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At least 721 records · Page 40

System identification computational considerations.

System identification methods may be accurately characterized as inverse computational problems. Three approaches to the computational problem are considered. Equation error methods are based on regression analysis techniques. Attention is given to the maximum conditional likelihood estimate and the maximum unconditional likelihood (Bayesian) estimate. Gradient dependent algorithms for solving the minimization problems are discussed, taking into account Gaussian methods, quadratic model methods, and the homogeneous function model method of Jacobson and Oksman. Some advanced methods are also examined.

Bowles, R. L.↗

The helium abundance of Saturn from Voyager measurements

The helium abundance in the atmosphere of Saturn is obtained from Voyager measurements by two methods. The first method combines infrared spectra and vertical profiles derived from radio occultation measurements and yields a hydrogen mole fraction of q = 0.963 + or - 0.024 corresponding to a helium mass fraction of Y = 0.06 + or - 0.05. The estimated errors are primarily due to uncertainties in the radio occultation profile and in the abundance of methane, which contributes significantly to the mean molecular weight. The second method is based on the direct inversion of infrared spectra and yields values consistent with those from the first method; however, examination of the sensitivities of the two methods indicates that in the Saturnian case the first approach provides more accurate results. Comparison of the helium abundance of Saturn with that of Jupiter and the sun suggests that helium precipitation is significant in Saturn but may not have begun in Jupiter.

Conrath, B. J.↗

Ionospheric profile inversion using oblique-incidence ionograms

Some of the elementary methods used in deriving true-height profiles from oblique-incidence ionograms are reviewed. The two principal methods presented are oblique-to-vertical transformation and direct inversion of the oblique-incidence ionogram. Limitations in oblique-incidence inversion due to magnetic-field effects, horizontal gradients, and absolute time delay are discussed.

Nielson, D. L.↗

Evaluation of the Abel inversion integral in O-mode plasma reflectometry using Chebyshev–Gauss quadrature

The Abel transform is often used to reconstruct plasma density profiles from O-Mode polarized reflectometry diagnostics. However, standard numerical trapezoidal evaluation of the Abel inversion integral can be computationally expensive for a large number of evaluation points, and an endpoint singularity exists on the upper-bound of the integral, which can result in an increased error. In this work, Chebyshev–Gauss quadrature is introduced as a new method to evaluate the Abel inversion integral for the problem of O-Mode plasma reflectometry. Here, the method does not require numerical evaluation of an integral singularity and is shown to have similar accuracy compared to existing methods while being computationally efficient.

47 OTHER INSTRUMENTATION↗

Technical Report on Subsurface Monitoring of the Brady Hot Spring Geothermal Site, Nevada, based upon Full Waveform Inversion

Abilities to accurately characterize the subsurface in a geothermal setting is key to assess and support production. An important element of geothermal reservoir monitoring is also the ability to investigate fluid transport within fracture network. This report focuses on improving subsurface imaging and monitoring in geothermal settings using full waveform inversion based on the adjoint method and time-lapse imaging. To assess our method, we rely on a dense seismic dataset collected in 2016 at the Brady Hot Springs geothermal site in Nevada for the DOE-funded project Poroelastic Tomography by Adjoint Inverse Modeling of Data from Seismology, Geodesy, and Hydrology. This dataset captures subsurface changes across four stages of geothermal power plant operations, which involve varying rates of fluid injection and extraction. Two velocity models were previously derived from this dataset using different methods: one based on travel times and another on sweep interferometry. Our first step is to refine these models using adjoint tomography, which has been applied successfully at global and regional-scales but is less common at the reservoir-scale. Two approaches are then explored for time-lapse analysis: directly comparing refined tomographic models from different stages or backpropagating waveform differences relative to a baseline tomographic model. The main take away is that both approaches highlight similar reservoir behaviors, but the latter approach is more computationally effective in capturing small-scale changes in subsurface properties. For this work, we leverage the use of Salvus (www.mondaic.com), an end-to-end seismic imaging solution, relying on the spectral element method to compute forward and adjoint simulations, and developed by Mondaic Ltd. It includes integrated workflow management that handles waveform and metadata, launches simulations, computes waveform misfits and adjoint sources, and iterates for model updates by nonlinear optimization.

