Gradient Corrections Research Articles

A mortar segment-to-segment contact method for stabilized total-Lagrangian smoothed particle hydrodynamics

A segment-to-segment mortar frictionless contact method for total-Lagrangian smoothed particle hydrodynamics is presented in this work. The smoothed particle hydrodynamics method employs Lagrangian kernel, kernel gradient correction, and hourglass control to improve its accuracy, convergence property, and stability. Two formulations, the node-to-segment and mortar segment-to-segment, are employed to solve contact problems. The enforcement of contact constraints is performed using the penalty method and perturbed Lagrange method in the node-to-segment and mortar formulations, respectively. The algorithms and implementations of the two contact formulations are detailed. The performance of the two contact formulations is checked with several numerical examples. It is found that the mortar formulation gives robust simulations and more accurate results.

Online identification of optimal efficiency of multi-stack fuel cells(MFCS)

With the development of fuel cells, the demand for high-power fuel cells has gradually increased, but the multi-stack fuel cell system(MFCS) has received wide attention due to the existing technical barriers. The optimal efficiency of the multi-stack fuel cell system is the target, and the power distribution point of the multi-stack fuel cell is obtained by combining the KKT condition. Equipped with the recursive gradient correction method, the online identification of the optimal efficiency of the system is realized. The results are compared with the average distribution and Daisy-chain methods, and the online identification algorithm results in the highest optimal efficiency and the lowest hydrogen consumption. It was validated on two 1kW air-cooled fuel cell systems.

The magnetic field dependent displacement effect and its correction in reference and relative dosimetry

Objective. This study investigates the perturbation correction factors of air-filled ionization chambers regarding their depth and magnetic field dependence. Focus has been placed on the displacement or gradient correction factor Additionally, the shift of the effective point of measurement that can be applied to account for the gradient effect has been compared between the cases with and without magnetic field. Approach. The perturbation correction factors have been simulated by stepwise modifications of the models of three ionization chambers (Farmer 30013, Semiflex 3D 31021 and PinPoint 3D 31022, all from PTW Freiburg). A 10 cm × 10 cm 6 MV photon beam perpendicular to the chamber’s axis was used. A 1.5 T magnetic field was aligned parallel to the chamber’s axis. The correction factors were determined between 0.4 and 20 cm depth. The shift of from the chamber’s reference point was determined by minimizing the variation of the ratio between dose-to-water and the dose-to-air along the depth. Main Results. The perturbation correction factors with and without magnetic field are depth dependent in the build-up region but can be considered as constant beyond the depth of dose maximum. Additionally, the correction factors are modified by the magnetic field. at the reference depth is found to be larger in 1.5 T magnetic field than in the magnetic field free case, where an increase of up to 1% is observed for the largest chamber (Farmer 30013). The magnitude of for all chambers decreases by 40% in a 1.5 T magnetic field with the sign of remains negative. Significance. In reference dosimetry, the change of in a magnetic field can be corrected by applying the magnetic field correction factor when the chamber is positioned with its at the depth of measurement. However, due to the depth dependence of the perturbation factors, it is more convenient to apply the -shift during chamber positioning in relative dosimetry.

A Unified Pansharpening Model Based on Band-Adaptive Gradient and Detail Correction.

Pansharpening is used to fuse a panchromatic (PAN) image with a multispectral (MS) image to obtain a high-spatial-resolution multispectral (HRMS) image. Traditional pansharpening methods face difficulties in obtaining accurate details and have low computational efficiency. In this study, a unified pansharpening model based on the band-adaptive gradient and detail correction is proposed. First, a spectral fidelity constraint is designed by keeping each band of the HRMS image consistent with that of the MS image. Then, a band-adaptive gradient correction model is constructed by exploring the gradient relationship between a PAN image and each band of the MS image, so as to adaptively obtain an accurate spatial structure for the estimated HRMS image. To refine the spatial details, a detail correction constraint is defined based on the parameter transfer by designing a reduced-scale parameter acquisition model. Finally, a unified model is constructed based on the gradient and detail corrections, which is then solved by an alternating direction multiplier method. Both reduced-scale and full-scale experiments are conducted on several datasets. Compared with state-of-the-art pansharpening methods, the proposed method can achieve the best results in terms of fusion quality and has high efficiency. Specifically, our method improves the SAM and ERGAS metrics by 17.6% and 21.2% respectively compared to the traditional approach with the best average values, and improves these two metrics by 4.3% and 10.3% respectively compared to the learning-based approach with the best average values.

