Numerical Correction Method Research Articles

Research on the modulation aberration numerical correction method of interference signals for high aspect ratio samples utilizing coherence scanning interferometry.

Coherence scanning interferometry (CSI) is a non-destructive method for measuring the microstructure surface topography, but it fails to retrieve the bottom topography because the detection light is blocked by the sidewalls of the high aspect ratio (HAR) samples. Our team has proposed CSI technology with the detection light transparent to the sample to measure the surface topography thus ensuring the numerical aperture of the detection light with high throughput. However, a dedicated optical path to monitor the aberrations caused by the modulation from the sample is necessary and a complex optical path is added for aberration correction, which inevitably increases the design complexity and component costs of the optical system. This paper proposes a numerical correction method for sample-induced aberration of interference signals for HAR samples utilizing coherence scanning interferometry, without the need to modify the optical system. Aberration-modulated PSF is calculated for deconvolution of the interference signal affected by aberrations to solve the issues of low signal-to-noise ratio and interference fringe widening. The study integrates a rigorous numerical electromagnetic field solution to quantify the modulation aberrations of detection light by a transparent trench. A three-dimensional point spread function (3D-PSF) model based on the angular spectrum method (ASM) is employed to calculate the 3D-PSF of the system modulated by the sample, and then the impact of aberrations on the PSF is analyzed. The initial values of HAR trench width and depth are obtained from the raw interference signal collected by experiments and use the initial values to match the corresponding 3D-PSF. The HAR microstructure topography construction is completed based on the corrected interference signal. The effectiveness of our method is validated through experiments conducted on three HAR trench samples, with depths ranging from 100 µm to 300 µm and widths ranging from 10 µm to 30 µm.

A gas-surface interaction algorithm for discrete velocity methods in predicting rarefied and multi-scale flows: For Maxwell boundary model

The discrete velocity method (DVM) for rarefied flows and the unified methods (based on the DVM framework) for flows in all regimes, from continuum one to free molecular one, have worked well as precise flow solvers over the past decades and have been successfully extended to other important physical fields. Both DVM and unified methods endeavor to model the gas-gas interaction physically. However, for the gas-surface interaction (GSI) at the wall boundary, they have only use the full accommodation boundary up to now, which can be viewed as a rough Maxwell boundary with a fixed accommodation coefficient (AC) at unity, deviating from the real value. For example, the AC for metal materials typically falls in the range of 0.8 to 0.9. To overcome this bottleneck and extend the DVM and unified methods to more physical boundary conditions, an algorithm for Maxwell boundary with an adjustable AC is established into the DVM framework. The Maxwell boundary model splits the distribution of the bounce-back molecules into specular ones and Maxwellian (normal) ones. Since the bounce-back molecules after the spectral reflection does not math with the discrete velocity space (DVS), both macroscopic conservation (from numerical quadrature) and microscopic consistency in the DVS are hard to achieve in the DVM framework. In this work, this problem is addressed by employing a combination of interpolation methods for mismatch points in DVS and an efficient numerical error correction method for micro-macro consistency. On the other hand, the current Maxwell boundary for DVM takes the generality into consideration, accommodating both the recently developed efficient unstructured velocity space and the traditional Cartesian velocity space. Moreover, the proposed algorithm allows for calculations of both monatomic gases and diatomic gases with internal degrees in DVS. Finally, by being integrated with the unified gas-kinetic scheme within the DVM framework, the performance of the present GSI algorithm is validated through a series of benchmark numerical tests across a wide range of Knudsen numbers.

The characteristics and corrections of ventral support interferences in the transonic-speed wind tunnel for the blended-wing-body aircraft

For the problem of ventral support interference in a transonic-speed wind tunnel with the blended-wing-body aircraft NPU-BWB-300 installed, the numerical simulation method based on Reynolds-averaged Navier–Stokes (RANS) equations is used to study the influence law of aerodynamic characteristic interference with the variation of Mach numbers and angles of attack. Moreover, the characteristics of ventral support interference for blended-wing-body aircraft and conventional aircraft are compared. The relevant mechanism of the generation and change of ventral support interference is revealed by employing analysis of the body surface pressure, the shock wave of the strut, and the separation area between the strut and the aircraft. The aerodynamic characteristic interference obtained from the numerical simulation is linearized based on the principle of the least square method. Afterward, a numerical simulation correction method of ventral support interference in the transonic-speed wind tunnel for the blended-wing-body aircraft is developed. Finally, the test results after the corrections of ventral support interferences in the transonic-speed wind tunnel for NPU-BWB-300 are obtained, which is significant for the evaluation of current aerodynamic performances and subsequent optimization designs.

