Gradient Corrections Research Articles

A Software Tool for the True Height Analysis of Ionograms Using the Iterative Gradient Correction (IGC) Method

AbstractDeriving the precise true height electron density profile from the measured ionosonde virtual heights is quite a challenging problem. Recently, Ankita and Tulasi Ram (2023, https://doi.org/10.1029/2023RS007808) presented a new method, Iterative Gradient Correction (IGC) method, for true height analysis that uses HF radio wave propagation path computations to reconstruct the true height profile. Through iterative corrections on electron density gradients between successive points, the IGC method minimizes errors below a specified tolerance at each point and reconstructs a complete electron density profile. The derived profiles from the IGC method are found to be accurate when compared with Incoherent Scatter Radar and Global Navigation Satellite System—Radio Occultation observations. To facilitate true height analysis by IGC method for a wider user community, a MATLAB‐based software has been developed and is outlined in this report. The software can be installed on any Windows platform and is designed with a user‐friendly interface for easy and efficient application by the users. It can analyze multiple scaled ionograms in a single run and outputs the real height profiles in ASCII format. Further, the software also captures important ionospheric parameters such as the base altitudes and peak frequencies of E‐ and F‐layers (e.g., hE, hF, foE, and foF2) etc., from the computed true height profiles and tabulates in a separate output file for the ready use. The software also provides the option for extrapolation of true height profile into top‐side ionosphere up to a user‐specified height and reconstructs the complete vertical electron density profile.

Improved mesh-free SPH approach for loose top coal caving modeling

This study presents an innovative model in computational geotechnical engineering by improving the Smoothed Particle Hydrodynamics (SPH) method for simulating loose particle dynamics in coal caving processes. The improved model integrates an elastic-perfectly plastic constitutive model with the Drucker-Prager yield criterion and includes several improvements aimed at boosting accuracy, stability, and efficiency. These improvements include gravity loading coupled with particle damping, first-order stress field smoothing, and kernel gradient correction. A series of numerical experiments validates the effectiveness of the improved SPH model, demonstrating its capability to predict large deformations and track the evolution of the coal-rock interface in coal caving processes. Furthermore, the study analyzes the model's sensitivity to material parameters such as the angle of friction and material density, which aids in configuring the model for distinct coal mining situations. Results show that the non-cohesive elastic-perfectly plastic constitutive model can effectively simulate the flow behavior of granular particles, and the landslide simulation results are in good agreement with the experiments. The improved SPH algorithm with stress smoothing technique solves the problem of numerical noise, and the “double peak” stress distribution around the coal outlet is identified. The established SPH model offers an effective tool for understanding dynamics behaviors of loose top coal. Significantly, the model requires only five material parameters, which can be identified through standard experiments, avoiding the typically arduous process of parameter selection or calibration commonly existing in Discrete Element Method simulations.

An improved smoothed particle hydrodynamics method for modeling multiphase flows

Multiphase flows are prevalent in both natural and engineered systems. The study of multiphase flow problems using numerical simulation is challenging due to the presence of high nonlinearities and moving interfaces. In this paper, an improved multiphase smoothed particle hydrodynamics (SPH) model is proposed for simulating multiphase flows. In the improved multiphase SPH model, an improved interface repulsive force model is proposed to reduce the interpenetration of particles at the multiphase interface and make the multiphase interface smooth and clear, and an improved kernel gradient correction is introduced to optimize the computational results. In addition, the particle shifting technology is applied to make the particle distribution uniform. Five numerical examples including the Rayleigh–Taylor instability, non-Boussinesq lock-exchange problem, square droplet deformation, single bubble rise, and circular droplet oscillation are investigated to verify the correctness and effectiveness of the improved multiphase SPH model. The results demonstrate that the improved multiphase SPH approach is effective in modeling multiphase flows.

