Gradient Corrections Research Articles

Scale-Aware Edge-Preserving Image Filtering via Iterative Global Optimization

Presently, few filters are able to smooth images in a scale-aware manner like Gaussian filtering while not blurring the edges of large-scale features, whereas this kind of filter can be important in many visual applications requiring scale-aware manipulation while avoiding halos. In this paper, we propose a filtering technique through iterative global optimization (IGO), enabling to achieve both good scale-aware and edge-preserving performance. Our method is based on a filtering idea of selective gradient suppression and guidance gradient correction in the framework of IGO, which has the advantages of avoiding halos and preventing oversharpening of edges, and a scale-aware measure can be introduced to further control the way of gradient suppression. The proposed measure is spatially varying and oriented by coarse-scale local extrema at each pixel to better preserve the natural boundaries of large-scale structures. Besides, we show that our method can be fast implemented with a sequence of 1-D filtering. In the experiments, we demonstrate the effectiveness of our method by comparing it with current state-of-the-art filtering methods and using it in a variety of applications.

An SPH multi‐fluid model based on quasi buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios

SummaryWe introduce a smoothed particle hydrodynamics (SPH) concept for the stabilization of the interface between 2 fluids. It is demonstrated that the change in the pressure gradient across the interface leads to a force imbalance. This force imbalance is attributed to the particle approximation implicit to SPH. To stabilize the interface, a pressure gradient correction is proposed. In this approach, the multi‐fluid pressure gradients are related to the (gravitational and fluid) accelerations. This leads to a quasi‐buoyancy correction for hydrostatic (stratified) flows, which is extended to nonhydrostatic flows. The result is a simple density correction that involves no parameters or coefficients. This correction is included as an extra term in the SPH momentum equation. The new concept for the stabilization of the interface is explored in 5 case studies and compared with other multi‐fluid models. The first case is the stagnant flow in a tank: The interface remains stable up to density ratios of 1:1000 (typical for water and air), in combination with artificial wave speed ratios up to 1:4. The second and third cases are the Rayleigh‐Taylor instability and the rising bubble, where a reasonable agreement between SPH and level‐set models is achieved. The fourth case is an air flow across a water surface up to density ratios of 1:100, artificial wave speed ratios of 1:4, and high air velocities. The fifth case is about the propagation of internal gravity waves up to density ratios of 1:100 and artificial wave speed ratios of 1:4. It is demonstrated that the quasi‐buoyancy model may be used to stabilize the interface between 2 fluids up to high density ratios, with real (low) viscosities and more realistic wave speed ratios than achieved by other weakly compressible SPH multi‐fluid models. Real wave speed ratios can be achieved as long as the fluid velocities are not very high. Although the wave speeds may be artificial in many cases, correct and realistic wave speed ratios are essential in the modelling of heat transfer between 2 fluids (eg, in engineering applications such as gas turbines).

Simultaneous identification and optimization of biochemical processes under model-plant mismatch using output uncertainty bounds

The method of simultaneous identification and optimization aims at satisfying the conditions of optimality while providing accurate predictions of the process outputs. The model parameters are updated in a run-to-run procedure as to account for changes in operating points and to correct for errors in the predicted gradients of the cost-function and constraints. To make this parameter updating step more robust, we propose a parameter identification objective that includes a ratio of the sum of squared errors to a parametric gradient sensitivity function. This results in an identified set of parameters which provide larger sensitivities for the subsequent gradient correction step thus leading to faster convergence to the optimum. Moreover, worst-case uncertainty bounds on the model outputs are utilized to enforce an adequate model fitting. This is especially valuable when identifying dynamic metabolic models with many parameters. The resulting improvements are illustrated using two simulated cell culture processes.

Theoretical foundations of quantum hydrodynamics for plasmas

Quantum hydrodynamics (QHD) theory for finite temperature plasmas is consistently derived in the framework of the local density approximation of the free energy with first order density gradient correction. Previously known results are revised and improved with a clear description of the underlying approximations. A fully non-local Bohm potential, which goes beyond all previous results and is linked to the electron polarization function in the random phase approximation, for the QHD model is presented. The dynamic QHD exchange correlation potential is introduced in the framework of local field corrections and considered for the case of the relaxation time approximation. Finally, the range of applicability of the QHD is discussed.

