multi-Gaussian Model Research Articles

Multi-Gaussian Stratified Modeling and Characterization of Multi-process Surfaces

Surface serves as the fingerprint of a component. Most researchers understood surface topography from a single-stratum viewpoint, some ones have focused on a bi-Gaussian stratified model that respects formation mechanism, but few studies have considered a multi-Gaussian stratified possibility. A multi-Gaussian stratified model of surface topography is developed based on the existing bi-Gaussian stratified surface theory. The bi-Gaussian characterizing method, on the basis of linear regression, is revised to differentiate the mixed multiple Gaussian components. The model and the method are demonstrated on simulated multi-Gaussian stratified surfaces and real engineering surfaces manufactured by turning, rough lapping, and fine lapping. The results reveal the existence of multi-Gaussian stratified feature on multi-process surfaces in industry, and improve the stratified surface theory.

An improved Richardson-Lucy iterative algorithm for C-scan image restoration and inclusion size measurement

The accuracy of measuring inclusion size in direct C-scan image of immersion ultrasonic testing is restricted by the lateral resolution of the focused transducer, even if a high frequency is used, and the blurred edge due to scattering of sound waves at inclusions. In this work, an improved image restoration method that is based on the Richardson-Lucy (RL) iterative algorithm is proposed, which is used to restore the C-scan image and improve the accuracy of inclusion size measurement in immersion ultrasonic testing. For the improved RL iterative algorithm, the point spread function (PSF) is derived based on the multi-Gaussian beam model and Kirchhoff approximation, which considers the propagation properties of sound waves at water-steel interface and the spectral characteristics of the transducer with high frequency. In order to determine the final iteration number, the relationship between final iteration number and size of the inclusion in the image is established by restoring the simulated C-scan image and further calibrated with size correction factor. The size correction factor considers the effect of sound attenuation and electro-mechanical transformation encountered in practical testing equipment. Experimental results show that the inclusion sizes measured in restored C-scan images agree well with the optical micrograph results, which prove the effectiveness of the proposed method.

Liquid Level Measurement Model Outside of Closed Containers Based on Continuous Sound Wave Amplitude.

This research put forward an exogenous liquid level measurement method based on continuous sound wave amplitude. The distribution of round piston transducers in the sound field of a metal solid was analyzed by building 15 Multi-Gaussian Beam superposition models; the calculation method for echo sound pressure was worked out according to the reflection and refraction properties of ultrasonic wave. The continuous wave with three amplitudes was used as the driving source of ultrasonic sensor, and two single-crystal sensors with the same diameter were used as the transmitting terminal and receiving terminal of ultrasonic waves to carry out experiments for four groups of containers of different wall thickness and to compare the characteristics of echo energy of driving sources with three amplitudes above and below the liquid levels with different wall thickness. Two groups of sensors of different diameters were used to measure the liquid levels of experimental models, and the measuring errors of the two groups of sensors were analyzed and compared. The experimental result shows that the measuring error of the model is less than 5 mm, so it is applicable to the level measurement of liquids or liquid mixtures in many sectors.

Three dynamically distinct stellar populations in the halo of M49

Context. M49 (NGC 4472) is the dominant galaxy in subcluster B of the Virgo Cluster, and a benchmark for studying the build-up of the extended halos of brightest group galaxies in the outskirts of galaxy clusters. Aims. We investigate the kinematics in the outer halo of M49, look for substructures, and describe the transition to the surrounding intra-group light. Methods. As kinematic tracers, we use planetary nebulae (PNe), combining kinematics from the extended Planetary Nebula Spectrograph (PN.S) early-type galaxy survey with our recent deep photometric sample. We study the position-velocity-plane for bright and faint PN populations out to 95 kpc radius, and employ a multi-Gaussian model for the velocity distribution to identify stellar populations with distinct kinematics and histories. Results. We report the detection of stellar-kinematic substructure associated with the interaction of M49 with the dwarf irregular galaxy VCC 1249. We find two kinematically distinct PN populations associated with the main M49 halo and the extended intra-group light (IGL). These have velocity dispersions σhalo ≃ 170 km s−1 and σIGL ≃ 400 km s−1 at 10–80 kpc radii. The overall luminosity profile and velocity dispersion at ~80 kpc are consistent with a flat circular velocity curve extrapolated from X-ray observations. The dispersion of the PNe associated with the IGL joins onto that of the satellite galaxies in subcluster B at ~100 kpc radius. This is the first time that the transition from halo to IGL is observed based on the velocities of individual stars. Conclusions. Therefore the halo of M49, consisting of at least three distinct components, has undergone an extended accretion history within its parent group potential. The blue colours of the IGL component are consistent with a population of stars formed in low-mass galaxies at redshift ~0.5 that has since evolved passively, as suggested by other data.