Experimental and numerical determination of the fatigue notch factor in as‐built wire arc additive manufacturing steel components

AbstractParts manufactured by wire arc additive manufacturing (WAAM) are characterized by a peculiar surface morphology, namely, surface waviness, that negatively affects the fatigue performance. To exploit the full potential of WAAM and minimize the need for postproduction work, it is crucial to utilize the components in the as‐built state. This is because conventional machining techniques, typically employed for postprocessing operations, severely curtail the freedom of geometry of the components. This study focuses on an experimental and numerical characterization of the notch effect of the surface waviness for an AISI 308 LSi stainless steel. This is done by quantifying the fatigue notch factor in a probabilistic fashion, considering the results of ad‐hoc designed fatigue tests. A finite element model is developed by considering a 3D scan of the geometry of WAAMed plates, allowing to determine the theoretical stress concentration factor. The fatigue notch factor is also estimated from the numerical model by making use of the gradient correction according to the FKM guidelines. To validate the numerical approach, test data produced for different testing conditions are correlated by using the local stress approach, showing that classical methods are also applicable to additive manufactured parts.

A Quasi-Newton Trust-Region Method for Well Location Optimization Under Uncertainty

Summary Subsurface development involves well-placement decisions considering the highly uncertain understanding of the reservoir in the subsurface. The simultaneous optimization of a large number of well locations is a challenging problem. Traditional gradient-based methods can be adapted for well location optimization (WLO) when these problems are converted into real-valued representations and equipped with protocols to handle noisy objective functions. However, their application to large-scale scenarios often remains impractical. This impracticality arises because computing gradients of the objective function can be prohibitively expensive in realistic settings, particularly without using the adjoint method. In this paper, we explore the application of a novel quasi-Newton trust-region (TR) method that employs the stochastic simplex approximate gradient (StoSAG). We have implemented the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton updating algorithm together with line-search (LS) and TR optimization strategies. The StoSAG-based optimization methods have been applied to a realistic synthetic reservoir featuring 26 wells considering two distinct cases: Each includes 20 realizations of porosity and permeability. The first case exhibits mild heterogeneity, while the second exhibits significant heterogeneity with a large correlation length. We have conducted a series of runs to evaluate the performance of these algorithms in addition to comparisons to the finite-difference (FD) and particle-swarm-optimization (PSO) algorithms. We introduce a novel approach to enhance the accuracy of StoSAG gradients by proposing modified StoSAG formulations. These formulations are tailored to exploit the structure of the objective function and to capture the relationships between its components and the individual optimization parameters. This approach involves using a correction matrix W informed by problem-specific knowledge. The entries of W vary from 0 to 1 and are proportional to the interference effects the neighboring wells have on each other. We determine those entries (or weights) based on the radii of investigation around the wells and the distance between the well pairs. Results indicate that the steepest-descent (SD) algorithm coupled with StoSAG has superior performance to PSO and FD. Although the objective function is prone to numerical noise and not continuously differentiable with respect to well locations, StoSAG overcomes this challenge because it acts as a smooth approximation. Comparative tests further confirm that the TR-BFGS is more effective than the LS-BFGS. Moreover, we show that using the proposed gradient correction procedure results in a significant acceleration in convergence, indicating an enhancement in the StoSAG gradient approximation quality. This enhancement allows the TR-BFGS algorithm to achieve considerably higher performance than SD, illustrating that the accuracy of the BFGS approximation benefits from improved gradient quality.

Causality and stability in relativistic hydrodynamic theory - a choice to be endured

In this work, it has been indicated that the key features requisite for preserving causality and stability of the popularly existing relativistic hydrodynamic theories, can be translated into each other. It has been shown here, that a generic ‘fluid frame transformation’ including all orders of gradient corrections can recast a stable-causal hydrodynamic theory that (i) only includes fundamental fluid variables (velocity and temperature) but requires to be in a general hydrodynamic frame other than the Landau or Eckart, to a theory that is (ii) pathology free in Landau frame but needs newer degrees of freedom. Since frame choice provides the first principle field definitions and degrees of freedom indicate the number of conserved quantities, the causality and stability of a theory seem to require a consensus between the two unless the derivative correction goes to infinity. The key finding of this work is to indicate a connection between these different formalisms, that lead to a causal and stable hydrodynamic theory.

