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NASA NTRS1972

Recent results of nonlinear estimators applied to hereditary systems.

An application of the extended Kalman filter to delayed systems to estimate the state and time delay is presented. Two nonlinear estimators are discussed and the results compared with those of the Kalman filter. For all the filters considered, the hereditary system was treated with the delay in the pure form and by using Pade approximations of the delay. A summary of the convergence properties of the filters studied is given. The results indicate that the linear filter applied to the delayed system performs inadequately while the nonlinear filters provide reasonable estimates of both the state and the parameters.

Schiess, J. R.↗

NASA NTRS2018

On the Limitations of Variational Bias Correction

Satellite radiances are the largest dataset assimilated into Numerical Weather Prediction (NWP) models, however the data are subject to errors and uncertainties that need to be accounted for before assimilating into the NWP models. Variational bias correction uses the time series of observation minus background to estimate the observations bias. This technique does not distinguish between the background error, forward operator error, and observations error so that all these errors are summed up together and counted as observation error. We identify some sources of observations errors (e.g., antenna emissivity, non-linearity in the calibration, and antenna pattern) and show the limitations of variational bias corrections on estimating these errors.

Moradi, Isaac↗

NASA NTRS2000

Stress Recovery and Error Estimation for Shell Structures

The Penalized Discrete Least-Squares (PDLS) stress recovery (smoothing) technique developed for two dimensional linear elliptic problems is adapted here to three-dimensional shell structures. The surfaces are restricted to those which have a 2-D parametric representation, or which can be built-up of such surfaces. The proposed strategy involves mapping the finite element results to the 2-D parametric space which describes the geometry, and smoothing is carried out in the parametric space using the PDLS-based Smoothing Element Analysis (SEA). Numerical results for two well-known shell problems are presented to illustrate the performance of SEA/PDLS for these problems. The recovered stresses are used in the Zienkiewicz-Zhu a posteriori error estimator. The estimated errors are used to demonstrate the performance of SEA-recovered stresses in automated adaptive mesh refinement of shell structures. The numerical results are encouraging. Further testing involving more complex, practical structures is necessary.

Yazdani, A. A.↗

DOE OSTI2015

Linear functional minimization for inverse modeling

In this paper, we present a novel inverse modeling strategy to estimate spatially distributed parameters of nonlinear models. The maximum a posteriori (MAP) estimators of these parameters are based on a likelihood functional, which contains spatially discrete measurements of the system parameters and spatiotemporally discrete measurements of the transient system states. The piecewise continuity prior for the parameters is expressed via Total Variation (TV) regularization. The MAP estimator is computed by minimizing a nonquadratic objective equipped with the TV operator. We apply this inversion algorithm to estimate hydraulic conductivity of a synthetic confined aquifer from measurements of conductivity and hydraulic head. The synthetic conductivity field is composed of a low-conductivity heterogeneous intrusion into a high-conductivity heterogeneous medium. Our algorithm accurately reconstructs the location, orientation, and extent of the intrusion from the steady-state data only. Finally, addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.

47 OTHER INSTRUMENTATION↗

NASA NTRS2005

X-43A Rudder Spindle Fatigue Life Estimate and Testing

Fatigue life analyses were performed using a standard strain-life approach and a linear cumulative damage parameter to assess the effect of a single accidental overload on the fatigue life of the Haynes 230 nickel-base superalloy X-43A rudder spindle. Because of a limited amount of information available about the Haynes 230 material, a series of tests were conducted to replicate the overload and in-service conditions for the spindle and corroborate the analysis. Both the analytical and experimental results suggest that the spindle will survive the anticipated flight loads.

Glaessgen, Edward H.↗

NASA NTRS1987

Estimation of squeeze-film damping and inertial coefficients from experimental free-decay data

The results are given for an experimental program concerned with a parametric identification of the damping and inertial coefficients of a cylindrical squeeze-film bearing, through an analysis of transient response data. The results enable the operating range for which a linear model of the squeeze-film is appropriate to be determined. Comparisons are made between the estimated coefficients and theoretical predictions. Presentation is by courtesy of the Council of the Institution of Mechanical Engineers, London.

