Splitting Method Research Articles

Distributed Charging Strategy of PEVs in SCS with Feeder Constraints Based on Generalized Nash Equilibria

In this article, a distributed charging strategy problem for plug-in electric vehicles (PEVs) with feeder constraints based on generalized Nash equilibria (GNE) in a novel smart charging station (SCS) is investigated. The purpose is to coordinate the charging strategies of all PEVs in SCS to minimize the energy cost of SCS. Therefore, we build a non-cooperative game framework and propose a new price-driven charging control game by considering the overload constraint of the assigned feeder, where each PEV minimizes the fees it pays to satisfy its optimal charging strategy. On this basis, the existence of GNE is given. Furthermore, we employ a distributed algorithm based on forward–backward operator splitting methods to find the GNE. The effectiveness of the employed algorithm is verified by the final simulation results.

A formulated method for streams splitting in heat exchanger network design using pinch analysis

Abstract Thermal processes constitute a significant portion of energy consumption in the industrial sector. In this context, Pinch Analysis has emerged as a powerful method for achieving substantial energy savings. By systematically analyzing process streams and their heat transfer characteristics, Pinch Analysis enables the identification of heat re-covery opportunities, leading to the design of an optimized heat exchangers network (HEN) that minimizes energy requirements. In this study, a formulated stream split-ting method is proposed to design feasible Minimum Energy Requirement (MER) heat exchangers network. This method aims to achieve two main goals. Firstly, it gives a practical formulated method to help the designer when splitting streams and focuses on splitting the streams in such a way that creates sub-streams with the exact enthalpy required to satisfy heat exchanges with a specific number of streams, in order to minimize the need for process-utility heat exchangers whenever possible. Additionally, the method aims to eliminate exergy destruction caused by temperature differences in the mixer used to recombine the split streams, by ensuring an isothermal mixture of streams, preventing unnecessary energy losses. The design of the heat exchanger net-work is conducted using the HINT software, allowing for a comprehensive and detailed analysis of each step. The results obtained shows that the heat exchangers network attained not only achieves the minimum energy consumption but also mitigates exergy destruction and avoid unnecessary process-utility heat exchangers, resulting in enhanced overall system performance

Analysis and Design of Adjustable-Gap Double-Side Axial Flux Permanent Magnet Hysteresis Damper

In this paper, a novel adjustable gap double-side axial flux permanent magnet hysteresis damper (AGDSAPHD) is proposed, of which the torque can be adjusted by changing the air gap and the magnetic field angle between the upper and lower stators at the same time. To analyze and design, a modified vector Jiles-Atherton (JA) hysteresis model is used for simulating the magnetic flux distribution and the hysteresis torque of AGDSAPHD. The eddy currents in the AGDSAPHD are analyzed, which have a great influence on the output torque when the rotational speed is fast. A splitting method used in the rotor of the AGDSAPHD is proposed to reduce the effect of eddy currents. The heat distribution of the AGDSAPHD is calculated to determine its slip power and operating mode. A prototype is built and tested to verify the reliability of the analysis. The experiments prove that the modified vector JA model has high computational accuracy in calculating the hysteresis effects of the AGDSAPHD. A splitting method used in the rotor can greatly reduce the eddy current torque. AGDSAPHD has a greater torque adjustment range and better temperature stability than the traditional one.

A uniform kernel trick for high and infinite-dimensional two-sample problems

We use a suitable version of the so-called ”kernel trick” to devise two-sample tests, especially focussed on high-dimensional and functional data. Our proposal entails a simplification of the practical problem of selecting an appropriate kernel function. Specifically, we apply a uniform variant of the kernel trick which involves the supremum within a class of kernel-based distances. We obtain the asymptotic distribution of the test statistic under the null and alternative hypotheses. The proofs rely on empirical processes theory, combined with the delta method and Hadamard directional differentiability techniques, and functional Karhunen-Loève-type expansions of the underlying processes. This methodology has some advantages over other standard approaches in the literature. We also give some experimental insight into the performance of our proposal compared to other kernel-based approaches (the original proposal by Borgwardt et al. (2006) and some variants based on splitting methods) as well as tests based on energy distances (Rizzo et al., 2017).

