Estimation Of Correlation Length Research Articles

Method for auto-alignment and determination of parameter space in dual-phase grating interferometry

X-ray dual-phase grating interferometry provides quantitative micro-structural information beyond the optical resolution through its tunable correlation length. Ensuring optimal performance of the set-up requires accurate correlation length estimation and precise alignment of the gratings. This paper presents an automated procedure for determining the complete geometrical parameters of the interferometer set-up with a high degree of precision. The algorithm’s effectiveness is then evaluated through a series of experimental tests, illustrating its accuracy and robustness.

Uncertainty quantification in the bearing capacity estimation for shallow foundations in sandy soils

ABSTRACT In geotechnical engineering, is well known that the theoretical Bearing capacity (BC) differs from the real behaviour of the foundation, especially when theoretical BC was obtained from in-situ test equations or through shear strength properties obtained by laboratory or correlations. The scope of this work is to quantify the uncertainty of the different BC methods of a shallow foundation supported by an anthropic sandy soil tested in the Texas A&M University. Uncertainty was classified according to a degree associated with human errors, laboratory tests, traditional BC models and BC obtained by in-situ test equations. The results show that the choice of the most appropriate friction angle (ϕ') correlation is ambiguous and can generate important uncertainties with possible BC overestimations. As the exploration and/or calculation method becomes more sophisticated (e.g. Finite elements (FE) and Random Finite elements (RFEM)), the bias will be lower. However, as evidenced, the FE and RFEM bias is linked to the quality of the laboratory results and the correlation length estimation in RFEM. Finally, it is concluded that the BC uncertainty is directly related to the model selection and the derivation of the input parameters and not the method degree of uncertainty.

Reverse Problem in Surface Texture Analysis-One-Process Profile Modeling on the Basis of Measured Two-Process Profile after Machining or Wear.

The method of the base (valley) one-process profile modeling on the basis of the measured two-process profile was developed. The base one-process random profile of the Gaussian ordinate distribution is characterized by the standard deviation of the profile height and the correlation length. The problem of estimation of the correlation length of this one-process profile exists. In the procedure of the correlation length estimation, information about the averaged shape of the autocorrelation functions of many one-process profiles after the same type of machining is required. The correlation length of the base one-process profile can be obtained on the basis of the vertical truncation of the measured two-process profile. The average error of the correlation length estimation was not higher than 7%, while the maximum error was not larger than 14%. This method can be extended to simulate the one-process texture of 3D (areal) surface topography.

Direct simulation of two-dimensional isotropic or anisotropic random field from sparse measurement using Bayesian compressive sampling

Random field theory has been increasingly adopted to simulate spatially varying environmental properties and hydrogeological data in recent years. In a two-dimensional (2D) stochastic analysis, variation of the environmental properties or hydrogeological data along different directions can be similar (i.e., isotropic) or quite different (i.e., anisotropic). To model the spatially isotropic or anisotropic variability in a stochastic analysis, conventional random field generators generally require a vast amount of measurement data to identify the random field parameters (e.g., mean, variance, and correlation structure and correlation length in different directions). However, measurement data available in practice are usually sparse and limited. The random field parameters estimated from sparse measurements might be unreliable, and the subsequent random field modeling or stochastic analysis might be misleading. This underscores the significance and challenge of generating 2D isotropic or anisotropic random fields from sparse measurements. This paper develops a novel 2D random field generator, which does not require a parametric form of correlation function or estimation of correlation length and other random field parameters, and directly generates 2D isotropic or anisotropic random field samples from sparse measurements. The proposed generator is highly efficient because simulation of a 2D random field is achieved by generation of a short 1D random vector. The effectiveness and applicability of the proposed generator are illustrated using isotropic and anisotropic numerical examples.

Optimal channels for channelized quadratic estimators.