Roberts, J. B.↗

NASA NTRS2002

Classification image analysis: estimation and statistical inference for two-alternative forced-choice experiments

We consider estimation and statistical hypothesis testing on classification images obtained from the two-alternative forced-choice experimental paradigm. We begin with a probabilistic model of task performance for simple forced-choice detection and discrimination tasks. Particular attention is paid to general linear filter models because these models lead to a direct interpretation of the classification image as an estimate of the filter weights. We then describe an estimation procedure for obtaining classification images from observer data. A number of statistical tests are presented for testing various hypotheses from classification images based on some more compact set of features derived from them. As an example of how the methods we describe can be used, we present a case study investigating detection of a Gaussian bump profile.

Non-NASA Center↗

DOE OSTI2019

Optical-property coefficient estimation of bulky medium in experiments with a succinctly analytical calculation

Diffuse optical imaging enables to reconstruct distribution of optical properties, absorption and scattering coefficients, in tissue for breast cancer detection based on diffusion equation with the help of the initial guess obtained from measured data. To estimate the initial guess of the optical-property coefficients, an analytical solution of diffusion equation can be used and compared with the measured data. The analytical solution for a homogeneous infinite medium can be obtained in the frequency domain, expressing that the photon intensity and the phase lag relative to the distance between source and detector in a linear relationship. In this study, a succinct calculation using the trigonometric relation is proposed to estimate the optical-property coefficients. A tank-type and a cylinder Lipovenoes phantoms with two concentrations of 1.25% and 2.5% are employed and measured for verification. It is found that the method proposed here shows better results and results in estimation errors of 0–14.81% for μ{sub a} and 20–42% for μ{sub s}′.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Identification and system parameter estimation methods for a Pyrofusion neutron source - 372

Pyrofusion sources are compact, low power systems which are capable of producing short intense pulses of neutrons from D-D fusion reactions. A model structure has been derived from the underlying physics principles and it is shown that the dominant non-linear dynamics pose significant challenges to the system control. This paper presents the methods under development to construct, estimate and analyse nonlinear grey-box models of Pyrofusion systems from measured data. The methods have been trialled on data sets obtained from the publications of previous Pyrofusion research groups. The results indicate the promising potential application of these methods to the system identification of profusion device characteristics to support model verification, pulse characterisation and prediction of operational capabilities. The identified models are shown to exhibit satisfactory analogous cause-and-effect behaviour. (authors)

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2017

Towards optimal extraction of cosmological information from nonlinear data

One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics of clusters, density peaks or voids etc.), along with the corresponding covariance matrices. However, this approach is computationally prohibitive and has not been shown to be exhaustive in terms of information content. Here we instead develop a hierarchical Bayesian approach, expanding the likelihood around the maximum posterior of linear modes, which we solve for using optimization methods. By integrating out the modes using perturbative expansion of the likelihood we construct an initial power spectrum estimator, which for a fixed forward model contains all the cosmological information if the initial modes are gaussian distributed. We develop a method to construct the window and covariance matrix such that the estimator is explicitly unbiased and nearly optimal. We then generalize the method to include the forward model parameters, including cosmological and nuisance parameters, and primordial non-gaussianity. We apply the method in the simplified context of nonlinear structure formation, using either simplified 2-LPT dynamics or N-body simulations as the nonlinear mapping between linear and nonlinear density, and 2-LPT dynamics in the optimization steps used to reconstruct the initial density modes. We demonstrate that the method gives an unbiased estimator of the initial power spectrum, providing among other a near optimal reconstruction of linear baryonic acoustic oscillations.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1996

Closed-Loop System Identification Experience for Flight Control Law and Flying Qualities Evaluation of a High Performance Fighter Aircraft

This paper highlights some of the results and issues associated with estimating models to evaluate control law design methods and design criteria for advanced high performance aircraft. Experimental fighter aircraft such as the NASA-High Alpha Research Vehicle (HARV) have the capability to maneuver at very high angles of attack where nonlinear aerodynamics often predominate. HARV is an experimental F/A-18, configured with thrust vectoring and conformal actuated nose strakes. Identifying closed-loop models for this type of aircraft can be made difficult by nonlinearities and high order characteristics of the system. In this paper, only lateral-directional axes are considered since the lateral-directional control law was specifically designed to produce classical airplane responses normally expected with low-order, rigid-body systems. Evaluation of the control design methodology was made using low-order equivalent systems determined from flight and simulation. This allowed comparison of the closed-loop rigid-body dynamics achieved in flight with that designed in simulation. In flight, the On Board Excitation System was used to apply optimal inputs to lateral stick and pedals at five angles at attack : 5, 20, 30, 45, and 60 degrees. Data analysis and closed-loop model identification were done using frequency domain maximum likelihood. The structure of identified models was a linear state-space model reflecting classical 4th-order airplane dynamics. Input time delays associated with the high-order controller and aircraft system were accounted for in data preprocessing. A comparison of flight estimated models with small perturbation linear design models highlighted nonlinearities in the system and indicated that the closed-loop rigid-body dynamics were sensitive to input amplitudes at 20 and 30 degrees angle of attack.

