Search NASA⌕ Search

SEARCH · Search NASA

Results for “linear estimation”

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 865 records · Page 48

Generalized Jeans' Escape of Pick-Up Ions in Quasi-Linear Relaxation

Jeans escape is a well-validated formulation of upper atmospheric escape that we have generalized to estimate plasma escape from ionospheres. It involves the computation of the parts of particle velocity space that are unbound by the gravitational potential at the exobase, followed by a calculation of the flux carried by such unbound particles as they escape from the potential well. To generalize this approach for ions, we superposed an electrostatic ambipolar potential and a centrifugal potential, for motions across and along a divergent magnetic field. We then considered how the presence of superthermal electrons, produced by precipitating auroral primary electrons, controls the ambipolar potential. We also showed that the centrifugal potential plays a small role in controlling the mass escape flux from the terrestrial ionosphere. We then applied the transverse ion velocity distribution produced when ions, picked up by supersonic (i.e., auroral) ionospheric convection, relax via quasi-linear diffusion, as estimated for cometary comas [1]. The results provide a theoretical basis for observed ion escape response to electromagnetic and kinetic energy sources. They also suggest that super-sonic but sub-Alfvenic flow, with ion pick-up, is a unique and important regime of ion-neutral coupling, in which plasma wave-particle interactions are driven by ion-neutral collisions at densities for which the collision frequency falls near or below the gyro-frequency. As another possible illustration of this process, the heliopause ribbon discovered by the IBEX mission involves interactions between the solar wind ions and the interstellar neutral gas, in a regime that may be analogous [2].

Moore, T. E.↗

Dynamic of Langmuir and Ion-Sound Waves in Type 3 Solar Radio Sources

The evolution of Langmuir and ion-sound waves in type 3 sources is investigated, incorporating linear growth, linear damping, and nonlinear electrostatic decay. Improved estimates are obtained for the wavenumber range of growing waves and the nonlinear coupling coefficient for the decay process. The resulting prediction for the electrostatic decay threshold is consistent with the observed high-field cutoff in the Langmuir field distribution. It is shown that the conditions in the solar wind do not allow a steady state to be attained; rather, bursty linear and nonlinear interactions take place, consistent with the highly inhomogeneous and impulsive waves actually observed. Nonlinear growth is found to be fast enough to saturate the growth of the parent Langmuir waves in the available interaction time. The resulting levels of product Langmuir and ion-sound waves are estimated theoretically and shown to be consistent with in situ ISEE 3 observations of type 3 events at 1 AU. Nonlinear interactions slave the growth and decay of product sound waves to that of the product Langmuir waves. The resulting probability distribution of ion-sound field strengths is predicted to have a flat tail extending to a high-field cutoff. This prediction is consistent with statistics derived here from ISEE 3 observations. Agreement is also found between the frequencies of the observed waves and predictions for the product S waves. The competing processes of nonlinear wave collapse and quasilinear relaxation are discussed, and it is concluded that neither is responsible for the saturation of Langmuir growth. When wave and beam inhomogeneities are accounted for, arguments from quasi-linear relaxation yield an upper bound on the Langmuir fields that is too high to be relevant. Nor are the criteria for direct wave collapse of the beam-driven waves met, consistent with earlier simulation results that imply that this process is not responsible for saturation of the beam instability. Indeed, even if the highest observed Langmuir fields are assumed to he part of a long-wavelength 'condensate' produced via electrostatic decay, they still fall short of the relevant requirements for wave collapse. The most stringent requirement for collapse is that collapsing wave packets not be disrupted by ambient density fluctuations in the solar wind. Fields of several mV m(exp -1) extending over several hundred km would be needed to satisfy this requirement; at 1 AU such fields are rare at best.

