Parabolic Fitting Method Research Articles

TwoPhaseFlow: A Framework for Developing Two Phase Flow Solvers in OpenFOAM

We present a new OpenFOAM based open-source framework, TwoPhaseFlow, enabling fast implementation and testing of new phase change and surface tension force models for two-phase flows including interfacial heat and mass transfer. Capitalizing on the runtime-selection mechanism in OpenFOAM, the new models can easily be selected and benchmarked against analytical solutions and existing models. The framework currently includes the following three interface curvature calculation methods for surface tension: 1) the height function method, 2) the parabolic fit method and 3) the reconstructed distance function method. As for phase change, two models are available: 1) Interface heat resistance and 2) direct heat flux. These can be combined in three solvers: 1) InterFlow for isothermal, incompressible two-phase flow, 2) compressibleInterFlow for compressible, non-isothermal two-phase flow and 3) multiRegionPhaseChangeFlow for compressible, non-isothermal two-phase flow with conjugated heat transfer. By design, addition of new models and solvers is straightforward and users are encouraged to contribute their specific models, solvers, and validation cases to the library.

Parabolic fitting method for quality factor estimation

The quality factor [Formula: see text] has a wide application range in seismic data processing and interpretation. Compared with the commonly used methods of Q estimation (e.g., the spectral ratio method and the centroid frequency shift method), the logarithmic spectral area difference (LSAD) method exhibits better noise immunity. However, the LSAD method uses the area difference in one frequency band, and the [Formula: see text] values estimated using this method are still unstable under the influence of noise. We have developed a new parabolic fitting (PF) method to estimate Q. This method is an extension of the LSAD method. We derive an analytical relationship between [Formula: see text] and area difference curve of the logarithmic amplitude spectra. Using the logarithmic area difference of multiple frequency bands to fit the parabola, we improve the accuracy and stability of [Formula: see text] estimation. In addition, the PF method does not require special assumptions regarding the source wavelet. We test the PF method in the presence of noise and at varying bandwidths and compare the results with those obtained using the LSAD method. The results of the theoretical examples indicate that the PF method is noise resistant and stable. Applying the PF method to real zero-offset vertical seismic profiling records also indicates that the proposed method can reasonably and stably estimate the [Formula: see text] value of the formation.

Alternating prestress monitoring of steel strands based on the magnetoelastic inductance method

Alternating prestress is difficult to measure. By analyzing the inverse magnetostriction effect and the magnetic hysteresis, a theoretical model was established to describe the prestress-inductance relationship. The results of the prestress monitoring experiment showed that the inductance was influenced by the irreversible magnetization, the plastic deformation, and the hysteresis effect. Keeping the stress range constant, the inductance range was unaffected by the number of load cycles. The inductance can be used to judge whether the prestress is reasonable. The parabolic fitting method was employed to establish the mapping from the inductance to the prestress. When the stress range was 10% design prestress or 20% design prestress, the prestress monitoring error, less than 12.56% or 18.77%, was close to the magnetoelastic method and the frequency-based method. Based on the proposed calculation method, the MI method could monitor the alternating prestress of steel strands.

Improved multi-order parameter and multi-component model of polycrystalline solidification

• The grain boundary energy can be predicted even at larger undercoolings by tuning the coefficient of the new introduced interpolation function. • The kinetic coefficient can be adjusted to match the grain boundary migration situation encountered during solid state transition. • A self-consistent nucleation method was successfully incorporated into the model through introduction of noise effects. Accurate nucleation driving force is used and temperature dependent noise amplitude expression is given. • Through employing the parabolic free energy fitting technique, the developed model can be effectively used to study the entire solidification process for a variety of alloys. Temperature dependent phase field parameters selection strategy is proposed and proved. • Two solid phases nucleation of Al-Cu alloy is realized through self-consistent noise term. This approach is suitable to study multiple solid phase solidification phenomena. In this paper, we present an improved multi-order parameter model for multi-component model of polycrystalline solidification. We introduce an interpolation function in the phase field dynamical equation to obtain controllable grain boundary energy at large undercooling. The same interpolation function is also employed in the kinetics coefficient to allow for better control of grain boundary migration. Temperature dependent phase field parameters and noise terms are consistently coupled into the dynamics of a binary system in a manner that allows for quantitative simulations in the thin interface limit. The model is applied to multi-phase solidification in Al-Cu alloy, where a parabolic fitting method is employed to model the free energy of Al-Cu phases and two-phase nucleation is demonstrated in directional solidification.

WSSNet: Aortic Wall Shear Stress Estimation Using Deep Learning on 4D Flow MRI.

Wall shear stress (WSS) is an important contributor to vessel wall remodeling and atherosclerosis. However, image-based WSS estimation from 4D Flow MRI underestimates true WSS values, and the accuracy is dependent on spatial resolution, which is limited in 4D Flow MRI. To address this, we present a deep learning algorithm (WSSNet) to estimate WSS trained on aortic computational fluid dynamics (CFD) simulations. The 3D CFD velocity and coordinate point clouds were resampled into a 2D template of 48 × 93 points at two inward distances (randomly varied from 0.3 to 2.0 mm) from the vessel surface (“velocity sheets”). The algorithm was trained on 37 patient-specific geometries and velocity sheets. Results from 6 validation and test cases showed high accuracy against CFD WSS (mean absolute error 0.55 ± 0.60 Pa, relative error 4.34 ± 4.14%, 0.92 ± 0.05 Pearson correlation) and noisy synthetic 4D Flow MRI at 2.4 mm resolution (mean absolute error 0.99 ± 0.91 Pa, relative error 7.13 ± 6.27%, and 0.79 ± 0.10 Pearson correlation). Furthermore, the method was applied on in vivo 4D Flow MRI cases, effectively estimating WSS from standard clinical images. Compared with the existing parabolic fitting method, WSSNet estimates showed 2–3 × higher values, closer to CFD, and a Pearson correlation of 0.68 ± 0.12. This approach, considering both geometric and velocity information from the image, is capable of estimating spatiotemporal WSS with varying image resolution, and is more accurate than existing methods while still preserving the correct WSS pattern distribution.