Murphy, Patrick C.↗

DOE OSTI2018

On the Solvability of a Boundary-Value Problem for a Second-Order Singular Quasilinear Equation

We obtain solvability conditions for a two-point boundary-value problem for a second-order quasilinear equation. The equation is singular with respect to the independent variable. The result is based on the properties of the Green operator of the corresponding linear problem. In particular, we prove its boundedness and obtain an upper estimate of its norm. Conditions of existence of a solution of the original problem are obtained from the solvability condition of an auxiliary operator equation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Slow-scale split-step tau-leap method for stiff stochastic chemical systems

Tau-leaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. A motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and systems biology. It is known that the dynamical behavior of biochemical systems is often intrinsically stiff representing a serious challenge for their numerical approximation. The naive extension of stiff deterministic solvers to stochastic integration often yields numerical solutions with either impractically large relaxation times or incorrectly resolved covariance. In this paper, we propose a splitting heuristic which helps to resolve some of these issues. The proposed integrator contains a number of unknown parameters which are estimated for each particular problem from the moment equations of the corresponding linearized system. We show that this method is able to reproduce the exact mean and variance of the linear scalar test equation and demonstrates a good accuracy for the arbitrarily stiff systems at least in the linear case. The numerical examples for both linear and nonlinear systems are also provided, and the obtained results confirm the efficiency of the considered splitting approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Kinetic model-based group contribution method for derived cetane number prediction of oxygenated fuel components and blends

A four-step autoignition model was used to derive an expression for the ignition delay (ID) measured in ignition quality testers (IQT) with the derived cetane number (DCN) determined from this ID using the ASTM D6890 standard correlation. The model predicts DCN for individual compounds and blends as a function of each compound's global initiation and net chain branching rate constants. Expressions for these values were determined assuming they could be related to the functional groups present in each compound. Measurement data for 125 compounds and 94 binary and ternary blends (including oxygenates: alcohols, aldehydes, esters, ethers, and ketones), from literature and from measurements performed in our lab, were used to obtain the dependence of the measured ignition delay on each functional group. The new kinetic model-based group contribution method was able to predict the ignition delay of both pure compounds and blends, with an average DCN error of 4.4 (19%) and 2.8 (11%), respectively. Here, the blend model was also used to develop an ID mixing rule by incorporating existing IQT ignition delay data for each compound. Use of the mixing rule gave an average DCN error of 3.6 (16%) for blends. Both the blend model and mixing rule were found to be superior compared to standard linear by volume fraction or mole fraction mixing rules commonly used to estimate the DCN of mixtures.

42 ENGINEERING↗

DOE OSTI2019

Characterization of laboratory-scale hydraulic fracturing for EGS

To investigate the impact of reservoir stimulation by hydraulic fracturing, a series of advanced lab-scale block tests were conducted with multiple measurement methods to characterize the fracture and to assess the operation and the performance of an enhanced or engineered geothermal system (EGS). The stimulation test samples were 330-mm cubic blocks of Sierra White granite with one injection well and four producers drilled into it. Acoustic emissions generated during the fracture initiation and propagation were monitored with twenty AE sensors mounted on all sides of the block to help characterize the fracture initiation and propagation process. The recorded AE signals were analyzed to obtain the event location and the failure mechanism. The localized AE events shows that due to the low viscosity of the fracturing fluid (water), the fracture propagated rapidly and took only about 1.4 s to reach near the block surface. During the fracturing phase, about 47 percent of the events were determined to be shear/mixed mode failure events, 28 percent tensile failure events, and 25 percent compressional failure events. Just after the simulation, a step-rate (constant flowrate) injection test was carried out to investigate the reservoir injectivity enhancement. During this phase additional compressional failure events were observed and the percentages of tensile failure and shear/mixed mode failure decreased. The dramatic increase of the injection rate with small increments of the injection pressure demonstrates the nonlinear response of the fracture to effective normal stress variation with much higher fracture opening increase during the low effective normal stress interval. Hydraulic fracturing tests under different stress levels show that more AE hits/events are recorded when the rock block is under higher applied stress. The reconstructed 3D fracture geometry shows good agreement with the AE monitoring results. After fracturing, a tracer test was carried out and the fracture aperture was estimated to be around 139 μm. The tracer recovery curve shows two linear portions of the tracer tail on a semi-log plot similar to that observed in some field data and predicted by numerical modeling. Laser scanning of the fracture surfaces indicates that the induced fracture has a rough surface with a joint roughness coefficient (JRC) of 12.98 and tortuosity of 1.10, both of which are slightly larger than that from the Brazilian test fracture on the same rock. The thin section and SEM observations show that the fracture follows the weak boundaries between the Quartz and Albite grains or the weak beddings in the grains.