Robinson, P. A.↗

A Novel Machine Learning Method for Surface PM2.5 Estimations from Geostationary Satellites

Particulate matter (PM) with a diameter of less or equal to 2.5 μm, known as PM , affects human health as it penetrates the respiratory system. The Environmental Protection Agency (EPA) measures the atmospheric concentration of PM using air quality monitors stationed throughout the Continental United States (CONUS). Such measurements are points on a spatial domain and therefore, might not be representative of the air quality at nearby areas considering that the composition of the atmosphere is highly variable from place to place. Satellite based AOD permits a spatially uniform means of estimating PM and new geostationary satellites provide high temporal and spatial resolution estimation of AOD. However, the concentration of PM is non-linearly dependent on other atmospheric parameters that include relative humidity, temperature, and height of the planetary boundary layer. This information may be estimated at similar spatial and temporal resolutions as AOD from numerical modeling such as from the National Oceanic and Atmospheric Administration’s (NOAA) High Resolution Rapid Refresh (HRRR) model which resolves near real-time atmospheric conditions over the CONUS. The estimation of PM concentration is a multi-parametric problem that considers the effect of temporal dependencies among the different parameters. Deep learning approaches are appropriate for such complex estimation problems as they intrinsically capture relations among multiple non-linear parameters. This study compares deep-learning methods to traditional regression analysis to demonstrate the capabilities of these methods in predicting PM2.5 concentrations. Additionally, a novel ensemble learning approach is employed to identify scientific processes that could further improve the estimation of PM concentration. Utilizing Long Short-Term Memory (LSTM) neural networks, which are suitable for multivariate time series estimation problems as they are capable of learning long-term dependencies, individual models are created for each EPA station and trained on the aforementioned dataset collocated over each station. Individual station models are merged if the model's performance is improved by reducing the root mean squared error (RMSE) metric. This ensemble training method ultimately reduces the RMSE value. Evaluation of these results provide insights into physical processes and related observable parameters that may contribute to PM concentrations. Identified parameters evaluated to be statistically different between the merged and unmerged models are expected to improve overall performance. These new parameters are then utilized for reevaluation of the deep learning methods with an extreme gradient boosting model with an RMSE of 5.5 providing the best results.

George Priftis↗

LuGo: An enhanced quantum phase estimation implementation

Quantum Phase Estimation (QPE) is a cardinal algorithm in quantum computing that plays a crucial role in various applications, including cryptography, molecular simulation, and solving systems of linear equations. However, the standard implementation of QPE faces challenges related to time complexity and circuit depth, which limit its practicality for large-scale computations. We introduce LuGo, a novel framework designed to enhance the performance of QPE by reducing circuit duplication, as well as using parallelization techniques to achieve faster generation of the QPE circuit and gate reduction. We validate the effectiveness of our framework by generating quantum linear solver circuits, which require both QPE and inverse QPE, to solve linear systems of equations. LuGo achieves significant improvements in both computational efficiency and hardware requirements without compromising on accuracy. Compared to a standard QPE implementation, LuGo reduces time consumption to generate a circuit that solves a 2 6 × 2 6 system matrix by a factor of 50.68 and over 31× reduction of quantum gates and circuit depth, with no fidelity loss on an ideal quantum simulator. Furthermore, we demonstrated the versatility and scalability of LuGo enabled HHL algorithm by simulating a canonical Hele-Shaw fluid problem using a quantum simulator. With these advantages, LuGo paves the way for more efficient implementations of QPE, enabling broader applications across several quantum computing domains.

Quantum algorithm↗

The determination of third order linear models from a seventh order nonlinear jet engine model

Results are presented that demonstrate how good reduced-order models can be obtained directly by recursive parameter identification using input/output (I/O) data of high-order nonlinear systems. Three different methods of obtaining a third-order linear model from a seventh-order nonlinear turbojet engine model are compared. The first method is to obtain a linear model from the original model and then reduce the linear model by standard reduction techniques such as residualization and balancing. The second method is to identify directly a third-order linear model by recursive least-squares parameter estimation using I/O data of the original model. The third method is to obtain a reduced-order model from the original model and then linearize the reduced model. Frequency responses are used as the performance measure to evaluate the reduced models. The reduced-order models along with their Bode plots are presented for comparison purposes.

