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Linearization
Kinds of Linearization Terms modified by Linearization Selected AbstractsINPUT-STATE LINEARIZATION OF A ROTARY INVERTED PENDULUMASIAN JOURNAL OF CONTROL, Issue 1 2004Chih-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] SVG Linearization and AccessibilityCOMPUTER GRAPHICS FORUM, Issue 4 2002Ivan Herman Abstract The usage of SVG (Scaleable Vector Graphics) creates new possibilities as well as new challenges for theaccessibility of Web sites. This paper presents a metadata vocabulary to describe the information content ofan SVG file geared towards accessibility. When used with a suitable tool, this metadata description can helpin generating a textual ("linear") version of the content, which can be used for users with disabilities or withnon-visual devices. Although this paper concentrates on SVG, i.e. on graphics on the Web, the metadata approach and vocabularypresented below can be applied in relation to other technologies, too. Indeed, accessibility issues have a muchwider significance, and have an effect on areas like CAD, cartography, or information visualization. Hence, theexperiences of the work presented below may also be useful for practitioners in other areas. ACM CSS: I.3.4 Graphics Utilities,Graphics Packages, I.3.6 Methodology and Techniques,Graphics datastructures and data types, Standards, K.4.2 Social Issues,Assistive technologies for persons with disabilities [source] Linearization of second-order calibration curves in stable isotope dilution,mass spectrometryFLAVOUR AND FRAGRANCE JOURNAL, Issue 3 2001Laurent B. Fay Abstract The quantification of compounds using isotope dilution mass spectrometry requires the establishment of calibration curves prior to determination of any unknown sample. When calibration over a wide concentration range is required and/or when an overlap exists between internal standard and analyte ions (if mono- or di-isotopically-labelled internal standards are used), second-order calibration curves are obtained. In this paper we have compared several calculation methods to linearize such calibration curves. We found that the method published by Bush and Trager6 gives a satisfactory linear relationship between the corrected amount ratio y = Ql(Qu+tQl) (the value Qu being the amount of unlabelled analyte, Ql the amount of labelled internal standard and t, the fixed fraction of the internal standard, which is identical to the unlabelled analyte) and the ratio of unlabelled to labelled ion intensities. All the other calculation methods that have been published so far have failed to linearize the second-order calibration curve build-up over a wide concentration range. Copyright © 2001 John Wiley & Sons, Ltd. [source] Stabilized finite element method for viscoplastic flow: formulation with state variable evolutionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003Antoinette M. Maniatty Abstract A stabilized, mixed finite element formulation for modelling viscoplastic flow, which can be used to model approximately steady-state metal-forming processes, is presented. The mixed formulation is expressed in terms of the velocity, pressure and state variable fields, where the state variable is used to describe the evolution of the material's resistance to plastic flow. The resulting system of equations has two sources of well-known instabilities, one due to the incompressibility constraint and one due to the convection-type state variable equation. Both of these instabilities are handled by adding mesh-dependent stabilization terms, which are functions of the Euler,Lagrange equations, to the usual Galerkin method. Linearization of the weak form is derived to enable a Newton,Raphson implementation into an object-oriented finite element framework. A progressive solution strategy is used for improving convergence for highly non-linear material behaviour, typical for metals. Numerical experiments using the stabilization method with hierarchic shape functions for the velocity, pressure and state variable fields in viscoplastic flow and metal-forming problems show that the stabilized finite element method is effective and efficient for non-linear steady forming problems. Finally, the results are discussed and conclusions are inferred. Copyright © 2002 John Wiley & Sons, Ltd. [source] Nonlinear Control VIA Generalized Feedback Linearization Using Neural NetworksASIAN JOURNAL OF CONTROL, Issue 2 2001Graham C. Goodwin ABSTRACT A novel approach to nonlinear control, called Generalized Feedback Linearization (GFL), is presented. This new strategy overcomes one important drawback of the well known Feedback Linearization strategy, in the sense that it is able to handle a broader class of nonlinear systems, namely those having unstable zero dynamics. It is shown that the use of a nonlinear predictor for the system output is a key feature in the derivation of the control strategy. For certain types of systems this predictor can be found as a nonlinear function of the system input and output, allowing an output feedback control solution. The use of Artificial Neural Networks (ANN) to directly parameterize the predictor of the controlled variable when an explicit model for the system is not available, is investigated via computer simulations. This approach is based on the functional approximation capability of multi layer ANN. [source] Post-earthquake bridge repair cost and repair time estimation methodologyEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 