Trajectory Sensitivity Method and Master-Slave Synchronization to Estimate Parameters of Nonlinear Systems

A combination of trajectory sensitivity method and master-slave synchronization was proposed to parameter estimation of nonlinear systems. It was shown that master-slave coupling increases the robustness of the trajectory sensitivity algorithm with respect to the initial guess of parameters. Since synchronization is not a guarantee that the estimation process converges to the correct parameters, a conditional test that guarantees that the new combined methodology estimates the true values of parameters was proposed. This conditional test was successfully applied to Lorenz's and Chua's systems, and the proposed parameter estimation algorithm has shown to be very robust with respect to parameter initial guesses and measurement noise for these examples. Copyright (C) 2009 Elmer P. T. Cari et al.

GENERALIZED FINITE ELEMENT METHOD FOR NONLINEAR THREE-DIMENSIONAL ANALYSIS OF SOLIDS

The Generalized Finite Element Method (GFEM) is employed in this paper for the numerical analysis of three-dimensional solids tinder nonlinear behavior. A brief summary of the GFEM as well as a description of the formulation of the hexahedral element based oil the proposed enrichment strategy are initially presented. Next, in order to introduce the nonlinear analysis of solids, two constitutive models are briefly reviewed: Lemaitre`s model, in which damage and plasticity are coupled, and Mazars`s damage model suitable for concrete tinder increased loading. Both models are employed in the framework of a nonlocal approach to ensure solution objectivity. In the numerical analyses carried out, a selective enrichment of approximation at regions of concern in the domain (mainly those with high strain and damage gradients) is exploited. Such a possibility makes the three-dimensional analysis less expensive and practicable since re-meshing resources, characteristic of h-adaptivity, can be minimized. Moreover, a combination of three-dimensional analysis and the selective enrichment presents a valuable good tool for a better description of both damage and plastic strain scatterings.

An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations

The applicability of a meshfree approximation method, namely the EFG method, on fully geometrically exact analysis of plates is investigated. Based on a unified nonlinear theory of plates, which allows for arbitrarily large rotations and displacements, a Galerkin approximation via MLS functions is settled. A hybrid method of analysis is proposed, where the solution is obtained by the independent approximation of the generalized internal displacement fields and the generalized boundary tractions. A consistent linearization procedure is performed, resulting in a semi-definite generalized tangent stiffness matrix which, for hyperelastic materials and conservative loadings, is always symmetric (even for configurations far from the generalized equilibrium trajectory). Besides the total Lagrangian formulation, an updated version is also presented, which enables the treatment of rotations beyond the parameterization limit. An extension of the arc-length method that includes the generalized domain displacement fields, the generalized boundary tractions and the load parameter in the constraint equation of the hyper-ellipsis is proposed to solve the resulting nonlinear problem. Extending the hybrid-displacement formulation, a multi-region decomposition is proposed to handle complex geometries. A criterium for the classification of the equilibrium`s stability, based on the Bordered-Hessian matrix analysis, is suggested. Several numerical examples are presented, illustrating the effectiveness of the method. Differently from the standard finite element methods (FEM), the resulting solutions are (arbitrary) smooth generalized displacement and stress fields. (c) 2007 Elsevier Ltd. All rights reserved.

Galerkin Method and Weighting Functions Applied to Nonlinear H(infinity) Control with Output Feedback

This paper considers two aspects of the nonlinear H(infinity) control problem: the use of weighting functions for performance and robustness improvement, as in the linear case, and the development of a successive Galerkin approximation method for the solution of the Hamilton-Jacobi-Isaacs equation that arises in the output-feedback case. Design of nonlinear H(infinity) controllers obtained by the well-established Taylor approximation and by the proposed Galerkin approximation method applied to a magnetic levitation system are presented for comparison purposes.

An improved novel method for solving nonlinear boundary value problems

A modified formula for the integral transform of a nonlinear function is proposed for a class of nonlinear boundary value problems. The technique presented in this paper results in analytical solutions. Iterations and initial guess, which are needed in other techniques, are not required in this novel technique. The analytical solutions are found to agree surprisingly well with the numerically exact solutions for two examples of power law reaction and Langmuir-Hinshelwood reaction in a catalyst pellet.

A filter inexact-restoration method for nonlinear programming

A new iterative algorithm based on the inexact-restoration (IR) approach combined with the filter strategy to solve nonlinear constrained optimization problems is presented. The high level algorithm is suggested by Gonzaga et al. (SIAM J. Optim. 14:646–669, 2003) but not yet implement—the internal algorithms are not proposed. The filter, a new concept introduced by Fletcher and Leyffer (Math. Program. Ser. A 91:239–269, 2002), replaces the merit function avoiding the penalty parameter estimation and the difficulties related to the nondifferentiability. In the IR approach two independent phases are performed in each iteration, the feasibility and the optimality phases. The line search filter is combined with the first one phase to generate a “more feasible” point, and then it is used in the optimality phase to reach an “optimal” point. Numerical experiences with a collection of AMPL problems and a performance comparison with IPOPT are provided.

The potential field method and the nonlinear attractor dynamics approach: what are the differences?

One of the most popular approaches to path planning and control is the potential field method. This method is particularly attractive because it is suitable for on-line feedback control. In this approach the gradient of a potential field is used to generate the robot's trajectory. Thus, the path is generated by the transient solutions of a dynamical system. On the other hand, in the nonlinear attractor dynamic approach the path is generated by a sequence of attractor solutions. This way the transient solutions of the potential field method are replaced by a sequence of attractor solutions (i.e., asymptotically stable states) of a dynamical system. We discuss at a theoretical level some of the main differences of these two approaches.