Lalonde, Rick J.↗

Taylor approximation variance reduction for approximation errors in PDE-constrained Bayesian inverse problems

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a computationally cheaper alternative to the accurate parameter-to-observable mappings and/or may ignore additional unknowns or sources of uncertainty. The Bayesian approximation error (BAE) approach provides a means to account for the induced uncertainties and approximation errors, i.e. the errors between the accurate parameter-to-observable mapping and the surrogate. The statistics of these errors are, however, in general unknown a priori, and are thus calculated using Monte Carlo sampling. Although the sampling is typically carried out offline, i.e. before considering the data, the process can still represent a computational bottleneck. In this work, we develop a scalable computational approach for reducing the costs associated with the sampling stage of the BAE approach. Specifically, we consider the Taylor expansion of the accurate and surrogate forward models with respect to the uncertain parameter fields either as a control variate for variance reduction or as a means to directly and efficiently approximate the mean and covariance of the approximation errors. We propose efficient methods for evaluating the expressions for the mean and covariance of the Taylor approximations based on linear(-ized) PDE solves. Furthermore, the proposed approach is independent of the dimension of the uncertain parameter, depending instead on the intrinsic dimension of the data, ensuring scalability to high-dimensional problems. The potential benefits of the proposed approach are demonstrated for two high-dimensional inverse problems governed by PDE examples, namely for the estimation of a distributed Robin boundary coefficient in a linear diffusion problem, and for a coefficient estimation problem governed by a nonlinear diffusion problem.

Bayesian approximation error↗

Quantitative comparison of impurity transport in turbulence reduced and enhanced scenarios at Wendelstein 7-X

We assess the turbulent particle transport being responsible for the limitation of the confinement and, thus, the overall performance of the neoclassically optimized stellarator Wendelstein 7-X. The radial particle transport is experimentally inferred from the evaluation of impurity injection into turbulence reduced and enhanced plasma scenarios revealing a completely different confinement behavior. The impact of the density gradient on the turbulent ion transport is theoretically estimated using large-scale non-linear gyro-kinetic simulations enabling, for the first time in Wendelstein 7-X, a quantitative comparison to the experimentally assessed impurity transport properties. We demonstrate that impurity transport in most of the Wendelstein 7-X discharges, up to now impossible to cover only with neoclassical estimations, is dominated by turbulence and can be modelled via gyro-kinetic simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Stability regions for multiloop LQ-regulated systems with state estimators

This note investigates the closed-loop stability of linear, time-invariant systems controlled by linear-quadratic-Gaussian (LQG) type controllers, when the actuators have nonlinearities. The nonlinearities N(sigma) are assumed to violate the standard LQ robustness condition either for values of sigma away from sigma = 0, or in a neighborhood of sigma = 0. The cases with an exponentially stable state estimator, and an estimator with ultimately bounded estimation error are considered, and expressions are obtained for the regions of attraction and ultimate boundedness.

Joshi, S. M.↗

Spectral moment estimation in MST radars

Signal processing techniques used in Mesosphere-Stratosphere-Troposphere (MST) radars are reviewed. Techniques which produce good estimates of the total power, frequency shift, and spectral width of the radar power spectra are considered. Non-linear curve fitting, autocovariance, autocorrelation, covariance, and maximum likelihood estimators are discussed.

Woodman, R. F.↗

Bayesian Framework for Multi-Timescale State Estimation in Low-Observable Distribution Systems

To support the smart grid paradigm, there has been a significant increase in sensor deployments and metering infrastructure in distribution systems. However, the measurements provided by these sensors and metering devices are typically sampled at different rates and could suffer from losses during the aggregation process. It is crucial to effectively reconcile the time-series measurements for a reliable state estimation. While weighted least squares has been the traditional approach for state estimation, sparsity-based approaches like matrix completion have become popular due to their superior performance in low-observability conditions. This paper proposes a Bayesian framework for both multi-timescale data aggregation and matrix completion based state estimation. Specifically, the multiscale time-series data aggregated from heterogenous sources are reconciled using a multitask Gaussian process that exploits the spatio-temporal correlations. Here, the resulting consistent timeseries alongwith the confidence bound on the imputations are fed into a Bayesian matrix completion method augmented with linearized power-flow constraints to accurately estimate the states in low-observability conditions. Results on three phase unbalanced IEEE 37 and IEEE 123 bus test systems reveal the superior performance of the proposed Bayesian framework. The computational complexity for the proposed Bayesian framework is also quantified.