3 2010Kevin R. Mackie Abstract While structural engineers have traditionally focused on individual components (bridges, for example) of transportation networks for design, retrofit, and analysis, it has become increasingly apparent that the economic costs to society after extreme earthquake events are caused at least as much from indirect costs as direct costs due to individual structures. This paper describes an improved methodology for developing probabilistic estimates of repair costs and repair times that can be used for evaluating the performance of new bridge design options and existing bridges in preparation for the next major earthquake. The proposed approach in this paper is an improvement on previous bridge loss modeling studies,it is based on the local linearization of the dependence between repair quantities and damage states so that the resulting model follows a linear relationship between damage states and repair points. The methodology uses the concept of performance groups (PGs) that account for damage and repair of individual bridge components and subassemblies. The method is validated using two simple examples that compare the proposed method to simulation and previous methods based on loss models using a power,law relationship between repair quantities and damage. In addition, an illustration of the method is provided for a complete study on the performance of a common five-span overpass bridge structure in California. Intensity-dependent repair cost ratios (RCRs) and repair times are calculated using the proposed approach, as well as plots that show the disaggregation of repair cost by repair quantity and by PG. This provides the decision maker with a higher fidelity of data when evaluating the contribution of different bridge components to the performance of the bridge system, where performance is evaluated in terms of repair costs and repair times rather than traditional engineering quantities such as displacements and stresses. Copyright © 2009 John Wiley & Sons, Ltd. [source] Stability improvement in power systems with non-linear TCSC control strategiesEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 6 2000X. Lei In this paper, a non-linear control scheme for the TCSC (thyristor-controlled series compensator) to dampen power oscillations and to improve the transient stability of power systems is presented. Based on an one-machine-infinite-bus system, a non-linear mathematical model is established which is proven as an affine nonlinear system. With the help of the feedback linearization technique, the affine non-linear model is exactly transferred to a linear model, and then the control scheme is designed for the TCSC based on the global linearization, where the input signal uses local measurements only. The effectiveness and robustness of the proposed non-linear control scheme are demonstrated with an one-machine test system, where the TCSC modelling and power system simulations are performed by using the program system NETOMAC. In comparison with a conventional control scheme, significant improvements of dynamical performance in the test power' system are achieved by the proposed non-linear control strategy for the TCSC. [source] Spectral Theory for Perturbed SystemsGAMM - MITTEILUNGEN, Issue 1 2009Fritz Colonius Abstract This paper presents an overview of topological, smooth, and control techniques for dynamical systems and their interrelations for the study of perturbed systems. We concentrate on spectral analysis via linearization of systems. Emphasis is placed on parameter dependent perturbed systems and on a comparison of the Markovian and the dynamical structure of systems with Markov diffusion perturbation process. A number of applications is provided (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A hybrid fast algorithm for first arrivals tomographyGEOPHYSICAL PROSPECTING, Issue 5 2009Manuela Mendes ABSTRACT A hybrid algorithm, combining Monte-Carlo optimization with simultaneous iterative reconstructive technique (SIRT) tomography, is used to invert first arrival traveltimes from seismic data for building a velocity model. Stochastic algorithms may localize a point around the global minimum of the misfit function but are not suitable for identifying the precise solution. On the other hand, a tomographic model reconstruction, based on a local linearization, will only be successful if an initial model already close to the best solution is available. To overcome these problems, in the method proposed here, a first model obtained using a classical Monte Carlo-based optimization is used as a good initial guess for starting the local search with the SIRT tomographic reconstruction. In the forward problem, the first-break times are calculated by solving the eikonal equation through a velocity model with a fast finite-difference method instead of the traditional slow ray-tracing technique. In addition, for the SIRT tomography the seismic energy from sources to receivers is propagated by applying a fast Fresnel volume approach which when combined with turning rays can handle models with both positive and negative velocity gradients. The performance of this two-step optimization scheme has been tested on synthetic and field data for building a geologically plausible velocity model. This is an efficient and fast search mechanism, which permits insertion of geophysical, geological and geodynamic a priori constraints into the grid model and ray path is completed avoided. Extension of the technique to 3D