Influential Factors of Internal Magnetic Field Gradient in Reservoir Rock and Its Effects on NMR Response

Nuclear magnetic resonance (NMR) plays a significant role in porous media analysis and petroleum exploration, but its response is significantly influenced by the internal magnetic field gradient in fluid saturated porous medium, which obviously limits the accuracy of rock core analysis and logging interpretation. The influential factors of the internal magnetic field gradient in formation and its influences on NMR response are studied in this paper, based on NMR mechanism through one- and two-dimensional core NMR experiments. The results indicate that the internal magnetic field gradient is positively correlated with the static magnetic field strength and the magnetic susceptibility difference between pore fluid and solid grains, while it presents negative correlation with pore radius. The internal magnetic field gradient produces an additional diffusion relaxation in hydrogen relaxation system and accelerates the attenuation of magnetization vector. As a result, T2 spectrum shifts to the left and NMR porosity and diffusion coefficient of the fluid could be inaccurate. This research sets a foundation for the NMR porosity correction and fluid distribution on T2-G maps based on the internal magnetic field gradient correction.

Strong anharmonicity in the phonon spectra of PbTe and SnTe from first principles

At room temperature, PbTe and SnTe are efficient thermoelectrics with a cubic structure. At low temperature, SnTe undergoes a ferroelectric transition with a critical temperature strongly dependent on the hole concentration, while PbTe is an incipient ferroelectric. By using the stochastic self-consistent harmonic approximation, we investigate the anharmonic phonon spectra and the occurrence of a ferroelectric transition in both systems. We find that vibrational spectra strongly depend on the approximation used for the exchange-correlation kernel in density-functional theory. If gradient corrections and the theoretical volume are employed, then the calculation of the phonon frequencies as obtained from the diagonalization of the free-energy Hessian leads to phonon spectra in good agreement with experimental data for both systems. In PbTe we evaluate the linear thermal expansion coefficient $\ensuremath{\gamma}=2.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{4.pt}{0ex}}{\text{K}}^{\ensuremath{-}1}$, finding it to be in good agreement with experimental value of $\ensuremath{\gamma}=2.04\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{4.pt}{0ex}}{\text{K}}^{\ensuremath{-}1}$. Furthermore, we study the phonon spectrum and we do reproduce the transverse optical mode phonon satellite detected in inelastic neutron scattering and the crossing between the transverse optical and the longitudinal acoustic modes along the $\mathrm{\ensuremath{\Gamma}}\mathrm{X}$ direction. The phonon satellite becomes broader at high temperatures but its energy is essentially temperature independent, in agreement with experiments. We decompose the self-consistent harmonic free energy in second-, third-, and fourth-order anharmonic terms. We find that the third- and fourth-order terms are small. However, treating the third-order term perturbatively on top of the second-order self-consistent harmonic free energy overestimates the energy of the satellite associated with the transverse optical mode. On the contrary, a perturbative treatment on top of the harmonic Hamiltonian breaks down and leads to imaginary phonon frequencies already at 300 K. In the case of SnTe, we describe the occurrence of a ferroelectric transition from the high-temperature $Fm\overline{3}m$ structure to the low-temperature $R3m$ one. The transition temperature is, however, underestimated with respect to the experimental one. No satellites are present in the SnTe phonon spectra despite a not negligible anharmonic broadening of the zone-center TO mode.

Asymptotic Stability of Economic NMPC: The Importance of Adjoints

Recently, it has been shown in a sampled-data continuous-time setting that under certain regularity assumptions a simple linear end penalty enforces exponential stability of Economic (nonlinear) Model Predictive Control (EMPC) without terminal constraints. This paper investigates the same framework in the discrete-time case, i.e. we establish sufficient conditions for asymptotic stability of the optimal steady state under an EMPC scheme without terminal constraints. The key ingredient is a linear end penalty that can be understood as a gradient correction of the stage cost by means of the adjoint/dual variable of the underlying steady-state optimization problem. Although almost all stability proofs for EMPC focus on primal variables, our developments elucidate the importance of the adjoints for achieving asymptotic stability without terminal constraints. Moreover, we propose an adaptive gradient correction strategy which alleviates the need for solving explicitly the steady-state optimization. Finally, we draw upon two simulation examples to illustrate our results.

