Iterative Solution Algorithm Research Articles

Two-dimensional vehicular movement modelling at intersections based on optimal control

Modeling traffic flow at intersections is essential for the design, control, and management of intersections. A challenging feature of microscopic modeling vehicular movement at intersections is that drivers can choose among an infinite number of alternative traveling paths and speeds. This makes it fundamentally different from structured straight road sections with lanes. This study proposes a novel method to model the trajectories of vehicles in two-dimensional space and speed. Based on optimal control theory, it assumes drivers schedule their driving behavior, including the steering and acceleration, to minimize the predicted costs. The costs contain the running costs, which consist of the travel time and driving smoothness (longitudinally and laterally), and the terminal cost, which penalizes the deviations from the desired final state. Different than conventional methods, the vehicle motion dynamics are formulated in distance rather than in time. The model is solved by an iterative numerical solution algorithm based on the Minimum Principle of Pontryagin. The descriptive power, plausibility, and accuracy of the proposed model are investigated by comparing the calculated results under several cases, which can be solved from symmetry or analytically. The proposed model is further calibrated and validated using empirical trajectory data, and the quality of the predicted trajectory is confirmed. Qualitatively, the optimal trajectory changes in the range of the shortest path and smoothest path under different weights of the running cost. The proposed model can be used as a starting point and extended with more considerations of intersection operation in the real world for future applications.

Decentralized-distributed robust electric power scheduling for multi-microgrid systems

This paper proposes a novel decentralized-distributed (DD) adaptive robust optimization (ARO) method to address the efficient distributed scheduling of multi-microgrid systems involving various entities, uncertainties and accidental communication failures. To avoid an unavailable coordination center of the whole network, a DD-ARO model is firstly proposed based on the parallelizing-distributed (PD) framework, which allocates the task of tie-line power coordination in the virtual center to the neighboring stakeholders. According to the properties of nonlinear ARO, a modified analytical target cascading method is further developed to formulate the consistency constraints on shared tie-lines, thus guaranteeing the optimality and enhancing the solution quality of the DD-ARO model. Finally, an iterative solution algorithm is proposed to efficiently solve the resulting multi-level non-convex DD-ARO model. Case studies and computational results illustrate the effectiveness of the DD-ARO approach for an AC/DC hybrid multi-microgrid system under normal and faulty communications.

Sensor Location Strategy and Scaling Rate Inference for Origin-Destination Demand Estimation

The goal of sample-data-based origin-destination (O-D) demand estimation is to aggregate the location data into the traffic network. Inevitably, the scaling rate, which expands the estimated O-D demands to the population level, should be generated. In this paper, a two-stage optimization model is explored for determining the sensor location and stochastic scaling rate. In the first stage, a sensor deployment model identifies the optimal sensor location strategy by minimizing the variability of the scaling rate under a budget constraint. In the second stage, a Bayesian-based scaling rate inference model leverages the prior information and the data that were observed at the identified sensor locations to derive the stochastic scaling rate. The Bayesian-based scaling rate inference model is a bilevel program, which seeks the maximum a posteriori (MAP) scaling rate conditioned by the observed link flows in the upper level and optimizes the stochastic user equilibrium (SUE) in the lower level. To reflect the interactive relationships between the sensor location and the stochastic scaling rate inference, an integrating model is built. A sequential identifying sensor location algorithm that avoids matrix inversions was proposed to solve the sensor deployment model, and an iterative solution algorithm was developed to solve the Bayesian-based scaling rate inference model. The results from numerical experiments demonstrate that the sensor deployment model could provide the most reliable scheme of sensor locations, thereby contributing to the reliable estimation of the stochastic scaling rate. The results also demonstrate that both the endogenous information (prior information on the scaling rate) and exogenous factors (link flows) can facilitate a more accurate scaling rate inference.