data and also to the solution of ,static correction' problems is easily feasible. [source] Traveltime computation with the linearized eikonal equation for anisotropic mediaGEOPHYSICAL PROSPECTING, Issue 4 2002Tariq Alkhalifah A linearized eikonal equation is developed for transversely isotropic (TI) media with a vertical symmetry axis (VTI). It is linear with respect to perturbations in the horizontal velocity or the anisotropy parameter ,. An iterative linearization of the eikonal equation is used as the basis for an algorithm of finite-difference traveltime computations. A practical implementation of this iterative technique is to start with a background model that consists of an elliptically anisotropic, inhomogeneous medium, since traveltimes for this type of medium can be calculated efficiently using eikonal solvers, such as the fast marching method. This constrains the perturbation to changes in the anisotropy parameter , (the parameter most responsible for imaging improvements in anisotropic media). The iterative implementation includes repetitive calculation of , from traveltimes, which is then used to evaluate the perturbation needed for the next round of traveltime calculations using the linearized eikonal equation. Unlike isotropic media, interpolation is needed to estimate , in areas where the traveltime field is independent of ,, such as areas where the wave propagates vertically. Typically, two to three iterations can give sufficient accuracy in traveltimes for imaging applications. The cost of each iteration is slightly less than the cost of a typical eikonal solver. However, this method will ultimately provide traveltime solutions for VTI media. The main limitation of the method is that some smoothness of the medium is required for the iterative implementation to work, especially since we evaluate derivatives of the traveltime field as part of the iterative approach. If a single perturbation is sufficient for the traveltime calculation, which may be the case for weak anisotropy, no smoothness of the medium is necessary. Numerical tests demonstrate the robustness and efficiency of this approach. [source] Implicit integration of a mixed isotropic,kinematic hardening plasticity model for structured claysINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2008Angelo Amorosi Abstract In recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterized by complex formulations, often leading to non-trivial problems in their numerical integration in finite elements codes. The paper describes a fully implicit stress-point algorithm for the numerical integration of a single-surface mixed isotropic,kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterizing the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterized by an ellipsoid-shaped yield function, inside which a stress-dependent reversible stiffness is accounted for by a non-linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam-Clay one to include plastic strain-driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space. The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global-level Newton,Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem. Copyright © 2007 John Wiley & Sons, Ltd. [source] Analysis of the solid phase stress tensor in multiphase porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2007William G. Gray Abstract Conservation equations for mass, momentum, energy, and entropy are formulated for the phases and interfaces of a three-phase system consisting of a solid and two immiscible fluids. The microscale equations are averaged to the macroscale by integration over a representative elementary volume. Thermodynamic statements for each of the phases and interface entities are also formulated at the microscale and then averaged to the macroscale. This departure from most uses of thermodynamics in macroscale analysis ensures consistency between models and parameters at the two scales. The expressions for the macroscale rates of change of internal energy are obtained by differentiating the derived forms for energy and making use of averaging theorems. These thermodynamic expressions, along with the conservation equations, serve as constraints on the entropy inequality. A linearization of the resulting equations is employed to investigate the theoretical origins of the Biot coefficient that relates the hydrostatic part of the total stress tensor to the normal force applied at the solid surface by the pore fluids. The results here are placed in the context of other formulations and expressions that appear in the literature. Copyright © 2006 John Wiley & Sons, Ltd. [source] Steady infiltration from buried point source into heterogeneous cross-anisotropic unsaturated soilINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2004G. J. Chen Abstract The paper presents the analytical solution for the steady-state infiltration from a buried point source into two types of heterogeneous cross-anisotropic unsaturated half-spaces. In the first case, the heterogeneity of the soil is modelled by an exponential relationship between the hydraulic conductivity and the soil depth. In the second case, the heterogeneous soil is represented by a multilayered half-space where each layer is homogeneous. The hydraulic conductivity varies exponentially with moisture potential and this leads to the linearization of the Richards equation governing unsaturated flow. The analytical solution is obtained by using the Hankel integral transform. For the multilayered case, the