Successive Iteration Method Research Articles

Extended Model Predictive Control Based on Multi-Structure RBF Networks: Design and Application to Clutch Control

For many control systems in engineering practice, the nonlinear, slow time varying and multistage dynamics make it difficult to realize precise control. Therefore, the extended model predictive control (EMPC) based on multi-structure radial basis function neural networks (MSRBFNN) is proposed in this paper. To begin with, the standard model predictive model (MPC) is established from system analysis or identification to formulate the problem with known disturbances. Secondly, the original MPC is extended with radial basis function neural networks (RBFNN) to deal with the nonlinearity and slow time varying dynamics of the system. Further, considering that a single RBFNN is too complicated to cope with the multistage dynamics of the system for real time application, the MSRBFNN, composed of a series of simpler RBFNNs, is designed to replace the original RBFNN. The running system can then switch between different RBFNNs at different working conditions. Finally, a successive iteration method is introduced to derive the controller with nonlinear compensations and the stability issue is also discussed. Application to the dry clutch control system shows that the proposed method has a much better performance than the standard MPC. Moreover, it can also be extended to other similar nonlinear control systems.

Study on the Unsteady Creep of Composite Beams with an Irregular Laminar Fibrous Structure Made from Nonlinear Hereditary Materials

The creep of homogenous and hybrid composite beams of an irregular laminar fibrous structure is investigated. The beams consist of thin walls and flanges (load-carrying layers). The walls may be reinforced longitudinally or crosswise in the plane, and the load-carrying layers are reinforced in the longitudinal direction. The mechanical behavior of phase materials is described by the Rabotnov nonlinear hereditary theory of creep taking into account their possible different resistance to tension and compression. On the basis of hypotheses of the Timoshenko theory, with using the method of time steps, a problem is formulated for the inelastic bending deformation of such beams with account of the weakened resistance of their walls to the transverse shear. It is shown that, at discrete instants of time, the mechanical behavior of such structures can formally be described by the governing relations for composite beams made of nonlinear elastic anisotropic materials with a known initial stress state. The method of successive iterations, similar to the method of variable parameters of elasticity, is used to linearize the boundary-value problem at each instant of time. The bending deformation is investigated for homogeneous and reinforced cantilever and simply supported beams in creep under the action of a uniformly distributed transverse load. The cross sections of the beams considered are I-shaped. It is found that the use of the classical theory for such beams leads to the prediction of indefensibly underestimated flexibility, especially in long-term loading. It is shown that, in beams with reinforced load-carrying layers, the creep mainly develops due to the shear strains of walls. It is found that, in short- and long-term loadings of composite beams, the reinforcement structures rational by the criterion of minimum flexibility are different.

Local discontinuous Galerkin method for elliptic interface problems

AbstractIn this paper, the minimal dissipation local discontinuous Galerkin method is studied to solve the elliptic interface problems in two-dimensional domains. The interface may be arbitrary smooth curves. It is shown that the error estimates in L2-norm for the solution and the flux are O(h2|logh|) and O(h|logh1/2), respectively. In numerical experiments, the successive substitution iterative methods are used to solve the LDG schemes. Numerical results verify the efficiency and accuracy of the method.

Decomposition of conditional probability for high-order symbolic Markov chains.

The main goal of this paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate on a decomposition procedure for the conditional probability function of sequences considered to be high-order Markov chains. We represent the conditional probability function as the sum of multilinear memory function monomials of different orders (from zero up to the chain order). This allows us to introduce a family of Markov chain models and to construct artificial sequences via a method of successive iterations, taking into account at each step increasingly high correlations among random elements. At weak correlations, the memory functions are uniquely expressed in terms of the high-order symbolic correlation functions. The proposed method fills the gap between two approaches, namely the likelihood estimation and the additive Markov chains. The obtained results may have applications for sequential approximation of artificial neural network training.