Wavelet Phase Coherence Analysis between the Respiratory Activity and the Microcirculation—The Effects of Type 1 Diabetes

The microvascular perfusion is modulated by physiological functions, which have been associated with specific frequency ranges. Although cardio-respiratory interactions have been widely analyzed at a macrocirculation level, only few studies have been conducted with the aim to understand the effect of breathing on the peripheral circulation. Diabetic microangiopathy is characterized by structural and functional alterations of the blood microvessels, which reflect in a modification of the physical properties of peripheral microvascular beds, such as vascular stiffness. A wavelet phase coherence (WPC) analysis was performed to elucidate the time-phase relationship between the respiratory activity and vascular-dependent features of the peripheral pulse, reconstructed by means of a novel multi-Gaussian modeling algorithm. The present WPC analysis was conducted on a group of 24 healthy volunteers, mean age 30±15 years, in comparison with 21 type-1 diabetic (T1D) subjects, mean age 26±3 years, in order to detect the effects of T1D on the physiological coupling between breathing and microcirculation. The peripheral cutaneous perfusion was assessed on the pulp of the index finger with the laser Doppler flowmetry (LDF) technique, while the respiratory signal was simultaneously recorded with a wearable chest band. In 17 out of the 24 control subjects involved (i.e., 71%), significant WPC values were identified in the respiratory frequency range (0.145-0.6 Hz), with respect to the area beneath the diastolic portion of the peripheral pulse (median WPC: 77.9%). This outcome indicates that the diastolic phase of the pulse exhibits a marked periodicity linked to the breathing activity. The analysis conducted on the T1D group highlighted a loss of synchronization, with significant WPC levels found in only 33% of the investigated subjects. These results suggest that the proposed method is able to detect the detrimental effects of T1D on the blood microcirculation. Disclosure A. Perrella: None. M. Sorelli: None. P. Francia: None. L. Capirchio: None. R. Anichini: Advisory Panel; Self; Abbott. Speaker's Bureau; Self; Novartis Pharmaceuticals Corporation, Boehringer Ingelheim GmbH. Advisory Panel; Self; Eli Lilly and Company, AstraZeneca. Speaker's Bureau; Self; Merck & Co., Inc., Takeda Development Centre Europe Ltd.. Advisory Panel; Self; Sanofi, Janssen Pharmaceuticals, Inc.. Research Support; Self; Grünenthal Group. A. de Bellis: Speaker's Bureau; Self; Eli Lilly and Company, AstraZeneca, Novo Nordisk A/S. Research Support; Self; Grünenthal Group. M. Gulisano: None. L. Bocchi: None.

A method for efficient Bayesian optimization of self-assembly systems from scattering data

BackgroundThe ability of collections of molecules to spontaneously assemble into large functional complexes is central to all cellular processes. Using the viral capsid as a model system for complicated macro-molecular assembly, we develop methods for probing fine details of the process by learning kinetic rate parameters consistent with experimental measures of assembly. We have previously shown that local rule based stochastic simulation methods in conjunction with bulk indirect experimental data can meaningfully constrain the space of possible assembly trajectories and allow inference of experimentally unobservable features of the real system.ResultsIn the present work, we introduce a new Bayesian optimization framework using multi-Gaussian process model regression. We also extend our prior work to encompass small-angle X-ray/neutron scattering (SAXS/SANS) as a possibly richer experimental data source than the previously used static light scattering (SLS). Method validation is based on synthetic experiments generated using protein data bank (PDB) structures of cowpea chlorotic mottle virus. We also apply the same approach to computationally cheaper differential equation based simulation models.ConclusionsWe present a flexible approach for the global optimization of computationally costly objective functions associated with dynamic, multidimensional models. When applied to the stochastic viral capsid system, our method outperforms a current state of the art black box solver tailored for use with noisy objectives. Our approach also has wide applicability to general stochastic optimization problems.