15 GEOTHERMAL ENERGY↗

Differential programming enabled functional imaging with Lorentz transmission electron microscopy

Abstract Lorentz transmission electron microscopy is an advanced characterization technique that enables the simultaneous imaging of both the microstructure and functional properties of materials. Information such as magnetization and electric potentials is carried by the phase of the electron wave, and is lost during image acquisition. Various methods have been proposed to retrieve the phase of the electron wavefunction using intensities of the acquired images, most of which work only in the small defocus limit. Imaging at strong defoci not only carries more quantitative phase information, but is essential to the study of weak magnetic and electrostatic fields at the nanoscale. In this work we develop a method based on differentiable programming to solve the inverse problem of phase retrieval. We show that our method maintains a high spatial resolution and robustness against noise even at the upper defocus limit of the microscope. More importantly, our proposed method can go beyond recovering just the phase information. We demonstrate this by retrieving the electron-optical parameters of the contrast transfer function alongside the electron exit wavefunction.

97 MATHEMATICS AND COMPUTING↗

Spread Spectrum Time Domain Reflectometry and Steepest Descent Inversion to Measure Complex Impedance

In this paper, we present a method for estimating complex impedances using reflectometry and a modified steepest descent inversion algorithm. We simulate spread spectrum time domain reflectometry (SSTDR), which can measure complex impedances on energized systems for an experimental setup with resistive and capacitive loads. A parametric function, which includes both a misfit function and stabilizer function, is created. The misfit function is a least squares estimate of how close the model data matches observed data. The stabilizer function prevents the steepest descent algorithm from becoming unstable and diverging. Steepest descent iteratively identifies the model parameters that minimize the parametric function. We validate the algorithm by correctly identifying the model parameters (capacitance and resistance) associated with simulated SSTDR data, with added 3 dB white Gaussian noise. With the stabilizer function, the steepest descent algorithm estimates of the model parameters are bounded within a specified range. Furthermore, the errors for capacitance (220pF to 820pF) and resistance (50 Ω to 270 Ω) are < 10%, corresponding to a complex impedance magnitude |R +1/jωC| of 53 Ω to 510 Ω.

14 SOLAR ENERGY↗

Deep Learning for Full Waveform Inversion of Elastic Active-Source Seismic Data to Estimate P-Wave Velocity Models

Seismic imaging methods are critical for Global Security and Energy & Homeland Security missions and activities that rely on subsurface characterization, but traditional methods remain computationally expensive and require significant labor hours and expertise to execute. Within the past few years, machine learning (ML), namely deep learning (DL), has been used to develop data-driven end-to-end full waveform inversion (FWI) methods to estimate 2D P-wave velocity (Vp) models in a fraction of the time as conventional FWI. These methods, however, are trained on simplistic acoustic wave seismic data and Vp models that are not realistic nor representative of real-world observations, leaving a large gap between the state-of-the-art and deployable, feasible, and practical DL FWI methods. Here, we generate a synthetic active-source, 3D, elastic wave seismic data set and a variety of Vp models with realistic geologic structure for training DL FWI methods. We evaluate six different methods that have performed well for acoustic DL FWI or medical imaging tasks using our more realistic dataset. We find that these six trained models do not match the performance of published acoustic end-to-end DL FWI methods, indicating more training data may be needed, physics may need to be incorporated to achieve good accuracy at the sacrifice of the end-to-end advantage, and/or novel methods need to be developed to enable end-to-end DL FWI methods to perform well for real-world seismic data.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

3D strain field reconstruction by inversion of dynamical scattering

Strain governs not only the mechanical response of materials but also their electronic, optical, and catalytic properties. For this reason, the measurement of the 3D strain field is crucial for a detailed understanding and for further development of material properties through strain engineering. However, measuring strain variations along the electron beam direction has remained a major challenge for (scanning-) transmission electron microscopy (S/TEM). In this article, we present a method for 3D strain field determination using 4D-STEM. The method is based on the inversion of dynamical diffraction effects, which occur at strain field variations along the beam direction. We test the method against simulated data with a known ground truth and demonstrate its application to an experimental 4D-STEM dataset from an inclined pseudomorphically grown Al0.47Ga0.53N layer.

