Nonlinear elasto-plastic analysis of slack and taut cable structures

This paper presents the geometrically nonlinear analysis of the slack and taut cable structures considering the material inelasticity subjected to self-weight, pretension, and external loads. The finite element procedure is briefly summarized using the Lagrangian formulation associated with isoparametric interpolation polynomials and the Newton–Raphson iterative scheme with incremental load. The simple and efficient method to determine the initial equilibrium state of the slack cable systems under self-weight as well as support motions is presented using the penalty method. The numerical algorithm to evaluate the tangent modulus of elasticity of cable is presented based on the iterative scheme. The accuracy and reliability of the present study are verified by comparing the predictions with those generated by well-reported slack and taut cable structure problems. The effect of the yielding of cable segments on displacements and stresses of cable structures is investigated.     

Convergence acceleration for the iterative solution of the equations X = AX + f

A method is presented for accelerating the convergent iterative procedures of solving the system of linear equations X = AX + f. The method is also applicable to divergent iterative schemes if the number of eigenvalues of A that are greater in absolute value than unity is not very large. The method is particularly advantageous if the matrix A has not been explicitly constructed because of extensive storage requirements and if it is not possible to use the alhorithms (such as the Chebyshev and Lanzcos polynomial methods) which are designed with respect to the position of eigenvalues of A in the complex plane.     

Numerical solutions of nonlinear problems of continua—II. Survey of incompressibility constraints and software aspects

In Part I [Comput. Struct. 19, 865–877 (1984)], a comprehensive survey is provided for the formulation and solution techniques of finite element applications in nonlinear continuum mechanics problems. In this paper we extend the survey to cover incompressibility constraints and software aspects. Various methods of incorporating incompressibility constraints in the finite element formulation are discussed. The extension of these methods to account for nonlinear structural analysis is discussed. An emphasis is put on the numerical aspects of various techniques. In the software aspects, a discussion of various tools for solving nonlinear continuum mechanics problems is given. These are the general purpose programs, the special purpose programs, and the programming systems. A practical working practical example is outlined to aid in the assessment of various tools in view of specific problem requirements.     

Nonlinear topology optimization of layered shell structures

Topology stiffness (compliance) design of linear and geometrically nonlinear shell structures is solved using the SIMP approach together with a filtering scheme. A general anisotropic multi-layer shell model is employed to allow the formation of through-the-thickness holes or stiffening zones. The finite element analysis is performed using nine-node Mindlin-type shell elements based on the degenerated shell approach, which are capable of modeling both single and multi-layered structures exhibiting anisotropic or isotropic behavior. The optimization problem is solved using analytical compliance and constraint sensitivities together with the Method of Moving Asymptotes (MMA). Geometrically nonlinear problems are solved using iterative Newton–Raphson methods and an adjoint variable approach is used for the sensitivity analysis. Several benchmark tests are presented in order to illustrate the difference in optimal topologies between linear and geometrically nonlinear shell structures.     

Recovering temperature-dependent heat conductivity in 2D and 3D domains with homogenization functions as the bases

The paper solves the parameters identification problem in a nonlinear heat equation with homogenization functions as the bases, which are constructed from the boundary data of the temperature in the 2D and 3D space-time domains. To satisfy the over-specified Neumann boundary condition, a linear equations system is derived and then used to determine the expansion coefficients of the solution. Then, after back substituting the solution and collocating points to satisfy the governing equations, the space-time-dependent and temperature-dependent heat conductivity functions in 2D and 3D nonlinear heat equations are identified by solving other linear systems. The novel methods do not need iteration and solving nonlinear equations, since the unknown heat conductivities are retrieved from the solutions of linear systems. The solutions and the heat conductivity functions recovered are quite accurate in the entire space-time domain. We find that even for the inverse problems of nonlinear heat equations, the homogenization functions method is easily used to recover 2D and 3D space-time-dependent and temperature-dependent heat conductivity functions. It is interesting that the present paper makes a significant contribution to the engineering and science in the field of inverse problems of heat conductivity, merely solving linear equations and without employing iteration and solving nonlinear equations to solve nonlinear inverse problems.

     

Nonlinear Iterative Multiuser Detection and Equalization for CDMA Receivers in the Presence of Interchip Interference

Perreau, S. L., and White L. B., Nonlinear Iterative Multiuser Detection and Equalization for CDMA Receivers in the Presence of Interchip Interference, Digital Signal Processing11 (2001) 94–109This paper addresses the problem of (nonlinear) iterative multiuser detection (MUD) for synchronous CDMA. In the literature, there are several related methods for solving this problem. These methods involve a linear estimator combined with nonlinear detection of the transmitted symbols but generally do not apply per-symbol iteration. However, the convergence analysis of iterative schemes has not been addressed yet (to our knowledge). In this paper, we present a new algorithm for MUD and provide a convergence analysis for an approximation to it. We believe this approach yields an understanding not only of the behavior of our proposed scheme but also of other possible iterative algorithms for MUD.     