Accelerating Image-Domain-Warping Virtual View Synthesis on GPGPU

The image-domain-warping (IDW) method can effectively create high-quality virtual views. However, the IDW algorithm is very complex, and the software implementation for this method is far from real-time. In this paper, we propose an IDW-based view synthesis acceleration method on general-purpose computing on a graphics processing unit (GPGPU). Our method makes two main contributions. First, at the algorithm level, we employ FAST for sparse disparity estimation and adopt the successive over-relaxation iterative method to calculate warps. Second, at the platform level, two computation-intensive modules (data extraction and view synthesis) in IDW are offloaded to GPU using efficient data-level parallelism strategies. Experimental results demonstrate that our proposed acceleration method can speed up the original IDW algorithm by more than 110x, and HD stereo three-dimensional video can be converted to 8-view 4 K video (each view has an approximate 720P resolution) in real-time on a hybrid CPU + GPU (NVIDIA GTX980) platform.

A superlinear iteration method for calculation of finite length journal bearing's static equilibrium position.

Solving the static equilibrium position is one of the most important parts of dynamic coefficients calculation and further coupled calculation of rotor system. The main contribution of this study is testing the superlinear iteration convergence method—twofold secant method, for the determination of the static equilibrium position of journal bearing with finite length. Essentially, the Reynolds equation for stable motion is solved by the finite difference method and the inner pressure is obtained by the successive over-relaxation iterative method reinforced by the compound Simpson quadrature formula. The accuracy and efficiency of the twofold secant method are higher in comparison with the secant method and dichotomy. The total number of iterative steps required for the twofold secant method are about one-third of the secant method and less than one-eighth of dichotomy for the same equilibrium position. The calculations for equilibrium position and pressure distribution for different bearing length, clearance and rotating speed were done. In the results, the eccentricity presents linear inverse proportional relationship to the attitude angle. The influence of the bearing length, clearance and bearing radius on the load-carrying capacity was also investigated. The results illustrate that larger bearing length, larger radius and smaller clearance are good for the load-carrying capacity of journal bearing. The application of the twofold secant method can greatly reduce the computational time for calculation of the dynamic coefficients and dynamic characteristics of rotor-bearing system with a journal bearing of finite length.

Accelerating Flash Calculation using Compositional Space for Compositional Simulation

Compositional simulation is often required for modeling complex oil recovery processes, such as CO2 enhanced oil recovery (Chen and Reynolds, 2016; Dai et al., 2014). Flash calculation using Equation of State (EOS) is very CPU expensive in compositional simulation. Conventional approaches for initial guess of K-values usually have several levels of limitations. This paper reports our research motivated to provide trustworthy initial guess for flash calculation and further improve flash performance in isothermal processes. Reservoir fluid composition changes are categorized into two different scenarios: (a) slightly varying or constant composition changes in depletion process; and (b) sharp varying composition in gas injection process. Scenario (a) is reasonably parameterized as a compositional space of K-value and vapor mole fraction varied with pressure. Considering the actual simulation of gas injection process, a compositional space is defined via introducing a key pseudo composition as a controlling variable in addition to pressure. Flash calculation is formulated through direct solution of those non-linear equations in phase-split calculation, and solved by combining successive substitution iteration (SSI) and Newton-Raphson (NR) method. Using interpolation from the constructed compositional space, it is found that the initial guess of K-values for flash calculation are always obtained with safeguard. A variety of fluid samples has been applied for testing this new flash technique. The results show that initial guesses of K-values based on Wilson’s correlation results cause much more flash iterations and even failures in some gas injection examples. On the other hand, the proposed method shows significant advantages in reducing the number of flash iterations in all examples. In addition, the SSI procedure in flash can even be bypassed and only NR procedure and a simple Rachford-Rice Equation Preconditioning is sufficient.