Niermann, Laura↗

Multidisciplinary Design Optimization of Low-Boom Supersonic Aircraft with Mission Constraints

Conceptual design of low-boom supersonic aircraft is heavily dictated by aircraft volume and lift distributions. These unique design characteristics make it a challenge to enforce mission requirements (such as static margins and trim requirements) during design optimization. This low-boom design challenge is resolved by using reversed equivalent area targets for low-fidelity low-boom inverse design and a block coordinate optimization (BCO) method for multidisciplinary design optimization (MDO). The corresponding low-boom MDO problem includes aircraft mission constraints on ranges, cruise speeds, trim for low-boom cruise, static margins for takeoff/cruise/landing, takeoff/landing field lengths, approach velocity, and tail rotation angles for trim at takeoff/landing, as well as fuselage volume constraints for passengers and main gear storage. The BCO method is developed to optimally resolve the conflicts between the low-boom inverse design objective and other design constraints. This method is successfully applied to design a low-boom supersonic configuration that carries 40 passengers, flies a low-boom mission with cruise Mach of 1.6 and range of 2,500 nm, and cruises overwater at Mach 1.8 with range of 3,600 nm. The generated configuration satisfies all specified mission constraints and has the potential to match a reversed equivalent area target with ground noise level below 70 PLdB.

Multidisciplinary design optimization↗

Improved definition of crustal anomalies for Magsat data

A scheme was developed for separating the portions of the magnetic field measured by the Magsat 1 satellite that arise from internal and external sources. To test this method, a set of sample coefficients were used to compute the field values along a simulated satellite orbit. This data was then used to try to recover the original coefficients. Matrix inversion and recursive least squares methods were used to solve for the input coefficients. The accuracy of the two methods are compared.

Source record↗

Affine Generalized Inverse for Optimal Control Allocation

This research is a follow on to the "Optimal Control Prediction Method for Control Allocation" paper in which the Prediction Method iterative algorithm was introduced. Previously, the Prediction Method was shown to provide optimal control allocation solutions over the entire Attainable Moment Set for the Moore-Penrose and the generalized (weighted) inverse. As an extension to the Prediction Method, this paper introduces a family of Moore Penrose Affine Generalized Inverses, applicable for all moments, which compute control allocation solutions using a constant matrix and fixed null-space vector. The Moore-Penrose Affine Generalized Inverse is proven to yield equivalent solutions to those of the Prediction Method and therefore is guaranteed to yield Moore-Penrose optimal control allocation solutions. While the Prediction Method is applicable for any moment along an a priori specified moment direction, the Affine Generalized Inverse is shown to yield optimal control allocation solutions in a neighborhood of the given moment which is not restricted to a specified moment direction. Furthermore, the Affine Generalized Inverse is shown to provide the time derivative of optimal control allocation solutions and to facilitate maintaining solutions within control effector rate limitations. The Moore-Penrose Affine Generalized Inverse is broadened to encompass any arbitrary (weighted) Affine Generalized Inverse. Finally, a method of creating a moment lookup table is outlined to utilize the Affine Generalized Inverse as an offline control allocation solution for all moments in the Attainable Moment Set.

