Discrete Iteration Research Articles

Evaluation of Grid Support Capacity From Electrified Railways

High power level and temporal operation flexibility endow electric trains with great potential for improving grid resilience. It becomes crucial to quantify the grid support capacity (GSC) from large-scale electrified railways. This paper innovatively proposes a hierarchical train coordination and trajectory regulation method to evaluate and deliver the GSC from electrified railways. In the light of the mechanical energy consumption analysis of train running, the energy-oriented train operation model is proposed to avoid the nonlinear differential dynamics of train kinetics when coordinating large-scale trains. Then the aggregation and disaggregation of trains for grid support can be formulated as linear and convex quadratic programming problems respectively. To closely follow the reference power and enhance the feasibility of train operation, a novel iterative discretization approach is proposed to generate the precise reference trajectory. A sliding mode controller with disturbance bound adaption is devised to overcome the modeling errors and disturbances when deploying GSC in realistic environment. Comprehensive numerical examples verify the effectiveness of the proposed scheme, and demonstrate the significant grid support potential from collaborative electrified railways.

Analysis and Control of Chaos in Current Mode Controlled Superbuck Converter for Photovoltaic Systems

Background: Superbuck converter is a strong nonlinear system. However, with the changes in parameters, Superbuck converter performance may be reduced due to nonlinear phenomena, such as bifurcation, chaos, etc. Current mode controlled Superbuck converters have been extensively applied in photovoltaic (PV) systems that require a stable output voltage. Superbuck converters, as nonlinear circuits, exhibit plentiful nonlinear phenomena, such as bifurcation and chaos. In this study, we analyze and control the nonlinear phenomena in the current mode controlled Superbuck converter. The piecewise switching model and discrete iteration mapping model of the Superbuck converter are established. The evolution process of the Superbuck converter from steady state to bifurcation and chaos is revealed when the reference current, input voltage, and load are used as bifurcation parameters, and the bifurcation forms of the converter are all period-doubling bifurcations. The stability criterion of Superbuck converter under current mode has been deduced from reference current by analyzing the stability of the converter. Through the resonant parametric perturbation (RPP) method, the chaos control of the Superbuck converter has been realized for the first time. The converter changes from a chaotic state to a stable single-cycle state about 0.4ms after control and the output voltage ripple is reduced from 3.905V to 0.679V, which effectively improves the output stability of the converter. Objective: This study aimed to analyze and control nonlinear phenomena in current-mode controlled Superbuck converters. Method: Bifurcation diagram, time-domain waveform diagram, phase portrait and Poincare section are used as analytical methods for the nonlinear dynamic characteristics of Superbuck converters. The chaotic control method of the Superbuck converter is Resonant Parameter Perturbation (RPP). Results: After applying RPP control to the Superbuck converter in the chaotic state, it is converted into a single-cycle stable state in about 0.4ms. After the converter is controlled, the output current ripple is reduced from 0.71479A to 0.31A, and the output voltage ripple is reduced from 3.905V to 0.679V. Conclusion: With the increase in the reference current, the decrease in the input voltage, or the increase in the load, the system enters the chaotic state through the period-doubling bifurcation path. In this study, the chaos control of the Superbuck converter is carried out for the first time, and the control method used is the resonant parametric perturbation method. After RPP control, the converter is changed from an unstable, chaotic state to a stable period state in about 0.4ms.