Fretting fatigue in dovetail assembly and bridge-flat model: Verification of a life prediction model based on stress gradient

The dovetail assembly and the bridge-flat model are two typical fretting fatigue tests. This article concentrates on the fretting fatigue of the dovetail assembly, utilizing a sub-scaled specimen tested under cyclic loading. Simultaneously, fretting tests on the bridge-flat and combined high and low cycle fatigue tests on the dovetail assembly were conducted. These tests were analyzed in conjunction with the dovetail assembly to understand the stress state characteristics in the contact region. The results from both tests and finite element analysis highlight that fretting leads to a significant reduction in fatigue life, primarily attributed to stress concentration at the edges of the contact area. Building upon the method of stress gradient correction, a life prediction model for fretting fatigue is proposed, demonstrating good accuracy in predicting fretting fatigue life.

AAPM WGTG51 Report 385: Addendum to the AAPM's TG-51 protocol for clinical reference dosimetry of high-energy electron beams.

An Addendum to the AAPM's TG-51 protocol for the determination of absorbed dose to water is presented for electron beams with energies between 4MeV and 22MeV ( ). This updated formalism allows simplified calibration procedures, including the use of calibrated cylindrical ionization chambers in all electron beams without the use of a gradient correction. New data are provided for electron beams based on Monte Carlo simulations. Implementation guidance is provided. Components of the uncertainty budget in determining absorbed dose to water at the reference depth are discussed. Specifications for a reference-class chamber in electron beams include chamber stability, settling, ion recombination behavior, and polarity dependence. Progress in electron beam reference dosimetry is reviewed. Although this report introduces some major changes (e.g., gradient corrections are implicitly included in the electron beam quality conversion factors), they serve to simplify the calibration procedure. Results for absorbed dose per linac monitor unit are expected to be up to approximately 2% higher using this Addendum compared to using the original TG-51protocol.

An efficient truncation scheme for Eulerian and total Lagrangian smoothed particle hydrodynamics methods

In smoothed particle hydrodynamics (SPH) method, the particle-based approximations are implemented via kernel functions, and the evaluation of performance involves two key criteria: numerical accuracy and computational efficiency. In the SPH community, the Wendland kernel reigns as the prevailing choice due to its commendable accuracy and reasonable computational efficiency. Nevertheless, there exists an urgent need to enhance computational efficiency while upholding accuracy. In this paper, we employ a truncation approach to limit the compact support of the Wendland kernel to 1.6h. This decision is based on the observation that particles within the range of 1.6h to 2h make negligible contributions to the SPH approximation. To decrease numerical errors from SPH approximation and the truncation method, we incorporate the Laguerre–Gauss kernel for particle relaxation to obtain the high-quality particle distribution with reduced residue [Wang et al., “A fourth-order kernel for improving numerical accuracy and stability in Eulerian and total Lagrangian SPH,” arXiv:2309.01581 (2023)], and the kernel gradient correction to rectify integration errors. A comprehensive set of numerical examples including fluid dynamics in Eulerian formulation and solid dynamics in total Lagrangian formulation are tested and have demonstrated that truncated and non-truncated Wendland kernels enable achieving the same level of accuracy but the former significantly increases the computational efficiency.

Generalized Semiclassical Ehrenfest Method: A Route to Wave Function-Free Photochemistry and Nonadiabatic Dynamics with Only Potential Energies and Gradients.

We reconsider recent methods by which direct dynamics calculations of electronically nonadiabatic processes can be carried out while requiring only adiabatic potential energies and their gradients. We show that these methods can be understood in terms of a new generalization of the well-known semiclassical Ehrenfest method. This is convenient because it eliminates the need to evaluate electronic wave functions and their matrix elements along the mixed quantum-classical trajectories. The new approximations and procedures enabling this advance are the curvature-driven approximation to the time-derivative coupling, the generalized semiclassical Ehrenfest method, and a new gradient correction scheme called the time-derivative matrix (TDM) scheme. When spin-orbit coupling is present, one can carry out dynamics calculations in the fully adiabatic basis using potential energies and gradients calculated without spin-orbit coupling plus the spin-orbit coupling matrix elements. Even when spin-orbit coupling is neglected, the method is useful because it allows calculations by electronic structure methods for which nonadiabatic coupling vectors are unavailable. In order to place the new considerations in context, the article starts out with a review of background material on trajectory surface hopping, the semiclassical Ehrenfest scheme, and methods for incorporating decoherence. We consider both internal conversion and intersystem crossing. We also review several examples from our group of successful applications of the curvature-driven approximation.