Nuclear mass parabola and its applications * * Supported by National Natural Science Foundation of China, (11961131010, 11422548 and U1867212), and the Foundation of Guangxi innovative team (2017GXNSFGA198001, 2016GXNSFFA380001), and innovation fund of undergraduate at Anyang Normal University (ASCX/2019-Z055)

We propose a method for extracting the properties of the isobaric mass parabola based on the total double -decay energies of isobaric nuclei. Two important parameters of the mass parabola, the location of the most -stable nuclei and the curvature parameter , are obtained for 251 A values, based on the total double -decay energies of nuclei compiled in the AME2016 database. The advantage of this approach is that the pairing energy term caused by the odd-even variation can be removed in the process, as well as the mass excess of the most stable nuclide for the mass number A, which are employed in the mass parabolic fitting method. The Coulomb energy coefficient MeV is determined by the mass difference relation for mirror nuclei, and the symmetry energy coefficient is also studied by the relation .

An investigation on the bending straightening process of D-type cross section shaft

D-type cross section shaft is widely used in many industrial fields. As a crucial factor, the shaft straightness has potential significant impact on its working performance, thus the bending straightening process becomes an essential correction step in shaft manufacturing. With a piecewise linearized elastic-plastic stress-strain relation, the bending straightening process of both side-cut and flat-cut D-type cross section shaft is modeled and deduced as a straightening prediction model. The prediction model can provide an accurate and practical relation between the straightening press curvature and the initial bending curvature. For the straightening process simulation, systematic D-type shaft stress and deformation models are built by using classic principle of material mechanics. Three-point parabola method and parabolic fitting method are both proposed for the curvature conversion in the straightening process. To verify the theoretical straightening prediction model, some specialized D-type shaft specimens are designed and manufactured, and a parameter calibration method of straightening prediction model is proposed. Finally, experimental research and comparison analysis are carried out to verify the correctness and feasibility of the straightening prediction model, and a straightening process flowchart is presented as an application guideline of current models and methods.

Comparison of shift estimation strategies in spectral elastography

This paper compares the performance of various spectral shift estimators for use in spectral elastography, namely, the normalized cross-correlation (NCC), sum squared difference (SSD) and sum absolute difference (SAD). Simulation and experimental results demonstrate that the spectral SSD-based elastographic method exhibits no marked difference in performance compared to the more computationally costly NCC-based approach, which has conventionally been the preferred estimator in spectral elastography. The spectral SAD-based strain estimator, despite being computationally less burdening, failed to exhibit performance comparable to that of the NCC- and SSD-based techniques. Furthermore, though spectral subsample estimation techniques using a cosine-fit interpolation method outperformed that of the parabolic-fit method in terms of both reduced bias errors and standard deviations, the latter was analyzed in this study due to computational simplicity. The role of spectral density was evaluated without and with parabolic-based subsample interpolation. Based on minimizing computational complexity, it is concluded that a (low density) spectral SSD strain estimator coupled with parabolic-based subsample estimation is the preferred choice for spectral elastography.

Interpolation methods for time-delay estimation using cross-correlation method for blood velocity measurement

The cross-correlation method (CCM) for blood flow velocity measurement using Doppler ultrasound is based on time delay estimation of echoes from pulse-to-pulse. The sampling frequency of the received signal is usually kept as low as possible in order to reduce computational complexity, and the peak in the correlation function is found by interpolating the correlation function. The parabolic-fit interpolation method introduces a bias at low sampling rate to the ultrasound center frequency ratio. In this study, four different methods are suggested to improve the estimation accuracy: (1) Parabolic interpolation with bias-compensation, derived from a theoretical signal model. (2) Parabolic interpolation combined with linear filter interpolation of the correlation function. (3) Parabolic interpolation to the complex correlation function envelope. (4) Matched filter interpolation applied to the correlation function. The new interpolation methods are analyzed both by computer simulated signals and RF-signals recorded from a patient with time delay larger than 1/f(0), where f(0) is the center frequency. The simulation results show that these methods are more accurate than the parabolic-fit method. From the simulation, the worst estimation accuracy is about 1.25% of 1/f(0) for the parabolic-fit interpolation, and it is improved by the above methods to less than 0.5% of 1/f(0) when the sampling rate is 10 MHz, the center frequency is 2.5 MHz and the bandwidth is 1 MHz. This improvement also can be observed in the experimental data. Furthermore, the matched filter interpolation gives the best performance when signal-to-noise ratio (SNR) is low. This is verified both by simulation and experimentation.

A bat-like sonar system for obstacle localization

An active wide-beam sonar system that mimics the sensor configuration of echolocating bats is described for applications in sensor-based robotics. Obstacles in a two-dimensional (2-D) environment are detected and localized using time-of-flight (TOF) measurements of their echoes. The standard threshold detector produces a biased TOF estimate. An unbiased TOF estimate is derived by a parametric fit to the echo waveform, motivated by experimental observations of actual sonar signals. This novel method forms a tradeoff between the complexity of the optimum estimator and the biased threshold detector. Using the TOF information from both methods, the range and azimuth of an obstacle are estimated. Localization is most accurate if the obstacle is located along the system line-of-sight and improves with decreasing range. Standard deviations of the range and azimuth estimators are compared to the Cramer-Rao lower bounds. The parabolic fit method has large variance but zero bias at large deviations from the line-of-sight. The system operation is generalized from isolated obstacles to extended obstacles.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>