Origin-Destination Demand Reconstruction Using Observed Travel Time under Congested Network

Two bi-level models to reconstruct origin-destination (O-D) demand under congested network are explored in terms of the observed link and route travel times, where one model inputs the known trajectories of observed route travel times and the other model uses both known and unknown trajectories of observed route travel times. The proposed models leverage both the link and route traffic information to determine the network O-D demand that minimizes the distances between the observed and estimated traffic information (O-D, link and route travel times) in the upper-level, and optimize the stochastic user equilibrium (SUE) in the lower-level. Meanwhile, the observed information of travel time can capture the relationships between traffic flow and travel cost/time in congested network. The K-means (hard assignment) and Gaussian mixture model (GMM, soft assignment) clustering methods are presented to identify the trajectories of observed route travel times. An iterative solution algorithm is proposed to solve the built O-D reconstruction models, where the method of gradient descent, the method of successive average and Expectation-Maximization (EM) algorithm are used to solve the upper-level model, lower level model, and GMM, respectively. Results from numerical experiments demonstrate the superiority of the travel time based model over the traditional flow based method in congested traffic network, and also suggest that using both the route and link information outperforms only using link information in the reconstruction of O-D demand.

Joint Resource Management With Distributed Uplink Power Control in Full-Duplex OFDMA Networks

Resource allocation problems in full-duplex orthogonal frequency division multiple access (FD-OFDMA) networks are challenging due to their combinatorial, non-convex nature. In this paper, user pairing, subcarrier and power allocation in a single cell FD-OFDMA network are considered. A joint optimization problem is formulated to maximize the network's sum rate while satisfying downlink (DL) and uplink (UL) transmission power’ constraints. Due to the sheer complexity of the proposed formulation, mainly due to its combinatorial nature, an efficient, iterative two-step solution algorithm for the joint problem is proposed. In the first step, based on defining the DL user equipment (UE) signal to noise ratio (SNR) threshold, which is the least SNR that can be detected by the DL-UE, an algorithm is proposed for user pairing and subcarrier assignment. In the second step, the power allocation problem for the assigned users’ pairs is formulated and solved using the Alternating Direction Method of Multipliers (ADMM) in the high signal-to-interference-noise ratio regime. Finally, numerical results are presented to validate the performance of the proposed algorithms. We show that the performance of our proposed computationally-efficient two-step algorithm is very close to the sum rate upper bound derived from solving the dual problem.

Dynamic response of vertically loaded rectangular barrettes in multilayered viscoelastic soil

Rectangular barrettes have been increasingly used as foundations for many infrastructure projects, but the vertical vibration of a barrette has been rarely addressed theoretically. This paper presents an analysis method of dynamic response for a rectangular barrette subjected to a time-harmonic vertical force with the aid of a modified Vlasov foundation model in multilayered viscoelastic soil. The barrette-soil system is modeled as a continuum, the vertical continuous displacement model for the barrette and soil is proposed. The governing equations of the barrette-soil system and the boundary conditions are obtained and the vertical shaft resistance of barrette is established by employing Hamilton's principle for the system and thin layer element, respectively. The physical meaning of the governing equations and shaft resistance is interpreted. The iterative solution algorithm flow is proposed to obtain the dynamic response of barrette. Good agreement of the analysis and comparison confirms the correctness of the present solution. A parametric study is further used to demonstrate the effects of cross section aspect ratio of barrettes, depth of soil column, and module ratio of substratum to the upper soil layers on the complex barrette-head stiffness and the resistance stiffness.

Steady State Energy Flow Analysis for Energy Internet Planning

The planning and design of energy Internet is an important work. The basis of this work is energy flow analysis of the design network. In this paper, the energy flow analysis model of typical gas-electricity interconnection system is established. The mismatch equations and iterative algorithm for energy flow solution are given. The effectiveness of the algorithm is verified by a typical gas-electric interconnection example.

On the stability of projected dynamical system for generalized variational inequality with hesitant fuzzy relation

In this paper, we investigate the projected dynamical system associated with the generalized variational inequality with hesitant fuzzy relation. We establish the equivalence between the generalized variational inequality with hesitant fuzzy relation and the fuzzy fixed point problem. And we analyze the existence theorem and iterative algorithm of solutions to such problem. Furthermore, using the projection method, we propose a projection neural network for solving the generalized variational inequality with hesitant fuzzy relation and discuss the stability of the proposed projected dynamical system.