We present a new method for computing optimized channels for estimation tasks that is feasible for high-dimensional image data. Maximum-likelihood (ML) parameter estimates are challenging to compute from high-dimensional likelihoods. The dimensionality reduction from M measurements to L channels is a critical advantage of channelized quadratic estimators (CQEs), since estimating likelihood moments from channelized data requires smaller sample sizes and inverting a smaller covariance matrix is easier. The channelized likelihood is then used to form ML estimates of the parameter(s). In this work we choose an imaging example in which the second-order statistics of the image data depend upon the parameter of interest: the correlation length. Correlation lengths are used to approximate background textures in many imaging applications, and in these cases an estimate of the correlation length is useful for pre-whitening. In a simulation study we compare the estimation performance, as measured by the root-mean-squared error (RMSE), of correlation length estimates from CQE and power spectral density (PSD) distribution fitting. To abide by the assumptions of the PSD method we simulate an ergodic, isotropic, stationary, and zero-mean random process. These assumptions are not part of the CQE formalism. The CQE method assumes a Gaussian channelized likelihood that can be a valid for non-Gaussian image data, since the channel outputs are formed from weighted sums of the image elements. We have shown that, for three or more channels, the RMSE of CQE estimates of correlation length is lower than conventional PSD estimates. We also show that computing CQE by using a standard nonlinear optimization method produces channels that yield RMSE within 2% of the analytic optimum. CQE estimates of anisotropic correlation length estimation are reported to demonstrate this technique on a two-parameter estimation problem.

Comparison of beam emission spectroscopy and gas puff imaging edge fluctuation measurements in National Spherical Torus Experiment

In this study, the close physical proximity of the Gas Puff Imaging (GPI) and Beam Emission Spectroscopy (BES) diagnostics on the National Spherical torus Experiment (NSTX) is leveraged to directly compare fluctuation measurements, and to study the local effects of the GPI neutral deuterium puff during H-mode plasmas without large Edge Localized Modes. The GPI and BES views on NSTX provide partially overlapping coverage of the edge and scrape-off layer (SOL) regions above the outboard midplane. The separation in the toroidal direction is 16 °, and field lines passing through diagnostic views are separated by ∼ 20 cm in the direction perpendicular to the magnetic field. Strong cross-correlation is observed, and strong cross-coherence is seen for frequencies between 5 and 15 kHz. Also, probability distribution functions of fluctuations measured ∼ 3 cm inside the separatrix exhibit only minor deviations from a normal distribution for both diagnostics, and good agreement between correlation length estimates, decorrelation times, and structure velocities is found at the ±40% level. While the two instruments agree closely in many respects, some discrepancies are observed. Most notably, GPI normalized fluctuation levels exceed BES fluctuations by a factor of ∼ 9. BES mean intensity is found to be sensitive to the GPI neutral gas puff, and BES normalized fluctuation levels for frequencies between 1 and 10 kHz are observed to increase during the GPI puff.

Validation of the AIEM Through Correlation Length Parameterization at Field Scale Using Radar Imagery in a Semi-Arid Environment

This letter aimed to validate the advanced integral equation model (AIEM) through different correlation length parameterizations using radar imagery for field-scale studies in a semi-arid environment. This letter compared backscattering coefficients simulated from the AIEM and retrieved from the synthetic aperture radar imagery of a study site in Sardinia. Two treatments for the correlation length were adopted, i.e., in situ measurements and empirically based correlation length estimation. The results showed an overestimation of backscattering coefficients of 2.5 dB with a root mean square error (RMSE) of 3.1 dB for HH and VV polarizations and an underestimation of 27.7 dB and an RMSE of 31.0 dB for HV polarization from the AIEM parameterized by in situ measurements. When using the AIEM with an empirical correlation length, a bias of less than 1.0 dB was found with an RMSE of 1.7 dB for HH and VV polarizations and an overestimation of 1.1 dB and an RMSE of 5.1 dB for HV polarization. Better results were obtained with surface soil moisture (SSM) measured at 10 cm than at 5 cm. Promising soil moisture data retrieval from the SAR imagery is expected from using the empirical correlation length-parameterized AIEM for field-scale purposes in semi-arid environments.

