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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A Convex Data-Driven Approach for Nonlinear Control Synthesis

We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. We propose a data-driven approach to stabilize the systems when only sample trajectories of the dynamics are accessible. Our method is built on the density-function-based stability certificate that is the dual to the Lyapunov function for dynamic systems. Unlike Lyapunov-based methods, density functions lead to a convex formulation for a joint search of the control strategy and the stability certificate. This type of convex problem can be solved efficiently using the machinery of the sum of squares (SOS). For the data-driven part, we exploit the fact that the duality results in the stability theory can be understood through the lens of Perron–Frobenius and Koopman operators. This allows us to use data-driven methods to approximate these operators and combine them with the SOS techniques to establish a convex formulation of control synthesis. The efficacy of the proposed approach is demonstrated through several examples.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

Vibration response of spacecraft shrouds to in-flight fluctuating pressures

Results are presented for the vibration response of a spacecraft shroud to a range of in-flight fluctuation pressures. An Atlas-Agena 15 degree cone-cylinder shroud was analyzed during the present study, and three critical flight Mach numbers were considered. At transonic Mach numbers, the aerodynamic flow over the shroud is complex, involving zones of regular attached flow, separated flow, shock wave oscillation, and modified attached flows induced by local thickening of the boundary layer. The overall shroud vibration levels for a particular Mach number were determined by initially calculating the mean square acceleration levels induced by the fluctuating pressures distributed over an individual zone, and then summing mean square acceleration levels in one-third octave bands over all zones.

Cockburn, J. A.↗
DOE OSTI2024

Remark on Algorithm 1012: Computing Projections with Large Datasets

In ACM TOMS Algorithm 1012, the DELAUNAYSPARSE software is given for performing Delaunay interpolation in medium to high dimensions. When extrapolating outside the convex hull of the training set, DELAUNAYSPARSE calls the nonnegative least squares solver DWNNLS to compute projections onto the convex hull. However, DWNNLS and many other available sum-of-squares optimization solvers were not intended for usage with many variable problems, which result from the large training sets that are typical in machine learning applications. Thus, a new PROJECT subroutine is given, based on the highly customizable quadratic program solver BQPD. This solution is shown to be as robust as DELAUNAYSPARSE for projection onto both synthetic and real-world datasets, where other available solvers frequently fail. Although it is intended as an update for DELAUNAYSPARSE, due to the difficulty and prevalence of the problem, this solution is likely to be of external interest as well.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1971

A method of computing periods of cyclic phenomena.

Use of an analysis of Expected Mean Square Deviations to search for periodicities in an observational data sample is described. The statistic for testing the null hypothesis of nonperiodicity is derived from a partitioning of the total sum of squared deviations from the mean. Unlike most existing methods, the present one does not require equally spaced observations. No assumptions are made concerning the statistical nature of spacing intervals. The method is illustrated by numerical examples.

Jurkevich, I.↗
NASA NTRS1976

Canonical analysis for increased classification speed and channel selection

The quadratic form can be expressed as a monotonically increasing sum of squares when the inverse covariance matrix is represented in canonical form. This formulation has the advantage that, in testing a particular class hypothesis, computations can be discontinued when the partial sum exceeds the smallest value obtained for other classes already tested. A method for channel selection is presented which arranges the original input measurements in that order which minimizes the expected number of computations. The classification algorithm was tested on data from LARS Flight Line C1 and found to reduce the sum-of-products operations by a factor of 6.7 in comparison with the conventional approach. In effect, the accuracy of a twelve-channel classification was achieved using only that CPU time required for a conventional four-channel classification.

