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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Recursive mass matrix factorization and inversion: An operator approach to open- and closed-chain multibody dynamics

This report advances a linear operator approach for analyzing the dynamics of systems of joint-connected rigid bodies.It is established that the mass matrix M for such a system can be factored as M=(I+H phi L)D(I+H phi L) sup T. This yields an immediate inversion M sup -1=(I-H psi L) sup T D sup -1 (I-H psi L), where H and phi are given by known link geometric parameters, and L, psi and D are obtained recursively by a spatial discrete-step Kalman filter and by the corresponding Riccati equation associated with this filter. The factors (I+H phi L) and (I-H psi L) are lower triangular matrices which are inverses of each other, and D is a diagonal matrix. This factorization and inversion of the mass matrix leads to recursive algortihms for forward dynamics based on spatially recursive filtering and smoothing. The primary motivation for advancing the operator approach is to provide a better means to formulate, analyze and understand spatial recursions in multibody dynamics. This is achieved because the linear operator notation allows manipulation of the equations of motion using a very high-level analytical framework (a spatial operator algebra) that is easy to understand and use. Detailed lower-level recursive algorithms can readily be obtained for inspection from the expressions involving spatial operators. The report consists of two main sections. In Part 1, the problem of serial chain manipulators is analyzed and solved. Extensions to a closed-chain system formed by multiple manipulators moving a common task object are contained in Part 2. To retain ease of exposition in the report, only these two types of multibody systems are considered. However, the same methods can be easily applied to arbitrary multibody systems formed by a collection of joint-connected regid bodies.

Rodriguez, G.↗
NASA NTRS1995

Analytical and phenomenological studies of rotating turbulence

A framework, which combines mathematical analysis, closure theory, and phenomenological treatment, is developed to study the spectral transfer process and reduction of dimensionality in turbulent flows that are subject to rotation. First, we outline a mathematical procedure that is particularly appropriate for problems with two disparate time scales. The approach which is based on the Green's method leads to the Poincare velocity variables and the Poincare transformation when applied to rotating turbulence. The effects of the rotation are now reflected in the modifications to the convolution of a nonlinear term. The Poincare transformed equations are used to obtain a time-dependent analog of the Taylor-Proudman theorem valid in the asymptotic limit when the non-dimensional parameter mu is identical to Omega(t) approaches infinity (Omega is the rotation rate and t is the time). The 'split' of the energy transfer in both direct and inverse directions is established. Secondly, we apply the Eddy-Damped-Quasinormal-Markovian (EDQNM) closure to the Poincare transformed Euler/Navier-Stokes equations. This closure leads to expressions for the spectral energy transfer. In particular, an unique triple velocity decorrelation time is derived with an explicit dependence on the rotation rate. This provides an important input for applying the phenomenological treatment of Zhou. In order to characterize the relative strength of rotation, another non-dimensional number, a spectral Rossby number, which is defined as the ratio of rotation and turbulence time scales, is introduced. Finally, the energy spectrum and the spectral eddy viscosity are deduced.

Mahalov, Alex↗
NASA NTRS2000

Spaceborne Radar Measurements of Rainfall Vertical Velocity

This paper studies the performance of a spaceborne precipitation radar in measuring vertical Doppler velocity of rainfall. As far as a downward pointing precipitation radar is concerned, one of the major problems affecting Doppler measurement at the nadir direction arises from the Non-Uniform Beam-Filling effect (NUBF). That is, when significant variation in rain rate is present within the radar IFOV (Instrument Field of View) in the along track direction. the Doppler shift caused by the radial component of the horizontal speed of the satellite is weighted differently among the portions of IFOV. The effects of this non-uniform weighting may dominate any other contribution. Under this condition, shape, average value and width of the Doppler spectrum may not be directly correlated with the vertical velocity of the precipitating particles. However, by using an inversion technique which over-samples the radar measurements in the along track direction, we show that the shift due to NUBF can be evaluated, and that the NUBF induced errors on average fall speed can be reduced.

Im, Eastwood↗
NASA NTRS2005

Coronal Diagnostics of Intermediate Activity Star XI Boo A

The analysis of Xi Boo A proved difficult to adapt to our line-by-line approach because of the strong wings of the RGS instrumental profile, as has been detailed in earlier reports. While progress was also delayed because of problems in using SAS v4, we succeeded in the past year or so to bring the analysis to conclusion. Abundances have been derived using both EPIC and RGS data, confirming earlier EUVE findings of a mild solar-like FIP effect, though with some evidence of a turn-up in abundances of elements with higher FIP. Plasma densities appear normal for a moderately active stellar corona. Xi Boo A nicely bridges the gap between the very active stars and stars like the Sun, and it indeed does appear that these are the stars in which the solar-like FIP effects begins to change to the "inverse FIP" type of effect seen in the very active stars. Probing this divide was the main goal of the proposal. These results are in the process of being prepared for publication, though we have not decided the target journal as yet.