Reinforcement learning control with function approximation via multivariate simplex splines

SummaryIn the field of optimal control for continuous nonlinear systems, function approximation methods are often employed to overcome the curse of dimensionality. Compared to other global function approximators like neural networks, multivariate splines can be easily evaluated and adapted on a local basis with linearity in the parameters. In this work, a multivariate spline based reinforcement learning (RL) strategy is proposed for solving the continuous‐time nonlinear control problem. Based on the classic value iteration method, multivariate splines are integrated into RL algorithms to approximate continuous value functions and policy functions from discrete action and value samples. Hence, the determined splines with updated coefficients can be utilized in continuous control of nonlinear systems. In the simulation experiment, the performance of the spline‐based RL control is evaluated in controlling an under‐actuated inverted pendulum. The proposed method is compared with the value iteration based discrete control strategy and the neural network based continuous control strategy. The simulation results indicate that the proposed method based on multivariate splines has better control performance with less state oscillations, energy consumption and convergence time in comparison with discrete value iteration and neural network based RL, and the adoption of simplex splines improves the function approximation efficiency with less computation time than neural network optimization.

CNN-Based Temporal Video Segmentation Using a Nonlinear Hyperbolic PDE-Based Multi-Scale Analysis

An automatic temporal video segmentation framework is introduced in this article. The proposed cut detection technique performs a high-level feature extraction on the video frames, by applying a multi-scale image analysis approach combining nonlinear partial differential equations (PDE) to convolutional neural networks (CNN). A nonlinear second-order hyperbolic PDE model is proposed and its well-posedness is then investigated rigorously here. Its weak and unique solution is determined numerically applying a finite difference method-based numerical approximation algorithm that quickly converges to it. A scale-space representation is then created using that iterative discretization scheme. A CNN-based feature extraction is performed at each scale and the feature vectors obtained at multiple scales are concatenated into a final frame descriptor. The feature vector distance values between any two successive frames are then determined and the video transitions are identified next, by applying an automatic clustering scheme on these values. The proposed PDE model, its mathematical investigation and discretization, and the multi-scale analysis based on it represent the major contributions of this work. Some temporal segmentation experiments and method comparisons that illustrate the effectiveness of the proposed framework are finally described in this research paper.

Isogeometric algorithm for one-step inverse forming of sheet metal

The isogeometric one-step inverse forming method aims to predict the shape of blanks and the formability of stamping parts using accurate geometry without meshing. In this paper, the discrete surface Ricci flow algorithm in computational conformal geometry is introduced as an unfolding algorithm for one-step inverse forming of isogeometric membrane elements. A combination of discrete surface Ricci flow algorithm and elastic iteration is proposed to predict the initial solution. It is proved applicable, even for the extremely curled parts which have negative angles and vertical walls. In addition, we propose a method that the external force of the punch is equivalent to the control point by means of Greville abscissae. A nonlinear equation system is established based on the principle of minimum potential energy. The Newton–Raphson iteration is used to calculate the blank shape and the thickness distribution of the stamping parts. The examples of square box, flower box, and L shape prove that the algorithm can predict the contour of the initial configuration and the formability of sheet metal stamping.

A dynamic fracture model combining with Laplace transform and synchronous iteration method for transient behavior analysis of a four-zone system

A robust and generic semi-analytical model with the capture of dynamic fracture behaviors under long-term pumping rate condition is developed for transient flow analysis in this four-zone system. To characterize the variations of fracture length, the improved pressure-dependent dynamic fracture factor is introduced and incorporated into this model. The Laplace domain with predetermined time discretization and synchronous iteration technique are deployed to obtain the solutions of pressure and pumping rate with the least computational burden. Meanwhile, the stability and convergence of this semi-analytical model can be met within the discrete time. Furthermore, the pressure and pumping rate solutions of this model under the static fracture condition are in good agreement with those of the constant length fracture, which verifies the reliability of this model.The dynamic fracture model with the four -zone system develops five flow stages on the dimensionless pressure and its derivative curves: fracture bilinear flow, dynamic fracture flow, inner area linear flow, transitional flow and boundary-dominated flow. The dynamic fracture behavior is mainly reflected in the obviously positive upwards and pressure derivative curve presents a higher than unit slope. Moreover, the significant decrease of flow rate indicates that fracture closure could result in a rapid decline in pumping rate, which might be the reason why the pumping rate decrease quickly during the long-term pumping period. As the shrinkage coefficient increases, fractures are closed from abruptly to gradually, and typical signatures of fracture closure may be hidden if the shrinkage factor is too small, which may be caused by the instantaneous pressure depletion in the fractures. With the decrease of retained fracture coefficient, there is greater in the positive upward of transient pressure behavior and a lower in pumping rate. As a result, the flow rate will be seriously overestimated if the fracture closure is not considered especially for the tight formation.