Real option pricing under the regime-switching model with jumps on a finite time horizon

We consider an irreversible investment decision problem on a finite time horizon where an instantaneous cash flow process of a firm follows a regime-switching jump-diffusion (RSJD) model. The value of a project can be derived from a partial integro-differential equation (PIDE) and then we obtain a closed-form solution of the PIDE. It is proved that the value of the project converges to the solution on an infinite time horizon problem as the lifetime of the project tends to infinity. Moreover, the value function of a real option with a finite expiration date can be evaluated by solving a linear complementarity problem (LCP) under the RSJD model. We apply a 2-step backward differentiation formula (BDF2 method) combined with an operator splitting method to solve the LCP and then it has the second-order convergence rate in the discrete ℓ2-norm with respect to the time and spatial variables. The stability of the proposed method to solve the LCP is also proved in the discrete ℓ2-norm. Finally, a variety of numerical experiments are carried out to determine the optimal investment time and the numerical results on the finite time horizon are analyzed.

Стационарное протекание несжимаемой вязкой жидкости сквозь двухмерный разветвленный канал

The results of a numerical experiment for the problem of an incompressible viscous fluid stationary flow through a branched planar (two-dimensional) channel are presented. The region in which the flow occurs simulates either blood vessels or a river delta. The finite element method and a modification of the penalty method, as well as the splitting method, are used for calculations. The implementation of the calculation algorithm is using with the help the package FreeFem++. The main goal, in addition, of course, to study the properties and structure of the stationary flow, is to demonstrate the effectiveness of the proposed modification of the penalty method. It is assumed that the region has one input boundary section through which the liquid flows into the region, and several (five) boundary sections through which the liquid flows out of the region. The remaining sections of the region boundary are considered impermeable to liquid. The boundary condition corresponding to the Poiseuille flow in a plane rectilinear channel is set at the input section. Three types of boundary conditions are considered on the output boundary secctions. 1. The boundary conditions correspond to the conditions of conservation of motion of luid particles i. e. the material derivative of the velocity is zero. 2. The boundary conditions correspond to the setting of the flow velocity. 3. The boundary conditions correspond to the setting of the same pressure. The stationary solution is constructed by the relaxation method. In fact, a non-stationary problem is solved over a sufficiently large time interval. As an initial condition for a non-stationary problem, a flow is chosen that is a Poiseuille flow in some region near the input boundary. The dependence of the convergence rate of the relaxation method on the initial data is investigated. It is found that the Poiseuille flow, given at the input section of the boundary of the region, induces similar Poiseuille flows at the output boundaries sections of the region in all these cases of boundary conditions. For a region with five sections of the output boundaries for some configuration of the region, the presence of stationary vortex flows (‘maelstorm’) is found.

Fractional guidance-based level set evolution for noisy image segmentation with intensity inhomogeneity

Intensity inhomogeneity (IIH) and noise are ubiquitous in images acquired by a variety of imaging modalities, which pose an ongoing challenge for segmentation methods used in many applications. This paper proposes a level set evolution equation based on fractional derivative to address the IIH and noise issues in image segmentation, which integrates the information from the input and guidance images. The proposed model is a linear diffusion equation of level set function with nonlinear edge-stopping and guidance sources, in which the edge-stopping source is derived from the input image and a local statistical model (Bayesian formulation) in the level set framework, whereas the guidance source is derived from the guidance image and the fitting term of the popular Chan-Vese model. The guidance source ensures swift contour movement toward the boundary of the objects and enhances the robustness to noise and contour initialization, while the edge-stopping source is used to stop the evolving contour on the boundary of the objects later in the evolution. To tackle the challenge of obtaining accurate guidance images for many applications, an adaptive variable-order of fractional derivative robust to IIH and noise is introduced to generate the desired guidance image from the input image. The proposed diffusion equation with sources is solved numerically by the series splitting method and finite difference scheme. Experimental results on synthetic and real images show that the proposed model has higher performance in terms of accuracy and efficiency of segmentation, compared to several state-of-the-art level set models.

Riemannian quantum circuit optimization for Hamiltonian simulation

Hamiltonian simulation, i.e. simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful approximation can lead to relatively deep circuits. Here we start from the insight that for translation invariant systems, the gates in such circuit topologies can be further optimized on classical computers to decrease the circuit depth and/or increase the accuracy. We employ tensor network techniques and devise a method based on the Riemannian trust-region algorithm on the unitary matrix manifold for this purpose. For the Ising and Heisenberg models on a one-dimensional lattice, we achieve orders of magnitude accuracy improvements compared to fourth-order splitting methods. The optimized circuits could also be of practical use for the time-evolving block decimation algorithm.

An effective numerical method for the vector-valued nonlocal Allen–Cahn equation

Nonlocal Allen–Cahn model and their numerical schemes have received great attention in the literature as nonlocal model becomes popular in various fields. Our main idea in this work is to consider the vector-valued nonlocal Allen–Cahn model, which is a coupled system of nonlinear partial differential equations. Then, with the help of the operator splitting method and finite difference method, a fully-decoupled and energy stable numerical scheme for the vector-valued nonlocal Allen–Cahn model is proposed. Furthermore, we prove the modified energy dissipation law is unconditionally guaranteed and it is closely related to classical energy up to O(τ). Finally, numerical examples are carried out to verify the efficiency and accuracy of the proposed scheme.