Privacy-Preserving Optimal Dispatch for an Integrated Power Distribution and Natural Gas System in Networked Energy Hubs

Energy hubs (EHs) are deployed to supply multi-energy demands economically in the integrated energy systems while considering physical and operational constraints of individual energy systems. This paper presents a decentral framework for the optimal dispatch of integrated power distribution and natural gas system (IDGS) in networked energy hubs. The IDGS operator (IDGSO) is charged with delivering a constrained optimal dispatch while preserving the privacy of participants’ data. First, a comprehensive optimization model is proposed in this paper using the mixed-integer second-order cone programming and sequential second-order cone (SOC) algorithms to guarantee the exactness of SOC relaxation. In this optimization process, we consider advanced control methods, such as remotely controlled switches and static var compensators, and propose two improvements including initial point setting and a special type of cutting plane to obtain a fast and feasible solution. Next, we apply Benders decomposition for decentralizing the decision-making process in accordance with the practical leader–follower relationship between IDGSO and EHOs (EH operators) and preserving private operation data of individual EHOs. Finally, we present numerical case studies, which illustrate the effectiveness of the proposed iterative model and solution algorithm for enhancing the operation of EHs.

Precise time-domain expanding boundary element method for solving phase change problems

In this article, the precise time-domain expanding boundary element method (PTEBEM) is applied to solving phase change problems. In the present method, the recursive formulation of the governing equation is derived by expanding time-dependent physical quantities at discrete time intervals. Then the recursive equation is solved by the radial integration boundary element method, where the radial integral method is used to transform the domain integral into the boundary integral. Moreover, in order to guarantee the accuracy and efficiency, a self-adaptive check scheme is introduced to evaluate the recursive times in a time step. Simultaneously, the front-tracking method is used to simulate the motion of the moving boundary. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing PTEBEM. To verify the present method, several typical examples are given. Satisfactory results are obtained in comparison with reference solutions.

Nonlinear Hermitian generalized hygrothermoelastic stress and wave propagation analyses of thick FGM spheres exhibiting temperature, moisture, and strain-rate material dependencies

The present article is dedicated to the dynamic stress and displacement distributions and hygrothermoelastic wave propagation and reflection responses of FG hollow spheres subjected to thermomechanical shocks. The strain-rate and temperature dependencies of the material properties are accounted for. Hence, the material properties of the sphere are dependent on coordinates, time, loading rate, temperature, and ambient humidity. Furthermore, material degradation due to moisture absorption is considered. It is the first time that such a complex and more realistic combination is taken into account in the wave propagation analysis. The nonlinear coupled Lord-Shulman-type generalized hygrothermoelasticity equations that are developed by the inclusion of the moisture absorption state variable into the free energy function, are solved by using a Galerkin-type finite element method, iterative solution algorithm, and a second-order Runge-Kutta time integration procedure. Results are extracted by using the C1-continuous Hermitian rather than common C0-continuous Lagrangian elements to guarantee exact continuity of the stresses at the mutual boundaries of the elements and preclude the numerical locking phenomenon. Comprehensive sensitivity analyses including the effects of various factors are performed. Results reveal the significant effects of the temperature, strain-rate, and moisture absorption on both the material properties and constitutive law and consequently, on the transient stress distribution and the hygrothermoelastic wave propagation/reflection phenomenon. Furthermore, the results confirm that in the FG structures, the thermal and stress wavefronts travel with variable and time-dependent speeds.

A Review of Numerical Modeling and Experimental Analysis of Combustion in Moving Grate Biomass Combustors