MAP-SNN: Mapping spike activities with multiplicity, adaptability, and plasticity into bio-plausible spiking neural networks.

Spiking Neural Networks (SNNs) are considered more biologically realistic and power-efficient as they imitate the fundamental mechanism of the human brain. Backpropagation (BP) based SNN learning algorithms that utilize deep learning frameworks have achieved good performance. However, those BP-based algorithms partially ignore bio-interpretability. In modeling spike activity for biological plausible BP-based SNNs, we examine three properties: multiplicity, adaptability, and plasticity (MAP). Regarding multiplicity, we propose a Multiple-Spike Pattern (MSP) with multiple-spike transmission to improve model robustness in discrete time iterations. To realize adaptability, we adopt Spike Frequency Adaption (SFA) under MSP to reduce spike activities for enhanced efficiency. For plasticity, we propose a trainable state-free synapse that models spike response current to increase the diversity of spiking neurons for temporal feature extraction. The proposed SNN model achieves competitive performances on the N-MNIST and SHD neuromorphic datasets. In addition, experimental results demonstrate that the proposed three aspects are significant to iterative robustness, spike efficiency, and the capacity to extract spikes' temporal features. In summary, this study presents a realistic approach for bio-inspired spike activity with MAP, presenting a novel neuromorphic perspective for incorporating biological properties into spiking neural networks.

Continuous and discrete dynamical sampling

In this paper we study the continuous dynamical sampling problem at infinite time in a complex Hilbert space H. We find necessary and sufficient conditions on a bounded linear operator A∈B(H) and a set of vectors G⊂H, in order to obtain that {etAg}g∈G,t∈[0,∞) is a semi-continuous frame for H. We study if it is possible to discretize the time variable t and still have a frame for H. We also relate the continuous iteration etA on a set G to the discrete iteration (A′)n on G′ for an adequate operator A′ and set G′⊂H.

Penalty Methods for Bilateral XVA Pricing in European and American Contingent Claims by a PDE Model

Taking into account default risk in the valuation of financial derivatives has become increasingly important, especially after the 2007-2008 financial crisis. Under some assumptions, the valuation of financial derivatives, including a value adjustment to account for default risk (the so-called XVA), gives rise to a nonlinear PDE. We propose numerical methods for handling the nonlinearity in this PDE, the most efficient of which are discrete penalty iteration methods. We first formulate a penalty iteration method for the case of European contingent claims, and study its convergence. We then extend the method to the case of American contingent claims, resulting in a double-penalty iteration. We also propose boundary conditions and their discretization for the XVA PDE problem in the cases of call and put options, as well as the case of a forward contract. Numerical results demonstrate the effectiveness of our methods.

Well and ICV management in a carbonate reservoir with high gas content

The management of oil fields that present high gas content is challenging, mainly in cases where this represents a bottleneck for oil production due to gas platform constraints. One way to deal with this problem is with the use of ICVs (Interval Control Valves), which enables the production to be controlled by zones in the wells.In this work, we propose a methodology using reactive control rules for producers and ICVs, with GOR as monitoring variable, to improve the economic performance of the field. We compare the management of the field in three ways: (a) well management by shutting down producers when they reach an uneconomic GOR limit, (b) the use of ICVs on-off type and (c) application of multi-position type ICVs. We extend the application of algorithm IDLHC (Iterative Discrete Latin Hypercube) for the optimization process in this context. This study is made in a synthetic simulation case (Lira1_2022) with characteristics of a Brazilian pre-salt carbonate field with karstic features, high CO2 content and using WAG (Water-Alternate-Gas) injection as recovery mechanism.The results demonstrated that the use of ICVs has a great potential to increase the performance of the field, both in economic and production indicators, when compared to well shut-in management. Both ICV on-off and multi-position types achieved similar results, with a slight advantage to the multi-position type ICVs. The improvement in the field's performance was mainly caused by the interference among zones and wells, in which the closure of less productive wells, or zones, reflected in improvements in other more productive wells.