An Adaptive Policy Evaluation Network Based on Recursive Least Squares Temporal Difference With Gradient Correction

Reinforcement learning (RL) is an important machine learning paradigm that can be used for learning from the data obtained by the human–computer interface and the interaction in human-centered smart systems. One of the essential problems in RL algorithms is the value functions. Value functions are usually estimated via linearly parameterized value functions. Prior RL algorithms that generalize in this way required learning times tuning the linear weights leaving out the basis function. In fact, basis functions in value function approximation also have a significant influence on the performance. In this paper, a new adaptive policy evaluation network based on recursive least squares temporal difference (TD) with gradient correction (adaptive RC network) is proposed. Basis functions in the proposed algorithm were adaptive optimized, mainly aiming at the widths. In the proposed algorithm, TD error and value function were estimated by RC algorithm and value function approximation. The gradient derived from the squares of TD error was used to update the widths of basis functions. Therefore, the RC network can adjust its network parameters in an adaptive way with a self-organizing approach according to the progress in learning. Empirical results based on the three RL benchmarks show the performance and applicability of the proposed adaptive RC network.

Adaptation strategies for tracking constraints under plant-model mismatch

Optimal operating conditions for a process plant are typically obtained via model-based optimization. However, due to modeling errors, the operating conditions found are often sub-optimal or, worse, they can violate critical process constraints. Hence, model corrections become a necessity and are done by exploiting measured process data. To this end, either model parameters are adapted and/or correction terms are added to the model-based optimization problem. The modifier-adaptation methodology does the latter by adding bias and gradient correction terms that are called modifiers. The role of modifiers and model parameters are often seen as competing, and which one of the two is better suited to track the optimality conditions is an open problem. This paper attempts to shed light on finding a synergy between the model parameters and the modifiers in the case when tracking constraints is sufficient for near-optimal performance. We demonstrate through the simulation study of a batch-to-batch optimization problem that a set of model parameters can be selected that mirror the role of modifiers. The modifiers are then added only when there is insufficient number of mirror parameters for independent constraint tracking.

Enforcing Model Adequacy in Real-Time Optimization via Dedicated Parameter Adaptation

Iterative real-time optimization schemes that employ modifier adaptation add bias and gradient correction terms to the model that is used for optimization. These affine corrections lead to meeting the first-order necessary conditions of optimality of the plant despite plant-model mismatch. However, since the added terms do not include curvature information, satisfaction of the second-order sufficient conditions of optimality is not guaranteed, and the model might be deemed inadequate for optimization. In the context of modifier adaptation, this paper proposes to include a dedicated parameter-estimation step such that also the second-order optimality conditions are met at the plant optimum. In addition, we propose a procedure to select the best parameters to adapt based on a local sensitivity analysis. A simulation study dealing with product maximization in a fed-batch reactor demonstrates that the proposed scheme can both select the right parameters and determine their values such that modifier adaptation can drive the plant to optimality fast and without oscillations.

Experimental Design in Simultaneous Identification and Optimization of Batch Processes under Model-Plant Mismatch

Model-plant mismatch commonly arises from simplifications and assumptions during the development of first-principles models. Hence, when employing such models in iterative optimization schemes, structural mismatch may lead to inaccurate prediction of the necessary conditions of optimality. This results in convergence to a predicted optimum which does not coincide with the actual process optimum. The method of simultaneous identification and optimization aims to correct for errors in the predicted gradients of the cost and constraints by adapting the model parameters. In a former implementation of this approach, the gradients have been corrected only locally at the current operating point. To achieve a better prediction of the cost function over a wider range of input conditions, we propose to consider cost measurements from previous batch experiments combined with an optimal experimental design of future experiments. Using this approach, it is possible to achieve a better prediction, especially around the optimum, and to make the gradient correction step less susceptible to uncertainty in local gradient measurements. The improvements are illustrated using a simulated run-to-run optimization study of a cell-culture process.