A Gaussian beam method for ultrasonic non-destructive evaluation modeling

The propagation of high-frequency ultrasonic body waves can be efficiently estimated with a semi-analytic Dynamic Ray Tracing approach using paraxial approximation. Although this asymptotic field estimation avoids the computational cost of numerical methods, it may encounter several limitations in reproducing identified highly interferential features. Nevertheless, some can be managed by allowing paraxial quantities to be complex-valued. This gives rise to localized solutions, known as paraxial Gaussian beams. Whereas their propagation and transmission/reflection laws are well-defined, the fact remains that the adopted complexification introduces additional initial conditions. While their choice is usually performed according to strategies specifically tailored to limited applications, a Gabor frame method has been implemented to indiscriminately initialize a reasonable number of paraxial Gaussian beams. Since this method can be applied for an usefully wide range of ultrasonic transducers, the typical case of the time-harmonic piston radiator is investigated. Compared to the commonly used Multi-Gaussian Beam model [1], a better agreement is obtained throughout the radiated field between the results of numerical integration (or analytical on-axis solution) and the resulting Gaussian beam superposition. Sparsity of the proposed solution is also discussed.

A non-stationary geostatistical approach to multigaussian kriging for local reserve estimation

Multigaussian kriging technique has many applications in mining, soil science, environmental science and other fields. Particularly, in the local reserve estimation of a mineral deposit, multigaussian kriging is employed to derive panel-wise tonnages by predicting conditional probability of block grades. Additionally, integration of a suitable change of support model is also required to estimate the functions of the variables with larger support than that of the samples. However, under the assumption of strict stationarity, the grade distributions and important recovery functions are estimated by multigaussian kriging using samples within a supposedly spatial homogeneous domain. Conventionally, the underlying random function model is required to be stationary in order to carry out the inference on ore grade distribution and relevant statistics. In reality, conventional stationary model often fails to represent complicated geological structure. Traditionally, the simple stationary model neither considers the obvious changes in local means and variances, nor is it able to replicate spatial continuity of the deposit and hence produces unreliable outcomes. This study deals with the theoretical design of a non-stationary multigaussian kriging model allowing change of support and its application in the mineral reserve estimation scenario. Local multivariate distributions are assumed here to be strictly stationary in the neighborhood of the panels. The local cumulative distribution function and related statistics with respect to the panels are estimated using a distance kernel approach. A rigorous investigation through simulation experiments is performed to analyze the relevance of the developed model followed by a case study on a copper deposit.

Detecting Vascular Age Using the Analysis of Peripheral Pulse.

proposing an approach for the assessment of vascular ageing based on a support vector machine (SVM) learning from features of the pulse contour. the supervised classifier was trained and validated over 20935 models of pulse wave, obtained with a multi-Gaussian decomposition algorithm, applied to laser Doppler flowmetry signals of 54 healthy, non-smoker subjects. the multi-Gaussian model showed a mean R2 of 0.98 and an average normalized root mean square error of 0.90, demonstrating the ability to reconstruct the pulse shape. Over 30 training and validation experiments, the SVM showed a mean Pearson's r of 0.808 between the rate of waves classified as old and the age of the subjects, along with an average area under the ROC curve of 0.953. the SVM showed the capability to discriminate differently aged individuals. the proposed method might detect the ageing-related modifications of the vascular tree; furthermore, since diabetes promotes vascular alterations comparable to ageing, this approach may be also suitable for the screening of diabetic angiopathy.