Transient Coupled Borehole/Formation Fluid-Flow Model for Interpretation of Oil/Water Production Logs

Summary Interpretation of two-phase production logs (PLs) traditionally constructs borehole fluid-flow models decoupled from the physics of reservoir rocks. However, quantifying formation dynamic petrophysical properties from PLs requires simultaneous modeling of both borehole and formation fluid-flow phenomena. This paper develops a novel transient borehole/formation fluid-flow model that allows quantification of the effect of formation petrophysical properties on measurements acquired with production-logging tools (PLTs). We invoke a 1D, isothermal, two-fluid formulation to simulate borehole fluid-phase velocity, pressure, volume fraction, and density in oil/water-flow systems. The developed borehole fluid-flow model implements oil-dominant and water-dominant bubbly flow regimes with the inversion point taking place approximately when the oil volume fraction is equal to 0.5. Droplet diameter is dynamically modified to simulate interfacial drag effects, and to effectively account for variations of slip velocity in the borehole. Subsequently, a new successive iterative method interfaces the borehole and formation fluid-flow models by introducing appropriate source terms into the borehole fluid-phase mass-conservation equations. The novel iterative coupling method integrated with the developed borehole fluid-flow model allows dynamic modification of reservoir boundary conditions to accurately simulate transient behavior of borehole crossflow taking place across differentially depleted rock formations. In the case of rapid variations of near-borehole properties, frequent borehole/formation communication inevitably increases the computational time required for fluid-flow simulation. Despite this limitation, in a two-layer reservoir model penetrated by a vertical borehole, the coupling method accurately quantifies a 14% increase of volume-averaged oil-phase relative permeability of the low-pressure layer caused by through-the-borehole cross-communication of differentially depleted layers. Sensitivity analyses indicate that the alteration of near-borehole petrophysical properties primarily depends on formation average pressure, fluid-phase density contrast, and borehole-deviation angle. A practical application of the new coupled fluid-flow model is numerical simulation of borehole production measurements to estimate formation average pressure from two-phase selective-inflow-performance (SIP) analysis. This study suggests that incorporating static (shut-in) PL passes into the SIP analysis could result in misleading estimation of formation average pressure.

Convergence on successive over-relaxed iterative methods for non-Hermitian positive definite linear systems

Some convergence conditions on successive over-relaxed (SOR) iterative method and symmetric SOR (SSOR) iterative method are proposed for non-Hermitian positive definite linear systems. Some examples are given to demonstrate the results obtained.

Nonlinear impulsive differential and integral inequalities with integral jump conditions

Some new nonlinear impulsive differential inequalities and integral inequalities with integral jump conditions for discontinuous functions are established using the method of successive iteration. These jump conditions at a discontinuous point are related to the integral conditions of the past state, which can be used in the qualitative analysis of the solutions to certain nonlinear impulsive differential systems.

Boundary value problems of fractional q-difference Langevin equations

In this paper, we study the existence of positive solutions of a class of fractional q-difference Langevin equations with Caputo fractional derivative and nonlocal four-point boundary conditions. By means of fixed-point theorems and successive iteration method, some results on the existence, multiplicity and uniqueness of positive solutions are obtained.

Boundary value problems of fractional q-difference Langevin equations

In this paper, we study the existence of positive solutions of a class of fractional q-difference Langevin equations with Caputo fractional derivative and nonlocal four-point boundary conditions. By means of fixed-point theorems and successive iteration method, some results on the existence, multiplicity and uniqueness of positive solutions are obtained.

A Decomposition Method for a Unilateral Contact Problem with Tresca Friction Arising in Electro-elastostatics

This article is concerned with the numerical modeling of unilateral contact problems in an electro-elastic material with Tresca friction law and electrical conductivity condition. First, we prove the existence and uniqueness of the weak solution of the model. Rather than deriving a solution method for the full coupled problem, we present and study a successive iterative (decomposition) method. The idea is to solve successively a displacement subproblem and an electric potential subproblem in block Gauss-Seidel fashion. The displacement subproblem leads to a constraint non-differentiable (convex) minimization problem for which we propose an augmented Lagrangian algorithm. The electric potential unknown is computed explicitly using the Riesz's representation theorem. The convergence of the iterative decomposition method is proved. Some numerical experiments are carried out to illustrate the performances of the proposed algorithm.

The Riemann-Hilbert problem for mixed complex equations of first order with degenerate rank 0

This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed (ellipti-chyperbolic) complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem and prove the uniqueness of solutions for the boundary value problem. Afterwards, by using the method of successive iteration, the existence and estimates of solutions for the boundary value problem are verified. The above problem possesses the important applications to the Tricomi problem of mixed type equations of second order. In this article, the proof of Holder continuity of a singular double integer is very difficult and interesting as in this Section 4 below.

