Home About us Contact
|
Home About us Contact | ||
|
|
||
Jacobian Matrix (jacobian + matrix)
Selected AbstractsStrategies for the numerical integration of DAE systems in multibody dynamicsCOMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 2 2004E. Pennestrě Abstract The number of multibody dynamics courses offered in the university is increasing. Often the instructor has the necessity to go through the steps of an algorithm by working out a simple example. This gives the student a better understand of the basic theory. This paper provides a tutorial on the numerical integration of differential-algebraic equations (DAE) arising from the dynamic modeling of multibody mechanical systems. In particular, some algorithms based on the orthogonalization of the Jacobian matrix are herein discussed. All the computational steps involved are explained in detail and by working out a simple example. It is also reported a brief description and an application of the multibody code NumDyn3D which uses the Singular Value Decomposition (SVD) approach. © 2004 Wiley Periodicals, Inc. Comput Appl Eng Educ 12: 106,116, 2004; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20005 [source] A Rosenbrock-W method for real-time dynamic substructuring and pseudo-dynamic testingEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 9 2009C. P. Lamarche Abstract A variant of the Rosenbrock-W integration method is proposed for real-time dynamic substructuring and pseudo-dynamic testing. In this variant, an approximation of the Jacobian matrix that accounts for the properties of both the physical and numerical substructures is used throughout the analysis process. Only an initial estimate of the stiffness and damping properties of the physical components is required. It is demonstrated that the method is unconditionally stable provided that specific conditions are fulfilled and that the order accuracy can be maintained in the nonlinear regime without involving any matrix inversion while testing. The method also features controllable numerical energy dissipation characteristics and explicit expression of the target displacement and velocity vectors. The stability and accuracy of the proposed integration scheme are examined in the paper. The method has also been verified through hybrid testing performed of SDOF and MDOF structures with linear and highly nonlinear physical substructures. The results are compared with those obtained from the operator splitting method. An approach based on the modal decomposition principle is presented to predict the potential effect of experimental errors on the overall response during testing. Copyright © 2009 John Wiley & Sons, Ltd. [source] Steady-state power flow and voltage control by unified power-flow controllers, part 2: ApplicationsEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 2 2000Y. H. Song The unifiedpower-flowcontroller(UPFC) isa powerfuldeviceforthe reliejroj'transmission constraints. Part 1 of the paper proposes novel steady-state modelling and control algorithms for the study of UPFC, which use power-injection models to derive control parameters for UPFC to achieve the required line active power control and bus-voltage support. The proposed method does not change the symmetrical structures of Jacobian matrix, avoids the initialisations of control parameters and can cover a wide control range of UPFC due to the characteristics of optimal multiplier power-flow algorithms employed. This paper describes in detail the applications of the proposed theory in a 28-node system. The convergence of controlled power flow is analysed. Control performance has been evaluated. The numerical results presented clearly illustrate the effectiveness of the proposed approach. [source] A review of the adjoint-state method for computing the gradient of a functional with geophysical applicationsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2006R.-E. Plessix SUMMARY Estimating the model parameters from measured data generally consists of minimizing an error functional. A classic technique to solve a minimization problem is to successively determine the minimum of a series of linearized problems. This formulation requires the Fréchet derivatives (the Jacobian matrix), which can be expensive to compute. If the minimization is viewed as a non-linear optimization problem, only the gradient of the error functional is needed. This gradient can be computed without the Fréchet derivatives. In the 1970s, the adjoint-state method was developed to efficiently compute the gradient. It is now a well-known method in the numerical community for computing the gradient of a functional with respect to the model parameters when this functional depends on those model parameters through state variables, which are solutions of the forward problem. However, this method is less well understood in the geophysical community. The goal of this paper is to review the adjoint-state method. The idea is to define some adjoint-state variables that are solutions of a linear system. The adjoint-state variables are independent of the model parameter perturbations and in a way gather the perturbations with respect to the state variables. The adjoint-state method is efficient because only one extra linear system needs to be solved. Several applications are presented. When applied to the computation of the derivatives of the ray trajectories, the link with the propagator of the perturbed ray equation is established. [source] 2D data modelling by electrical resistivity tomography for complex subsurface geologyGEOPHYSICAL PROSPECTING, Issue 2 2006E. Cardarelli ABSTRACT A new tool for two-dimensional apparent-resistivity data modelling and inversion is presented. The study is developed according to the idea that the best way to deal with ill-posedness of geoelectrical inverse problems lies in constructing algorithms which allow a flexible control of the physical and mathematical elements involved in the resolution. The forward problem is solved through a finite-difference algorithm, whose main features are a versatile user-defined discretization of the domain and a new approach to the solution of the inverse Fourier transform. The inversion procedure is based on an iterative smoothness-constrained least-squares algorithm. As mentioned, the code is constructed to ensure flexibility in