Acheson, Michael J.↗

Adjoint Klein-Nishina Sampling Methods: Efficiency, Speed and Applications

Three new rejection sampling methods for generating samples from the adjoint Klein-Nishina cross section are discussed: the two-branch rejection sampling procedure, the three-branch linear rejection sampling procedure and the three-branch inverse rejection sampling procedure. These methods have all been implemented in the Framework for REsearch in Nuclear ScIence and Engineering (FRENSIE). The efficiency and sample generation rate of each of these methods are evaluated to characterize the methods and to make recommendations regarding their use. The use of these methods in realistic transport simulations is also evaluated by incorporating a scattering function into the sampling process. Furthermore, the results of an infinite medium problem are presented to verify that the sampling procedure can be used in an adjoint Monte Carlo simulation to generate results that are in agreement with an equivalent forward simulation.

97 MATHEMATICS AND COMPUTING↗

Validation of Spherically Symmetric Inversion by Use of a Tomographically Reconstructed Three-Dimensional Electron Density of the Solar Corona

Determining the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (spherically symmetric inversion, SSI) was developed in the 1950s and has been widely applied to interpret various observations. However, to date there is no study of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 solar radius as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066).We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally smaller than about a factor of two; the former has the lower peak but extends more in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50 deg. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt), as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with the reconstruction by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.

corona↗

Inversion of dynamical Bragg intensities to complex structure factors by iterated projections. For Ultramic. 2020. ("Pico" Festschrift, May 2021)

We discuss a method for recovering complex structure factors from many simultaneously excited Bragg beam intensities is described. The method is applied to simulated transmission electron diffraction data over a wide range of crystal thickness and beam energies. The method is based on iterated projections between structure and scattering matrices, which are related by a matrix unitary transformation, exponential, which we invert. The algorithm removes multiple-scattering perturbations from diffraction data and might be extended to other fields, including X-ray and neutron diffraction and cryo-electron microscopy. Because coherent multiple scattering involves interference between Bragg beams, the method also solves the phase problem. Unlike dynamical inversion from electron microscope images or ptychography data, the method, which starts with Bragg beam intensities, provides complex structure factors unaffected by focusing errors or resolution limitations imposed by lenses. We provide inversions from simulated data with 441 simultaneously excited Bragg beams over a range of thickness and beam energy. We discuss the retrieval of chirality information from enantiomorphs, the efficient incorporation of symmetry information using the irreducible representation of the group of structure matrices, and the effect of HOLZ lines to provide three-dimensional information.

97 MATHEMATICS AND COMPUTING↗

The updated statistical inversion technique to the evaluation of Umkehr observations

In the present study the standard retrieval Umkehr method to estimate the vertical distribution of ozone was updated using a statistical approach to the mathematical inversion scheme. The vertical ozone profile covariance matrix was used as a priori information for the inverse problem. A new method of the ozonesonde data organization according to air mass types helped to improve the covariance matrix quality. A retrieval method was developed using eigenvector technique. An optimal vertical ozone profile resolution was determined from the mathematical inversion scheme analysis based on the same technique. The sun radiation transfer was accounted for multiple scattering and atmospheric sphericity in this calculation. The retrievals using actual Umkehr Dobson spectrophotometer observations were also performed to provide the comparison of the standard and updated methods with concurrent ozone sound data at Boulder U.S. The comparison has revealed that the present method has some advantages in both resolution and accuracy, as compared to the standard one, especially for the atmospheric layers below ozone maximum.

Frolov, Alexander D.↗

Observation of polarization density waves in SrTiO 3

The nature of the incipient ferroelectric transition in SrTiO 3 has been a long-standing puzzle in condensed matter physics. One explanation involves the competition between ferroelectricity and an instability characterized by the mesoscopic modulation of the polarization. These polarization density waves, which should intensify near the quantum critical point, break local inversion symmetry and are difficult to characterize with conventional X-ray scattering methods. Here, in this study, we probe inversion symmetry breaking at finite momenta and visualize the instability of the polarization at the nanometre scale in SrTiO3 by combining a femtosecond X-ray free-electron laser with terahertz coherent control methods. We found polar-acoustic collective modes that are soft, particularly at the tens of nanometre scale. These precursor collective excitations provide evidence for the conjectured mesoscopic-modulated phase in SrTiO 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