combination of a special forward and backward transfer matrix techniques makes the numerical evaluation of the solution very accurate and efficient. The correctness of both formulations is validated by comparison with alternative solutions for two different cases. The results from typical cases are presented to illustrate the influence on the flow field of the cross-anisotropic hydraulic conductivity, the soil heterogeneity and the depth of the source. Copyright © 2004 John Wiley & Sons, Ltd. [source] Direct assessment of structural resistance against pressurized fractureINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2003G. Bolzon Abstract The determination of the load bearing capacity of hydraulic structures such as dams, reservoirs and retaining walls requires the consideration of mixed-mode fracture, possibly driven by the fluid pressure, in correspondence to artificial and natural joints (or cracks, in the latter case). A friction-cohesive softening interface model with coupled degradation of normal and tangential strength is introduced here to account for the essential features of the joint behaviour; its predictive capability is assessed through extensive calculations. Alternative numerical techniques resting on the discrete-crack approach are considered, focusing on simplified approaches for the direct appraisal of the structural resistance. Comparison is made with the results of evolutionary analyses, based on a priori piecewise linearization of the interface model and on ,exact integration'. Copyright © 2003 John Wiley & Sons, Ltd. [source] Solving limit analysis problems: an interior-point methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2005F. Pastor Abstract This paper exposes an interior-point method used to solve convex programming problems raised by limit analysis in mechanics. First we explain the main features of this method, describing in particular its typical iteration. Secondly, we show and study the results of its application to a concrete limit analysis problem, for a large range of sizes, and we compare them for validation with existing results and with those of linearized versions of the problem. As one of the objectives of the work, another classical problem is analysed for a Gurson material, to which linearization or conic programming does not apply. Copyright © 2005 John Wiley & Sons, Ltd. [source] A dual mortar approach for 3D finite deformation contact with consistent linearizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010Alexander Popp Abstract In this paper, an approach for three-dimensional frictionless contact based on a dual mortar formulation and using a primal,dual active set strategy for direct constraint enforcement is presented. We focus on linear shape functions, but briefly address higher order interpolation as well. The study builds on previous work by the authors for two-dimensional problems. First and foremost, the ideas of a consistently linearized dual mortar scheme and of an interpretation of the active set search as a semi-smooth Newton method are extended to the 3D case. This allows for solving all types of nonlinearities (i.e. geometrical, material and contact) within one single Newton scheme. Owing to the dual Lagrange multiplier approach employed, this advantage is not accompanied by an undesirable increase in system size as the Lagrange multipliers can be condensed from the global system of equations. Moreover, it is pointed out that the presented method does not make use of any regularization of contact constraints. Numerical examples illustrate the efficiency of our method and the high quality of results in 3D finite deformation contact analysis. Copyright © 2010 John Wiley & Sons, Ltd. [source] A contact algorithm for frictional crack propagation with the extended finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2008Fushen Liu Abstract We present an incremental quasi-static contact algorithm for path-dependent frictional crack propagation in the framework of the extended finite element (FE) method. The discrete formulation allows for the modeling of frictional contact independent of the FE mesh. Standard Coulomb plasticity model is introduced to model the frictional contact on the surface of discontinuity. The contact constraint is borrowed from non-linear contact mechanics and embedded within a localized element by penalty method. Newton,Raphson iteration with consistent linearization is used to advance the solution. We show the superior convergence performance of the proposed iterative method compared with a previously published algorithm called ,LATIN' for frictional crack propagation. Numerical examples include simulation of crack initiation and propagation in 2D plane strain with and without bulk plasticity. In the presence of bulk plasticity, the problem is also solved using an augmented Lagrangian procedure to demonstrate the efficacy and adequacy of the standard penalty solution. Copyright © 2008 John Wiley & Sons, Ltd. [source] A two-dimensional stochastic algorithm for the solution of the non-linear Poisson,Boltzmann equation: validation with finite-difference benchmarks,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2006Kausik Chatterjee Abstract This paper presents a two-dimensional floating random walk (FRW) algorithm for the solution of the non-linear Poisson,Boltzmann (NPB) equation. In the past, the FRW method has not been applied to the solution of the NPB equation which can be attributed to the absence of analytical expressions for