Dynamic 18F-FET PET/CT to differentiate recurrent primary brain tumor and brain metastases from radiation necrosis after single-session robotic radiosurgery

ObjectiveCyberknife robotic radiosurgery (RRS) provides single-session high-dose radiotherapy of brain tumors with a steep dose gradient and precise real-time image-guided motion correction. Although RRS appears to cause more radiation necrosis (RN), the radiometabolic changes after RRS have not been fully clarified. 18F-FET-PET/CT is used to differentiate recurrent tumor (RT) from RN after radiosurgery when MRI findings are indecisive. We explored the usefulness of dynamic parameters derived from 18F-FET PET in differentiating RT from RN after Cyberknife treatment in a single-center study population. MethodsWe retrospectively identified brain tumor patients with static and dynamic 18F-FET-PET/CT for suspected RN after Cyberknife. Static (tumor-to-background ratio) and dynamic PET parameters (time-activity curve, time-to-peak) were quantified. Analyses were performed for all lesions taken together (TOTAL) and for brain metastases only (METS). Diagnostic accuracy of PET parameters (using mean tumor-to-background ratio >1.95 and time-to-peak of 20 min for RT as cut-offs) and their respective improvement of diagnostic probability were analyzed. ResultsFourteen patients with 28 brain tumors were included in quantitative analysis. Time-activity curves alone provided the highest sensitivities (TOTAL: 95%, METS: 100%) at the cost of specificity (TOTAL: 50%, METS: 57%). Combined mean tumor-to-background ratio and time-activity curve had the highest specificities (TOTAL: 63%, METS: 71%) and led to the highest increase in diagnosis probability of up to 16% p. – versus 5% p. when only static parameters were used. ConclusionsThis preliminary study shows that combined dynamic and static 18F-FET PET/CT parameters can be used in differentiating RT from RN after RRS.

Key technologies of 18 MeV self-extraction cyclotron

In this work, an 18 MeV self extraction high current cyclotron is designed, which provides a feasible design scheme for the self extraction system. For the main magnet, it is designed by restricting the parameter change of the main magnetic field through “three judgments”. For the self extraction system, the phase space suitable for particle extraction is scanned by injecting the phase space, and the gradient correction magnet is used to increase the acceptance of the extracted beam. For the harmonic coil, through the second harmonic change of the magnetic field, the beam characteristics are analyzed and the position of the harmonic coil is determined. Under the condition of scanning different harmonic coil surface currents, the extraction of the beam is obtained, and then the phase space of the beam is pushed to the acceptance. In order to match the radial dimension and the axial dimension of the target beam and obtain a stronger beam, the magnetic channel of the double structure is selected and the related design idea is given. The final beam size is 30.5 mm × 12.9 mm, the particles that can be extracted account for 82.62% of the successfully accelerated particles.

A Combined State of Charge Estimation Method for Lithium‐Ion Batteries Using Cubature Kalman Filter and Least Square with Gradient Correction

AbstractReliable state of charge (SOC) is the core of the energy storage system for electric vehicles. An efficient method of parameter identification and SOC estimation for lithium‐ion batteries (LIBs) using cubature Kalman filter (CKF) and least square with gradient correction is proposed. Firstly, the recursive gradient correction (RGC) strategy is introduced based on the recursive least square with forgetting factor (FFRLS) method, and a novel way is proposed for a simplified equivalent circuit model (ECM) based LIBs parameter identification using the combination of RGC and FFRLS method. Then, on the basis of CKF, the singular value decomposition (SVD) is used instead of the Cholesky decomposition to solve the non‐positive definiteness matrix for cubature transformation in the priori estimated covariance, thereby improving the effect of SOC estimation. Finally, the dynamic stress test (DST) and the federal urban driving schedule (FUDS) are used to verify the effect of the proposed method. The test results reflect that the combination of RGCFFRLS‐SVDCKF method and simplified ECM have advantages in terms of LIBs SOC estimation convergence ability and tracking accuracy, and the SOC estimation error can converge to 1% and 1.5% error boundary when the initial SOC are 0.5 and 0.8, respectively. In addition, the robustness of the proposed method is verified. Compared with the FFRLS‐EKF method, the proposed RGCFFRLS‐SVDCKF method has better precision and robustness to noise disturbance.