Eppler, W.↗
NASA NTRS1994

Analysis of cloud top height and cloud coverage from satellites using the O2 A and B bands

Cloud height and cloud coverage detection are important for total ozone retrieval using ultraviolet and visible scattered light. Use of the O2 A and B bands, around 761 and 687 nm, by a satellite-borne instrument of moderately high spectral resolution viewing in the nadir makes it possible to detect cloud top height and related parameters, including fractional coverage. The measured values of a satellite-borne spectrometer are convolutions of the instrument slit function and the atmospheric transmittance between cloud top and satellite. Studies here determine the optical depth between a satellite orbit and the Earth or cloud top height to high accuracy using FASCODE 3. Cloud top height and a cloud coverage parameter are determined by least squares fitting to calculated radiance ratios in the oxygen bands. A grid search method is used to search the parameter space of cloud top height and the coverage parameter to minimize an appropriate sum of squares of deviations. For this search, nonlinearity of the atmospheric transmittance (i.e., leverage based on varying amounts of saturation in the absorption spectrum) is important for distinguishing between cloud top height and fractional coverage. Using the above-mentioned method, an operational cloud detection algorithm which uses minimal computation time can be implemented.

Kuze, Akihiko↗
NASA NTRS1976

Multivariate normality

Sets of experimentally determined or routinely observed data provide information about the past, present and, hopefully, future sets of similarly produced data. An infinite set of statistical models exists which may be used to describe the data sets. The normal distribution is one model. If it serves at all, it serves well. If a data set, or a transformation of the set, representative of a larger population can be described by the normal distribution, then valid statistical inferences can be drawn. There are several tests which may be applied to a data set to determine whether the univariate normal model adequately describes the set. The chi-square test based on Pearson's work in the late nineteenth and early twentieth centuries is often used. Like all tests, it has some weaknesses which are discussed in elementary texts. Extension of the chi-square test to the multivariate normal model is provided. Tables and graphs permit easier application of the test in the higher dimensions. Several examples, using recorded data, illustrate the procedures. Tests of maximum absolute differences, mean sum of squares of residuals, runs and changes of sign are included in these tests. Dimensions one through five with selected sample sizes 11 to 101 are used to illustrate the statistical tests developed.

Crutcher, H. L.↗
DOE OSTI2023

Estimating and Calibrating DER Model Parameters Using Levenberg–Marquardt Algorithm in Renewable Rich Power Grid

The proliferation of inverter-based distributed energy resources (IBDERs) has increased the number of control variables and dynamic interactions, leading to new grid control challenges. For stability analysis and designing appropriate protection controls, it is important that IBDER models are accurate. This paper focuses on the accurate estimation and parameter calibration of DER_A, a recently proposed aggregated IBDER model. In particular, we focus on the parameters of the reactive power–voltage regulation module. We formulate the problem of parameter tuning as a non-linear least square minimization problem and solve it using the Levenberg–Marquardt (LM) method. The LM method is primarily chosen due to its flexibility in adaptively selecting between the steepest descent and Gauss–Newton methods through a damping parameter. The LM approach is used to minimize the error between the actual measurements and the estimated response of the model. Further, the computational challenges posed by the numerical calculation of the Jacobian are tackled using a quasi-Newton root-finding approach. The proposed method is validated on a real feeder model in the northeastern part of the United States. The feeder is modeled in OpenDSS and the measurements thus obtained are fed to the DER_A model for calibration. The simulation results indicate that our approach is able to successfully calibrate the relevant model parameters quickly and with high accuracy, with a total sum of square error of 3.57 × 10 –7 .

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Causality, unitarity, and the weak gravity conjecture

We consider the shift of charge-to-mass ratio for extremal black holes in the context of effective field theory, motivated by the Weak Gravity Conjecture. We constrain extremality corrections in different regimes subject to unitarity and causality constraints. In the asymptotic IR, we demonstrate that for any supersymmetric theory in flat space, and for all minimally coupled theories, logarithmic running at one loop pushes the Wilson coefficient of certain four-derivative operators to be larger at lower energies, guaranteeing the existence of sufficiently large black holes with Q > M. We identify two exceptional cases of nonsupersymmetric theories involving large numbers of light states and Planck-scale nonminimal couplings, in which the sign of the running is reversed, leading to black holes with negative corrections to Q/M in the deep IR, but argue that these do not rule out extremal black holes as the requisite charged states for the WGC. We separately show that causality and unitarity imply that the leading threshold corrections to the effective action from integrating out massive states, in any weakly coupled theory, can be written as a sum of squares and is manifestly positive for black hole backgrounds. Quite beautifully, the shift in the extremal Q/M ratio is directly proportional to the shift in the on-shell action, guaranteeing that these threshold corrections push Q > M in compliance with the WGC. Our results apply for black holes with or without dilatonic coupling and charged under any number of U(1)s.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

