. The computational efficiency of the new algorithms stems from adaptive thresholds for convergence, recursive fading memory estimation of the sample cross-correlations of the innovations, and accelerated stochastic gradient descent algorithms. The comparative evaluation of the proposed methods on a number of test cases demonstrates their computational efficiency and accuracy.

Adaptive Kalman filtering↗
NASA NTRS1979

Modeling of terrain gradient for stochastically spaced rows of a measurement matrix

Terrain gradients are employed to evaluate passable regions for unmanned martian roving vehicle. Range data matrix is displaced randomly row wise at the shallow elevation angles near the skyline. The magnitude of the measurement noise in the elevation angles can approach that of the spacing of the same angle. By using a variable incremental data spacing scanning scheme, one can estimate this signal noise ratio. It is found that the error in slope estimate at far distance becomes large for a given elevation angle error. Evaluation of the in-path slopes can be expressed in terms of the inverse of the range slopes. This is because of the fact that the elevation angle is considered as a random variable while the range data are relatively less noisy. An error analysis is performed and it is found that the change of slope is a nonlinear function of the error in elevation angle.

Mediavilla, R.↗
NASA NTRS1991

Estimation of optical flow in airborne electro-optical sensors by stochastic approximation

The essence of motion or range estimation by passive electrooptical means is the ability to determine the correspondence of picture elements in pairs of image frames and to estimate their coordinates and their disparity (relative shifts) in the image plane of an electrooptical imaging sensor. The disparity can be in successive frames due to self-motion or in simultaneous frames of a stereo pair. A key issue is to provide these estimates on-line. This paper describes the theoretical background of such an interframe shift estimator. It is based on a stochastic gradient algorithm, specifically implementing a form of stochastic approximation, which can achieve rapid convergence of the shift estimate. Analytical and numerical simulation examples for random texture and isolated features validate the feasibility and the effectiveness of the estimator.

Merhav, S. J.↗
NASA NTRS1977

Estimation of terrain iso-gradients from a stochastic range data measurement matrix

The problem of estimating terrain iso-gradients for an autonomous roving vehicle is complicated by the measurement error inherent in the range data matrix. In this paper, the in-path and cross-path slopes at each data point in the multivariable range matrix are expressed in terms of parameters at that data point and those at its surrounding points. The sensitivity in the change of these slopes - due to the errors in measurements in range, elevation angle and azimuth angle are formulated. These sensitivities are used to determine the appropriate statistics of the gradient, which are then used to describe the terrain with a known probability of accuracy.

Shen, C. N.↗
NASA NTRS1973

Stochastic estimates of gradient from laser measurements for an autonomous Martian roving vehicle

The general problem of estimating the state vector x from the state equation h = Ax where h, A, and x are all stochastic, is presented. Specifically, the problem is for an autonomous Martian roving vehicle to utilize laser measurements in estimating the gradient of the terrain. Error exists due to two factors - surface roughness and instrumental measurements. The errors in slope depend on the standard deviations of these noise factors. Numerically, the error in gradient is expressed as a function of instrumental inaccuracies. Certain guidelines for the accuracy of permissable gradient must be set. It is found that present technology can meet these guidelines.

Burger, P. A.↗
NASA NTRS1973

Stochastic estimates of gradient from laser measurements for an autonomous Martian Roving Vehicle

The general problem presented in this paper is one of estimating the state vector x from the state equation h = Ax, where h, A, and x are all stochastic. Specifically, the problem is for an autonomous Martian Roving Vehicle to utilize laser measurements in estimating the gradient of the terrain. Error exists due to two factors - surface roughness and instrumental measurements. The errors in slope depend on the standard deviations of these noise factors. Numerically, the error in gradient is expressed as a function of instrumental inaccuracies. Certain guidelines for the accuracy of permissable gradient must be set. It is found that present technology can meet these guidelines.-

Shen, C. N.↗
NASA NTRS1971

A stochastic constrained optimization technique and its application to detector array processing.

A stochastic projected gradient algorithm is proposed which can be used for finding a constrained optimum point for a concave or convex objective function subject to nonlinear constraints which form a connected region even when only a noisy estimate of the objective function is available. For a constraint described by a single linear equation, convergence to the constrained optimum value is proved, and the rate of convergence of the algorithm to the constrained optimum value is determined. The algorithm is applied to the nonlinear problem of obtaining automatically an array of detectors which forms a beam in a desired direction in space in the presence of interfering noise so as to maximize the SNR subject to a constraint on the super-gain ratio.