A new method for measuring the 3D turbulent velocity dispersion of molecular clouds

ABSTRACT The structure and star formation activity of a molecular cloud are fundamentally linked to its internal turbulence. However, accurately measuring the turbulent velocity dispersion is challenging due to projection effects and observational limitations, such as telescope resolution, particularly for clouds that include non-turbulent motions, such as large-scale rotation. Here, we develop a new method to recover the 3D turbulent velocity dispersion (σv,3D) from position–position–velocity (PPV) data. We simulate a rotating, turbulent, collapsing molecular cloud, and compare its intrinsic σv,3D with three different measures of the velocity dispersion accessible in PPV space: (1) the spatial mean of the 2nd-moment map, σi, (2) the standard deviation of the gradient/rotation-corrected 1st-moment map, σ(c − grad), and (3) a combination of (1) and (2), called the ‘gradient-corrected parent velocity dispersion’, $\sigma _{\mathrm{(p}-\mathrm{grad)}}=(\sigma _{\mathrm{i}}^2+\sigma _{(\mathrm{c}-\mathrm{grad)}}^2)^{1/2}$. We show that the gradient correction is crucial in order to recover purely turbulent motions of the cloud, independent of the orientation of the cloud with respect to the line of sight. We find that with a suitable correction factor and appropriate filters applied to the moment maps, all three statistics can be used to recover σv,3D, with method 3 being the most robust and reliable. We determine the correction factor as a function of the telescope beam size for different levels of cloud rotation, and find that for a beam full width at half-maximum f and cloud radius R, the 3D turbulent velocity dispersion can best be recovered from the gradient-corrected parent velocity dispersion via $\sigma _{v,\mathrm{3D}}= \left[(-0.29\pm 0.26)\, f/R + 1.93 \pm 0.15\right] \sigma _{\mathrm{(p}-\mathrm{grad)}}$ for f/R < 1, independent of the level of cloud rotation or LOS orientation.

Study of BP neural network based on improved particle swarm algorithm

This paper uses first-order difference to transform non-smooth data into smooth time series data, determines the p and q parameters in the model by judging the trailing and truncated nature of ACF, PACF, and finally establishes the ARIMA model after ACI, BCI detection. According to the parameters of the neural network randomly selected similar to the initial spatial position of the particles in the particle swarm algorithm, the improved particle swarm algorithm is used instead of the gradient correction method to precisely adjust the parameters and establish the BP neural network, which improves the robustness and accuracy of the prediction model.

Handling Measurement Delay in Iterative Real-Time Optimization Methods

This paper is concerned with the real-time optimization (RTO) of chemical plants, i.e., the optimization of the steady-state operating points during operation, based on inaccurate models. Specifically, modifier adaptation is employed to cope with the plant-model mismatch, which corrects the plant model and the constraint functions by bias and gradient correction terms that are computed from measured variables at the steady-states of the plant. This implies that the sampling time of the iterative RTO scheme is lower-bounded by the time to reach a new steady-state after the previously computed inputs were applied. If analytical process measurements (PAT technology) are used to obtain the steady-state responses, time delays occur due to the measurement delay of the PAT device and due to the transportation delay if the samples are transported to the instrument via pipes. This situation is quite common because the PAT devices can often only be installed at a certain distance from the measurement location. The presence of these time delays slows down the iterative real-time optimization, as the time from the application of a new set of inputs to receiving the steady-state information increases further. In this paper, a proactive perturbation scheme is proposed to efficiently utilize the idle time by intelligently scheduling the process inputs taking into account the time delays to obtain the steady-state process measurements. The performance of the proposed proactive perturbation scheme is demonstrated for two examples, the Williams–Otto reactor benchmark and a lithiation process. The simulation results show that the proposed proactive perturbation scheme can speed up the convergence to the true plant optimum significantly.