The Reservoir Temperature Estimator (RTEst): A multicomponent geothermometry tool

The Reservoir Temperature Estimator (RTEst) is a multicomponent geothermometry tool for estimating reservoir geochemical parameters including reservoir temperature, CO 2 fugacity, mass of water lost or gained, and a reaction factor. It estimates these parameters and their associated uncertainties by minimizing an objective function that is the weighted sum of squares of the saturation indices of a user-selected set of minerals believed to be equilibrated with the reservoir fluid. RTEst accomplishes these estimates by combining the geochemical modeling capabilities of The Geochemist’s Workbench® with the optimization/parameter estimation resources of PEST®. An included interface aids the user in selecting plausible mineral phases to comprise the objective function and calculates their weighting factors. The working principles of RTEst are described and its efficacy is illustrated by presenting results of its application to various geothermal fields with known conditions. These examples show RTEst can account for the alteration of ascending reservoir fluid by mineral (calcite) re-equilibration with changes in temperature, reconstruct waters with CO 2 loss, correct for the deficit of water and other volatiles (CO 2,gas , H 2 S gas ) from boiling, and determine the amount of mixing of thermal and non-thermal waters. RTEst can use data with basis species below detection limit, missing, or unreliable either by assuming equilibrium with a controlling mineral (fixed-analyte method) or by treating the analyte concentration as an optimization parameter. The inverse of variance weighting method included in RTEst provides more representative results than either the normalization or unit weighting methods. Finally, the ability of RTEst to calculate reservoir temperatures, gas fugacity, and mixing fractions demonstrates its usefulness as a tool for evaluating geothermal systems.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Rapid Tuning of Synchrotron Surrogate Model at the Recycler Ring

The 8 GeV proton-storage Recycler Ring (RR) is essential for reaching megawatt beam intensity goals for the DUNE neutrino beam at Fermilab. Custom shims on each RR permanent magnet were designed to cancel manufacturing defects and bring magnetic fields to the design values. Remaining imperfections cause the observed tune variation vs energy to deviate from what is calculated using the design fields. Using the POUNDERS (“Practical Optimization Using No Derivatives for sums of Squares”) optimization method with Synergia in the loop, we demonstrate rapid convergence to a set of additive, higher-order multipole moments of these magnetic shims which reproduce that observed variation, and show that the convergence advantage grows with the parameter-space dimensionality.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Transient Safety Filter Design for Grid-Forming Inverters

Unlike conventional generators, inverter-based generation are fundamentally incapable of providing rotational inertia. While grid-forming inverters alleviate some of that problem by synthesizing small inertia via feedback control, additional control mechanisms are needed to ensure safety and security during transients. In this paper, we propose novel real-time safety-constrained feedback controllers (``safety filters'') for droop-based (grid-forming) inverters to ensure transient security of the grid. The safety filter acts as a buffer between the network operational layer and the inverter-control layer, and only lets those dispatch control signals pass to the inverter droop-controller, which are guaranteed to not violate the safety specifications (frequency, voltage, current limits). Using a distributed barrier certificates method, we construct sector-like conditions on the control policies, which guarantee the satisfaction of transient safety specifications. Sum-of-square programming is used to synthesize the safety filters. Numerical simulation results are provided to illustrate the performance of the proposed filter on inverter-based microgrids.

Kundu, Soumya↗
DOE OSTI2022

Distributed Transient Safety Verification via Robust Control Invariant Sets: A Microgrid Application

Modern safety-critical energy infrastructures are increasingly operated in a hierarchical and modular control framework which allows for limited data exchange between the modules. In this context, it is important for each module to synthesize and communicate constraints on the values of exchanged information in order to assure system-wide safety. To ensure transient safety in inverter-based microgrids, we develop a set invariance-based distributed safety verification algorithm for each inverter module. Applying Nagumo's invariance condition, we construct a robust polynomial optimization problem to jointly search for safety-admissible set of control set-points and design parameters, under allowable disturbances from neighbors. We use sum-of-squares (SOS) programming to solve the verification problem and we perform numerical simulations using grid-forming inverters to illustrate the algorithm.