Drake, Jeremy↗
DOE OSTI2020

Hyper-Differential Sensitivity Analysis of Uncertain Parameters in PDE-Constrained Optimization

Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose additional complexity, namely, uncertain parameters in the PDEs. Uncertainty quantification (UQ) is necessary to characterize, prioritize, and study the influence of these uncertain parameters. Sensitivity analysis, a classical tool in UQ, is frequently used to study the sensitivity of a model to uncertain parameters. In this article, we introduce "hyper-differential sensitivity analysis" which considers the sensitivity of the solution of a PDE-constrained optimization problem to uncertain parameters. Our approach is a goal-oriented analysis which may be viewed as a tool to complement other UQ methods in the service of decision making and robust design. We formally define hyper-differential sensitivity indices and highlight their relationship to the existing optimization and sensitivity analysis literatures. Assuming the presence of low rank structure in the parameter space, computational efficiency is achieved by leveraging a generalized singular value decomposition in conjunction with a randomized solver which converts the computational bottleneck of the algorithm into an embarrassingly parallel loop. Two multi-physics examples, consisting of nonlinear steady state control and transient linear inversion, demonstrate efficient identification of the uncertain parameters which have the greatest influence on the optimal solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

WellPINN: Accurate Well Representation for Transient Fluid Pressure Diffusion in Subsurface Reservoirs With Physics‐Informed Neural Networks

Accurate representation of pumping wells is essential for reliable reservoir characterization and simulation of operational scenarios in subsurface flow models. Physics-informed neural networks (PINNs) are emerging as a promising alternative to numerical models for reservoir modeling, offering seamless integration of monitoring data and governing physical equations. However, existing PINN-based studies face major challenges in capturing fluid pressure near wells when using a source/sink term, particularly during the early stages after pumping begins. We address this problem by introducing WellPINN, a workflow in which an initially trained PINN infers fluid pressure across the entire reservoir domain using a large equivalent well radius. This initial PINN solution is then locally refined around the well by a set of subdomain PINNs that are trained for smaller equivalent well radii. Continuity across these subdomain interfaces as well as at the initial condition is ensured by hard-constraining each PINN on its subdomain boundary. Our results demonstrate WellPINN as the first workflow of its kind to focus on accurate inference of fluid pressure from pumping rates throughout the entire injection period, significantly advancing the potential of PINNs for inverse modeling and operational scenario simulations. All data and code for this paper are openly available at https://doi.org/10.20350/DIGITALCSIC/17260.

58 GEOSCIENCES↗
DOE OSTI2020

Three-Dimensional Imaging Lidar for Characterizing Particle Fields and Organisms in the Mesopelagic Zone

The ocean’s mesopelagic zone is largely uncharacterized despite its vital role in sustaining ocean ecosystems. The composition, cycling, and fate of particle fields in the mesopelagic lacks an integrative multi-scale understanding of organism migration patterns, distribution, and diversity. This problem is addressed by combining complementary technologies with overlapping size spectra, including profiler mounted optical scattering sensors, profiler, and ship mounted acoustic devices, and a custom Unobtrusive Multi-Static Lidar Imager (UMSLI). This unique sensor suite can observe distributions of particles including organisms over a six order of magnitude dynamic size range, from microns to meters. Overlapping size ranges between different methods allows for cross-validation. This work focuses on the lidar imaging measurements and optical backscattering and attenuation, covering a combined particle size range of 0.1 mm to several cm. Particles at the small end of this range are sized using an existing backscattering time series inversion method after Briggs et al. (2013). Larger particles are resolved with UMSLI over an expanding volume using three-dimensional photo-realistic laser serial imaging. UMSLI’s image rectifying ability over time allows for derivation of particle concentration, size, and spatial distribution. Technical details on the development and post-processing methods for the novel UMSLI system are provided. Image resolved particle size distributions (PSDs) revealed a size shift from smaller to larger particles (>0.5 mm) as indicated by flatter slopes from dawn (slope = 2.6) to dusk (slope = 3.0). PSD trends are supported by an optical backscatter and transmissometer time series inversion analysis. Size shifts in the particle field are largely attributed to aggregation effects. Images support evidence of temporal variation between dusk and dawn stations through statistical analysis of particle concentrations for particle sizes 0.50–5.41 mm. Spatial analysis of the particle field revealed a dominantly uniform distributed marine snow background. The importance and potential of integrated approaches to studying particle and organism dynamics in ocean environments are discussed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

