Discrete Iteration Research Articles

Discrete Spectrum Iteration Based Comprehensive Stability Assessment Method for the Delayed Cyber-Physical System With Electric-Vehicle Frequency Regulation

Nowadays, the increasing penetration of renewable energies often leads to system frequency variation due to the intermittent outputs, which limits the utilization of renewable electricity and brings higher requirements to frequency regulation. Aggregated electric vehicles (EVs) are suggested to be used as good regulation resources because of the vehicle-to-grid (V2G) capability and quick response characteristic. However, the participation of EVs inevitably leads to cyber delays due to their underlying communication infrastructure and scheduling, which may cause instability. To guarantee the system stability, this paper investigates the stability of a grid frequency regulation system with electric vehicle (EV) aggregators embedded by cyber delays in the cyber system. A comprehensive stability assessment method is proposed in this paper based on the discrete spectrum iteration. A stability assessment method flow is designed with only five stages: 1) system initialization and modeling; 2) spectrum transformation; 3) Chebyshev discretization; 4) Krylov subspace projection dimension reduction; 5) Newton correction. Comprehensive case studies are performed on the cyber regulation systems with single, double, and three EV aggregators to extract the stability region and to validate the proposed approach. It is revealed that the controller gain, the ratio between the participation ratios of each aggregator, and that between EV and grid are important factors for determining the stability of the regulation system at a given controller gain. Besides, the criterion of the stability region changing with the three factors is proposed. It is found that the mass utilization of electric vehicles in the frequency control disrupts system stability due to the aggregation delay and thus the stability region can be divided into several intervals and presents periodicity. It is expected that the proposed criteria can help to guide the determination of delay requirements for EV aggregators participating in frequency regulation service.

A numerical study on the non‐isothermal flow characteristics and hydrate risk of CO2 in buried transmission pipelines under the gas‐phase transportation mode

AbstractWith the development and progress of carbon dioxide (CO2) capture and storage technology, the study of the flow assurance of CO2 in transmission pipelines needs to be further deepened. In this study, aiming at the gas‐phase transportation mode of CO2, first, a new prediction model of temperature, pressure as well as hydrate formation risk in buried CO2 transmission pipelines is established. Second, the model solving methods of differential discretization and piecewise iteration are introduced in detail. Third, model validation and sensitivity analysis of typical transmission parameters are performed. The results show that: (a) there is good agreement between the model prediction results and software simulation results. (b) The subcooling and the length of the hydrate formation region increase with the increase in the transmission rate. Appropriate increase in the CO2 transmission rate can reduce the risk of hydrate formation in CO2 transmission pipelines. (c) The subcooling and the length of the hydrate formation region decrease as the transmission temperature increases. In order to prevent hydrate risk in the CO2 transmission process, low transmission temperatures should be avoided. (d) The subcooling and the length of the hydrate‐formation area increase first and then decrease as the transmission pressure increases. Appropriate increase in CO2 transmission pressure is conducive to avoiding hydrate formation risk. This study provides basic theoretical guidance for optimizing transmission parameters and risk assessment of hydrate formation in CO2 transmission pipelines. © 2019 Society of Chemical Industry and John Wiley & Sons, Ltd.

A Novel Iterative Discrete Estimation Algorithm for Low-Complexity Signal Detection in Uplink Massive MIMO Systems

In this paper, a novel iterative discrete estimation (IDE) algorithm, which is called the modified IDE (MIDE), is proposed to reduce the computational complexity in MIMO detection in uplink massive MIMO systems. MIDE is a revision of the alternating direction method of multipliers (ADMM)-based algorithm, in which a self-updating method is designed with the damping factor estimated and updated at each iteration based on the Euclidean distance between the iterative solutions of the IDE-based algorithm in order to accelerate the algorithm’s convergence. Compared to the existing ADMM-based detection algorithm, the overall computational complexity of the proposed MIDE algorithm is reduced from O N t 3 + O N r N t 2 to O N t 2 + O N r N t in terms of the number of complex-valued multiplications, where Ntand Nr are the number of users and the number of receiving antennas at the base station (BS), respectively. Simulation results show that the proposed MIDE algorithm performs better in terms of the bit error rate (BER) than some recently-proposed approximation algorithms in MIMO detection of uplink massive MIMO systems.