Winkler, L. P.↗
NASA NTRS1972

Adaptive nonlinear optimization of the signal-to-noise ratio of an array subject to a constraint.

Investigation of a stochastic projected gradient algorithm which can be used to find a constrained optimum point for a concave or convex objective function subject to nonlinear constraints. When the constraint consists of only one linear equation, convergence to the constrained optimum value is proven, and bounds are obtained for the rate of convergence of the algorithm to the constrained optimum value. This algorithm is then applied to the nonlinear problem of automatically making an array of detectors form a beam in a desired direction in space when unknown interfering noise is present so as to maximize the signal-to-noise ratio subject to a constraint on the supergain ratio.

Winkler, L. P.↗
NASA NTRS1991

Programming Probabilistic Structural Analysis for Parallel Processing Computer

The ultimate goal of this research program is to make Probabilistic Structural Analysis (PSA) computationally efficient and hence practical for the design environment by achieving large scale parallelism. The paper identifies the multiple levels of parallelism in PSA, identifies methodologies for exploiting this parallelism, describes the development of a parallel stochastic finite element code, and presents results of two example applications. It is demonstrated that speeds within five percent of those theoretically possible can be achieved. A special-purpose numerical technique, the stochastic preconditioned conjugate gradient method, is also presented and demonstrated to be extremely efficient for certain classes of PSA problems.

Sues, Robert H.↗
NASA NTRS2009

Oxygen Ion Heat Rate within Alfvenic Turbulence in the Cusp

The role that the cleft/cusp has in ionosphere-magnetosphere coupling makes it a dynamic and important region. It is directly exposed to the solar wind, making it possible for the entry of electromagnetic energy and precipitating electrons and ions from dayside reconnection and other dayside events. It is also a significant source of ionospheric plasma, contributing largely to the mass loading of the magnetosphere with large fluxes of outflowing ions. Crossing the cusp/cleft near 5100 km, the Polar instruments observe the common correlation of downward Poynting flux, ion energization, soft electron precipitation, broadband extremely low-frequency (BB-ELF) emissions, and density depletions. The dominant power in the BB-ELF emissions is now identified to be from spatially broad, low frequency Alfv nic structures. For a cusp crossing, we determine using the Electric Field Investigation (EFI), that the electric and magnetic field fluctuations are Alfv nic and the electric field gradients satisfy the inequality for stochastic acceleration. With all the Polar 1996 horizontal crossings of the cusp, we determine the O+ heating rate using the Thermal Ion Dynamics Experiment (TIDE) and Plasma Wave Investigation (PWI). We then compare this heating rate to other heating rates assuming the electric field gradient criteria exceeds the limit for stochastic acceleration for the remaining crossings. The comparison suggests that a stochastic acceleration mechanism is operational and the heating is controlled by the transverse spatial scale of the Alfvenic waves.

Coffey, Victoria N.↗
NASA NTRSDate not supplied

Differential Equation Approximation Using Gradient-Boosted Quantile Regression

The operation of cyber-physical-human (CPH) systems is subject to various epistemic and aleatory uncertainties. Overall trustworthiness of CPH systems relies on the trustworthiness of its components and their interactions. It is important that computational models comprising the cyber component of CPH provide predictions accompanied by a measure of confidence in model outcomes. Uncertainty quantification (UQ) and propagation are especially important in safety critical CPH systems. Gradient-boosted trees is a modeling approach capable both of learning the dynamics of a system and performing UQ. In this paper, we devise a method for using gradient boosting to learn the dynamics of a second order differential equation and estimate uncertainty at the same time. We do this by creating a custom loss function that trains the model to approximate the second derivative of a noisy time series, and to penalize based on a parameter that corresponds to the desired quantile. The resulting gradient boosting model can simulate stochastic trajectories of the system given a single starting point, that is, it can estimate both the expected trajectory and its uncertainty. We show that the uncertainty estimation is well calibrated and that the model can learn the dynamics even in the presence of noise. We demonstrate the approach on a simple cartpole system.