A Bayesian Approach to Regional Decadal Predictability: Sparse Parameter Estimation in High-Dimensional Linear Inverse Models of High-Latitude Sea Surface Temperature Variability

Stochastic reduced models are an important tool in climate systems whose many spatial and temporal scales cannot be fully discretized or underlying physics may not be fully accounted for. One form of reduced model, the linear inverse model (LIM), has been widely used for regional climate predictability studies—typically focusing more on tropical or midlatitude studies. However, most LIM fitting techniques rely on point estimation techniques deriving from fluctuation–dissipation theory. In this methodological study we explore the use of Bayesian inference techniques for LIM parameter estimation of sea surface temperature (SST), to quantify the skillful decadal predictability of Bayesian LIM models at high latitudes. We show that Bayesian methods, when compared to traditional point estimation methods for LIM-type models, provide better calibrated probabilistic skill, while simultaneously providing better point estimates due to the regularization effect of the prior distribution in high-dimensional problems. We compare the effect of several priors, as well as maximum likelihood estimates, on 1) estimating parameter values on a perfect model experiment and 2) producing calibrated 1-yr SST anomaly forecast distributions using a preindustrial control run of the Community Earth System Model (CESM). Finally, we employ a host of probabilistic skill metrics to determine the extent to which an LIM can forecast SST anomalies at high latitudes. We find that the choice of prior distribution has an appreciable impact on estimation outcomes, and priors that emphasize physically relevant properties enhance the model’s ability to capture variability of SST anomalies.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1942

A Study of the Effect of Increased Size and Speed of Pursuit Airplanes on the Aileron Balancing Problem

The present trend is toward faster and larger pursuit airplanes. Because both speed and size increase the aileron control forces, the design of ailerons for manual operation is becoming increasingly difficult. In order to obtain a clearer picture of the future problem of balancing ailerons, and inspection has been made of the effects of airplane size and speed on the control forces. Computations were made of the aileron control forces required to meet specified rolling conditions for plain ailerons on wings with spans from 40 to 80 feet and for speeds up to 500 miles per hour. The rolling conditions were specified by two alternative criterions. One was the rolling criterion pb/2V of reference 1. For reasons, which will be discussed later, a value of 0.09 rather than the recommended value of 0.07 was assigned to this criterion. For the criterion pb/2V, the required value of the rolling velocity p varies inversely with the airplane span b. There is some question as to whether the rolling velocity of a pursuit airplane can be permitted to decrease simply because its size is increased. For the second criterion, therefore, the rolling velocity is independent of span (p/V is a constant). The value assigned to this criterion was so chosen that for a wing of 40-foot span the value of pb/2V would be 0.09. The computations neglected compressibility effects. Available experimental data and the results of tests given in reference 2 indicate that the effect of compressibility is to increase the control force. Recent flight tests have indicated that, with certain types of aileron, serious compressibility effects may cause discontinuity at speeds of approximately 400 miles per hour in the aileron control force curves.

Soule, H. A.↗
DOE OSTI2024

Graph-learning approach to combine multiresolution seismic velocity models

SUMMARY The resolution of velocity models obtained by tomography varies due to multiple factors and variables, such as the inversion approach, ray coverage, data quality, etc. Combining velocity models with different resolutions can enable more accurate ground motion simulations. Toward this goal, we present a novel methodology to fuse multiresolution seismic velocity maps with probabilistic graphical models (PGMs). The PGMs provide segmentation results, corresponding to various velocity intervals, in seismic velocity models with different resolutions. Further, by considering physical information (such as ray path density), we introduce physics-informed probabilistic graphical models (PIPGMs). These models provide data-driven relations between subdomains with low (LR) and high (HR) resolutions. Transferring (segmented) distribution information from the HR regions enhances the details in the LR regions by solving a maximum likelihood problem with prior knowledge from HR models. When updating areas bordering HR and LR regions, a patch-scanning policy is adopted to consider local patterns and avoid sharp boundaries. To evaluate the efficacy of the proposed PGM fusion method, we tested the fusion approach on both a synthetic checkerboard model and a fault zone structure imaged from the 2019 Ridgecrest, CA, earthquake sequence. The Ridgecrest fault zone image consists of a shallow (top 1 km) high-resolution shear-wave velocity model obtained from ambient noise tomography, which is embedded into the coarser Statewide California Earthquake Center Community Velocity Model version S4.26-M01. The model efficacy is underscored by the deviation between observed and calculated traveltimes along the boundaries between HR and LR regions, 38 per cent less than obtained by conventional Gaussian interpolation. The proposed PGM fusion method can merge any gridded multiresolution velocity model, a valuable tool for computational seismology and ground motion estimation.