Discretization of homogeneous systems using Euler method with a state-dependent step

Numeric approximations to the solutions of asymptotically stable homogeneous systems by Euler method, with a step of discretization scaled by the state norm, are investigated (for the explicit and implicit integration schemes). It is proven that for a sufficiently small discretization step the convergence of the approximating solutions to zero can be guaranteed globally in a finite or a fixed time depending on the degree of homogeneity of the system, but in an infinite number of discretization iterations. The maximal admissible step can be estimated by analyzing the system properties on the sphere. It is shown that the absolute and relative errors of the discretizations are globally bounded functions, thus the approximations approaching the solutions with the step converging to zero. In addition, it is established that the proposed discretization approach preserves robustness with respect to exogenous perturbations. Efficiency of the designed discretization algorithms is demonstrated in simulations.

Distortion-aware image retargeting based on continuous seam carving model

The seam-carving algorithm is a classic context-aware image retargeting method and has been extensively studied for years; however, distortions exist as the discrete iteration of least- energy computation. We propose a continuous seam carving model through the just noticeable distortion (JND) detection at every iteration and accumulative energy weight. The JND of every pixel is calculated by the minimal just-noticeable distortion energy of adjacent-pixel conflicting displacements between seam carving iterations. The mean field approximation is used to efficiently solve the problem. In this way, the proposed energy weight can accumulatively calculate the JND information of recent k iterations and passed down to the next iteration for distortion avoidance. The superior performance of the proposed continuous seam carving model, as compared with state-of-art image retargeting approaches in RetargetMe database, was demonstrated experimentally.

A Contrastive Study of Two Heaviside-based Morphological Filters

Morphological filters can be used to eliminate the numerical instabilities in topology optimization results, including the checkerboard patterns, mesh-dependence and intermediate densities. In this paper, two morphological filters, namely Type 1 and Type 2 filters are constructed according to the morphology-based restriction schemes. Type 1 filters are constructed using the Heaviside filter and the improved Heaviside filter proposed by Sigmund and, Type 2 filters are constructed using the Heaviside filter and the improved Heaviside filter proposed by Guest. The optimization effects of the two kinds of morphological filters are investigated, including the convergence, the ability to obtain discrete designs, iteration times and compliances. Test results show that open and close filters exhibit better performances than the advanced filters, and the advanced filters are inclined to produce instabilities during the optimization process.

Rayleigh quotient minimization for absolutely one-homogeneous functionals

In this paper we examine the problem of minimizing generalized Rayleigh quotients of the form , where both J and H are absolutely one-homogeneous functionals. This can be viewed as minimizing J where the solution is constrained to be on a generalized sphere with , where H is any norm or semi-norm. The solution admits a nonlinear eigenvalue problem, based on the subgradients of J and H. We examine several flows which minimize the ratio. This is done both by time-continuous flow formulations and by discrete iterations. We focus on a certain flow, which is easier to analyze theoretically, following the theory of Brezis on flows with maximal monotone operators. A comprehensive theory is established, including convergence of the flow. We then turn into a more specific case of minimizing graph total variation on the L1 sphere, which approximates the Cheeger-cut problem. Experimental results show the applicability of such algorithms for clustering and classification of images.

Iterative Spatial Updating During Forward Linear Walking Revealed Using a Continuous Pointing Task

The continuous pointing task uses target-directed pointing responses to determine how perceived distance traveled is estimated during forward linear walking movements. To more precisely examine the regulation of this online process, the current study measured upper extremity joint angles and step-cycle kinematics in full vision and no-vision continuous pointing movements. Results show perceptual under-estimation of traveled distance in no-vision trials compared to full vision trials. Additionally, parsing of the shoulder plane of elevation trajectories revealed discontinuities that reflected this perceptual under-estimation and that were most frequently coupled with the early portion of the right foot swing phase of the step-cycle. This suggests that spatial updating may be composed of discrete iterations that are associated with gait parameters.