Parallel-vector computation with high-p element-by-element methods

A basic element-by-element formulation of the finite element method is presented. This is coupled with a bi-conjugate gradient iterative solver with Jacobi and block type preconditioners. A variety of performance calculations for linear and nonlinear test problems are presented. Results include parallel-vector perfor-mance studies on the Cray YMP and the Alliant FX/8.     

The intelligent critic framework for advanced optimal control

The idea of optimization can be regarded as an important basis of many disciplines and hence is extremely useful for a large number of research fields, particularly for artificial-intelligence-based advanced control design. Due to the difficulty of solving optimal control problems for general nonlinear systems, it is necessary to establish a kind of novel learning strategies with intelligent components. Besides, the rapid development of computer and networked techniques promotes the research on optimal control within discrete-time domain. In this paper, the bases, the derivation, and recent progresses of critic intelligence for discrete-time advanced optimal control design are presented with an emphasis on the iterative framework. Among them, the so-called critic intelligence methodology is highlighted, which integrates learning approximators and the reinforcement formulation.

     

Development of Box–Jenkins type time series models by combining conventional and orthonormal basis filter approaches

A unified scheme for developing Box–Jenkins (BJ) type models from input–output plant data by combining orthonormal basis filter (OBF) model and conventional time series models, and the procedure for the corresponding multi-step-ahead prediction are presented. The models have a deterministic part that has an OBF structure and an explicit stochastic part which has either an AR or an ARMA structure. The proposed models combine all the advantages of an OBF model over conventional linear models together with an explicit noise model. The parameters of the OBF–AR model are easily estimated by linear least square method. The OBF–ARMA model structure leads to a pseudo-linear regression where the parameters can be easily estimated using either a two-step linear least square method or an extended least square method. Models for MIMO systems are easily developed using multiple MISO models. The advantages of the proposed models over BJ models are: parameters can be easily and accurately determined without involving nonlinear optimization; a prior knowledge of time delays is not required; and the identification and prediction schemes can be easily extended to MIMO systems. The proposed methods are illustrated with two SISO simulation case studies and one MIMO, real plant pilot-scale distillation column.     

Modified alternating direction-implicit iteration method for linear systems from the incompressible Navier–Stokes equations

In order to solve the large sparse systems of linear equations arising from numerical solutions of two-dimensional steady incompressible viscous flow problems in primitive variable formulation, Ran and Yuan [On modified block SSOR iteration methods for linear systems from steady incompressible viscous flow problems, Appl. Math. Comput. 217 (2010), pp. 3050–3068] presented the block symmetric successive over-relaxation (BSSOR) and the modified BSSOR iteration methods based on the special structures of the coefficient matrices. In this study, we present the modified alternating direction-implicit (MADI) iteration method for solving the linear systems. Under suitable conditions, we establish convergence theorems for the MADI iteration method. In addition, the optimal parameter involved in the MADI iteration method is estimated in detail. Numerical experiments show that the MADI iteration method is a feasible and effective iterative solver.     

SChoA: a newly fusion of sine and cosine with chimp optimization algorithm for HLS of datapaths in digital filters and engineering applications

The spectral Legendre–Galerkin method for solving a two-dimensional nonlinear system of advection–diffusion–reaction equations on a rectangular domain is presented and compared with analytical solution. The proposed method is based on the Legendre–Galerkin formulation for the linear terms and computation of the nonlinear terms in the Chebyshev–Gauss–Lobatto points. The main difference of the spectral Legendre–Galerkin method presented in the current paper with the classic Legendre–Galerkin method is in treating the nonlinear terms and imposing boundary conditions. Indeed, in the spectral Legendre–Galerkin method the nonlinear terms are efficiently handled using the Chebyshev–Gauss–Lobatto points and also the boundary conditions are imposed strongly as collocation methods. Combination of the proposed method with a semi-implicit time integration method such as the Leapfrog–Crank–Nicolson scheme leads to reducing the complexity of computations and obtaining a linear algebraic system of equations. Efficiency and spectral accuracy of the proposed method are demonstrated numerically by some examples.

     

An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain

In this paper, we propose an iterative approach to increase the computation efficiency of the homotopy analysis method (HAM), a analytic technique for highly nonlinear problems. By means of the Schmidt–Gram process (Arfken et al., 1985)  [15], we approximate the right-hand side terms of high-order linear sub-equations by a finite set of orthonormal bases. Based on this truncation technique, we introduce the M$M$th-order iterative HAM by using each M$M$th-order approximation as a new initial guess. It is found that the iterative HAM is much more efficient than the standard HAM without truncation, as illustrated by three nonlinear differential equations defined in an infinite domain as examples. This work might greatly improve the computational efficiency of the HAM and also the Mathematica package BVPh for nonlinear BVPs.     