The Concavity of Conditional Maximum Likelihood Estimation for Logit Panel Data Models with Imputed Covariates

In estimating logistic regression models, convergence of the maximization algorithm is critical; however, this may fail. Numerous bias correction methods for maximum likelihood estimates of parameters have been conducted for cases of complete data sets, and also for longitudinal models. Balanced data sets yield consistent estimates from conditional logit estimators for binary response panel data models. When faced with a missing covariates problem, researchers adopt various imputation techniques to complete the data and without loss of generality; consistent estimates still suffice asymptotically. For maximum likelihood estimates of the parameters for logistic regression in cases of imputed covariates, the optimal choice of an imputation technique that yields the best estimates with minimum variance is still elusive. This paper aims to examine the behaviour of the Hessian matrix with optimal values of the imputed covariates vector, which will make the Newton–Raphson algorithm converge faster through a reduced absolute value of the product of the score function and the inverse fisher information component. We focus on a method used to modify the conditional likelihood function through the partitioning of the covariate matrix. We also confirm that the positive moduli of the Hessian for conditional estimators are sufficient for the concavity of the log-likelihood function, resulting in optimum parameter estimates. An increased Hessian modulus ensures the faster convergence of the parameter estimates. Simulation results reveal that model-based imputations perform better than classical imputation techniques, yielding estimates with smaller bias and higher precision for the conditional maximum likelihood estimation of nonlinear panel models.

Нитевой перинеальный лифтинг в эстетической гинекологии: путь от компромиссов к золотому сечению

Pelvic floor dysfunction found in women regardless of their age has long been and remains one of the most controversial issues of modern gyne-cology. Numerous correction methods, from extensive surgical interventions to minimally invasive approaches, have been often opposed one an-other. However, to date we have formulated a clear recommendation: defects of the pelvic fascia and pelvic floor muscle compartment are the un-contested imperative indications for reconstructive surgery. Meanwhile, the issue of correcting early signs of pelvic floor dysfunction in patients with no myofascial defects is still a matter of debate, since surgical correction is often impossible or even more often not feasible in such cases. In this regard, it is necessary to consider perineal thread lifting as one of the most advanced and effective methods for treatment of the gaping vaginal opening that does not require surgical correction.

Quantitative Study of Sensor-Pipe Distance in Noncontact Magnetic Detection of Ferromagnetic Pipelines

Non-contact magnetic detection technology has great application potential in buried oil and gas pipelines due to the non-contact online detection of pipeline damage. However, the non-contact magnetic detecting signal is affected by the distance between the magnetometer and the ferromagnetic pipeline, leading to missed detection of pipe defects. It is essential to calibrate the detection height for the non-contact magnetic detecting signal. In this paper, the spatial analytical model of non-contact magnetic signals above ferromagnetic pipelines is established. Then, a quantitative variation law of non-contact magnetic detecting signals is obtained under different pipe diameters and internal pressures. Next, a signal calculation model based on the detection height h is established. A detection height correction method is proposed to eliminate the influence of detection heights on the magnetic detecting signal. An experimental investigation is carried out to validate the accuracy of the numerical calculation results and correction method. The results indicate that the magnetic detecting signal has a second-order exponential relationship with the detection height h within 0.1 m - 2 m. The average error of the signal correction model is 6.37%. The modified magnetic detecting signal via the signal correction method can reflect the damage status of ferromagnetic pipelines.

Spatial biases revealed by LiDAR in a multiphysics WRF ensemble designed for offshore wind

Numerical weather predictions (NWPs) have become essential in offshore wind energy planning and operations. Thus, rigorous assessments of NWP model performance are critical to integrating offshore wind power into existing power systems. Taking advantage of two LiDAR buoys launched off the coast of New York in 2019, we assess the performance of a multiphysics Weather Research and Forecast (WRF) model ensemble with a 1.33-km spatial resolution for estimating the power system impacts associated with New York’s offshore wind target. Our work is the first to report WRF horizontal wind speed biases not only at multiple heights above sea level but also at two locations while still considering all seasons. WRF tends to overpredict wind speeds during spring and summer and underpredict wind speeds during winter. However, the patterns in wind speed biases differ substantially between the two buoys offering compelling evidence against spatially uniform biases, which impacts the performance of numerous bias correction methods frequently used to post-process WRF data. Therefore, additional measurements of wind speeds throughout the lower atmosphere are necessary to fully characterize bias patterns. With the recent goal set by the U.S. to install 30 GW of offshore wind by 2030 — largely along the East Coast, mispredictions carry important policy implications. Absent accurate offshore wind uncertainty forecasts, power system operators throughout the Eastern Interconnection will be forced to dispatch their most expensive and likely high emitting power plants to compensate for periods of underperformance.