volumetric Green's functions. Previous studies using the FRW method have examined only the linearized Poisson,Boltzmann equation. No such linearization is needed for the present approach. Approximate volumetric Green's functions have been derived with the help of perturbation theory, and these expressions have been incorporated within the FRW framework. A unique advantage of this algorithm is that it requires no discretization of either the volume or the surface of the problem domains. Furthermore, each random walk is independent, so that the computational procedure is highly parallelizable. In our previous work, we have presented preliminary calculations for one-dimensional and quasi-one-dimensional benchmark problems. In this paper, we present the detailed formulation of a two-dimensional algorithm, along with extensive finite-difference validation on fully two-dimensional benchmark problems. The solution of the NPB equation has many interesting applications, including the modelling of plasma discharges, semiconductor device modelling and the modelling of biomolecular structures and dynamics. Copyright © 2005 John Wiley & Sons, Ltd. [source] A spectral-element method for modelling cavitation in transient fluid,structure interactionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004M. A. Sprague Abstract In an underwater-shock environment, cavitation (boiling) occurs as a result of reflection of the shock wave from the free surface and/or wetted structure causing the pressure in the water to fall below its vapour pressure. If the explosion is sufficiently distant from the structure, the motion of the fluid surrounding the structure may be assumed small, which allows linearization of the governing fluid equations. In 1984, Felippa and DeRuntz developed the cavitating acoustic finite-element (CAFE) method for modelling this phenomenon. While their approach is robust, it is too expensive for realistic 3D simulations. In the work reported here, the efficiency and flexibility of the CAFE approach has been substantially improved by: (i) separating the total field into equilibrium, incident, and scattered components, (ii) replacing the bilinear CAFE basis functions with high-order Legendre-polynomial basis functions, which produces a cavitating acoustic spectral element (CASE) formulation, (iii) employing a simple, non-conformal coupling method for the structure and fluid finite-element models, and (iv) introducing structure,fluid time-step subcycling. Field separation provides flexibility, as it admits non-acoustic incident fields that propagate without numerical dispersion. The use of CASE affords a significant reduction in the number of fluid degrees of freedom required to reach a given level of accuracy. The combined use of subcycling and non-conformal coupling affords order-of-magnitude savings in computational effort. These benefits are illustrated with 1D and 3D canonical underwatershock problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] Finite element formulation for modelling large deformations in elasto-viscoplastic polycrystalsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004Karel Matou Abstract Anisotropic, elasto-viscoplastic behaviour in polycrystalline materials is modelled using a new, updated Lagrangian formulation based on a three-field form of the Hu-Washizu variational principle to create a stable finite element method in the context of nearly incompressible behaviour. The meso-scale is characterized by a representative volume element, which contains grains governed by single crystal behaviour. A new, fully implicit, two-level, backward Euler integration scheme together with an efficient finite element formulation, including consistent linearization, is presented. The proposed finite element model is capable of predicting non-homogeneous meso-fields, which, for example, may impact subsequent recrystallization. Finally, simple deformations involving an aluminium alloy are considered in order to demonstrate the algorithm. Copyright © 2004 John Wiley & Sons, Ltd. [source] Theory and numerics of geometrically non-linear open system mechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2003E. Kuhl Abstract The present contribution aims at deriving a general theoretical and numerical framework for open system thermodynamics. The balance equations for open systems differ from the classical balance equations by additional terms arising from possible local changes in mass. In contrast to existing formulations, these changes not only originate from additional mass sources or sinks but also from a possible in- or outflux of matter. Constitutive equations for the mass source and the mass flux are discussed for the particular model problem of bone remodelling in hard tissue mechanics. Particular emphasis is dedicated to the spatial discretization of the coupled system of the balance of mass and momentum. To this end we suggest a geometrically non-linear monolithic finite element based solution technique introducing the density and the deformation map as primary unknowns. It is supplemented by the consistent linearization of the governing equations. The resulting algorithm is validated qualitatively for classical examples from structural mechanics as well as for biomechanical applications with particular focus on the functional adaption of bones. It turns out that, owing to the additional incorporation of the mass flux, the proposed model is able to simulate size effects typically encountered in microstructural