Numerical simulations of thermal capillary migration of a droplet on a temperature gradient wall with smoothed particle hydrodynamics method

Thermal capillary migration is a phenomenon due to the Marangoni effect, which refers to the spontaneous motion of a liquid on a non-isothermal surface. Numerical simulation of thermal capillary migration of a droplet is extremely difficult due to the multi-physics field coupling and the violent motion of the droplet surface. In this paper, an improved smooth particle hydrodynamics (SPH) method is developed for simulating thermal capillary migration of a droplet driven by thermal gradient. In improved SPH model, an improved continuous surface force model is proposed to enhance the accuracy and stability of surface tension force calculation by introducing an improved surface tangential force. The contact angle model is utilized to model the surface wettability. The SPH method for simulating the thermal fluid flow is developed based on the continuum, momentum, and energy equations. In addition, kernel gradient correction and particle shifting technique are utilized to improve the accuracy and stability of the SPH method. The correctness and effectiveness of the improved SPH method are verified by numerical examples. Moreover, the motions of a droplet driven by thermal gradient under different conditions are investigated. Comparing with the results obtained by experiments and other resources, we can conclude that the improved SPH model is effective in modeling the thermal capillary migration of a droplet.

Efficient Asynchronous Federated Learning with Prospective Momentum Aggregation and Fine-Grained Correction

Asynchronous federated learning (AFL) is a distributed machine learning technique that allows multiple devices to collaboratively train deep learning models without sharing local data. However, AFL suffers from low efficiency due to poor client model training quality and slow server model convergence speed, which are a result of the heterogeneous nature of both data and devices. To address these issues, we propose Efficient Asynchronous Federated Learning with Prospective Momentum Aggregation and Fine-Grained Correction (FedAC). Our framework consists of three key components. The first component is client weight evaluation based on temporal gradient, which evaluates the client weight based on the similarity between the client and server update directions. The second component is adaptive server update with prospective weighted momentum, which uses an asynchronous buffered update strategy and a prospective weighted momentum with adaptive learning rate to update the global model in server. The last component is client update with fine-grained gradient correction, which introduces a fine-grained gradient correction term to mitigate the client drift and correct the client stochastic gradient. We conduct experiments on real and synthetic datasets, and compare with existing federated learning methods. Experimental results demonstrate effective improvements in model training efficiency and AFL performance by our framework.

Contact framework for total Lagrangian smoothed particle hydrodynamics using an adaptive hybrid kernel scheme

AbstractTotal Lagrangian SPH (TLSPH) offers many advantages that can overcome instability and computational time issues. However, it is not naturally applicable to problems with contact. Many problems in solid dynamics and structural analysis require contact definition. In order to use the total Lagrangian formulation, further development for the contact algorithm is required. This research proposes an algorithm to implement inter‐particle contact in TLSPH using an adaptive hybrid‐kernel scheme for the first time. A combination of the updated and total Lagrangian formulations at the contact surface is introduced, in which the kernel type change automatically when particles from a different body are detected. In kernel change from the updated to the total Lagrangian formulation, the gradient correction cannot be performed using a common correction method because different frames of reference are used. Therefore, a hybrid‐kernel correction technique is proposed to maintain the zeroth‐ and first‐order completeness. Then, the contact force is obtained from the inter‐particle force using the conservation of momentum. The proposed method does not require a user‐defined parameter that makes the application straightforward. Based on the test, the proposed method agrees well with the data available in published literature and the finite element method. Compared with the contact method in classical SPH, the proposed TLSPH shows a significant stability improvement.