The generalized Riemann problem scheme for a laminar two-phase flow model with two-velocities

In this paper, we propose a generalized Riemann problem (GRP) scheme for a laminar two-phase flow model. The model takes into account the distinctions between different densities and velocities, and is obtained by averaging vertical velocities across each layer for the two-phase flows. The rarefaction wave and the shock wave are analytically resolved by using the Riemann invariants and Rankine-Hugoniot condition, respectively. The source term is incorporated into the resolution of the GRP method. We further extend the GRP method to the two-dimensional (2-D) system, which is non-conservative. The Strang splitting method is applied, but it still can not provide explicit Riemann invariants and shock relations, which prevent us to apply the GRP method directly. Another splitting technique is also applied to the 2-D case, such that each split subsystem contains only one family of waves. Numerical experiments on some typical problems show that the proposed method achieves good performance.

Multi-back-propagation Algorithm for Signal Neural Network Decomposition

In this paper, a novel back-propagation error technique is presented. This neural network structure allows for two fundamental basic modes: (1) To decompose the neurones by transforming their variables, weights, and scalar functions into vectors. This conveys for the decomposition of the transfer function of every neurone (where the output variables are the components of the decomposition) and, consequently, to be written as the invariant sum of orthogonal functions, with the safeguard of preserving information This orthogonality is proven using Fourier theory. (2) In a second mode, a tuned neural network that occupies one of the channels of the neural network can see the weights of its supplementary channels adjusted to retain additional information. Only the decomposition algorithm of the network is presented here—Multi-back-propagation algorithm. The adopted methodology is validated step-by-step with some representative examples. Namely, to assess the performance of the splitting method, two different examples have been constructed from scratch: (1) a 2D classification problem and (2) a 3D surface. In both problems, the signal and transfer functions of the neural network are successfully decomposed without information losses. Therefore, since the main contribution of this work is to allow for the organisation of the information stored in neural network structure, through a split process, this promising method shows potential use in various areas—e.g. classification and/or pattern recognition problems, data analysis, modelling and so on. In the future, we expect to work further in the method computational aspects to render it more efficient, versatile and robust.

A Gaussian-mixture-model based peak splitting method in X-ray fluorescence for high concentration ratio solution

Simultaneous detection of multi-heavy metal ions in zinc sulfate solution facilitates the zinc hydrometallurgy process control. X-ray fluorescence spectrometry is widely used for composition detection due to its high detection speed and no sample pre-treatment. However, the high matrix ion-to-trace impurity ion ratio in zinc sulfate causes severe spectral overlap, hindering pure peak area acquisition—a vital feature in ion concentration detection. To address this, a peak-splitting method based on the Gaussian mixture model was proposed. Initially, two ion mixing spectra were obtained with optimized reagents. Subsequently, Gaussian models were established for the characteristic peak regions with varying distributions. Finally, the proposed model was combined with Chaotic Sparrow Search Algorithm to handle the overlapping peaks. The experimental results demonstrated superior stability and additivity compared to other methods. All coefficients of determination between single peak areas and ion concentrations exceeded 0.99, confirming the method's efficacy in resolving heavily masked overlapping peaks.

Prototype development and evaluation of a hyperspectral lidar optical receiving system.

As a new type of active Earth observation technology, airborne hyperspectral lidar combines the advantages of traditional lidar 3D information acquisition and passive hyperspectral imaging technology, and it can achieve integrated imaging detection with a high spatial and hyperspectral resolution. Thus, it has become an important future direction of Earth surface remote sensing technology. This article introduces the design and development of an airborne hyperspectral imaging lidar system. The hyperspectral lidar adopts a focal plane splitting method, combined with an array of 168 optical fibers, to couple wide-spectral-range laser echo signals one by one to the corresponding single tube detector, achieving efficient splitting and precise coupling of supercontinuum laser pulse echo signals. This article proposes a fast synchronous calibration method that is suitable for hyperspectral imaging lidar systems. Results show that the spectral range of the hyperspectral lidar system is 400-900 nm, and the spectral resolution of single-fiber detection is greater than 3 nm. Notably, this article focuses on analyzing the abnormal detection channels based on the calibration results. With the test results of adjacent channels combined, the reason for the abnormal spectral bandwidth of channel 17 is analyzed as an example. This research points out the direction for verifying the design parameters of the hyperspectral lidar prototype and lays an important foundation for airborne flight test of the hyperspectral lidar.