materials such as open-pored cellular solids, e.g. bones. Copyright © 2003 John Wiley & Sons, Ltd. [source] Volume-dependent pressure loading and its influence on the stability of structuresINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003T. Rumpel Abstract Deformation-dependent pressure loading on solid structures is created by the interaction of gas with the deformable surface of a structure. Such fairly simple load models are valid for static and quasi-static analyses and they are a very efficient tool to represent the influence of gas on the behaviour of structures. Completing previous studies on the deformation dependence of the loading with the assumption of infinite gas volumes, the current contribution is focusing on the influence of modifications of the size and shape of a finite volume containing the gas in particular on the stability of structures. The linearization of the corresponding virtual work expression necessary for a Newton-type solution leads to additional terms for the volume dependence. Investigating these terms the conservativeness of the problem can be proven by the symmetry of the linearized form. The discretization with finite elements leads to standard stiffness matrix forms plus the so-called load stiffness matrices and a rank-one update for each enclosed volume part, if the loaded surface segments are identical with element surfaces. Some numerical examples show first the effectiveness of the approach and the necessity to take the corresponding terms in the variational expression and in the following linearization into account, and second the particular influence of this term on the stability of structures is shown with some specific examples. Copyright © 2002 John Wiley & Sons, Ltd. [source] An improved weighting method with multibounds formulation and convex programming for multicriteria structural optimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2001W. H. Zhang Abstract This paper presents an improved weighting method for multicriteria structural optimization. By introducing artificial design variables, here called as multibounds formulation (MBF), we demonstrate mathematically that the weighting combination of criteria can be transformed into a simplified problem with a linear objective function. This is a unified formulation for one criterion and multicriteria problems. Due to the uncoupling of involved criteria after the transformation, the extension and the adaptation of monotonic approximation-based convex programming methods such as the convex linearization (CONLIN) or the method of moving asymptotes (MMA) are made possible to solve multicriteria problems as efficiently as for one criterion problems. In this work, a multicriteria optimization tool is developed by integrating the multibounds formulation with the CONLIN optimizer and the ABAQUS finite element analysis system. Some numerical examples are taken into account to show the efficiency of this approach. Copyright © 2001 John Wiley & Sons, Ltd. [source] Time-linearized time-harmonic 3-D Navier,Stokes shock-capturing schemesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2008J.-C. Chassaing Abstract In the present paper, a numerical method for the computation of time-harmonic flows, using the time-linearized compressible Reynolds-averaged Navier,Stokes equations is developed and validated. The method is based on the linearization of the discretized nonlinear equations. The convective fluxes are discretized using an O(,x) MUSCL scheme with van Leer flux-vector-splitting. Unsteady perturbations of the turbulent stresses are linearized using a frozen-turbulence-Reynolds-number hypothesis, to approximate eddy-viscosity perturbations. The resulting linear system is solved using a pseudo-time-marching implicit ADI-AF (alternating-directions-implicit approximate-factorization) procedure with local pseudo-time-steps, corresponding to a matrix-successive-underrelaxation procedure. The stability issues associated with the pseudo-time-marching solution of the time-linearized Navier,Stokes equations are discussed. Comparison of computations with measurements and with time-nonlinear computations for 3-D shock-wave oscillation in a square duct, for various back-pressure fluctuation frequencies (180, 80, 20 and 10,Hz), assesses the shock-capturing capability of the time-linearized scheme. Copyright © 2007 John Wiley & Sons, Ltd. [source] Efficient preconditioning of the discrete adjoint equations for the incompressible Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2005René Schneider Abstract Preconditioning of the discrete adjoint equations is closely related to preconditioning the linear systems arising in the Newton linearization of the discretized flow equations. We investigate the use of an optimal preconditioner for both problems on the example of a finite element discretization of the steady state incompressible Navier,Stokes equations. It is demonstrated that complications arising from the use of a zero mean pressure condition in the problem formulation can be overcome by modifying the preconditioner suitably. Copyright © 2005 John Wiley & Sons, Ltd. [source] Block preconditioners for the discrete incompressible Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3-4 2002Howard C. Elman Abstract We examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady-state Navier,Stokes equations. For steady-state problems, we show that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers. These characteristics are directly correlated with