An initial investigation of the non-isotropic feature of GNSS tropospheric delay

Tropospheric delay is a significant error source in Global Navigation Satellite Systems (GNSS) positioning. Slant Path Delay (SPD) is commonly derived by multiplying Zenith Tropospheric Delay (ZTD) with a mapping function. However, mapping functions, assuming atmospheric isotropy, restrict the accuracy of derived SPDs. To improve the accuracy, a horizontal gradient correction is introduced to account for azimuth-dependent SPD variations, treating the atmosphere as anisotropic. This study uncovers that, amidst atmospheric dynamics and spatiotemporal changes in moisture content, the SPD deviates from that based on traditional isotropy or anisotropy assumption. It innovatively introduces the concept that SPD exhibits non-isotropy with respect to azimuth angles. Hypothesis validation involves assessing SPD accuracy using three mapping functions at five International GNSS Service (IGS) stations, referencing the SPD with the ray-tracing method. It subsequently evaluates the SPD accuracy with horizontal gradient correction based on Vienna Mapping Function 3 (VMF3) estimation. Lastly, the non-isotropic of SPD is analyzed through the ray-tracing method. The results indicate the smallest residual (1.1–82.7 mm) between the SPDs with VMF3 and those with the ray-tracing. However, introducing horizontal gradient correction yields no significant improvement of SPD accuracy. Considering potential decimeter-level differences in SPD due to non-isotropic tropospheric delay across azimuth angles, a precise grasp and summary of these variations is pivotal for accurate tropospheric delay modeling. This finding provides vital support for future high-precision tropospheric delay modeling.

Gradient Correction for White-Box Adversarial Attacks.

Deep neural networks (DNNs) play key roles in various artificial intelligence applications such as image classification and object recognition. However, a growing number of studies have shown that there exist adversarial examples in DNNs, which are almost imperceptibly different from the original samples but can greatly change the output of DNNs. Recently, many white-box attack algorithms have been proposed, and most of the algorithms concentrate on how to make the best use of gradients per iteration to improve adversarial performance. In this article, we focus on the properties of the widely used activation function, rectified linear unit (ReLU), and find that there exist two phenomena (i.e., wrong blocking and over transmission) misguiding the calculation of gradients for ReLU during backpropagation. Both issues enlarge the difference between the predicted changes of the loss function from gradients and corresponding actual changes and misguide the optimized direction, which results in larger perturbations. Therefore, we propose a universal gradient correction adversarial example generation method, called ADV-ReLU, to enhance the performance of gradient-based white-box attack algorithms such as fast gradient signed method (FGSM), iterative FGSM (I-FGSM), momentum I-FGSM (MI-FGSM), and variance tuning MI-FGSM (VMI-FGSM). Through backpropagation, our approach calculates the gradient of the loss function with respect to the network input, maps the values to scores, and selects a part of them to update the misguided gradients. Comprehensive experimental results on ImageNet and CIFAR10 demonstrate that our ADV-ReLU can be easily integrated into many state-of-the-art gradient-based white-box attack algorithms, as well as transferred to black-box attacks, to further decrease perturbations measured in the l2 -norm.

Modeling Edge Flame Propagation for Flame Particle Tracking in the Forced Ignition Process of Turbulent Nonpremixed Jet Flame

ABSTRACT To ensure safe and reliable operation, ignition performance in propulsion and power devices needs to be thoroughly assessed. Reduced order models (ROMs) for ignition have gained increasing attention, given that first-principles models are restricted by immense computational costs that preclude rapid assessment for the design purpose. Currently, flame self-propagation is generally neglected in the ROM descriptions of ignition process and the impact on the flame front dynamics as well as the ignition probability map is not clear for low swirl or jet flames which are of interest for industrial applications. In this study, an empirical model for flame self-propagation is proposed to augment the capability of Lagrangian flame particle tracking method, a ROM model to predict ignition probability based on nonreacting flow field. The model adopts the classic scaling law of turbulent flame speed together with fuel gradient correction and flame self-propagation to mimic the edge flame dynamics during the ignition process. The model performances in terms of flame front dynamics and ignition probability map are quantified in a turbulent nonpremixed methane-air jet flame. Results reveal that only with flame self-propagation, the flame particle tracking can well capture the transient evolution of the leading flame front as observed in experiments. It is found that the predicted ignition probability map agrees well with experimental data with high ignition probability around the vicinity of the stoichiometric region at the downstream axial distance of 6 to 40 times the jet diameter. This study illustrates the importance to account for flame self-propagation to correctly predict ignition probability in jet dominant nonpremixed flames.