Discrete approximate iterative method for fuzzy investment portfolio based on transaction cost threshold constraint

Abstract There are many non-probability factors affecting financial markets and the return on risk assets is fuzzy and uncertain. The authors propose new risk measurement methods to describe or measure the real investment risks. Currently many scholars are studying fuzzy asset portfolios. Based on previous research and in view of the threshold value constraint and entropy constraint of transaction costs and transaction volume, the multiple-period mean value -mean absolute deviation investment portfolio optimization model was proposed on a trial basis. This model focuses on a dynamic optimization problem with path dependence; solving using the discrete approximate iteration method certifies the algorithm is convergent. Upon the empirical research on 30 weighted stocks selected from Shanghai Stock Exchange and Shenzhen Stock Exchange, a multi-period investment portfolio optimum strategy was designed. Through the empirical research, it can be found that the multi-period investments dynamic optimization model has linear convergence and is more effective. This is of great value for investors to develop a multi-stage fuzzy portfolio investment strategy.

Complex Dynamics of the Fractional-Order Rössler System and Its Tracking Synchronization Control

Numerical analysis of fractional-order chaotic systems is a hot topic of recent years. The fractional-order Rössler system is solved by a fast discrete iteration which is obtained from the Adomian decomposition method (ADM) and it is implemented on the DSP board. Complex dynamics of the fractional-order chaotic system are analyzed by means of Lyapunov exponent spectra, bifurcation diagrams, and phase diagrams. It shows that the system has rich dynamics with system parameters and the derivative order q. Moreover, tracking synchronization controllers are theoretically designed and numerically investigated. The system can track different signals including chaotic signals from the fractional-order master system and constant signals. It lays a foundation for the application of the fractional-order Rössler system.

Credibilitic Multiperiod Mean Semivariance Portfolio Selection with Transaction Costs

This paper proposes a credibilitic multiperiod mean-simivariance portfolio selection model with transaction costs, borrowing constraints, threshold constraints and cardinality constraints. In this model, the return rate of asset and the risk are quantified by credibilitic expected value and credibilitic semivariance, respectively. Threshold constraints limit the amount of capital to be invested in each stock and prevent very small investments in any stock. Based on credibilitic theories, the model is transformed into a mix integer dynamic optimization problem with path dependence. The proposed model is approximated to dynamic programming model. A novel discrete iteration method is designed to obtain the optimal portfolio strategy, and is proved linearly convergent. Finally, an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the Shanghai Stock Exchange.

A new methodology for history matching combining iterative discrete Latin Hypercube with multi-start simulated annealing

This paper introduces a new method for history matching, combining the Iterative Discrete Latin Hypercube (IDLHC) with multi-start Simulated Annealing methods. The proposed method, named IDLHCSA, combines the potential of the IDLHC in finding good matched models while preserving the diversity of solutions and the potential of the SA with local control in finding local (refined) solutions. The IDLHCSA was applied in two cases. The first is a simple reservoir model used as proof of concept. The second is a complex benchmark case (UNISIM-I-H) based on the Namorado field, located at the Campos Basin, Brazil. The robustness and effectiveness of the proposed method are demonstrated by comparison with other consolidated methods. It is demonstrated here that, when compared to other methodologies, the proposed method is more effective in finding multiple solutions for the history matching problem while maintaining solution diversity. The production forecast is analyzed and the predictive capacity of the matched models is assessed. The paper reveals that obtaining good matched models does not ensure reliable forecasts. The proposed method was able to find matched models which provided more reliable forecasts when compared to other methods.

RETRACTION: Peng Zhang, Chance-constrained multiperiod mean absolute deviation uncertain portfolio selection

In this paper, we propose a new multiperiod mean absolute deviation uncertain chance-constrained portfolio selection model with transaction costs, borrowing constraints, threshold constraints and cardinality constraints. In proposed model, the return rate of asset is quantified by uncertain expected value and the risk is characterized by uncertain absolute deviation. The chance constraints are that the uncertain expected return of the portfolio selection is bigger than the preset return of investors under the given confidence level. Cardinality constraints limit the number of assets in the optimal portfolio and threshold constraints limit the amount of capital to be invested in each asset and prevent very small investments in any asset. Based on uncertain theories, the model is converted to a dynamic optimization problem. Because of the transaction costs and cardinality constraints, the multiperiod portfolio selection is a mix integer dynamic optimization problem with path dependence, which is NP hard problem. The proposed model is approximated to a mix integer dynamic programming model. A novel discrete iteration method is designed to obtain the optimal portfolio strategy, and is proved linearly convergent. Finally, an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the Shanghai Stock Exchange.