Physical parameter estimation with MCMC from observations of Vela X-1

We present a parameter estimate for continua, and He-like triplets of the high resolution X-ray spectra with a Bayesian inference and a Markov Chain Monte Carlo (MCMC) tool. The method is applied for Vela X-1 with three different orbital phases ($\unicode[STIX]{x1D719}$), Eclipse, $\unicode[STIX]{x1D719}=0.25$, and $\unicode[STIX]{x1D719}=0.5$, which are adopted from the Chandra High-Energy Transmission Grating Spectrometer (HETGS). A parameterized two-component power-law model [Sako et al., Astrophys. J. 525, 921 (1999)] and a multi-Gaussian model are applied to model these continua and He-like triplets, respectively. A uniform distribution over each parameter is used as the prior belief. Posterior probability distribution functions of parameters and the covariances among them are explored by using the MCMC method. The main advantages are (i) all model-based parameters are set to be free instead of artificially fixing some of the parameters during the data-model fitting; (ii) the contributions from satellite lines are considered; (iii) backgrounds are treated as a correction to the observation errors; and (iv) the confidence interval of each parameter is given. The fitted results show that the column density of scatter component ($N_{\text{H}}^{\text{scat}}$) varies from phase to phase, which imply a non-spherical structure of the stellar wind in Vela X-1. Moreover, the wind velocities derived from main lines of each set of He-like triplets show better self-consistency than those in previous publications, which could provide a reliable approach for the diagnostics of photoionized plasma in astrophysical objects and the laboratory.

Calibration of focused circular transducers using a multi-Gaussian beam model

A new calibration method is proposed for characterizing spherically and cylindrically focused circular piston-like transducers. The calibration procedure employs a single frequency pulse-echo configuration with a large plane reflector. Analytical solutions based-on multi-Gaussian beam model are introduced to predict the received wave distributions, and a least squares fitting method for extracting the effective geometrical focal length and radius from the measurements near the transducer focus is described. The proposed method is easy to implement and can minimize errors due to measurements, uncertainties and material attenuation. Experimental results show good agreements with the theoretical predictions using the calibrated parameters and measurements.

Additional Sampling Layout Optimization Method for Environmental Quality Grade Classifications of Farmland Soil

Farmland soil environmental quality is important for farmland management. To precisely classify the environmental quality grades of farmland soil, additional samples may be required for multistage sampling or supplementary investigations. Compared with the sampling optimization methods used for mapping or estimating global means, environmental quality grade classifications are primarily focused on estimating the relationships between the values of unsampled locations and the thresholds that classify the environment quality grades. Such classifications must use a sampling layout optimization method to distribute additional sampling units into areas with a high risk of misclassification. To resolve such problems, this paper provides an additional sampling layout optimization method that initially develops a classification error index by building a multi-Gaussian model with the predicted values and error variances of unsampled locations and then calculates the probability of a threshold value occurring in the standardized Gaussian distribution. The average error indexes of all locations in the study area are then set as the objectivity function of the additional sampling layout optimization, and the spatial simulated annealing is adopted to obtain the optimized sampling layout by minimizing the objectivity function. The performance of the error index sampling layout optimization method was demonstrated in a case study using chromium concentration data for Hunan Province, China. The results showed that the additional samples generated by the proposed method produce lower and more stable classification error rates than the minimization of the mean of the shortest distances and spatially random sample methods. The proposed method can be used to improve the efficiency of additional sampling for environmental quality grade classifications of farmland soil.

The influence of riverbed heterogeneity patterns on river-aquifer exchange fluxes under different connection regimes

Riverbed hydraulic conductivity (K) is a critical parameter for the prediction of exchange fluxes between a river and an aquifer. In this study, the role of heterogeneity patterns was explored using the fully integrated hydrological model HydroGeoSphere simulating complex, variably saturated subsurface flow. A synthetic 3-D river-aquifer reference model was constructed with a heterogeneous riverbed using non-multi-Gaussian patterns in the form of meandering channels. Data assimilation was used to test the ability of different riverbed K patterns to reproduce hydraulic heads, riverbed K and river-aquifer exchange fluxes. Both fully saturated as well as variably saturated conditions underneath the riverbed were tested. The data assimilation experiments with the ensemble Kalman filter (EnKF) were carried out for four types of geostatistical models of riverbed K fields: (i) spatially homogeneous, (ii) heterogeneous with multi-Gaussian distribution, (iii) heterogeneous with non-multi-Gaussian distribution (channelized structures) and (iv) heterogeneous with non-multi-Gaussian distribution (elliptic structures). For all data assimilation experiments, state variables and riverbed K were updated by assimilating hydraulic heads. For saturated conditions, heterogeneous geostatistical models allowed a better characterization of net exchange fluxes than a homogeneous approximation. Among the three heterogeneous models, the performance of non-multi-Gaussian models was superior to the performance of the multi-Gaussian model, but the two tested non-multi-Gaussian models showed only small differences in performance from one another. For the variably saturated conditions both the multi-Gaussian model and the homogeneous model performed clearly worse than the two non-multi-Gaussian models. The two non-multi-Gaussian models did not show much difference in performance. This clearly shows that characterizing heterogeneity of riverbed K is important. Moreover, particularly under variably saturated flow conditions the mean and the variance of riverbed K do not provide enough information for exchange flux characterization and additional histogram information of riverbed K provides crucial information for the reproduction of exchange fluxes.