Thermocouple correction method evaluation for measuring steady high-temperature gas

When a thermocouple is used to measure a high-temperature gas flow, the measured temperature, i.e., the thermocouple bead temperature is not exactly the gas temperature. The bead temperature results from its energy balance. A few correction methods have been developed to fix the well-known error. However, the accuracy of the correction methods were not well validated because of the lack of a high temperature gas source with known temperature. The Hencken flame generates a near adiabatic combustion product and its temperature, composition and velocity can be calculated accurately. The S type thermocouples with different sizes are used to measure the Hencken flame temperature. With both the gas temperature and the measured temperature are known, the accuracy of the correction methods are evaluated. It is found that the 1D numerical correction method gives the best accuracy. The extrapolation method and some correction equations also give reasonable accuracy. Some correction methods need accurate thermocouple emissivity. With the CFD simulation of the detailed measurement process of the thermocouples, the emissivity is extracted. The advantages and disadvantages of different correction methods in practical measurements are also discussed.

Investigation of temperature correction methods for fine wire thermocouple losses in low‐pressure flat premixed laminar flames

Accurate temperature measurements in reactive combustion systems are crucial for kinetic and heat transfer studies. Intrusive temperature measurement methods, such as thermocouples, are still widely used in experimental combustion research applications. Thin wire customized type B thermocouples, (Pt Rh6%-Pt Rh30%), coated with BeO (Beryllium oxide) - Y2O3 (Yttrium oxide) anti-catalytic ceramic, are used in this study to measure the flame temperature at low pressure of three H2/CH4/CO-air flat flames at different equivalence ratios. In the range 500–1700 K, the measured flame temperatures are corrected for radiation losses with two different well-known approaches, the experimental electrical compensation method (ECM) and the numerical heat transfer correction method (HTM). Both methods are applied to the measured flame temperatures, and their performance and limits are assessed, highlighting the primary sources of uncertainties. This work aims to shed light on the crucial issues related to the temperature correction methods primarily used in the experimental combustion diagnostic. A strategy to reduce the uncertainties of the two methods is proposed and applied to the measured temperature flames. The propagation of the errors on the main parameters involved in the numerical correction method is carried out to estimate the final uncertainty of the corrected gas temperatures. Finally, a new approach is proposed to quantify the error incurred by neglecting conductive heat transfer between the thermocouple bead and the connecting thermocouple wires.

Optimization of the measurement of residual stresses by the incremental hole drilling method. Part I: Numerical correction of experimental errors by a configurable numerical–experimental coupling

The incremental hole drilling method is very effective in measuring the residual stress gradient in composite laminates. However, its reliability depends on the accuracy with which the calibration coefficients are determined. These coefficients are calculated using a finite element model. The samples’ features and the real experimental conditions must be taken into account in the simulation. Any mismatch can lead to inadequate calibration coefficients, thus introducing errors on residual stresses. Several calibration coefficients correction models exist for isotropic materials, but there is a lack of information on this subject concerning composite laminates. In this paper, the influence of three major experimental errors on the calibration coefficients is numerically investigated for composite laminates. The sensitivity of the coefficients to these errors is highlighted and a numerical correction method is proposed.

Inner Filter Effect Correction for Fluorescence Measurements in Microplates Using Variable Vertical Axis Focus.

The inner filter effect (IFE) hinders fluorescence measurements, limiting linear dependence of fluorescence signals to low sample concentrations. Modern microplate readers allow movement of the optical element in the vertical axis, changing the relative position of the focus and thus the sample geometry. The proposed Z-position IFE correction method requires only two fluorescence measurements at different known vertical axis positions (z-positions) of the optical element for the same sample. Samples of quinine sulfate, both pure and in mixtures with potassium dichromate, showed a linear dependence of corrected fluorescence on fluorophore concentration (R2 > 0.999), up to Aex ≈ 2 and Aem ≈ 0.5. The correction extended linear fluorescence response over ≈98% of the concentration range with ≈1% deviation of the calibration slope, effectively eliminating the need for sample dilution or separate absorbance measurements to account for IFE. The companion numerical IFE correction method further eliminates the need for any geometric parameters with similar results. Both methods are available online at https://ninfe.science.