요부 안정화운동이 대학생들의 자세균형, 어깨 기울기 및 거북목 자세에 미치는 영향

The purpose of this study was to measure and analyse the changes in postural balance, shoulder gradient and forward head posture after 8 weeks lumbar stabilization exercise by dividing the male and female college students who are attending universities into two groups: the group of lumbar tabilization exercise of 12 individuals and the control group of 15. The study findings are as follows: In Lt/Rt balance, especially in Lt, the group of stabilization exercise group increase by 0.14% and the control group by 2.89% and in Rt, the control group declined by 2.45%, whereas the group of stabilization exercise group increased by 0.13%, but there was no statistical significance. In shoulder gradient, especially in Lt, the group of stabilization exercise group got declined by 27.96%, which showed a statistically significant difference(p<.05) and the control group also got increase by 10.12%, which wasn’t statistically significant. In relation to forward head posture, the group of stabilization exercise group declined by 8.11% on average than the control group, which showed a statistically significant difference(p<.05). Taken together, it appears that the lumbopelvic stabilization exercise has a positive impact on shoulder gradient balance and correction of forward head posture in college students and thus is considered to be strongly encouraged in the clinical settings.

An Implicit SPH Formulation for Incompressible Linearly Elastic Solids

AbstractWe propose a novel smoothed particle hydrodynamics (SPH) formulation for deformable solids. Key aspects of our method are implicit elastic forces and an adapted SPH formulation for the deformation gradient that—in contrast to previous work—allows a rotation extraction directly from the SPH deformation gradient. The proposed implicit concept is entirely based on linear formulations. As a linear strain tensor is used, a rotation‐aware computation of the deformation gradient is required. In contrast to existing work, the respective rotation estimation is entirely realized within the SPH concept using a novel formulation with incorporated kernel gradient correction for first‐order consistency. The proposed implicit formulation and the adapted rotation estimation allow for significantly larger time steps and higher stiffness compared to explicit forms. Performance gain factors of up to one hundred are presented. Incompressibility of deformable solids is accounted for with an ISPH pressure solver. This further allows for a pressure‐based boundary handling and a unified processing of deformables interacting with SPH fluids and rigids. Self‐collisions are implicitly handled by the pressure solver.

Modeling of orthogonal cutting process of A2024-T351 with an improved SPH method

Modeling the cutting process is traditionally based on the finite element method (FEM). All element-based numerical methods, however, have difficulties in handling with extremely large deformation and material fragmentation that always occur in cutting processes. In contrast, mesh-free methods such as smoothed-particle hydrodynamics (SPH) have a lot of attractive features in solving extremely large deformation problems. This work introduces first an improved SPH method and then applies it to further develop a cutting model for A2024-T351 materials to predict cutting forces and chip morphology under different cutting conditions. The improvement to the traditional SPH is achieved through modifying schemes for approximating density (density correction) and kernel gradient (kernel gradient correction). The simulation results demonstrate the improved SPH is more stable and accurate compared with the traditional SPH that is implemented in the commercial code LS-DYNA® and element-based numerical methods in FEM models. Numerical tests show that the improved SPH cutting model better explains the shear-localized chip formation and correctly estimates the chip morphology as well as the cutting forces.

Gradient correction and Bohm potential for two‐ and one‐dimensional electron gases at a finite temperature

From the static polarization function of electrons in the random phase approximation, the quantum Bohm potential for the quantum hydrodynamic description of electrons and the density gradient correction to the Thomas–Fermi free energy at a finite temperature for the two‐ and one‐dimensional cases are derived. The behaviour of the Bohm potential and of the density gradient correction as a function of the degeneracy parameter is discussed. Based on recent developments in the fluid description of quantum plasmas, the Bohm potential for the high‐frequency domain is presented.

Simulations for soil explosion and its effects on structures using SPH method

The numerical simulation of landmine detonation is an extremely difficult task. In this paper, the Smoothed Particle Hydrodynamics (SPH) method is employed to tackle explosion in soil with extremely large deformation and the effects of blast on structures. Firstly, the basic idea of the SPH method and techniques related to the Monaghan-type artificial viscosity, interface treatment with high density ratio, boundary condition implementation, artificial stress, kernel gradient correction, and physical variables update are elaborated. Then three benchmark problems are carried out to validate the explosion, soil and structure models, respectively. Afterwards, the simulations of the explosion in soil and its loading on structures have been conducted on the basis of the verification of these three models. It was observed that the numerical calculations are in good agreement with the experimental results, which shows that the SPH method can handle large deformation problems with high density ratio effectively.