Convergence Analysis and Quality Criteria for an Iterative Schematization of Networks

Schematic networks are linear abstractions of functional networks, such as route networks. Lines in the original network are modified in order to produce a schematic network which satisfies a set of constraints chosen to design the network. A method is described which accomplishes this line transformation using an iterative improvement technique driven by design constraints. The method maintains topological characteristics of the network by the use of simple geometric operations and tests. The iterative process can be repeated until the line displacements become small enough or until it meets user defined stopping criteria. Experimental results are provided to examine the acceptability of outcomes and the convergence of the applied iterative technique. Criteria for measuring the quality of results, as well as for stopping the iterative approach are presented.

L2–L∞ fuzzy control for Markov jump systems with neutral time-delays

The L₂–L_∞ fuzzy control problem is considered for nonlinear stochastic Markov jump systems with neutral time-delays. By means of Takagi–Sugeno fuzzy models, the fuzzy controller systems and the overall closed-loop fuzzy dynamics are constructed. A sufficient condition is firstly established on the stochastic stability using stochastic Lyapunov–Krasovskii functional. Then in terms of linear matrix inequalities techniques, the sufficient conditions on the existence of mode-dependent state feedback L₂–L_∞ fuzzy controller are presented and proved respectively for constant and time varying case. Finally, the design problems are formulated as optimization algorithms. Simulation results are exploited to illustrate the effectiveness of the developed techniques.     

Structural topology synthesis with dynamics and nonlinearities using equivalent linear systems

Topology optimization for nonlinear and dynamic problems is expensive because of the necessity to solve the equations of motion at every optimization iteration in order to evaluate the objective function and constraints. In this work, an iterative methodology is developed using the concept of an equivalent linear system for the topology synthesis of structures undergoing nonlinear and dynamic response, using minimal nonlinear response evaluations. The approach uses equivalent loads obtained from nonlinear dynamic analysis to perform optimization iterations, during the course of which the nonlinear and dynamic system is continuously approximated. In this process, the optimization is decoupled from the nonlinear dynamic analysis. Results are presented for various kinds of nonlinear and dynamic problems showing the effectiveness of the developed approach.     

Constrained multisine input signals for plant-friendly identification of chemical process systems

This paper considers the use of constrained minimum crest factor multisine signals as inputs for plant-friendly identification testing of chemical process systems. The methodology presented here effectively integrates operating restrictions, information-theoretic requirements, and state-of-the-art optimization techniques to design minimum crest factor multisine signals meeting important user-specified time and frequency domain properties. A series of optimization problem formulations relevant to problems in linear, nonlinear, and multivariable system identification are presented; these culminate with their application to the modeling of the Weischedel–McAvoy high-purity distillation column problem, a demanding nonlinear and highly interactive system. The effectiveness of these signals for modeling for control purposes and the ability to incorporate a priori nonlinear models in the signal design procedure are demonstrated in this distillation system case study.     

Electron image processing: 1978–1980

Computer processing of electron microscope images has developed and expanded rapidly since the preceding bibliography in this series appeared [P. W. Hawkes, Computer Graphics and Image Processing, 8, 1978, 406–446]. The publications listed are grouped into the following classes: general works; image formation; linear processing; nonlinear problems; image handling; and high resolution and lattice imagery.     

A meshless FPM model for solving nonlinear material problems with proportional loading based on deformation theory

In this work a methodology of meshless finite points method for the analysis of nonlinear material problems with proportional loading based on deformation theory is presented.In finite points method the approximation around each point is obtained by using weighted least square techniques. The discrete system of equation is constructed by means of a point collocation procedure. The non-dependence on a mesh or integration procedures is an important aspect which transforms the finite point method in a truly meshless technique.Hencky’s total deformation theory and an elastic approach is used on the determination of stress–strain fields. This approach introduces the concept of effective material properties which are considered as spatial field variables and to be functions of equilibrium stress state and material properties.The present results are in good agreement with those obtained by nonlinear finite element method and previous work in this meshless context. Nevertheless the present methodology is based on a strong formulation, keeping the meshless characteristics of FPM.     

LTI approximation of nonlinear systems via signal distribution theory

L₂ and L₁ optimal linear time-invariant (LTI) approximation of discrete-time nonlinear systems, such as nonlinear finite impulse response (NFIR) systems, is studied via a signal distribution theory motivated approach. The use of a signal distribution theoretic framework facilitates the formulation and analysis of many system modelling problems, including system identification problems. Specifically, a very explicit solution to the L₂ (least squares) LTI approximation problem for NFIR systems is obtained in this manner. Furthermore, the L₁ (least absolute deviations) LTI approximation problem for NFIR systems is essentially reduced to a linear programming problem. Active LTI modelling emphasizes model quality based on the intended use of the models in linear controller design. Robust stability and LTI approximation concepts are studied here in a nonlinear systems context. Numerical examples are given illustrating the performance of the least squares (LS) method and the least absolute deviations (LAD) method with LTI models against nonlinear unmodelled dynamics.