Robust Symbol Detection in Large-Scale Overloaded NOMA Systems

We a framework for the design of low-complexity and high-performance receivers for multidimensional overloaded non-orthogonal multiple access (NOMA) systems. The framework is built upon a novel compressed sensing (CS) regularized maximum likelihood (ML) formulation of the discrete-input detection problem, in which the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -norm is introduced to enforce adherence of the solution to the prescribed discrete symbol constellation. Unlike much of preceding literature,.g., (Assaf et al., 2020, Yeom et al., 2019, Nagahara, 2015, Naderpour and Bizaki, 2020, Hayakawa and Hayashi, 2017, Hayakawa and Hayashi, 2018, and Zeng et al., 2020), the method is not relaxed into the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm, but rather approximated with a continuous and asymptotically exact expression without resorting to parallel interference cancellation (PIC). The objective function of the resulting formulation is thus a sum of concave-over-convex ratios, which is then tightly convexified via the quadratic transform (QT), such that its solution can be obtained via the iteration of a simple closed-form expression that closely resembles that of the classic zero-forcing (ZF) receiver, making the method particularly suitable to large-scale set-ups. By further transforming the aforementioned problem into a quadratically constrained quadratic program with one convex constraint (QCQP-1), the optimal regularization parameter to be used at each step of the iterative algorithm is then shown to be the largest generalized eigenvalue of a pair of matrices which are given in closed-form. The method so obtained, referred to as the Iterative Discrete Least Square (IDLS), is then extended to address several factors of practical relevance, such as noisy conditions, imperfect channel state information (CSI), and hardware impairments, thus yielding the Robust IDLS algorithm. Simulation results show that the proposed art significantly outperforms both classic receivers, such as the linear minimum mean square error (LMMSE), and recent CS-based state-of-the-art (SotA) alternatives, such as the sum-of-absolute-values (SOAV) and the sum of complex sparse regularizers (SCSR) detectors. It is also shown via simulations that the technique can be integrated with existing iterative detection-and-decoding (IDD) methods, resulting in accelerated convergence.

Penalty methods for bilateral XVA pricing in European and American contingent claims by a partial differential equation model

Accounting for default risk in the valuation of financial derivatives has become increasingly important, especially since the 2007–8 financial crisis. Under some assumptions, the valuation of financial derivatives, including a value adjustment to account for default risk (the so-called XVA), gives rise to a nonlinear partial differential equation (PDE). We propose numerical methods for handling the nonlinearity in this PDE, the most efficient of which are the discrete penalty iteration methods. We first formulate a penalty iteration method for the case of European contingent claims and study its convergence. We then extend the method to the case of American contingent claims, which results in a double-penalty iteration. We also propose boundary conditions and their discretization for the XVA PDE problem in the case of a call option, a put option and a forward contract. Numerical results demonstrate the effectiveness of our methods.

Integrating machine learning with Markov chain and cellular automata models for modelling urban land use change