Geochemistry & Geophysics↗
NASA NTRS1976

Laser absorption phenomena in flowing gas devices

A theoretical and experimental investigation is presented of inverse Bremsstrahlung absorption of CW CO2 laser radiation in flowing gases seeded with alkali metals. In order to motivate this development, some simple models are described of several space missions which could use laser powered rocket vehicles. Design considerations are given for a test call to be used with a welding laser, using a diamond window for admission of laser radiation at power levels in excess of 10 kW. A detailed analysis of absorption conditions in the test cell is included. The experimental apparatus and test setup are described and the results of experiments presented. Injection of alkali seedant and steady state absorption of the laser radiation were successfully demonstrated, but problems with the durability of the diamond windows at higher powers prevented operation of the test cell as an effective laser powered thruster.

Chapman, P. K.↗
NASA NTRS1996

Dynamics and Control of Articulated Anisotropic Timoshenko Beams

The paper illustrates the use of continuum models in control design for stabilizing flexible structures. A 6-DOF anisotropic Timoshenko beam with discrete nodes where lumped masses or actuators are located provides a sufficiently rich model to be of interest for mathematical theory as well as practical application. We develop concepts and tools to help answer engineering questions without having to resort to ad hoc heuristic ("physical") arguments or faith. In this sense the paper is more mathematically oriented than engineering papers and vice versa at the same time. For instance we make precise time-domain solutions using the theory of semigroups of operators rather than formal "inverse Laplace transforms." We show that the modes arise as eigenvalues of the generator of the semigroup, which are then related to the eigenvalues of the stiffness operator. With the feedback control, the modes are no longer orthogonal and the question naturally arises as to whether there is still a modal expansion. Here we prove that the eigenfunctions yield a biorthogonal Riesz basis and indicate the corresponding expansion. We prove mathematically that the number of eigenvalues is nonfinite, based on the theory of zeros of entire functions. We make precise the notion of asymptotic modes and indicate how to calculate them. Although limited by space, we do consider the root locus problem and show for instance that the damping at first increases as the control gain increases but starts to decrease at a critical value, and goes to zero as the gain increases without bound. The undamped oscillatory modes remain oscillatory and the rigid-body modes go over into deadbeat modes. The Timoshenko model dynamics are translated into a canonical wave equation in a Hilbert space. The solution is shown to require the use of an "energy" norm which is no more than the total energy: potential plus kinetic. We show that, under an appropriate extension of the notion of controllability, rate feedback with a collocated sensor can stabilize the structure in the sense that all modes are damped and the energy decays to zero. An example, non-numeric, is worked out in some detail illustrating the concepts and theory developed.

Balakrishnan, A. V.↗
DOE OSTI2022

Computer Model Calibration with Time Series Data Using Deep Learning and Quantile Regression

Computer models play a key role in many scientific and engineering problems. One major source of uncertainty in computer model experiments is input parameter uncertainty. Computer model calibration is a formal statistical procedure to infer input parameters by combining information from model runs and observational data. The existing standard calibration framework suffers from inferential issues when the model output and observational data are high-dimensional dependent data, such as large time series, due to the difficulty in building an emulator and the nonidentifiability between effects from input parameters and data-model discrepancy. To overcome these challenges, we, in this work, propose a new calibration framework based on a deep neural network (DNN) with long short-term memory layers that directly emulates the inverse relationship between the model output and input parameters. Adopting the “learning with noise” idea, we train our DNN model to filter out the effects from data-model discrepancy on input parameter inference. We also formulate a new way to construct interval predictions for DNN using quantile regression to quantify the uncertainty in input parameter estimates. Through a simulation study and real data application with the Weather Research and Forecasting Model Hydrological modeling system (WRF-Hydro), we show our approach can yield accurate point estimates and well-calibrated interval estimates for input parameters.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

MAGSAT satellite magnetic anomaly map over South America

A scalar magnetic anomaly map was prepared for South America and adjacent marine areas directly from original MAGSAT orbits. Special problems associated with the separation of external field and crustal anomalies, and the reduction of data to a common altitude are addressed. External fields are manifested in a long-wavelength ring current effect, a medium-wavelength equatorial electrojet, and short-wavelength noise. The noise is reduced by selecting profiles from quiet periods (Kp or = 3), and the effect of the electrojet is minimized by drawing the data set from dawn profiles only. The ring current is corrected through the use of a standard equation, augmented by further digital band-pass filtering. Profiles thus filtered differ primarily in amplitude due solely to satellite altitude differences. These differences are normalized by an inversion of the profile data onto a grid of equivalent point dipoles, and recalculated at an altitude of 350 km. The low altitudes in the study area cause instability in the inversion, necessitating separate inversions of several sub-areas which are subsequently merged. Crustal anomalies reduced-to-the-pole exhibit marked correlations to known tectonic features.