Iterative Gradient Correction (IGC) Method for True Height Analysis of Ionograms

AbstractInversion of precise true height electron density profile from the measured virtual heights by the Ionosonde is a quite challenging and ill‐posed problem. In this paper, we present a new method to compute the true height profiles from ionograms that relies on computing the propagation path of radio waves with time. This method does not use predefined polynomial functions to fit the vertical electron density distribution; hence, it is free from fitting errors. Instead, this method implements iterative corrections in the electron density gradient between the successive points and progressively reconstructs the true height profile. This Iterative Gradient Correction (IGC) method assures minimizing the error to below a tolerance limit at all sampled points on the ionogram. The true height profiles derived from this method exhibit better accuracy than those derived from the widely used POLynomial ANalysis, particularly, at cusp and F2‐peak regions. Further, the IGC method gives the best results at higher sampling resolutions of ionograms and is less sensitive to scaling errors.

An efficient correction method in Riemann SPH for the simulation of general free surface flows

In this paper, a new efficient weighted correction method for weakly-compressible smoothed particle hydrodynamics is proposed and successfully implemented in the simulation of violent free-surface flow exhibiting breaking and impact events for the first time. It is well known that the original kernel gradient correction (KGC) encounters numerical instability resulting from matrix inversion. The present method remedies this issue by introducing a weighted average of the KGC matrix and the identity matrix, other than directly applying the KGC matrix, to achieve numerical stability meanwhile decrease numerical dissipation. To ensure momentum conservation, the correction is implemented in a particle-average pattern by rewriting the pressure term of the Riemann solution. Furthermore, the proposed weighted KGC scheme is incorporated into the dual-criteria time-stepping framework developed by Zhang et al. (2020) to achieve optimized computational efficiency. A set of numerical examples in both two- and three-dimensions are investigated to demonstrate that the present method can significantly reduce numerical dissipation meanwhile exhibit a smooth pressure field for general free-surface flows.

Potential effects of the hydrostatic pressure gradient on hyperemic and nonhyperemic pressure ratios.

When measuring hyperemic and nonhyperemic pressure ratios with traditional sensor-tipped wires, the inevitable hydrostatic pressure gradient (HPG) may influence treatment decisions. This study aimed to simulate and analyze the effect of a hydrostatic pressure gradient on different indices of functional lesion severity. A hypothetical Pd-Pa height difference and subsequent hydrostatic pressure gradient based on previous literature was applied to the pressure measurements from the CONTRAST study. The effect on three indices of functional lesion severity (FFR, Pd/Pa, and dPR) was assessed and possible reclassifications in functional significance by the different indices were analyzed. In 602 pressure tracings, simulated hydrostatic pressure gradients led to an absolute change in Pd of 3.18 ± 1.30 mmHg, resulting in an overall increase in FFR, Pd/Pa, and dPR of 0.02 ± 0.04 for all indices (P = 0.69). Reclassification due to the hydrostatic pressure gradient when using dichotomous cutoff values occurred in 13.4, 22.3, and 20.6% for FFR, Pd/Pa, and dPR, respectively. The effect of hydrostatic pressure gradient correction differed among the coronary arteries and was most pronounced in the left anterior descending. When considering the gray zone for the different functional indices, the hydrostatic pressure gradient resulted in reclassification in only one patient out of the complete patient population (1/602; 0.17%). The hydrostatic pressure gradient can influence functional lesion assessment when using dichotomous cutoff values. When taking the gray zone into account, its effect is limited.NEW & NOTEWORTHY This study systematically simulated the effect of hydrostatic pressure gradients (HPG) on real-world hyperemic and nonhyperemic pressure ratios, showing correction for HPG leads to reclassification in functional significance from 13.4 to 22.3% for different functional indices. This was most pronounced in nonhyperemic pressure ratios. A new pressure guidewire (Wirecath) is unaffected by HPG. The ongoing PW-COMPARE study (NCT04802681) prospectively analyzes the magnitude and importance of HPG by simultaneous FFR measurements.

A simple approach to Lieb–Thirring type inequalities

In [10] Nam proved a Lieb–Thirring Inequality for the kinetic energy of a fermionic quantum system, with almost optimal (semi-classical) constant and a gradient correction term. We present a stronger version of this inequality, with a much simplified proof. As a corollary we obtain a simple proof of the original Lieb–Thirring inequality.