Multiperiod mean absolute deviation uncertain portfolio selection with real constraints

Absolute deviation is a commonly used risk measure, which has attracted more attentions in portfolio optimization. Most of existing mean---absolute deviation models are devoted to stochastic single-period portfolio optimization. However, practical investment decision problems often involve the uncertain dynamic information. Considering transaction costs, borrowing constraints, threshold constraints, cardinality constraints and risk control, we present a novel multiperiod mean absolute deviation uncertain portfolio selection model, which an optimal investment policy can be generated to help investors not only achieve an optimal return, but also have a good risk control. In proposed model, the return rate of asset and the risk are quantified by uncertain expected value and uncertain absolute deviation, respectively. Cardinality constraints limit the number of risky assets in the optimal portfolio. Threshold constraints limit the amount of capital to be invested in each asset and prevent very small investments in any asset. Based on uncertainty theories, the model is transformed into a crisp dynamic optimization problem. Because of the transaction costs and cardinality constraints, the multiperiod portfolio selection is a mix integer dynamic optimization problem with path dependence, which is "NP hard" problem that is very difficult to solve. The proposed model is approximated to a mix integer dynamic programming model. A novel discrete iteration method is designed to obtain the optimal portfolio strategy and is proved linearly convergent. Finally, an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the Shanghai Stock Exchange.

Combining Minkowski and Chebyshev: New distance proposal and survey of distance metrics using k-nearest neighbours classifier

This work proposes a distance that combines Minkowski and Chebyshev distances and can be seen as an intermediary distance. This combination not only achieves efficient run times in neighbourhood iteration tasks in Z2, but also obtains good accuracies when coupled with the k-Nearest Neighbours (k-NN) classifier. The proposed distance is approximately 1.3 times faster than Manhattan distance and 329.5 times faster than Euclidean distance in discrete neighbourhood iterations. An accuracy analysis of the k-NN classifier using a total of 33 datasets from the UCI repository, 15 distances and values assigned to k that vary from 1 to 200 is presented. In this experiment, the proposed distance obtained accuracies that were better than the average more often than its counterparts (in 26 cases out of 33), and also obtained the best accuracy more frequently (in 9 out of 33 cases).

A linear Uzawa-type FEM–BEM solver for nonlinear transmission problems

We propose a fully discrete Uzawa-type iteration for the Johnson–Nédélec formulation of a Laplace-type transmission problem with possible (strongly monotone) nonlinearity in the interior domain. In each step, we sequentially solve one BEM for the weakly-singular integral equation associated with the Laplace-operator and one FEM for the linear Yukawa equation. In particular, the nonlinearity is only evaluated to build the right-hand side of the Yukawa equation. The algorithm includes the inexact solution of the BEM/FEM part by a preconditioned CG method. We prove that the proposed method leads to linear convergence with respect to the number of Uzawa iterations. Moreover, while the current analysis of a direct FEM–BEM discretization of the Johnson–Nédélec formulation requires some restrictions on the ellipticity (resp. strong monotonicity constant) in the interior domain, our Uzawa-type solver avoids such assumptions.

Modified discrete iterations for computing the inverse and pseudoinverse of the time-varying matrix

Abstract The general discretization scheme for transforming continuous-time ZNN models for matrix inversion and pseudoinversion into corresponding discrete-time iterative methods is developed and investigated. The proposed discrete-time ZNN models incorporate scaled Hyperpower iterative methods as well as the Newton iteration in certain cases. The general linear Multi-step method is applied in order to obtain the proposed discretization rule which comprises all previously proposed discretization schemes. Both the Euler difference rule and the Taylor-type difference rules are included in the general scheme. In particular, the iterative scheme based on the 4th order Adams–Bashforth method is proposed and numerically compared with other known iterative schemes. In addition, the ZNN model for computing the time-varying matrix inverse is extended to the singular or rectangular case for the pseudoinverse computation. Convergence properties of the continuous-time ZNN model in the case of the Moore–Penrose inverse and its discretization are also considered.