Analytical Diffraction Corrections for Circular Focused Transducers Expressed Using the Multi-Gaussian Beam Model

Analytical Diffraction Corrections for Circular Focused Transducers Expressed Using the Multi-Gaussian Beam Model

Calibration of focused ultrasonic transducers and absolute measurements of fluid nonlinearity with diffraction and attenuation corrections.

This paper presents analytical and experimental techniques for absolute determination of the acoustic nonlinearity parameter (β) in fluids using focused transducers. When focused transducers are used for β measurements, the geometrical and mechanical calibrations are generally required for accurate determination of the receiver transfer function from which the absolute pressure can be calculated. The fundamental and second harmonic wave amplitudes in harmonic generation measurements should be modified to account for beam diffraction and material absorption. All these issues are resolved in this study and the proposed technique is validated through the β measurement in water. An experimental method is developed to determine the effective radius and focal length of focused transducers. A simplified self-reciprocity calibration procedure for a broadband focused receiver is described. The diffraction and attenuation corrections for the fundamental and second harmonic waves are explicitly derived using the multi-Gaussian beam model, and the effects on the β determination are discussed. When the diffraction and attenuation corrections are all properly made, the measurement of β over a large range of propagation distances is possible with errors less than 8%.

Spectral Characteristics of the He i D3 Line in a Quiescent Prominence Observed by THEMIS

We analyze the observations of a quiescent prominence acquired by the Telescope Heliographique pour l'Etude du Magnetisme et des Instabilites Solaires (THEMIS) in the He I 5876 A (He I D3) multiplet aiming to measure the spectral characteristics of the He I D3 profiles and to find for them an adequate fitting model. The component characteristics of the He I D3 Stokes I profiles are measured by the fitting system approximating them with a double Gaussian. This model yields an He I D3 component peak intensity ratio of $5.5\pm0.4$, which differs from the value of 8 expected in the optically thin limit. Most of the measured Doppler velocities lie in the interval $\pm5$ km/s, with a standard deviation of $\pm1.7$ km/s around the peak value of 0.4 km/s. The wide distribution of the full-width at half maximum has two maxima at 0.25 A and 0.30 A for the He I D3 blue component and two maxima at 0.22 A and 0.31 A for the red component. The width ratio of the components is $1.04\pm0.18$. We show that the double-Gaussian model systematically underestimates the blue wing intensities. To solve this problem, we invoke a two-temperature multi-Gaussian model, consisting of two double-Gaussians, which provides a better representation of He I D3 that is free of the wing intensity deficit. This model suggests temperatures of 11.5 kK and 91 kK, respectively, for the cool and the hot component of the target prominence. The cool and hot components of a typical He I D3 profile have component peak intensity ratios of 6.6 and 8, implying a prominence geometrical width of 17 Mm and an optical thickness of 0.3 for the cool component, while the optical thickness of the hot component is negligible. These prominence parameters seem to be realistic, suggesting the physical adequacy of the multi-Gaussian model with important implications for interpreting He I D3 spectropolarimetry by current inversion codes.

A new evaluation of fission product yields for the neutron induced fission of U-233 and Th-232

Worldwide R&D efforts in establishing the reactor technology with the Thorium-Uranium (Th-U) fuel cycle have significantly grown in the recent past. The study of fission product yields has a major impact on the understanding of the fissioning process and plays a vital role in the development, design and safety analysis of advanced nuclear energy systems. A new evaluation of fission product yields based on a new database of measurements up to 2013 will allow more reliable and accurate model calculations of the Th-U fuel cycle. This work is undertaken to study the mass and charge distributions of fission products for the fuel nuclei U-233 and Th-232 induced by thermal, fast, and about 14MeV neutrons. First, the available experimental data is analyzed systematically and evaluated. Second, it is necessary to predict the unmeasured fission yields and their errors by the systematics, due to the lack of experimental data. The mass distributions are well described by a superposition of 5 Gaussian functions, which is called the Multi-Gaussian model. The charge distributions are calculated on the basis of ZP model. Their parameters are derived based on evaluated data. Finally, the fission product yield library related with the Th-U fuel cycle is well established. The evaluated data is improved compared to the major international evaluated libraries, including ENDF/B-VII.1, JENDL-4.0 and JEFF-3.2.