the convergence properties of iterative solvers, with convergence rates independent of mesh size and only mildly dependent on viscosity. For evolutionary problems, we show that implicit treatment of the time derivatives leads to systems for which convergence is essentially independent of viscosity. Copyright © 2002 John Wiley & Sons, Ltd. [source] Adaptive control of stochastic nonlinear systems with uncontrollable linearizationINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 7 2009Wang Qiang-de Abstract For a class of high-order stochastic nonlinear systems with uncontrollable linearization, this paper investigates the problem of adaptive global stability in probability. By using the tool of adaptive adding a power integrator, a feedback domination design approach is presented and a smooth controller is constructed. The closed-loop stochastic system is proved to be globally stable in probability and the states can be regulated to the origin almost surely. Copyright © 2008 John Wiley & Sons, Ltd. [source] Nonlinear reference tracking control of a gas turbine with load torque estimationINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 8 2008B. Pongrácz Abstract Input,output linearization-based adaptive reference tracking control of a low-power gas turbine model is presented in this paper. The gas turbine is described by a third-order nonlinear input-affine state-space model, where the manipulable input is the fuel mass flowrate and the controlled output is the rotational speed. The stability of the one-dimensional zero dynamics of the controlled plant is investigated via phase diagrams. The input,output linearizing feedback is extended with a load torque estimator algorithm resulting in an adaptive feedback scheme. The tuning of controller parameters is performed considering three main design goals: appropriate settling time, robustness against environmental disturbances and model parameter uncertainties, and avoiding the saturation of the actuator. Simulations show that the closed-loop system is robust with respect to the variations in uncertain model and environ-mental parameters and its performance satisfies the defined requirements. Copyright © 2007 John Wiley & Sons, Ltd. [source] Adaptive transfer function-based control of nonlinear process.INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 10 2007Case study: Control of temperature in industrial methane tank Abstract The state model-based transfer function models are applied for adaptation of linear controller and disturbance compensator in a feedback/feed-forward control system of nonlinear process. An advantage of the presented adaptation method is the avoidance of artificial disturbances or iterative identification procedures for on-line estimation of process dynamic parameters. The adaptation is based on linearization of the process model at each sampling time about the current state point, independent of the process being at steady-state or transient conditions. The linear time-varying dynamics model is updated on-line using measured values of process variables and reduced to the first-order plus time delay transfer function models in order to directly apply well-developed controller tuning rules. Computational aspects of the adaptation method are discussed and computation algorithms are presented. The adaptive feedback/feed-forward control system was applied for controlling temperature in industrial methane tank, dynamic parameters of which vary in a wide range due to variations of methane-tank process load and external conditions. The heat balance-based process state model is developed and validated using observation data of real plant. Computer simulation of the proposed control system performance under extreme operating conditions demonstrates fast adaptation of controller parameters, robust behaviour and significant improvement in the controllers' performance compared to that of fixed-gain controllers. Copyright © 2007 John Wiley & Sons, Ltd. [source] Dynamic model of one-cycle control for converters operating in continuous and discontinuous conduction modes,INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 5 2009N. Femia Abstract In this paper a new dynamic model of one-cycle-controlled converters operating either in continuous or in discontinuous conduction mode (DCM) is introduced. The static and dynamic behaviour is analysed by using sampled-data modelling combined with the small-signal linearization of the average model of the converter's power stage. The proposed model is valid for frequencies up to half the switching frequency and, while the other dynamic models presented in the literature cover continuous conduction mode only, it also gives an accurate prediction of the system's dynamic behaviour in the DCM. The model allows to determine the closed-form expression of the reference-to-output transfer function G of the system, which is a fundamental prerequisite for the design of a conventional output feedback control circuit aimed at improving the dynamic behaviour of the system in response to load variations. In this paper it is also shown that one-cycle control does not work properly in switching converters operating in deep DCM if some specific design constraints are not fulfilled. The theoretical predictions are confirmed by the results of suitable numerical simulations and laboratory experiments on a one-cycle-controlled buck-switching converter. Copyright © 2008 John Wiley & Sons, Ltd. 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