Modelling urban land use change is of profound concern to environmental scientists who have found cellular automata models very attractive for simulating urban dynamics. The quest for suitable predictive models to improve realistic simulation of urban land use change has resulted in the use of several notable cellular automata calibrations. Cellular automata model has become very attractive and one of the strongest models for urban growth simulation due to its simplicity and possibility of evolution. However, the inability of cellular automata to include driving forces of urban growth in the simulation process has warranted further cellular automata calibrations to minimize this weakness. To address this problem, and contrary to previous cellular automata calibrations, this research presents a novel integration of support vector machine, Markov chain and cellular automata for urban change modelling. Support vector machine is introduced as a machine learning technique to mine the impact of the explanatory variables that drive urban change. Markov chain is employed to mine the urban transition probabilities between the various urban epochs while cellular automata are used to implement the incremental discrete time steps based on neighbourhood interaction from an initial time to a future time. This modelling is implemented using Landsat data acquired in 1984, 2000 and 2015 over Lagos in Nigeria, Africa’s most populous city. Urban transitions (1984–2000 and 2000–2015) are used to simulate future urban state in 2030 and validation metrics include McNemar's test. The introduction of stochasticity into the model helps create the typical randomness inherent in the real world for deriving future urban forms through discrete cellular automata iterations. The high accuracy obtained in this experiment implies a substantial fit between the predicted and reference data. This outcome proves the robustness of this method for modelling urban change.

A novel method to determine the coupling scaling laws of vibration characteristics for rotor-bearing systems

The purpose of this article is to study the coupling effects of support stiffness on geometric scaling factor powers of the rotor-bearing system and predict vibration characteristics of a prototype by scaled models accurately. Associated to the least-squares–based similitude method, the discrete iteration method proposed evaluates the estimated scaling laws under variable (instable) powers and further broadens the restriction of boundary conditions in scaling laws, which is the main finding in this article. The discrete iteration method does not need to establish a physical model but directly uses input and output parameters to establish output scaling laws. The complete scaled model and geometric distorted model are selected as study cases to prove the effectiveness and accuracy of the discrete iteration method. The vibration characteristics of the rotor-bearing system are obtained by the finite element method with validation by experimental test for the natural characteristics. The comparison between the prediction results and those without the discrete iteration method shows that discrete iteration method can significantly improve the accuracy for predicting the prototype.

Distributed discrete-time event-triggered algorithm for economic dispatch problem

In this paper, a distributed discrete-time event-triggered algorithm is proposed to deal with the economic dispatch problem with equality constraint. The communication can be reduced and the energy of systems can be saved by adopting event-triggered communication mechanism. The Zeno behavior is naturally excluded based on discrete iteration scheme. Moreover, the proposed algorithm has been proved to be exponentially convergent with the aid of convex optimization and Lyapunov stability theory that the optimal value is obtained with discrete exponential convergence rate. Finally, the effectiveness of the proposed algorithm is verified via a numerical example.

A semantic relatedness preserved subset extraction method for language corpora based on pseudo-Boolean optimization

As language corpora have been playing an increasingly important role in the field of Artificial Intelligence (AI) research, lots of extremely large corpora are created. However, a larger corpora size not only increases power and accuracy but also brings redundancy. Therefore, researchers began to emphasize the study of appropriate subset extraction methods. Due to the trade-off between data sufficiency and redundancy, a group of interesting and challenging problems are emerged that are studied in this paper: (1) How to make the resulting subset include as much data as possible under some necessary constraints? (2) How to preserve the potential useful semantic relatedness included in the original corpora while reducing the size of the corpora? For these two problems, existing work mainly focuses on the methods to construct particular subsets for special usage. These methods are limited in their focus. In this paper, we try to address the problems listed above. First, considering the cubic and binary semantic relatedness among tokens, we construct a general system model and formulate the mix problem as a cubic pseudo-Boolean optimization problem. Then, by analyzing the characteristics of the objective function, we transfer the problem into the maximum flow problem of a corresponding graph. Third, we propose a new algorithm by introducing discrete Lagrangian iteration method. We prove that the objective function is supermodular, which allows us to use fast minimum cut algorithms in each iteration step to propose another fast algorithm. Finally, we experimentally validate our new algorithms on several randomly created corpora.