This Review covers the current state-of-the-art literature dealing with numerical modeling and experimental analysis of moving grate biomass combustors. The greatest attention is paid to the modeling of the thermochemical conversion in the fuel bed. Changes in the fuel characteristics are also tracked during the combustion. Such a review can facilitate understanding a more robust model from viewpoints of thermal performance, chemical and physical properties, pollutant emissions, and combustion stability. Different modeling approaches for the moving grate biomass furnaces are introduced, with a focus on the independent fuel bed modeling. Stepwise biomass fuel degradation inside the bed and corresponding individual mathematical models are described, followed by overbed combustion modeling. Numerical methods for the conservation equations of the combustion model are classified, and a general iterative solution algorithm is delivered. Various NOx formation mechanisms from the fuel-bed efflux and the combustion of hot zone gases are detailed, followed by the particle matter originating from inorganic materials. Air-staging, the flue gas recirculation mechanism, and restriction of the maximum flame temperature can significantly reduce the NOx concentration in the flue gases. Industrial biomass combustion systems are addressed in terms of different grate technologies, and a general laboratory-scale biomass reactor is portrayed. For future work, according to the gaps found in the literature, it is recommended that, considering the intensive inhomogeneity of the biomass fuels, the effects of the fuel uncertainties should be considered in the bed modeling. Furthermore, deep investigation of the infrared images captured from biomass combustion can provide a comprehensive tool for the combustion system analysis. More recommendations are given in the conclusion of this Review.

Online Measurement of Wet Gas by Modeling Frequency and Amplitude Characteristics of a Vortex Flowmeter

In this article, an accurate online measurement of gas flowrate in wet gas was developed by modeling the frequency and amplitude characteristics of a vortex flowmeter in annular mist flow. The low-frequency modulation behaviors of the vortex signals were analyzed by the ridge method based on continuous wavelet transform (CWT). It indicates that the instability of frequency and amplitude of the signals both enhance with the increase of liquid loading; and therefore, a feature extraction method based on ridge-averaged was proposed and validated by the tests. A film extraction device was developed to measure the flowrate of the liquid film and further obtain the droplet mass loading. Then, a uniform linear equation for the overreading was obtained experimentally on the basis of the scaling parameter analysis in particle-laden flow. A uniform exponential equation for the dimensionless signal amplitude of the sensor output was developed with droplet mass loading. Finally, a wet gas measurement model with the simultaneous equations from these two correlations was established and the iterative solution algorithm was given. In the present cases, the percentage errors (PEs) of the gas flowrate predicted by the modeling are within ±1.5% and the mean absolute PE is 0.37%. The method proposed in this article can achieve accurate measurement of gas flowrate by using only one vortex flowmeter and, hence, creates a simple inexpensive metering system for wet gas flow.

A parametric study on geometrically nonlinear behavior of curved beams with single and double link rods, and supported on moving boundary

The paper presents a parametric study on effect of several geometric parameters on stress and deformation behavior of non-uniform curved beam with moving boundary. The parameters, considered in the present study, are height to span ratio of curved beam, ratio of radius of roller support to height of beam and types of support connection mechanisms. Effect of these parameters is observed for different curved profile shapes. Non-uniform initial curvature and combined effects of bending, stretching and warping of beam cross-section due to shear deformation are considered in the derivation of nonlinear strain-displacement relation in body fitted curvilinear frame. Based on the derived nonlinear kinematics and assumptions of large deformation but small strain and moderate initial curvature, nonlinear system governing equation is derived through variational principle based minimization of total potential energy method. An iterative numerical solution algorithm is developed and implemented in the computational environment of MATLAB® software to solve the nonlinear governing equation. The complicating effect coming from moving boundary imposes a kinematic constraint on the solution field. Hence, the solution methodology not only ensures energy balance of the system, but also satisfies shear force balance at each incremental load step. The geometric nonlinear incremental curved beam model is validated with deflection and stress results of commercial finite element software ABAQUS®. The geometry of master leaf spring of a previously reported study is considered as curved beam for the purpose of validation. After the validation study, results are generated for different curved profiles with two different combinations of support connection mechanisms and different height to span ratio for each type of them. In addition, to observe effect of roller radius, results are generated with different roller radius to height ratio for each type of the two curved beam systems. Investigations are made on the effects of the geometric parameters, support connection mechanisms and curved profile shape on large deflection characteristics of curved beam and the present study leads towards several meaningful observations.

Dynamic soil structure interaction model for beams on viscoelastic foundations subjected to oscillatory and moving loads

A new method for dynamic analysis of Euler-Bernoulli beams resting on multi-layered viscoelastic soil is presented. The governing differential equations for beam and soil displacements are obtained using the extended Hamilton’s principle, and these equations are solved using one-dimensional finite element method and analytical solutions. An iterative solution algorithm is used in conjunction with an implicit time integration scheme to obtain beam and soil responses as functions of time. The developed model resembles the traditional two-parameter spring foundation model but the analysis shows that the traditional foundation spring parameters cannot be prescribed a priori but determined as part of the solution. The model produces accurate beam response as illustrated by comparisons with equivalent two-dimensional finite element analysis. A few problems are analyzed that illustrate the novel features of the dynamic foundation model.