An improved numerical method for variational image registration model with intensity correction

In this paper, we propose an efficient numerical method for registration and intensity correction of images. We first introduced a variational image registration model in our previous work. The variational minimization of the functional in the model is solved by using an alternating minimization method. In this work, we improve the numerical solution of the minimization problem by applying the Split Bregman method together with the alternating minimization method. As expected, our numerical experiments show that the proposed method converges rapidly and is significantly more accurate than the method used in our previous work.

Phase-corrected buffer averaging for enhanced OCT angiography using FDML laser.

Megahertz-rate optical coherence tomography angiography (OCTA) is highly anticipated as an ultrafast imaging tool in clinical settings. However, shot-noise-limited sensitivity is inevitably reduced in high-speed imaging systems. In this Letter, we present a coherent buffer averaging technique for use with a Fourier-domain mode-locked (FDML) laser to improve OCTA contrast at 1060 nm MHz-rate retinal imaging. Full characterization of spectral variations among the FDML buffers and a numerical correction method are also presented, with the results demonstrating a 10-fold increase in the phase alignment among buffers. Coherent buffer averaging provided better OCTA contrast than the conventional multi-frame averaging approach with a faster acquisition time.

Spatiotemporal dynamics of soil salinity in the Yellow River Delta under the impacts of hydrology and climate.

In recent years, soil salinization in the Yellow River Delta under the effects of hydrology, climate and human activities have become increasingly prominent. Based on the 20 Landsat series images of Hekou, Kenli, Dongying districts and Lijin County of Dongying City selected from 1985 to 2018, numerical regression correction method was used to perform image spectral consistency conversion. The partial least squares regression method was used to construct quantitative inversion models of soil salt content. The soil salt content of the study area were retrieved by the best salt prediction model. The temporal and spatial characteristics of soil salt changes in the Yellow River Delta were analyzed. The results showed that the soil salt inversion model constructed with 10 sensitive spectral indices performed higher prediction accuracy, with coefficient of determination R2=0.769 and RMSE=1.125 for calibration, R2=0.752 and RMSE=1.203 for validation, and relative prediction deviation (RPD)=2.08. Using the measured soil salt data in 2016 to verify the inversion accuracy of the model, the correlation between the measured value and the inverted value was 0.7279. The model was used to map the soil salinity of the Yellow River Delta based on 20 images from 1985 to 2018. The abnormal soil salinity retrieval values was all less than 10%. During the study period, the soil salinity showed an overall trend of rising first and then falling which was lowest in 1985 (3.14 g·kg-1) and highest in 1995 (5.86 g·kg-1). Spatially, the area of heavily saline soil and saline soil in the study area decreased, and that of mildly and moderately saline soil significantly increased (66.6%). The total area of saline soil showed an increasing trend. The effects of hydrological and climatic conditions on soil salinity exhibited hysteresis. The increases of temperature promoted soil salinity, with the relationship between the soil salinity and the average temperatures in the past six months and one year being significantly correlated (R=0.507 and 0.538). Soil salinity did not correlate with regional precipitation, and was most affected by the Yellow River streamflow in the previous season (R=-0.543).

A new numerical correction method for gamma spectra based on the system transformation theory of random signals

The conventional correction techniques for gamma spectra usually use approximate algorithms, the calculation procedures are tedious and complicated, the obtained corrected spectra are usually the channel domain spectra even if they are calibrated by energy. Moreover, the spectra are still dependent upon system parameters themselves such as the gain of amplifier and the offset of ADC etc. In this paper, a new numerical correction method of gamma spectra was developed on the basis of the system transformation theory of random signals. By transforming the measured spectrum from the channel domain to the energy domain, the theoretical deposition energy spectrum which is energy domain spectrum, rather than channel domain spectrum can be obtained without any algorithm approximation processing. The presented method makes it possible to compare and exchange the gamma-ray spectrum data that are measured under different conditions or by different spectrometer systems equipped with the same type of detectors. To validate the method, a set of NaI (Tl) gamma spectra and three sets of HPGe gamma spectra were collected. The results show that serious spectral drifts and intensity variation in NaI (Tl) gamma spectra were effectively eliminated. The maximum relative drift of peak position, the maximum relative variation of peak height and that of FWHM before correction were 65.03%, 40.37% and 61.65%, respectively, and after correction, they became 0.19%, 2.81% and 0.85%, respectively, indicating that the method has strong ability to correct gamma spectra. HPGe gamma spectra were also well corrected using the presented method, and were identified as gamma radiation fingerprints of nuclear materials. The results show that the method can also improve the confidence degree of identifying nuclear materials significantly.