Boundary-Free Analytic Magnetic Field Calculations Including Soft Iron and Permanent Magnets Using an Iterative Discretization Technique

An extremely fast magnetostatic magnetic field modeling method is developed that includes nonlinear relative permeabilities (or “magnetic saturation”) of soft magnetic materials with nonuniform magnetization. The model assumes regions of linearity within the material in order to apply analytic equations and superposition. This article presents the general theory and method for 3-D geometries, along with a 2-D axisymmetric example case study that is of interest for tubular linear actuator (or motor) design. The case study maximizes the average air-gap flux of an axially magnetized pole piece and shows a close correlation of the internal and external magnetic flux densities with a finite element analysis. This demonstrates the method as suitable for large parametric searches of topologies, toward the optimization of electrical machines, linear actuators, transformers, or more general 3-D electromagnetic problems.

CFD study of the PTS experiment in ROCOM test facility

With the aging of nuclear reactors, embrittlement of the reactor pressure vessel (RPV) steel, as a consequence of routine operations, is highly probable. To ensure operational integrity and safety, prediction and mitigation of compromising damage, brought on by pressurized thermal shock (PTS) following an emergency procedure, is of utmost importance. Computational fluid dynamics (CFD) codes can be employed to predict these events and have therefore been an acceptable method for such assessments. In this paper, CFD simulations of a density driven ECC state in the ROCOM facility are analyzed. Obtained numerical results are validated with the experimental measurements. Considerable attention is attributed to the boundary conditions and their influence, specifically outlet definitions, in order to determine and adequately replicate the non-active pumps in the facility. Consequent analyses focused on initial conditions as well as on the temporal discretization and inner iterations. Disparities due to different turbulent modelling approaches are investigated for standard RANS models. Based on observed trends for different cases, a definitive simulation setup has been established, results of which have been ultimately compared to the measurements.

Time-consistent multiperiod mean semivariance portfolio selection with the real constraints

In this paper, a new multiperiod mean semivariance portfolio selection with the transaction costs, borrowing constraints, threshold constraints and cardinality constraints is proposed. In the model, the return and risk of assets are characterized by mean value and semivariance, respectively. Because the semivariance operator is not separable, the optimal solution of the model is not time-consistent. The time-consistent strategy for this model can be obtained by using game approach. The time-consistent strategy, which is a mix integer dynamic optimization problem with path dependence, is approximately turned into a dynamic programming problem by approximate dynamic programming method. A novel discrete approximate iteration method is designed to obtain the optimal time-consistent strategy, and is proved linearly convergent. Finally, the comparison analysis of trade-off parameters is given to illustrate the idea of our model and the effectiveness of the designed algorithm.

Reducing uncertainties of reservoir properties in an automatized process coupled with geological modeling considering scalar and spatial uncertain attributes

The current work introduces an automatized process coupled with geological modeling to reduce uncertainty in reservoir properties. The method assimilates dynamic data of wells interactively, and applies the deviations to constrain uncertainties. The methodology deals with scalar (e.g. rock compressibility) and spatial (e.g. porosity) attributes at same time, employing specialized uncertainty reduction procedures. The procedure reduces the uncertainty of scalar attributes through Iterative Discrete Latin HyperCube method (IDLHC). To reduce uncertainties of spatial attributes, we worked on an extension of a regionalized co-simulation (co-DSS) method. The main contributions regard the proposition of update, at same time, both kinds of uncertainties (spatial and scalar); the definition of sequential rules, that simplify the process execution and avoiding subjectivities on the coupling of the geological modeling on data assimilation, as well as the automation of the process. The procedure was validated under a siliciclastic black-oil benchmark field (UNISIM-I-M), established based on Namorado Field, Campos Basin, Brazil. The procedure reduced the range of uncertainty of the scalar attributes, centralizing final PDFs with the values presented in the reference model, without collapse to a particular level, as well as preserved the geological consistency throughout data assimilation, obtaining porosity responses in agreement with the reference porosity distribution. The potential of the procedure is supported by the consistent production forecast observed in the outcomes.