Autonomous systems↗
NASA NTRS1993

Statistics of Experiments on Cluster Formation and Transport in a Gravitational Field

Metastable state relaxation in a gravitational field is investigated in the case of non-critical binary solutions. A relaxation description is presented in terms of the time-dependent Ginzburg-Landau formalism for a non-conserved order parameter. A new ansatz for solution of the corresponding partial nonlinear stochastic differential equation is discussed. It is proved that, for the supersaturated solution under consideration, the metastable state relaxation in a gravitational field leads to formation of solute concentration gradients due to the sedimentation of subcritical solute clusters. The pure discussion of the possible methods to compare theoretical results and experimental data related to solute sedimentation in a gravitational field is presented. It is shown that in order to describe these experiments it is necessary to deal both with the value of the solute concentration gradient and with its formation rate. The stochastic nature of the sedimentation process is shown.

Izmailov, Alexander F.↗
NASA NTRSDate not supplied

Gradient-Based Optimization of the Common Research Model Wing Subject to CFD-Based Gust and Flutter Constraints

The linearized frequency-domain method was recently implemented in the stabilized finite element solver in NASA’s FUN3D code. Previous work by the authors used this method for enforcing flutter constraints during gradient-based optimizations. More recently, the solver was expanded to account for continuous (also known as stochastic) gust responses. This paper expands on recent Common Research Model wing optimization work, which demonstrated gradient-based optimization with flutter and stochastic gust constraints, among others. While that work utilized FUN3D for static aeroelastic solutions but relied on doublet lattice aerodynamics for gust and flutter responses, the present work replaces these unsteady aerodynamic analyses with those of FUN3D’s linearized frequency-domain solver. With analytic derivatives available, gradient-based optimization is performed through the use of the OpenMDAO/MPhys libraries with over 700 shape, structural, and aerodynamic design variables and over 10 nonlinear constraints. Comparisons of analysis results and optimized designs are made between doublet lattice and linearized frequency-domain solutions.

aeroelasticity↗
NASA NTRS2004

Employing Sensitivity Derivatives for Robust Optimization under Uncertainty in CFD

A robust optimization is demonstrated on a two-dimensional inviscid airfoil problem in subsonic flow. Given uncertainties in statistically independent, random, normally distributed flow parameters (input variables), an approximate first-order statistical moment method is employed to represent the Computational Fluid Dynamics (CFD) code outputs as expected values with variances. These output quantities are used to form the objective function and constraints. The constraints are cast in probabilistic terms; that is, the probability that a constraint is satisfied is greater than or equal to some desired target probability. Gradient-based robust optimization of this stochastic problem is accomplished through use of both first and second-order sensitivity derivatives. For each robust optimization, the effect of increasing both input standard deviations and target probability of constraint satisfaction are demonstrated. This method provides a means for incorporating uncertainty when considering small deviations from input mean values.

Newman, Perry A.↗
NASA NTRS1974

A relation between cosmic-ray fluctuations, gradient, and diffusion coefficient

The motion of charged particles in a stochastic magnetic field is considered via a generalized quasi-linear expansion of Liouville's equation. The result is an equation relating cosmic-ray scintillations to particle gradients and to magnetic-field fluctuations (or diffusion coefficient). The resulting theory may be regarded as an example of a fluctuation-dissipation phenomenon, in which the diffusion coefficient plays the role of the dissipative parameter. The resonant interaction between particles and the random interplanetary magnetic field is considered explicitly, and it is shown that observed scintillations of high-energy (about 1 GeV) cosmic rays may be reasonably explained by the model.

Owens, A. J.↗
NASA NTRS2019

Sizing and Topology Design of an Aeroelastic Wingbox Under Uncertainty

The goals of this work are to use a nested optimizer to conduct simultaneous sizing (inner level) and topology (outer level) design of a wingbox, considering uncertainties in the safety factors used to define the aeroelastic constraints. These uncertainties, propagated via sampling-driven polynomial chaos, are explicitly introduced at the inner level of the method, during gradient-based sizing optimization, resulting in a stochastic optimal sizing distribution. Measures of robustness in the total structural mass are then passed to the outer level, where a global optimizer evolves the topology parameters. The results demonstrate design choices needed to improve robustness in the face of uncertain safety factors, and the various physical mechanisms driving this process.

Stanford, Bret K.↗