Nonlinear optimization for human-like synchronous movements of a dual arm-hand robotic system

In previous work we have presented a model capable of generating human-like movements for a dual arm-hand robot involved in human-robot cooperative tasks. However, the focus was on the generation of reach-to-grasp and reach-to-regrasp bimanual movements and no synchrony in timing was taken into account. In this paper we extend the previous model in order to accomplish bimanual manipulation tasks by synchronously moving both arms and hands of an anthropomorphic robotic system. Specifically, the new extended model has been designed for two different tasks with different degrees of difficulty. Numerical results were obtained by the implementation of the IPOPT solver embedded in our MATLAB simulator.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Nonlinear models and small sample performance of the generalized method of moments

In this paper I explore the issue of nonlinearity (both in the datageneration process and in the functional form that establishes therelationship between the parameters and the data) regarding the poorperformance of the Generalized Method of Moments (GMM) in small samples.To this purpose I build a sequence of models starting with a simple linearmodel and enlarging it progressively until I approximate a standard (nonlinear)neoclassical growth model. I then use simulation techniques to find the smallsample distribution of the GMM estimators in each of the models.

Prediction of Recanalization Trumps Prediction of Tissue Fate: The Penumbra: A Dual-edged Sword.

BACKGROUND AND PURPOSE: To determine whether infarct core or penumbra is the more significant predictor of outcome in acute ischemic stroke, and whether the results are affected by the statistical method used. METHODS: Clinical and imaging data were collected in 165 patients with acute ischemic stroke. We reviewed the noncontrast head computed tomography (CT) to determine the Alberta Score Program Early CT score and assess for hyperdense middle cerebral artery. We reviewed CT-angiogram for site of occlusion and collateral flow score. From perfusion-CT, we calculated the volumes of infarct core and ischemic penumbra. Recanalization status was assessed on early follow-up imaging. Clinical data included age, several time points, National Institutes of Health Stroke Scale at admission, treatment type, and modified Rankin score at 90 days. Two multivariate regression analyses were conducted to determine which variables predicted outcome best. In the first analysis, we did not include recanalization status among the potential predicting variables. In the second, we included recanalization status and its interaction between perfusion-CT variables. RESULTS: Among the 165 study patients, 76 had a good outcome (modified Rankin score ≤2) and 89 had a poor outcome (modified Rankin score >2). In our first analysis, the most important predictors were age (P<0.001) and National Institutes of Health Stroke Scale at admission (P=0.001). The imaging variables were not important predictors of outcome (P>0.05). In the second analysis, when the recanalization status and its interaction with perfusion-CT variables were included, recanalization status and perfusion-CT penumbra volume became the significant predictors (P<0.001). CONCLUSIONS: Imaging prediction of tissue fate, more specifically imaging of the ischemic penumbra, matters only if recanalization can also be predicted.

A frequency-domain pseudo-force method for dynamic structural analysis nonlinear systems and nonproportional damping

A frequency-domain method for nonlinear analysis of structural systems with viscous, hysteretic, nonproportional and frequency-dependent damping is presented. The nonlinear effects and nonproportional damping are considered through pseudo-force terms. The modal coordinates uncoupled equations are iteratively solved. The treatment of initial conditions in the frequency domain which is necessary for the treatment of the uncoupled equations is initially adressed.

Covalidation of Integral Transforms and Method of Lines in Nonlinear Convection-Diffusion with Mathematica

The Mathematica system (version 4.0) is employed in the solution of nonlinear difusion and convection-difusion problems, formulated as transient one-dimensional partial diferential equations with potential dependent equation coefficients. The Generalized Integral Transform Technique (GITT) is first implemented for the hybrid numerical-analytical solution of such classes of problems, through the symbolic integral transformation and elimination of the space variable, followed by the utilization of the built-in Mathematica function NDSolve for handling the resulting transformed ODE system. This approach ofers an error-controlled final numerical solution, through the simultaneous control of local errors in this reliable ODE's solver and of the proposed eigenfunction expansion truncation order. For covalidation purposes, the same built-in function NDSolve is employed in the direct solution of these partial diferential equations, as made possible by the algorithms implemented in Mathematica (versions 3.0 and up), based on application of the method of lines. Various numerical experiments are performed and relative merits of each approach are critically pointed out.

Estimating Nonlinear DSGE Models by the Simulated Method of Moments

This paper studies the application of the simulated method of moments (SMM) for the estimation of nonlinear dynamic stochastic general equilibrium (DSGE) models. Monte Carlo analysis is employed to examine the small-sample properties of SMM in specifications with different curvature. Results show that SMM is computationally efficient and delivers accurate estimates, even when the simulated series are relatively short. However, asymptotic standard errors tend to overstate the actual variability of the estimates and, consequently, statistical inference is conservative. A simple strategy to incorporate priors in a method of moments context is proposed. An empirical application to the macroeconomic effects of rare events indicates that negatively skewed productivity shocks induce agents to accumulate additional capital and can endogenously generate asymmetric business cycles.

Studies of nonlinear absorption and aggregation in aqueous solutions of rhodamine 6G using a transient thermal lens technique

Dual-beam transient thermal lens studies were carried out in aqueous solutions of rhodamine 6G using 532 nm pulses from a frequency-doubled Nd:YAG laser. The analysis of the observed data showed that the thermal lens method can effectively be utilized to study the nonlinear absorption and aggregation which are taking place in a dye medium.