Decay characterization of solutions to incompressible Navier–Stokes–Voigt equations

Recently, Niche [J. Differential Equations, 260 (2016), 4440–4453] established upper bounds on the decay rates of solutions to the 3D incompressible Navier–Stokes–Voigt equations in terms of the decay character r ∗ of the initial data in H 1 ( R 3 ). Motivated by this work, we focus on characterizing the large-time behavior of all space-time derivatives of the solutions for the 2D case and establish upper bounds and lower bounds on their decay rates by making use of the decay character and Fourier splitting methods. In particular, for the case − n 2 < r ∗ ⩽ 1, we verify the optimality of the upper bounds, which is new to the best of our knowledge. Similar improved decay results are also true for the 3D case.

Midpoint splitting methods for nonlinear space fractional diffusion equations

We propose a midpoint splitting method to solve nonlinear space fractional diffusion equations. We first discretize the equation in space using the weighted and shifted Grünwald difference (WSGD) operators. Then, we obtain the fully discrete scheme of the equation using the midpoint splitting method, which can alleviate computational costs and mitigate instability issues that may arise. We establish the stability result of the fully discrete scheme under certain conditions. Finally, we demonstrate its feasibility and efficiency through numerical examples.

The Cauchy problem for an inviscid and non-diffusive Oldroyd-B model in two dimensions

A two-dimensional inviscid and diffusive Oldroyd-B model was investigated by Elgindi and Rousset (2015) where the global existence and uniqueness of the strong solution were established for arbitrarily large initial data. As pointed out by Bhave et al. (1991), since the diffusion coefficient is significantly smaller than other effects, it is interesting to study the non-diffusive model. In the present work, we obtain the global-in-time existence and uniqueness of the strong solution to the non-diffusive model with small initial data by deriving some uniform regularity estimates and taking vanishing diffusion limits. In addition, the large time behavior of the solution is studied and the optimal time-decay rates for each order of spatial derivatives are obtained. The main challenges focus on the lack of dissipation and regularity effects of the system and on the slower decay in the two-dimensional settings. A combination of the spectral analysis and the Fourier splitting method is adopted.

A Building Model for Enhancing Information Systems Security

Today, electronic systems and information have become no less important than food and water for human life. No one can deny this fact. Electronic information systems contribute to the development of life in many areas. But some electronic information systems should not be available for anyone to use, such as reading, operating, modifying or destroying without permission. This type of electronic information systems must be protected in some way based on the related situation. . Password-based authentication is the first defense for most information systems. Password security enhances the security of the entire information system. Therefore, password protection models become very important in such cases to help users improve authentication security. Researchers published various methods based on salting, hashing, symmetric encryption, and key splitting methods. The paper conducted by Saleh Al-Asali describes a method for generating a suitable secret key that is easy to memorize and remember, as he succeeded in generating a password that is strong and easy to remember. This paper improves the previous method by adding some improvements mentioned in the section described in the suggested method.

New third-order convex splitting methods and analysis for the phase field crystal equation

New third-order convex splitting methods and analysis for the phase field crystal equation

The Second-Order Numerical Approximation for a Modified Ericksen–Leslie Model

In this study, two numerical schemes with second-order accuracy in time for a modified Ericksen–Leslie model are constructed. The highlight is based on a novel convex splitting method for dealing with the nonlinear potentials, which is integrated with the second-order backward differentiation formula (BDF2) and leap frog method for temporal discretization and the finite element method for spatial discretization. The unconditional energy stability of both schemes is further demonstrated. Finally, several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed schemes.

Mixed Gaussian-impulse noise removal using non-convex high-order TV penalty

To restore images with clear edge details and no staircase artifacts from degraded versions, this paper incorporates the ℓ2 plus ℓ0 data fidelity and non-convex high-order total variation regularizer to establish an optimization model for eliminating mixed Gaussian-impulse noise. Among them, the ℓ2 fidelity is adopted to suppress Gaussian noise, while the ℓ0-norm is more suitable for detecting and removing impulse noise. In addition, the non-convex regularization displays excellent performance in overcoming the staircase effect and preserving edge details. Computationally, by using the iteratively reweighted ℓ1 algorithm and variable splitting method, this work designs a modified alternating minimization method to solve the optimization problem we construct. In theory, the convergence proof of our resulting algorithm is also presented. Finally, in the experimental section, we conduct extensive numerical experiments on degraded images and compare with other existing techniques. From the intuitive effects and restoration accuracy, it follows that our newly proposed method is effective and competitive for image deblurring and mixed noise removal.