An improved total Lagrangian SPH method for modeling solid deformation and damage

Total Lagrangian - Smoothed Particle Hydrodynamics (TL-SPH) is a classical algorithm to improve the tensile instability encountered in the conventional Eulerian kernel-based SPH method for solid mechanics. Meanwhile, the gradient correction usually is employed in TL-SPH to enhance the consistency of approximation, which would generate unavoidable time costs. Therefore, a simplified gradient correction under the initial configuration is derived. Aiming at different particle configurations, the corresponding selection modes are provided and verified. Then the simplified gradient correction is introduced into TL-SPH, which is the Improved TL-SPH (ITL-SPH) method. Firstly, a classical example – elastic rubber collision is simulated to verify ITL-SPH has the same ability as TL-SPH to improve tensile instability. Then, the convergence and high efficiency of ITL-SPH is demonstrated via the uniaxial tension of a plate. Moreover, the plate with square and triangle holes also is simulated to show the adaptation and stability of ITL-SPH for the extreme boundary. Under the Total Lagrangian frame, the treatment to model the crack is necessary. So, this paper proposes a damage model and combines it with the ITL-SPH method for crack initiation and propagation, which is verified by the plate with holes and the notched beam examples.

Solving 2-D Slamming Problems by an Improved Higher-Order Moving Particle Semi-Implicit Method

Abstract A higher-order moving particle semi-implicit (MPS) method was further developed to solve 2-D water entry problems. To overcome the inconsistency in the original MPS methods, a pressure gradient correction was implemented to guarantee the first-order consistency of the gradient. The corrective matrix was modified by using the derivative of the kernel function. A particle shifting technique was also applied to improve the numerical stability. Validation studies were carried out for water entry of a rigid wedge with the tilting angles of 0, 10, and 20, and two rigid ship sections. Convergence studies were conducted on domain size, particle spacing, and time step. A particle convergence index method was proposed to evaluate numerical uncertainties in the improved MPS method. Uncertainties in numerical solutions due to spatial discretization were calculated. The predicted impact pressures and forces by the present method are in good agreement with experimental data. Introduction Slamming can cause local structural deformation and damages. It is important to solve highly nonlinear water-entry problems involving breaking free surfaces. Many studies on the impact of pressures/ loads during water entry or slamming have been performed using experiments, analytical solutions, and numerical simulations. Extensive drop tests have been conducted. For example, Bisplinghoff and Doherty (1952) carried out a series of experiments for free-fall wedges. Because ship motions in waves can lead to asymmetric water entry, wedges with different tilt angles were tested by Barjasteh et al. (2016). A more detailed review of studies based on theoretical, potential-flow, and computational fluid dynamics (CFD) methods is presented in the work of Peng and Qiu (2018).

Overcoming excessive numerical dissipation in SPH modeling of water waves

Excessive nonphysical energy dissipation is a problem in Smoothed Particle Hydrodynamics (SPH) when modeling free surface waves, resulting in a significant decrease in wave amplitude within a few wavelengths for progressive waves. This dissipation poses a limitation to the physical scale of SPH applications involving water wave propagation. Some prior solutions to this wave decay problem rely on elaborate schemes, which require a complex, or non-straightforward, implementation. Other approaches demand large smoothing lengths that lead to longer simulation times and potential degradation of the results. In this work we present an approach based on a kernel gradient correction. Our scheme is fully 3D and solves the main known drawbacks of kernel gradient corrections, such as instabilities and lack of momentum conservation. The latter is ensured by adopting an averaged correction matrix, so as to conserve reciprocity during particle interactions. We test our model with a standing wave in a basin and a progressive wave train in a wave tank, and in both cases no nonphysical decay occurs. A comparison to an approach based on large smoothing factors shows advantages both in quality of the results and simulation time.