Bouvier, Jean-Baptiste H.↗
DOE OSTI2022

Calibration and Localization of Optically Pumped Magnetometers Using Electromagnetic Coils

In this paper, we propose a method to estimate the position, orientation, and gain of a magnetic field sensor using a set of (large) electromagnetic coils. We apply the method for calibrating an array of optically pumped magnetometers (OPMs) for magnetoencephalography (MEG). We first measure the magnetic fields of the coils at multiple known positions using a well-calibrated triaxial magnetometer, and model these discreetly sampled fields using vector spherical harmonics (VSH) functions. We then localize and calibrate an OPM by minimizing the sum of squared errors between the model signals and the OPM responses to the coil fields. We show that by using homogeneous and first-order gradient fields, the OPM sensor parameters (gain, position, and orientation) can be obtained from a set of linear equations with pseudo-inverses of two matrices. The currents that should be applied to the coils for approximating these low-order field components can be determined based on the VSH models. Computationally simple initial estimates of the OPM sensor parameters follow. As a first test of the method, we placed a fluxgate magnetometer at multiple positions and estimated the RMS position, orientation, and gain errors of the method to be 1.0 mm, 0.2°, and 0.8%, respectively. Lastly, we calibrated a 48-channel OPM array. The accuracy of the OPM calibration was tested by using the OPM array to localize magnetic dipoles in a phantom, which resulted in an average dipole position error of 3.3 mm. The results demonstrate the feasibility of using electromagnetic coils to calibrate and localize OPMs for MEG.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

MODFLOW6 models used to evaluate potential stresses and hydrologic conditions driving water-level fluctuations in well ER-5-3-2, Frenchman Flat, Southern Nevada

The hydrograph for well ER-5-3-2 in Frenchman Flat, southern Nevada, has previously unexplained water-level fluctuations. Four, three-dimensional, groundwater models (MODFLOW 6) were developed to evaluate potential stresses and hydrologic conditions affecting the well ER-5-3-2 hydrograph. Four model scenarios were developed that simulated: (1) wellbore leakage without recharge, (2) wellbore leakage with recharge, (3) shallow (low transmissivity) and deep (high transmissivity) carbonate rocks, and (4) lateral heterogeneity of carbonate rocks. Input and output files for the four model scenarios are in the model and output directories, respectively. Hydraulic conductivity, specific storage, and wellbore-leakage rates (when simulated) were estimated with parameter estimation (PEST) by minimizing a weighted composite, sum-of-squares objective function. The objective function was informed by measurement and Tikhonov regularization observations. Measurement observations included drawdowns from the constant-rate aquifer test and water-level altitudes measured in well ER-5-3-2 from 2001-2021. Tikhonov regularization informed hydraulic conductivity and specific storage parameters that were insensitive to measurement observations, where homogeneity was the preferred relation. Batch files, executables, and MODFLOW 6, PEST, and post-processing utilities are in the ancillary directory. Supplementary data also are included in the ancillary directory, including site information, high-frequency water-level and aquifer-test data, transmissivity estimates, water-chemistry data, and water-temperature analyses. This USGS data release contains data, analyses, and model files for the simulations and analysis results described in U.S. Geological Survey Scientific Investigations Report (https://doi.org/10.3133/sir20225132).

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1972

Biased estimation for dynamic systems.

Optimization and regulation of static and dynamic systems require good estimates of the states of the system model and the parameters of the model in the presence of input and measurement noise. A biased estimator is proposed as an alternative to the familiar best linear unbiased estimator. Depending on the value of a constant, this biased estimator can be made unbiased and is then identical to the best linear unbiased estimator, thus permitting additional freedom of choice in design and application. The sum of squared errors of this bs tmator can be less than the best linear unbiased case. An existence theorem is established and various properties are discussed.

Chang, J. W.↗