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Linearization Method (linearization + method)

Distribution by Scientific Domains

Engineering	80%

Selected Abstracts

Efficiency of base isolation systems in structural seismic protection and energetic assessment

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 10 2003
Giuseppe Carlo Marano
Abstract This paper concerns the seismic response of structures isolated at the base by means of High Damping Rubber Bearings (HDRB). The analysis is performed by using a stochastic approach, and a Gaussian zero mean filtered non-stationary stochastic process is used in order to model the seismic acceleration acting at the base of the structure. More precisely, the generalized Kanai,Tajimi model is adopted to describe the non-stationary amplitude and frequency characteristics of the seismic motion. The hysteretic differential Bouc,Wen model (BWM) is adopted in order to take into account the non-linear constitutive behaviour both of the base isolation device and of the structure. Moreover, the stochastic linearization method in the time domain is adopted to estimate the statistical moments of the non-linear system response in the state space. The non-linear differential equation of the response covariance matrix is then solved by using an iterative procedure which updates the coefficients of the equivalent linear system at each step and searches for the solution of the response covariance matrix equation. After the system response variance is estimated, a sensitivity analysis is carried out. The final aim of the research is to assess the real capacity of base isolation devices in order to protect the structures from seismic actions, by avoiding a non-linear response, with associated large plastic displacements and, therefore, by limiting related damage phenomena in structural and non-structural elements. In order to attain this objective the stochastic response of a non-linear n -dof shear-type base-isolated building is analysed; the constitutive law both of the structure and of the base devices is described, as previously reported, by adopting the BWM and by using appropriate parameters for this model, able to suitably characterize an ordinary building and the base isolators considered in the study. The protection level offered to the structure by the base isolators is then assessed by evaluating the reduction both of the displacement response and the hysteretic dissipated energy. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Numerical aspects of a real-time sub-structuring technique in structural dynamics

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2007
R. Sajeeb
Abstract A time domain coupling technique, involving combined computational and experimental modelling, for vibration analysis of structures built-up of linear/non-linear substructures is developed. The study permits, in principle, one or more of the substructures to be modelled experimentally with measurements being made only on the interfacial degrees of freedom. The numerical and experimental substructures are allowed to communicate in real time within the present framework. The proposed strategy involves a two-stage scheme: the first is iterative in nature and is implemented at the initial stages of the solution in a non-real-time format; the second is non-iterative, employs an extrapolation scheme and proceeds in real time. Issues on time delays during communications between different substructures are discussed. An explicit integration procedure is shown to lead to solutions with high accuracy while retaining path sensitivity to initial conditions. The stability of the integration scheme is also discussed and a method for numerically dissipating the temporal growth of high-frequency errors is presented. For systems with non-linear substructures, the integration procedure is based on a multi-step transversal linearization method; and, to account for time delays, we employ a multi-step extrapolation scheme based on the reproducing kernel particle method. Numerical illustrations on a few low-dimensional vibrating structures are presented and these examples are fashioned after problems of seismic qualification testing of engineering structures using real-time substructure testing techniques. Copyright © 2007 John Wiley & Sons, Ltd. [source]

,, model reduction for uncertain two-dimensional discrete systems

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 4 2005
Huijun Gao
Abstract This paper investigates the problem of ,, model reduction for two-dimensional (2-D) discrete systems with parameter uncertainties residing in a polytope. For a given robustly stable system, our attention is focused on the construction of a reduced-order model, which also resides in a polytope and approximates the original system well in an ,, norm sense. Both Fornasini,Marchesini local state-space (FMLSS) and Roesser models are considered through parameter-dependent approaches, with sufficient conditions obtained for the existence of admissible reduced-order solutions. Since these obtained conditions are not expressed as strict linear matrix inequalities (LMIs), the cone complementary linearization method is exploited to cast them into sequential minimization problems subject to LMI constraints, which can be readily solved using standard numerical software. In addition, the development of zeroth order models is also presented. Two numerical examples are provided to show the effectiveness of the proposed theories. Copyright © 2005 John Wiley & Sons, Ltd. [source]

INPUT-STATE LINEARIZATION OF A ROTARY INVERTED PENDULUM

ASIAN JOURNAL OF CONTROL, Issue 1 2004
Chih-Keng Chen
ABSTRACT The aim of this paper is to design a nonlinear controller for the rotary inverted pendulum system using the input-state linearization method. The system is linearized, and the conditions necessary for the system to be linearizable are discussed. The range of the equilibriums of the system is also investigated. Further, after the system is linearized, the linear servo controllers are designed based on the pole-placement scheme to control the output tracking problem. The performance of the controller is studied with different system parameters. The computer simulations demonstrate that the controller can effectively track the reference inputs. [source]

Dynamic Conditionally Linear Mixed Models for Longitudinal Data

BIOMETRICS, Issue 1 2002
M. Pourahmadi
Summary. We develop a new class of models, dynamic conditionally linear mixed models, for longitudinal data by decomposing the within-subject covariance matrix using a special Cholesky decomposition. Here ,dynamic' means using past responses as covariates and ,conditional linearity' means that parameters entering the model linearly may be random, but nonlinear parameters are nonrandom. This setup offers several advantages and is surprisingly similar to models obtained from the first-order linearization method applied to nonlinear mixed models. First, it allows for flexible and computationally tractable models that include a wide array of covariance structures; these structures may depend on covariates and hence may differ across subjects. This class of models includes, e.g., all standard linear mixed models, antedependence models, and Vonesh-Carter models. Second, it guarantees the fitted marginal covariance matrix of the data is positive definite. We develop methods for Bayesian inference and motivate the usefulness of these models using a series of longitudinal depression studies for which the features of these new models are well suited. [source]