Numerical correction of finite difference solution for two-dimensional space-fractional diffusion equations with boundary singularity

In this paper, an efficient algorithm is presented by adopting the extrapolation technique to improve the accuracy of finite difference schemes for two-dimensional space-fractional diffusion equations with non-smooth solution. The popular fractional centered difference scheme is revisited and the stability and error estimation of numerical solution are given in maximum norm. Based on the analysis of leading singularity of exact solution for the underlying problem, the extrapolation technique and numerical correction method are exploited to enhance the accuracy and convergence rate of the computation. Two numerical examples are provided to validate the theoretical prediction and efficiency of the algorithm. It is shown that, by using the proposed algorithm, both accuracy and convergence rate of numerical solutions can be significantly improved and the second-order accuracy can even be recovered for the equations with large fractional orders.

Multiple comparison correction methods for whole-body magnetic resonance imaging.

.Purpose: Voxel-level hypothesis testing on images suffers from test multiplicity. Numerous correction methods exist, mainly applied and evaluated on neuroimaging and synthetic datasets. However, newly developed approaches like Imiomics, using different data and less common analysis types, also require multiplicity correction for more reliable inference. To handle the multiple comparisons in Imiomics, we aim to evaluate correction methods on whole-body MRI and correlation analyses, and to develop techniques specifically suited for the given analyses.Approach: We evaluate the most common familywise error rate (FWER) limiting procedures on whole-body correlation analyses via standard (synthetic no-activation) nominal error rate estimation as well as smaller prior-knowledge based stringency analysis. Their performance is compared to our anatomy-based method extensions.Results: Results show that nonparametric methods behave better for the given analyses. The proposed prior-knowledge based evaluation shows that the devised extensions including anatomical priors can achieve the same power while keeping the FWER closer to the desired rate.Conclusions: Permutation-based approaches perform adequately and can be used within Imiomics. They can be improved by including information on image structure. We expect such method extensions to become even more relevant with new applications and larger datasets.

Numerical method for axial motion artifact correction in retinal spectral-domain optical coherence tomography.

A numerical method that compensates image distortions caused by random fluctuations of the distance to an object in spectral-domain optical coherence tomography (SD OCT) has been proposed and verified experimentally. The proposed method is based on the analysis of the phase shifts between adjacent scans that are caused by micrometer-scale displacements and the subsequent compensation for the displacements through phase-frequency correction in the spectral space. The efficiency of the method is demonstrated in model experiments with harmonic and random movements of a scattering object as well as during in vivo imaging of the retina of the human eye.

Resting State fMRI: Going Through the Motions.

Resting state functional magnetic resonance imaging (rs-fMRI) has become an indispensable tool in neuroscience research. Despite this, rs-fMRI signals are easily contaminated by artifacts arising from movement of the head during data collection. The artifacts can be problematic even for motions on the millimeter scale, with complex spatiotemporal properties that can lead to substantial errors in functional connectivity estimates. Effective correction methods must be employed, therefore, to distinguish true functional networks from motion-related noise. Research over the last three decades has produced numerous correction methods, many of which must be applied in combination to achieve satisfactory data quality. Subject instruction, training, and mild restraints are helpful at the outset, but usually insufficient. Improvements come from applying multiple motion correction algorithms retrospectively after rs-fMRI data are collected, although residual artifacts can still remain in cases of elevated motion, which are especially prevalent in patient populations. Although not commonly adopted at present, “real-time” correction methods are emerging that can be combined with retrospective methods and that promise better correction and increased rs-fMRI signal sensitivity. While the search for the ideal motion correction protocol continues, rs-fMRI research will benefit from good disclosure practices, such as: (1) reporting motion-related quality control metrics to provide better comparison between studies; and (2) including motion covariates in group-level analyses to limit the extent of motion-related confounds when studying group differences.

Compensation for the Influence of Fluctuations in the Distance to the Object During Noncontact Probing in Spectral Domain Optical Coherence Tomography

We propose and experimentally test a numerical method for correction of the influence of fluctuations in the distance to objects during noncontact probing in optical coherence tomography. The method is based on the analysis of phase shifts of the neighboring scans, which are due to microscale displacements, and further compensation for these displacements by using phasefrequency correction in the spectral domain. Unlike the known correlation methods, the proposed method does not distort the represented shape of the object surface. Its operability is demonstrated in model experiments in the cases of harmonic and random types of the motion of the scattering object, as well as in vivo imaging of the structures of the human middle ear.