A new approach to continuous multi-scale analysis in nonrelativistic QED: ground states and photon number bounds for the spin-boson model with critical infrared singularity

We introduce a new method for the study of spectral problems in nonrelativistic quantum electrodynamics, NR QED. The method is based on the so-called Pizzo’s Method (Ann Henri Poincare 4(3):439–486, 2003) or multi-scale analysis. We use it to prove existence and uniqueness of ground-state eigenvalues for the spin-boson model with critical infrared behavior. Denoting by H the corresponding Hamiltonian, we construct its ground-state eigenvalue using a continuous family of infrared cutoff Hamiltonians \((H_t)_{t \ge 0}\) such that as the parameter t tends to infinity, the cutoff is removed. The continuous method we introduce in this paper enjoys many advantages (and it has no disadvantages) with respect to the discrete version (where the parameter t takes its values in a discrete set). The reason is that it is a natural extension of the discrete iteration method, and therefore, it incorporates at the same time both: tools from the discrete approach and techniques from the area of differential equations. Actually, in our proof the analysis of the cutoff Hamiltonians \((H_t)_{t \in [0, \infty )}\) is carried out with the help of our calculations and proofs in Bach et al. (J Math Anal Appl 453:773–797, 2017). However, our main argument borrows ideas from differential equations, more specifically Gronwall’s inequality. Furthermore, we prove that the expectation value of the photon number operator (\({\mathcal {N}}_\mathrm{ph}\)) on the ground state is bounded and, moreover, that the ground-state vector belongs to the domain of \({\mathcal {N}}^{1 -\epsilon }_\mathrm{ph}\), where \(\epsilon >0\) is as small as we want, depending on the coupling constant.

Multi-Scaling Homogenization Process for Nodular Cast Iron Using BEM

In this work, a multi-scaling homogenization process using boundary element formulation (BEM) for modeling a two-dimensional multi-phase microstructure containing irregular’s inclusions is presented. The BEM is very attractive for multiscale modeling tools for heterogeneous materials. In this approach, the iterative inhomogeneity discretization of the external boundary is disregarded, leading to a computational low cost. This approach was used for solving the elastic problem of a representative volume element (RVE) and the field theory medium. The main goal relies on finding the effective properties of micro-heterogeneous materials within a homogeneous and orthotropic matrix. Expressions for evaluating the effective properties under Plane Stress (PT) for orthotropic materials were also presented. Generally, the numerical models consider the graphite nodules as voids for GGG-40 and the roundness is close circular geometry. In this sense, a nodular cast iron GGG-40 microgram was obtained by X-ray computed tomography and Laser Confocal Microscope System, allowing the modeling of the true nodule shape. The numerical results showed good agreement with the experimental tests. The inclusions of graphite were considered as voids in the material matrix. Experimental stress–strain tests and micrographic analysis were used to determine the Young’s modulus, spatial distributions, as well as, nodule shape. The numerical in this work was compared with the obtained experimental results in this work. The comparison between the obtained experimental data with those available in the literature also showed good agreement.

Spread option pricing using ADI methods

Spread option contracts are becoming increasingly important, as they frequently arise in the energy derivative markets, e.g. exchange electricity for oil. In this paper, we study the pricing of European and American spread options. We consider the two-dimensional Black-Scholes Partial Differential Equation (PDE), use finite difference discretization in space and consider Crank-Nicolson (CN) and Modified Craig-Sneyd (MCS) Alternating Direction Implicit (ADI) methods for time stepping. In order to handle the early exercise feature arising in American options, we employ the discrete penalty iteration method, introduced and studied in Forsyth and Vetzal (2002), for one-dimensional PDEs discretized in time by the CN method. The main novelty of our work is the incorporation of the ADI method into the discrete penalty iteration method, in a highly efficient way, so that it can be used for two or higher-dimensional problems. The results from spread option pricing are compared with those obtained from the closed-form approximation formulae of Kirk (1995), Venkatramanan and Alexander (2011), Monte Carlo simulations, and the Brennan-Schwartz ADI Douglas-Rachford method, as implemented in MATLAB. In all spread option test cases we considered, including American ones, our ADI-MCS method, implemented on appropriate non-uniform grids, gives more accurate prices and Greeks than the MATLAB ADI method.