Gradient temporal-difference learning for off-policy evaluation using emphatic weightings

The problem of off-policy evaluation (OPE) has long been advocated as one of the foremost challenges in reinforcement learning. Gradient-based and emphasis-based temporal-difference (TD) learning algorithms comprise the major part of off-policy TD learning methods. In this work, we investigate the derivation of efficient OPE algorithms from a novel perspective based on the advantages of these two categories. The gradient-based framework is adopted, and the emphatic approach is used to improve convergence performance. We begin by proposing a new analogue of the on-policy objective, called the distribution-correction-based mean square projected Bellman error (DC-MSPBE). The key to the construction of DC-MSPBE is the use of emphatic weightings on the representable subspace of the original MSPBE. Based on this objective function, the emphatic TD with lower-variance gradient correction (ETD-LVC) algorithm is proposed. Under standard off-policy and stochastic approximation conditions, we provide the convergence analysis of the ETD-LVC algorithm in the case of linear function approximation. Further, we generalize the algorithm to nonlinear smooth function approximation. Finally, we empirically demonstrate the improved performance of our ETD-LVC algorithm on off-policy benchmarks. Taken together, we hope that our work can guide the future discovery of a better alternative in the off-policy TD learning algorithm family.

Chiral transport in curved spacetime via holography

We consider a holographic model of strongly interacting plasma with a gravitational anomaly. In this model, we compute parity-odd responses of the system at finite temperature and chemical potential to external electromagnetic and gravitational fields. Working within the linearized fluid/gravity duality, we performed the calculation up to the third order in gradient expansion. Besides reproducing the chiral magnetic (CME) and vortical (CVE) effects we also obtain gradient corrections to the CME and CVE due to the gravitational anomaly. Additionally, we find energy-momentum and current responses to the gravitational field similarly determined by the gravitational anomaly. The energy-momentum response is the first purely gravitational transport effect that has been related to quantum anomalies in a holographic theory.

Understanding the acceleration phenomenon via high-resolution differential equations

Gradient-based optimization algorithms can be studied from the perspective of limiting ordinary differential equations (ODEs). Motivated by the fact that existing ODEs do not distinguish between two fundamentally different algorithms—Nesterov’s accelerated gradient method for strongly convex functions (NAG-SC) and Polyak’s heavy-ball method—we study an alternative limiting process that yields high-resolution ODEs. We show that these ODEs permit a general Lyapunov function framework for the analysis of convergence in both continuous and discrete time. We also show that these ODEs are more accurate surrogates for the underlying algorithms; in particular, they not only distinguish between NAG-SC and Polyak’s heavy-ball method, but they allow the identification of a term that we refer to as “gradient correction” that is present in NAG-SC but not in the heavy-ball method and is responsible for the qualitative difference in convergence of the two methods. We also use the high-resolution ODE framework to study Nesterov’s accelerated gradient method for (non-strongly) convex functions, uncovering a hitherto unknown result—that NAG-C minimizes the squared gradient norm at an inverse cubic rate. Finally, by modifying the high-resolution ODE of NAG-C, we obtain a family of new optimization methods that are shown to maintain the accelerated convergence rates of NAG-C for smooth convex functions.

Development of High-Resolution Regional Climatology in the East/Japan Sea With a Primary Focus on Meridional Temperature Gradient Correction

In this study, we developed a new high-resolution regional climatology (0.1° by 0.1° by 19 levels) in the East/Japan Sea. National Centers for Environmental Information and Korea Oceanic Data Center already released the regional climatology of East Asian seas including the East/Japan Sea with 0.1° by 0.1° resolution. It provides a reliable temperature and salinity structure compared to previous 1° or 0.25° climatologies. However, this study found an abnormal meridional temperature gradient problem when calculating geostrophic currents based on this new climatology. Geostrophic currents show a strong repetitive eastward flow along the 1° latitudinal band especially in the East/Japan Sea, which corresponds with abnormal meridional temperature gradients at the same areas. This problem could be related to the objective analysis procedure generating the high-resolution climatology. Here, we reproduced a high-resolution climatology without the abnormal meridional temperature gradient problem by using the optimal interpolation method. Results show that the meridional gradient problem can partly be attributed to both the use of the World Ocean Atlas background field on the 1° grid, and the spatial distribution of World Ocean database observation data; however, these are not the primary causes. We corrected the abnormal temperature gradient by increasing the meridional decorrelation length scale without losing the meso-scale feature in the East/Japan Sea, as shown by the wavelet analysis. Improvement of the new gridded field is also validated by using serial hydrographic data and the altimetry-derived surface current product.