Spatial scales of tropical precipitation inferred from TRMM microwave imager data

The local spatial scales of tropical precipitating systems were studied using Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) rain rate imagery from the TRMM satellite. Rain rates were determined from TMI data using the Goddard Profiling (GPROF) Version 5 algorithm. Following the analysis of Ricciardulli and Sardeshmukh (RS), who studied local spatial scales of tropical deep convection using global cloud imagery (GCI) data, active precipitating months were defined alternatively as those having greater than either 0.1 mm/h or 1 mm/h of rain for more than 5% of the time. Spatial autocorrelation values of rain rate were subsequently computed on a 55/spl times/55 km grid for convectively active months from 1998 to 2002. The results were fitted to an exponential correlation model using a nonlinear least squares routine to estimate a spatial correlation length at each grid cell. The mean spatial scale over land was 90.5 km and over oceans was 122.3 km for a threshold of 0.1 mm/h of rain with slightly higher values for a threshold of 1 mm/h of rain. An error analysis was performed which showed that the error in these determinations was of order 2% to 10%. The results of this study should be useful in the design of convective schemes for general circulation models and for precipitation error covariance models for use in numerical weather prediction and associated data assimilation schemes. The results of the TMI study also largely concur with those of RS, although the more direct relationship between the TMI data and rain rate relative to the GCI imagery provide more accurate correlation length estimates. The results also confirm the strong impact of land in producing short spatial scale convective rain.

Correlation length as an indicator of critical point behavior prior to a large earthquake

A large earthquake preparation is often manifested in correlation of seismicity in an area whose characteristic dimension greatly exceeds a dimension of source of main shock. Zöller et al. [G. Zöller, S. Hainzl, J. Kurths, Observation of growing correlation length as an indicator for critical point behavior prior to large earthquakes, J. Geophys. Res. 106 (2001) 2167–2176] show the growth of correlation length of earthquakes prior to nine large earthquakes in California according to a power low. We argue that the algorithm of correlation length estimation proposed by Zöller et al. [G. Zöller, S. Hainzl, J. Kurths, Observation of growing correlation length as an indicator for critical point behavior prior to large earthquakes, J. Geophys. Res. 106 (2001) 2167–2176] can result in a decrease of correlation length preceding its precursory growth before large earthquakes if the area in which earthquake activity is correlated grows with time during a main shock preparation. The correlation length analysis of acoustic emission events recorded in laboratory experiments on destruction of rocks and correlation length analysis of intermediate magnitude earthquakes in the area of large earthquakes preparation on Kamchatka and in Italy confirms the theoretical argument. This effect can be considered as an additional premonitory pattern of large earthquake preparation.

Two-dimensional linear theory of radial correlation reflectometry diagnostics

The two-dimensional linear theory of radial correlation reflectometry applicable for the case of low turbulence level, when the probing line is observable in the spectrum of reflected wave, is developed. It is shown that the small angle scattering in the plasma volume makes a significant contribution to the fluctuation reflectometry signal complicating the turbulence correlation length measurements. The conditions under which the cut off backscattering plays the dominant role and the correlation length estimation is possible are discussed.

Stochastic Reservoir Modeling Constrained to Dynamic Data: Local Calibration and Inference of Structural Parameters

Summary This paper presents a new geostatistical approach, called the general-inversion method that incorporates dynamic data (pressure transient, well production, water cut) into a reservoir model. It essentially involves two basic tools: the fast-Fourier-transform moving-average (FFT-MA) generator and the gradual-deformation method. The FFT-MA generator produces unconditional Gaussian-related fields that can be perturbed on the basis of the gradual-deformation principles. Thus, the initial structure of the realizations is preserved. Integrating these two primary algorithms within an optimization process yields the general-inversion procedure. The method has at least three significant advantages. First, unlike the traditional inverse approaches, the general-inversion method easily accounts for the constraint relative to prior geostatistical information. Second, the permeability/porosity distribution can be perturbed globally or locally. And third, the method makes it possible to condition the permeability/porosity distribution and the structural (or geostatistical) parameters (mean, variance, correlation length) at the same time. Because of these distinct capabilities, the suggested inversion scheme can qualify as a general one. The suggested approach was applied to synthetic examples designed to address such key issues as characterization of permeability distribution, updating of a reservoir model to integrate newly obtained data, and estimation of correlation length from well data.