Auxiliary Principle and Iterative Algorithm for a Generalized Nonlinear Mixed Quasi-variational-like Inequality

In this paper, we employ the auxiliary principle technique to study a generalized nonlinear mixed quasi-variational-like inequality in Hilbert spaces. Fist, we establish the existence and uniqueness of solution of the corresponding auxiliary generalized nonlinear mixed quasi-variational-like inequality by making use of minimizing sequence of a convex function. Then based on the existence result, we construct an iterative algorithm for finding approximate solution to the exact solution of the generalized nonlinear mixed quasi-variational-like inequality. Our results extend, improve and unify some known results in the literature.

Dynamic Wave Propagation in Fiber Reinforced Piezoelectric Composites with Cracks

This paper presents the transient dynamic analysis of micro-cracks of arbitrary shape in two-dimensional, linear piezoelectric fiber reinforced composite materials. Interface cracks between fiber and matrix as well as cracks inside the matrix and fibers are investigated. For this purpose, a symmetric Galerkin time-domain boundary element method in conjunction with a multi-domain technique is developed. The time-domain fundamental solutions for linear piezoelectric materials are applied. The time discretization is performed by a collocation method. An explicit time-stepping scheme is obtained to compute the discrete boundary data including the generalized crack-opening-displacements (CODs). Iterative solution algorithms are implemented to solve the nonlinear semi-permeable electrical crack-face boundary conditions and for a crack-face contact analysis at time-steps when a physically unacceptable crack-face intersection occurs. Several numerical examples are presented to reveal the influences of the micro-cracks, the material combinations and the transient dynamic loading on the intensity factors and the scattered wave fields.

КОНЕЧНОЕ ЧИСЛО ИТЕРАЦИЙ В ДВУХЭТАПНЫХ АЛГОРИТМАХ ДЛЯ РЕШЕНИЯ ЗАДАЧ О РАВНОВЕСИИ

A two iterative two-stage proximal algorithms for the approximate solution of the equilibrium problem in a Hilbert space is considered. In this article we proved the convergence of algorithms in a finite number of iterations when the condition of sharpness is fulfilled.

Method for increasing the view field of THz holograms

In this paper we demonstrate the method of widefield amplitude-phase object images reconstruction from the spatially-limited broadband terahertz wavefield spectral components distributions in the Fresnel diffraction zone, based on the wave propagation equations iterative solution algorithm. Using of this method allows one to overpass the spatial resolution limit of an object image, reconstructed from the digital pulse terahertz hologram in low-frequency components of the THz radiation, used in the research. In its turn the created software allows to simulate the process of holograms registration in case of limited detector aperture and to reconstruct the full images of an object.

A spectral stochastic formulation for nonlinear framed structures

The present paper proposes a stochastic formulation which enables the effective coupling of spectral stochastic finite elements with geometrically nonlinear analysis of framed structures. This is achieved by projecting the stochastic part of the incremental displacements, formulated in the framework of a Newton–Raphson solution scheme, to a polynomial chaos expansion basis. The nonlinear solution is consequently achieved by introducing these expansion coefficients in the iterative solution algorithm as unknowns to be evaluated. With this approach, an augmented system of nonlinear equations is produced and the values of the coefficients are obtained through convergence of the iterative algorithm. In a similar to the deterministic problems manner, the nonlinear load or displacement control algorithms are extended to their stochastic counterparts and a discussion on the appropriate choice of such algorithms depending on the problem at hand is presented. This work focuses on stochastic beam finite element systems in which uncertainty is considered in the system properties. The efficiency of the proposed methodology is demonstrated in benchmark problems with strong geometrically nonlinear behavior. In order to verify the validity of the proposed approach the results obtained are compared to those of Monte Carlo simulations and fair accuracy can be reported.