A stabilised mixed meshfree method for incompressible media: Application to linear elasticity and Stokes flow

This paper addresses some problems of modelling incompressible media using meshfree methods with a stabilised mixed formulation. The aims of this paper are twofold: to avoid the volumetric locking that occurs at the incompressible limit; and to circumvent the inf–sup condition while approximating both displacement and pressure with the same set of nodes and shape functions. We employ a modified polynomial pressure projection stabilisation method to stabilise and filter spurious pressure modes, where the gradient is corrected as proposed by Duan et al. (2014). The gradient correction is used to counteract the lack of variational consistency when numerical integration of the rational shape functions is performed, a threat that could undermine the stabilisation effort. The resulting novel method passes the mixed patch tests, and is demonstrated to be effective and optimally accurate in linear elasticity and Stokes flow test cases.

Interaction of solid and polymeric lithium electrolytes with composites based on carbon fibers and silicon nanoclusters: Quantum-chemical modeling

In the framework of the search for promising electrodes and membranes for lithium-ion batteries, quantum-chemical modeling of the contact area of the solid (Li10GeP2S12) and polymeric LiNafion · nDMSO-based electrolytes with an anode as carbon fibers coated with silicon nanoclusters (Si n C m ) has been performed by the density functional theory method with inclusion of gradient correction and periodic conditions (PBE/PAW). It has been found that the polymeric electrolytes form a better contact with the electrode surface than the solid electrolytes. The barriers to lithium transport in the polymeric LiNafion · nDMSO-based electrolyte have been estimated at 0.3 eV, and those to Li migration from the electrolyte into the electrode have been estimated at 0.4 eV.

Mean stress effects in fretting fatigue life estimation method using fatigue damage gradient correction factor

In our previous study, we developed a fretting fatigue life estimation method that considers stress gradient effect [Journal of Mechanical Science and Technology 28 (2014) 2153–2159]. In this method, fatigue damage value at the cracking location is corrected with the factor that is a function of fatigue damage gradient, and the corrected value is treated as the fatigue damage value in plain fatigue for life estimation. In the present study, we examined the effect of mean stress on fatigue damage gradient correction function, because the reliability of the developed method was only verified at a stress ratio (R) of −1 in previous studies. Fretting fatigue experiments were conducted to obtain the fatigue life data of three different fretting pad shapes with R values ranging from −1.0 to 0.3. Finite element analyses were then conducted to evaluate the fatigue damage parameter in the cracking region. The results revealed that fretting fatigue life decreases at increased stress ratio. Furthermore, the fatigue damage gradient correction function was unaffected by the stress ratio, although it is affected by plastic deformation at the cracking location. Thus, a correction function for the occurrence of plastic deformation and another for the absence of plastic deformation are necessary. The developed method was demonstrated to predict the fretting fatigue life at various levels of stress ratio with the use of plain fatigue data.

Airy-averaged gradient corrections for two-dimensional fermion gases

Building on the discussion in Trappe et al. (2016), we present a systematic derivation of gradient corrections to the kinetic-energy functional and the one-particle density, in particular for two-dimensional systems. We derive the leading gradient corrections from a semiclassical expansion based on Wigner’s phase space formalism and demonstrate that the semiclassical kinetic-energy density functional at zero temperature cannot be evaluated unambiguously. In contrast, a density-potential functional description that effectively incorporates interactions provides unambiguous gradient corrections. Employing an averaging procedure that involves Airy functions, thereby partially resumming higher-order gradient corrections, we facilitate a smooth transition of the particle density into the classically forbidden region of arbitrary smooth potentials. We find excellent agreement of the semiclassical Airy-averaged particle densities with the exact densities for very low but finite temperatures, illustrated for a Fermi gas with harmonic potential energy. We furthermore provide criteria for the applicability of the semiclassical expansions at low temperatures. Finally, we derive a well-behaved ground-state kinetic-energy functional, which improves on the Thomas–Fermi approximation.