58 GEOSCIENCES↗

DOE OSTI2019

Effect of cobalt substitution on structure and magnetic properties of Nd 0.4 Zr 0.6 Fe 10–x Co x Si 2 (x = 0–3) alloys and their ribbons

This paper reports the stabilization of the RFe 12 -type based compounds where part of R and Fe are substituted with Zr and Co and Si, respectively, in order to examine whether these rare-earth-lean materials are suitable for applications as permanent magnets. Structural and magnetic characterization of the family of alloys with the general formula Nd 0.4 Zr 0.6 Fe 10–x Co x Si 2 (x = 0–3) and their melt-spun ribbons were carried out using X-ray diffraction and Mössbauer spectroscopy. The ThMn 12 -type structure is obtained for all samples as the majority phase with a minority α-Fe(CoSi) phase (less than 5 wt%) as it was estimated by XRD for x = 1 and 2. The Curie temperature increases linearly with Co substitution from 561 K for x = 0 to 712 K for x = 3. The saturation magnetization decreases slightly from 130.5 (x = 1) to 129.1 A·m 2 /kg (x = 3), while the anisotropy field is following the same trend.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Accurate prediction of short-range order and its effect on thermodynamic, structural, and electronic properties of disordered alloys: exemplified in archetypical Cu 3 Au

Electronic-structure methods based on density-functional theory (DFT) were used to quantify the effect of chemical short-range order (SRO) on thermodynamic, structural, and electronic properties of archetypal face-centered-cubic (fcc) Cu3Au alloy. We showed that SRO can be tuned to alter bonding and lattice dynamics (i.e., phonons) and detail how these properties are changed with SRO. Thermodynamically favorable SRO significantly improved the phase stability of fcc Cu3Au from -0.0343 eV-atom -1 to –0.0682 eV-atom -1 . We used our DFT-based linear-response theory to predict SRO and its electronic origin, and accurately estimate the observed transition temperature, ordering instability (L1 2 ), and Warren-Cowley SRO parameters, in agreement with experiments. The accurate prediction of real-space SRO gives an edge over computationally and resource intensive approaches such as monte-carlo methods or experiments, which will enable large scale molecular dynamic simulations by providing supercells with optimized SRO. Here we also analyzed phonon dispersion and estimated the vibrational entropy change (from 9kB at 300 K to 6kB at 100 K) in fcc Cu3Au. We established from SRO analysis that exclusion of chemical interactions may lead to a skewed view of true properties in chemically complex alloys. The first-principles methods described in this work are generally applicable to any arbitrary solid-solution alloys, including multi-principal-element alloys, therefore, holds promise for designing technologically useful materials.

36 MATERIALS SCIENCE↗

DOE OSTI2023

On the uncertainty of estimating photovoltaic soiling using nearby soiling data

The accumulation of dust on the surface of photovoltaic modules can reduce their performance and affect the cost competitiveness of this technology. This phenomenon is known as soiling and can be mitigated through appropriate corrective and/or preventive actions. In order to maximize its effectiveness, it is important to plan the soiling mitigation strategy even before the PV system is operational. This is typically done through a nearest neighbor approach, by estimating soiling using data from the nearest operational photovoltaic system. This work focuses on understanding the uncertainty related to this practice. For this purpose, the semi-variance function is used to study the dissimilarity between the soiling losses of two locations in California depending on their distance. The results show that, when the soiling loss at a nearby system is used to estimate soiling of a site, the uncertainty can be approximated to increase linearly at a rate of 0.08-0.10%/km up to 60 or 80 km. After this distance, the use of a nearest neighbor approach is no longer justified, as it produces an uncertainty as big as the average soiling loss of the sites in the dataset used in this study. In some conditions, uncertainties > 0% are found also for sites located within 25 km, meaning that even close-by systems might soil differently.

14 SOLAR ENERGY↗