Effects of measurement error and sampling resolution on estimates of atrial tissue recovery parameters.

We studied the effect of sampling resolution and measurement error on estimates of tissue recovery parameters using experimental and simulated data. Action potential duration (APD) was estimated from monophasic action potentials recorded at 250 sites (delta x = 3.5 mm) on the endocardium of the canine right atrium (n = 8) during control and acetylcholine perfusion. APD distributions were also simulated using a random number generator, then scaled and filtered to physiological values. The following parameters were estimated at increasing APD sampling interval and measurement error: mean APD, standard deviation of APD, mean APD gradient, standard deviation of APD gradient, APD wavelength, and APD correlation length. We found that large errors can result from APDs collected at inadequate sampling intervals and adequate sampling intervals may be 3-6 times less than the Nyquist interval. Large parameter errors also resulted from data with relatively low levels of measurement error. The effect of measurement error was dependent upon the standard deviation of APD, sampling resolution, and APD wavelength. Inadequate sampling resolution was the largest source of error in experimental parameter estimates. Estimates of mean and standard deviation of APD gradient decreased with spacing as estimates of correlation length and wavelength increased. Careful selection of spacing interval, taking into account the spatial complexity of recovery, as well as considerably low measurement errors will produce accurate estimates of gradients, correlation length, and wavelength.

Correlation length from cluster-diameter distribution

We report numerical estimates of correlation lengths in 2D Potts models from the asymptotic decay of the cluster-diameter distribution. Using this observable we are able to verify theoretical predictions for the correlation length in the disordered phase at the transition point for $q=10$, 15, and 20 with an accuracy of about $1%-2%$. This is a considerable improvement over previous measurements using the standard (projected) two-point function.

Correlation functions for sediment acoustic properties

Models for sediment volume scattering require knowledge of the correlation functions for sediment sound velocity and density (or porosity). High-resolution vertical correlation functions of these properties have been estimated using sediment porosity and compressional wave velocity data measured vertically at regular, closely spaced intervals from diver-collected core samples. Because the data series are truncated owing to a limited core length, the correlation functions were estimated using a first-order autoregressive model and autocorrelations were calculated with Burg’s algorithm. Correlation length estimates were from a variety of shallow-water sites. Relationships between grain size and correlation length are discussed.

First-order nature of pure gauge SU(3) deconfinement

We present further evidence that pure gauge deconfinement for N t = 4 is a first-order phase transition. Additional Monte Carlo runs on a 24 3 × 4 lattice have been carried out, and previous runs have been analyzed more thoroughly. Topics discussed are: reliable determination of the order of a phase transition in a finite volume, improved estimates of correlation lengths obtained from Polyakov loop correlations, and the resolution of the small systematic error seen previously in our results on a 16 3 spatial volume.

Magnetization and correlation length of the easy-plane ferromagnetic chain: Numerical analysis and application to (C6H

The ferromagnetic spin-(1/2 one-dimensional XXZ Heisenberg model is studied numerically by quantum Monte Carlo analysis and extrapolations in 1/N of finite-size chain data. Reliable magnetization and correlation-length estimates are presented and a quantitative agreement with recent experimental data on the compound (${\mathrm{C}}_{6}$${\mathrm{H}}_{11}$${\mathrm{NH}}_{3}$)${\mathrm{CuBr}}_{3}$ is found.

Results of an exact [formula omitted] scale transformation for two-dimensional lattice systems with O(2) and O(3) symmetry

The diagonal-to-diagonal transfer operator is considered on two-dimensional square lattices. A variational solution treating every second spin in an exact way is shown to yield very encouraging correlation length estimates for T> T c in the cases of the XY and Heisenberg spin models.