42 ENGINEERING↗

A Bayesian approach to nonlinear inversion

Powerful methods are now available for solving linear parametric inverse problems. However, many inverse problems which arise in geohysics are nonlinear. Fortunately, it is possible to treat most of these with the air of linear perturbation theory and liner inversion. But a convenient method is needed for assessing the importance of nonlinearity in these quasi-linear problems. The present paper provides such a method. Matsu'ura and Jackson (1984) have presented a simple algorithm for evaluating the asymptotic covariance matrix fo estimation errors. In the present investigation, aspects of linear inversion are discussed, taking into account linear parametric inverse problems, nonuniqueness, prior information, confidence limits, conditional and marginal statistics, the relative importance of the prior and observational data, and standardized variables. Attention is also given to nonlinear inversion, and the application of the considered approaches to a number of examples.

Jackson, D. D.↗

On optimal control of linear systems in the presence of multiplicative noise

This correspondence considers the problem of optimal regulator design for discrete time linear systems subjected to white state-dependent and control-dependent noise in addition to additive white noise in the input and the observations. A pseudo-deterministic problem is first defined in which multiplicative and additive input disturbances are present, but noise-free measurements of the complete state vector are available. This problem is solved via discrete dynamic programming. Next is formulated the problem in which the number of measurements is less than that of the state variables and the measurements are contaminated with state-dependent noise. The inseparability of control and estimation is brought into focus, and an 'enforced separation' solution is obtained via heuristic reasoning in which the control gains are shown to be the same as those in the pseudo-deterministic problem. An optimal linear state estimator is given in order to implement the controller.

Joshi, S. M.↗

Hand-held spectral radiometer to estimate gramineous biomass

A simple hand-held instrument has been designed and constructed to nondestructively estimate above-ground gramineous biomass using radiometric measurements. The prototype unit consists of a modified two-channel digital radiometer interfaced to a pocket calculator. A digital interface was constructed to join electronically and control the radiometer and calculator to enable the radiometer-calculator system to solve a linear conversion solution from radiometric units to estimated biomass. This instrument has been used to estimate radiometrically gramineous biomass in a more efficient fashion with a high degree of accuracy.

Pearson, R. L.↗

Relative-Error-Covariance Algorithms

Two algorithms compute error covariance of difference between optimal estimates, based on data acquired during overlapping or disjoint intervals, of state of discrete linear system. Provides quantitative measure of mutual consistency or inconsistency of estimates of states. Relative-error-covariance concept applied, to determine degree of correlation between trajectories calculated from two overlapping sets of measurements and construct real-time test of consistency of state estimates based upon recently acquired data.

Bierman, Gerald J.↗

Geometric Interpretation of the Cluster Location Problem Part I: Theory

We present a new framing of the seismic location problem using principles drawn from differential geometry. Our interpretation relies upon the common assumption that travel times observed across a network are continuous, differentiable functions of source location. In consequence, travel‐time functions constitute a differentiable map between the source region and a Riemannian manifold. The manifold is said to be the image of the source region embedded in a generally high‐dimension travel‐time vector space. A cluster of events in the source region has an image of discrete points on the manifold, that, except in the simplest cases, cannot be viewed directly. However, it is possible to project the image of a cluster into a tangent space of the manifold for direct visualization. The projection operator can be computed directly from the data without a velocity model, but produces a distorted rendering of the cluster geometry. With a model we can predict the distortions and correct them to estimate cluster geometry. We develop these points with the simplest possible example, one for which direct visualization of the manifold is possible, using the example as an introduction to the relevant concepts from differential geometry in a familiar setting. The tangent space, a local linearization of the manifold, plays a key role. We develop a metric to estimate the limits of linearization, that is, to determine when the curvature of the manifold invalidates the linear assumption. We also examine the interplay of model error, inadequate network geometry, and pick error. We then generalize our results from the simple case to the general case of 3D source regions observed by general networks. Although we do suggest a new “project and correct” method for location, we do not develop it into a practical algorithm. In conclusion, our intention rather is to highlight new analytical methods grounded in differential geometry.