Ridgway, J. R.↗
NASA NTRS1984

An investigation of the consistency of the ionospheric measurements of the photoelectron flux and solar EUV flux

This paper demonstrates that there is an inconsistency between ionospheric measurements of the photoelectron flux and the solar EUV flux. The problem which occurs for EUV wavelengths near 250 A or photoelectron energies near 35 eV has serious implications for theoretical photoelectron flux calculations and could help to explain up to 40 percent of the difference between calculated and measured photoelectron fluxes for electron energies below 35 eV. It is also shown that: (1) only photons with wavelengths shorter than 310 A are of importance in producing photoelectrons; (2) above 20 eV, the photoelectron flux is controlled by the production of primary photoelectrons, while below 20 eV the flux is controlled by degraded photoelectrons; (3) the calculated cascading production rate is insensitive to the cross sections used for the calculation; and (4) the photoelectron flux is inversely proportional to the total inelastic cross sections.

Richards, P. G.↗
NASA NTRS1992

Analytical multiple scattering correction to the Mie theory: Application to the analysis of the lidar signal

The contribution of the multiple scattering to the lidar signal is dependent on the optical depth tau. Therefore, the radar analysis, based on the assumption that the multiple scattering can be neglected is limited to cases characterized by low values of the optical depth (tau less than or equal to 0.1) and hence it exclude scattering from most clouds. Moreover, all inversion methods relating lidar signal to number densities and particle size must be modified since the multiple scattering affects the direct analysis. The essential requests of a realistic model for lidar measurements which include the multiple scattering and which can be applied to practical situations follow. (1) Requested are not only a correction term or a rough approximation describing results of a certain experiment, but a general theory of multiple scattering tying together the relevant physical parameter we seek to measure. (2) An analytical generalization of the lidar equation which can be applied in the case of a realistic aerosol is requested. A pure analytical formulation is important in order to avoid the convergency and stability problems which, in the case of numerical approach, are due to the large number of events that have to be taken into account in the presence of large depth and/or a strong experimental noise.

Flesia, C.↗
DOE OSTI2023

New approaches to an old problem: addressing spatial gaps in the World Stress Map

Abstract A well-recognized characteristic of the World Stress Map (WSM) database is the continued presence of large spatial gaps in the distribution of the data records despite the more than 40-year development history of the database. The current release has more than 30 000 high-quality (A–C) data records (often referred to as ‘stress indicators’), but while some continental areas (such as Australia) have seen a significant increase in spatial converge with the latest release, other continental regions (Africa, central Asia, most of South America) remain markedly sparse. In this contribution we (1) review the current state of the spatial distribution of stress indicators in the continental regions (above sea-level); (2) quantify the clustering of the stress indicators in the latest WSM release using the Hopkins statistic as a way to explore the current spatial distribution of the indicators and assess future WSM releases; and (3) present three approaches (joint inversion, seismic anisotropy and InSAR) that provide a way to fill in the gaps (both in the S Hmax orientation and principal stress magnitudes) in regions that lack active seismicity and where borehole drilling is cost prohibitive. These three approaches have the potential to guide procedures for improving a priori estimates of the ambient stress field in the Earth's crust and reduce the uncertainty in predicting both the magnitude and orientation of the principal tectonic stresses.

58 GEOSCIENCES↗
NASA NTRS1992

Multi-point inverse design of an infinite cascade of airfoils

This paper describes a practical method for the design of an infinite cascade in incompressible flow. The method is based on conformal mapping, and as a result it allows for multi-point design. The cascade blade to be determined is divided into a desired number of segments. Over each segment, the velocity distribution is prescribed together with an inlet or outlet flow angle at which this velocity distribution is to be achieved. In this way multi-point design requirements can be met. It is necessary to satisfy several conditions that arise to guarantee compatibility with the inlet and outlet flow as well as closure of the cascade blade. Satisfaction of these conditions does not necessarily result in a cascade with all the desired characteristics. For example, the cascade blades may be bulbous or crossed. Through Newton iteration, however, the desired characteristics may be prescribed by allowing for the adjustment of the design parameters that define the mathematical problem through conformal mapping. Several examples will be illustrated to demonstrate the capability of the method. It will be shown that the method is limited to the design of cascades with solidities of up to one.

Selig, Michael S.↗