A Review of Modeling Modification Methods for Mixed FE-SEA

Since the traditional deterministic method and classical statistical energy method have little room for improvement, more and more researches gradually turn to the combination of the two methods to solve the low and medium frequency “acoustic vibration” problem. However, in the application of mixed FE-SEA model, researchers found that when the coupling interface between FEA substructure and SEA statistical substructure is in the form of continuous interface, a very large finite element grid needs to be established at the boundary of the mixed model, which leads to huge time-consuming problem in the calculation of medium and low frequency of the mixed model. To solve this problem, the hybrid FE-SEA model needs to be improved and modified. In this paper, some common hybrid model correction methods, including deterministic subsystem edge gradient correction, are reviewed to provide theoretical support for the comprehensive study of hybrid model correction.

Coupling edge-based smoothed finite element method with smoothed particle hydrodynamics for fluid structure interaction problems

Numerical simulation of fluid structure interaction (FSI) problems is one of the most challenging topics in computational fluid dynamics. In this paper, coupling edge-based smoothed finite element method (ES-FEM) and smoothed particle hydrodynamics (SPH) method (ES-FEM-SPH) is proposed for solving FSI problems, where the edge-based smoothed finite element method is used to model the movement and deformation of structures, and the smoothed particle hydrodynamics is used to model the fluid flow. In ES-FEM, the gradient smoothing technique is applied over the smoothing domain and it can effectively overcome the ‘‘overly-stiff’’ effect in conventional FEM model. Some correction algorithms including density correction, kernel gradient correction and particle shift technique are integrated into the SPH method to improve computational stability and accuracy. A virtual particle coupling scheme is used to implement the coupling of ES-FEM and SPH with complex geometry interface. As ES-FEM is more accurate than conventional FEM, and it is expected that this ES-FEM-SPH coupling approach should be superior than existing FEM-SPH coupling approaches. A number of test examples with FSI are investigated with the presented ES-FEM-SPH, and compared with results from other approaches including FEM-SPH. From the obtained numerical results, we can conclude that the ES-FEM-SPH coupling approach is effective to simulate FSI problems.

Flat rotation curves of z ∼ 1 star-forming galaxies

ABSTRACT We investigate the shape of the rotation curves (RCs) of z ∼ 1 star-forming galaxies (SFGs) and compare them with local SFGs. For this purpose, we have used 344 galaxies from the K-band Multi-Object Spectrograph (KMOS) for Redshift One Spectroscopic Survey (KROSS). This sample covers the redshift range 0.57 ≤ z ≤ 1.04, the effective radii 0.69 ≤ Re [kpc] ≤ 7.76, and the stellar masses 8.7 ≤ log (M* [M⊙]) ≤ 11.32. Using 3DBAROLO, we extract the H α kinematic maps and corresponding RCs. The main advantage of 3DBAROLO is that it incorporates the beam smearing in the 3D observational space, which provide us with the intrinsic rotation velocity even in the low spatial resolution data. We have corrected the RCs for pressure support, which seems to be a more dominant effect than beam smearing in high-z galaxies. Only a combination of the three techniques (3D-kinematic modelling + 3D-beam smearing correction + pressure gradient correction) yields the intrinsic RC of an individual galaxy. Further, we present the co-added and binned RCs constructed out of 256 high-quality objects. We do not see any change in the shape of RCs with respect to the local SFGs. Moreover, we notice a significant evolution in the stellar-disc length (RD) of the galaxies as a function of their circular velocity. Therefore, we conclude that the stellar disc of SFGs evolves over cosmic time (from z ∼ 1) while the total mass stays constant (within ∼20 kpc).