Geostatistical modeling of the geological uncertainty in an iron ore deposit

This paper addresses the problem of quantifying the joint uncertainty in the grades of elements of interest (iron, silica, manganese, phosphorus and alumina), loss on ignition, granulometry and rock types in an iron ore deposit. Sampling information is available from a set of exploration drill holes. The methodology considers the construction of multiple rock type outcomes by plurigaussian simulation, then outcomes of the quantitative variables (grades, loss on ignition and granulometry) are constructed by multigaussian joint simulation, accounting for geological domains specific to each quantitative variable as well as for a stoichiometric closure formula linking these variables. The outcomes are validated by checking the reproduction of the data distributions and of the data values at the drill hole locations, and their ability to measure the uncertainty at unsampled locations is assessed by leave-one-out cross validation.Both the plurigaussian and multigaussian models offer much flexibility to the practitioner to face up to the complexity of the variables being modeled, in particular: (1) the contact relationships between rock types, (2) the geological controls exerted by the rock types over the quantitative variables, and (3) the cross-correlations and stoichiometric closure linking the quantitative variables. In addition to this flexibility, the use of efficient simulation algorithms turns out to be essential for a successful application, due to the high number of variables, data and locations targeted for simulation.

Identification of high-permeability subsurface structures with multiple point geostatistics and normal score ensemble Kalman filter

Alluvial aquifers are often characterized by the presence of braided high-permeable paleo-riverbeds, which constitute an interconnected preferential flow network whose localization is of fundamental importance to predict flow and transport dynamics. Classic geostatistical approaches based on two-point correlation (i.e., the variogram) cannot describe such particular shapes. In contrast, multiple point geostatistics can describe almost any kind of shape using the empirical probability distribution derived from a training image. However, even with a correct training image the exact positions of the channels are uncertain. State information like groundwater levels can constrain the channel positions using inverse modeling or data assimilation, but the method should be able to handle non-Gaussianity of the parameter distribution. Here the normal score ensemble Kalman filter (NS-EnKF) was chosen as the inverse conditioning algorithm to tackle this issue. Multiple point geostatistics and NS-EnKF have already been tested in synthetic examples, but in this study they are used for the first time in a real-world case study. The test site is an alluvial unconfined aquifer in northeastern Italy with an extension of approximately 3km2. A satellite training image showing the braid shapes of the nearby river and electrical resistivity tomography (ERT) images were used as conditioning data to provide information on channel shape, size, and position. Measured groundwater levels were assimilated with the NS-EnKF to update the spatially distributed groundwater parameters (hydraulic conductivity and storage coefficients). Results from the study show that the inversion based on multiple point geostatistics does not outperform the one with a multiGaussian model and that the information from the ERT images did not improve site characterization. These results were further evaluated with a synthetic study that mimics the experimental site. The synthetic results showed that only for a much larger number of conditioning piezometric heads, multiple point geostatistics and ERT could improve aquifer characterization. This shows that state of the art stochastic methods need to be supported by abundant and high-quality subsurface data.

Evaluating grain size in polycrystals with rough surfaces by corrected ultrasonic attenuation

Surface roughness of a sample has a great effect on the calculated grain size when measurements are based on ultrasonic attenuation. Combining modified transmission and reflection coefficients at the rough interface with a Multi-Gaussian beam model of the transducer, a comprehensive correction scheme for the attenuation coefficient is developed. An approximate inverse model of the calculated attenuation, based on Weaver’s diffuse scattering theory, is established to evaluate grain size in polycrystals. The experimental results showed that for samples with varying surface roughness and matching microstructures, the fluctuation of evaluated average grain size was ±1.17μm. For polished samples with different microstructures, the relative errors to optical microscopy were no more than ±3.61%. The presented method provides an effective nondestructive tool for evaluating the grain size in metals with rough surfaces.