ELECTRODYNAMIC CHARACTERISTICS OF A RADIAL IMPEDANCE VIBRATOR ON A PERFECT CONDUCTION SPHERE

A problem of the spherical antenna consisting of a thin radial monopole located on a perfectly conducting sphere is solved. The antenna is excited at the base by a voltage δ-generator. An approximate analytical solution of the integral equation for the current on a thin impedance vibrator was found by the method of successive iterations. The solution is physically correct for arbitrary dimensions of the spherical antenna and for any value of surface impedance distributed along the monopole. The validity of the problem formulation is provided by using the Green's function for the Hertz vector potential in unbounded space outside the perfectly conducting sphere and by writing the initial integral equation for the current on the monopole. Influence of the monopole dimensions and surface impedance upon the radiation characteristics and the input impedance of the spherical antenna is studied by numerical evaluations using zero order approximation. The input impedance of the monopole was determined by the method of induced electromotive forces (EMF) using the current distribution function thus obtained.

Strong convergence theorems for equilibrium problems involving a family of nonexpansive mappings

We give new hybrid variants of extragradient methods for finding a common solution of an equilibrium problem and a family of nonexpansive mappings. We present a scheme that combines the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this scheme is modified by projecting on a suitable convex set to get a better convergence property under certain assumptions in a real Hilbert space.

Generalized successive overrelaxation iterative method for a class of complex symmetric linear system of equations

In this paper, to solve a broad class of complex symmetric linear systems, we recast the complex system in a real formulation and apply the generalized successive overrelaxation (GSOR) iterative method to the equivalent real system. We then investigate its convergence properties and determine its optimal iteration parameter as well as its corresponding optimal convergence factor. In addition, the resulting GSOR preconditioner is used to precondition Krylov subspace methods such as the generalized minimal residual method for solving the real equivalent formulation of the system. Finally, we give some numerical experiments to validate the theoretical results and compare the performance of the GSOR method with the modified Hermitian and skew-Hermitian splitting iteration.

New Integral Inequalities with Weakly Singular Kernel for Discontinuous Functions and Their Applications to Impulsive Fractional Differential Systems

Some new integral inequalities with weakly singular kernel for discontinuous functions are established using the method of successive iteration and properties of Mittag-Leffler function, which can be used in the qualitative analysis of the solutions to certain impulsive fractional differential systems.

Improved Particle Swarm Optimization-Based Form-Finding Method for Suspension Bridge Installation Analysis

In this paper, an improved particle swarm optimization (IPSO) method, which is based on standard particle swarm optimization (PSO) and a changing range genetic algorithm (GA), is proposed, and it is applied in the form-finding analysis of a suspension bridge installation. The new method has been integrated into the successive iteration method of the form-finding analysis, and it transfers the usual iterative process of form-finding analysis into a single objective optimization problem. The computation formulation and computer code of the IPSO have been developed and implemented, and benchmark examples are studied to test the performance of the IPSO method through numerical experiments. The results show that IPSO can be used as a viable solution methodology for the form-finding analysis in various initial, boundary, and complicated load conditions to overcome the limitations of the conventional Newton-Raphson (N-R) iterative method. Furthermore, compared with GA, PSO, and GA-PSO, IPSO has greater accuracy and efficiency. Finally, the method is applied in an actual form-finding analysis of a multitower suspension bridge (Yingwuzhou Yangtze River Bridge) to validate the practicality and feasibility of the IPSO-based method in engineering design. The case study indicates that IPSO provides superior convergent solutions for the analysis considered here when compared to the N-R method, and the computation time is affordable for large-scale engineering bridge construction design and analysis.

A new modified SSOR iteration method for solving augmented linear systems

In this paper, we present a new symmetric successive over-relaxation method to find solution of the large sparse augmented linear systems, which is the extension of the symmetric successive overrelaxation iteration method. The convergence analysis of our method is also studied. Furthermore, the functional equation between the parameters and the eigenvalues of the relevant iteration matrix is obtained. Finally, numerical computations are presented to show the effectiveness of our algorithm.