East Pacific Ocean Islands↗

Estimation of RTT and Loss Rate of Wide-Area Connections Using MPI Measurements

Scientific computations are expected to be increasingly distributed across wide-area networks, and the Message Passing Interface (MPI) has been shown to scale to support their communications over long distances. These computations should account for certain network parameters to ensure an effective execution, for example, by avoiding highly congested and long connections. The execution times of MPI basic operations reflect the connection parameters, including the Round Trip Time (RTT) and loss rate. We describe five machine leaning methods to estimate the connection RTT and loss rate using execution times of MPI basic operations. We utilize execution time measurements of MPI Sendrecv operations collected over emulated 10 Gbps connections with 0-366 ms round-trip times, wherein the longest connection spans the globe, under up to 20% periodic losses. These methods provide disparate, namely, linear and non-linear, and smooth and non-smooth, estimates of RTT and loss rate. Our results show that accurate estimates can be generated at low loss rates but they become inaccurate at loss rates 10% and higher. Overall, these results constitute a case study of the strengths and limitations of machine learning methods in inferring network-level parameters using application-level measurements.

Rao, Nageswara S.↗

Hybrid state-space self-tuning control of uncertain linear systems

The paper presents a hybrid state-space self-tuner using a new dual-rate sampling scheme for digital adaptive control of continuous-time uncertain linear systems. A state-space-based recursive least-squares algorithm, together with a variable forgetting factor, is used for direct estimations of both the equivalent discrete-time uncertain linear system parameters and the associated discrete-time state of a continuous-time uncertain linear system from the sampled input and output data. An analogue optimal regional pole-placement design method is used for designing an optimal observer-based analogue controller. A suboptimal observer-based digital controller is then designed from the designed analogue controller using digital redesign technique. To enhance the robustness of parameter identification and state estimation algorithms, a dynamic bound for a class of uncertain bilinear parameters and a fast-rate digital controller are developed at each fast-sampling period. Also, to accommodate computation loads and computation delay for developing the advanced hybrid self-tuner, the designed analogue controller and observer gains are both updated at each slow-sampling period. This control technique has been successfully applied to benchmark control problems.

Shieh, L. S.↗

Foreground-immune CMB lensing reconstruction with polarization

Extragalactic foregrounds are known to generate significant biases in temperature based CMB lensing reconstruction. Several techniques, which include "source hardening'" and "shear-only estimators'' have been proposed to mitigate contamination and have been shown to be very effective at reducing foreground-induced biases. Here we extend both techniques to polarization, which will be an essential component of CMB lensing reconstruction for future experiments and investigate the "large lens'' limit analytically to gain insight on the origin and scaling of foreground biases, as well as the sensitivity to their profiles. Furthermore, using simulations of polarized point sources, we estimate the expected bias to both Simons Observatory and CMB-S4 like (polarization-based) lensing reconstruction, finding that biases to the former are minuscule while those to the latter are potentially non-negligible at small scales ($L$ ~ $1000-2000$). In particular, we show that for a CMB-S4 like experiment, an optimal linear combination of point-source hardened estimators can reduce the (point-source induced) bias to the CMB lensing power spectrum by up to two orders of magnitude, at a ~ 4% noise cost relative to the global minimum variance estimator.

79 ASTRONOMY AND ASTROPHYSICS↗