resolution. This is first achieved by starting the inversion from an arbitrarily defined model. In our approach, a Jacobian matrix is calculated at each iteration, using a generalization of Cohn's network sensitivity theorem. Another versatile feature is the issue of introducing a priori information about the solution. Regions of the domain can be constrained to vary between two limits (the lower and upper bounds) by using inequality constraints. A second possibility is to include the starting model in the objective function used to determine an improved estimate of the unknown parameters and to constrain the solution to the above model. Furthermore, the possibility either of defining a discretization of the domain that exactly fits the underground structures or of refining the mesh of the grid certainly leads to more accurate solutions. Control on the mathematical elements in the inversion algorithm is also allowed. The smoothness matrix can be modified in order to penalize roughness in any one direction. An empirical way of assigning the regularization parameter (damping) is defined, but the user can also decide to assign it manually at each iteration. An appropriate tool was constructed with the purpose of handling the inversion results, for example to correct reconstructed models and to check the effects of such changes on the calculated apparent resistivity. Tests on synthetic and real data, in particular in handling indeterminate cases, show that the flexible approach is a good way to build a detailed picture of the prospected area. [source] Coupled HM analysis using zero-thickness interface elements with double nodes.INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 18 2008Part I: Theoretical model Abstract In recent years, the authors have proposed a new double-node zero-thickness interface element for diffusion analysis via the finite element method (FEM) (Int. J. Numer. Anal. Meth. Geomech. 2004; 28(9): 947,962). In the present paper, that formulation is combined with an existing mechanical formulation in order to obtain a fully coupled hydro-mechanical (or HM) model applicable to fractured/fracturing geomaterials. Each element (continuum or interface) is formulated in terms of the displacements (u) and the fluid pressure (p) at the nodes. After assembly, a particular expression of the traditional ,u,p' system of coupled equations is obtained, which is highly non-linear due to the strong dependence between the permeability and the aperture of discontinuities. The formulation is valid for both pre-existing and developing discontinuities by using the appropriate constitutive model that relates effective stresses to relative displacements in the interface. The system of coupled equations is solved following two different numerical approaches: staggered and fully coupled. In the latter, the Newton,Raphson method is used, and it is shown that the Jacobian matrix becomes non-symmetric due to the dependence of the discontinuity permeability on the aperture. In the part II companion paper (Int. J. Numer. Anal. Meth. Geomech. 2008; DOI: 10.1002/nag.730), the formulation proposed is verified and illustrated with some application examples. Copyright © 2008 John Wiley & Sons, Ltd. [source] Coupled HM analysis using zero-thickness interface elements with double nodes,Part II: Verification and applicationINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 18 2008J. M. Segura Abstract In a companion Part I of this paper (Int. J. Numer. Anal. Meth. Geomech. 2008; DOI: 10.1002/nag.735), a coupled hydro-mechanical (HM) formulation for geomaterials with discontinuities based on the finite element method (FEM) with double-node, zero-thickness interface elements was developed and presented. This Part II paper includes the numerical solution of basic practical problems using both the staggered and the fully coupled approaches. A first group of simulations, based on the classical consolidation problem with an added vertical discontinuity, is used to compare both the approaches in terms of accuracy and convergence. The monolithic or fully coupled scheme is also used in an application example studying the influence of a horizontal joint in the performance of a reservoir subject to fluid extraction. Results include a comparison with other numerical solutions from the literature and a sensitivity analysis of the mechanical parameters of the discontinuity. Some simulations are also run using both a full non-symmetric and a simplified symmetric Jacobian matrix. On top of verifying the model developed and its capability to reflect the conductivity changes of the interface with aperture changes, the results presented also lead to interesting observations of the numerical performance of the methods implemented. Copyright © 2008 John Wiley & Sons, Ltd. [source] An integrated parameter identification method combined with sensor placement designINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2008Yiqian Li Abstract Material parameter identification based on in situ measurements plays a very important role in engineering. Since noises are inevitable in measurements and the parameter identification is inherently ill posed, it is necessary to consider some methods to stabilize the identification procedure. One choice is properly designing the sensor placement, which has attracted much attention over the past 30 years. Most existing sensor placement design methods are based on certain sensitivity analysis, which commonly requires evaluating Jacobian matrix for given parameters. However, the ,true' values of parameters are unknown at that moment, because sensor placement design is carried out before the parameter identification. Consequently, roughly estimated ,true' parameters have to be used and less optimal sensor placement could be obtained. To solve this problem, this paper presents an integrated method in which the parameter identification and sensor placement design are carried out alternatively. The validity of the proposed method is illustrated by two simple academic examples. Then it is implemented to detect damages in a real highway bridge. Copyright © 2007 John Wiley & Sons, Ltd. [source] Efficient solution techniques for implicit finite element schemes with flux limitersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2007M. MöllerArticle first published online: 20 MAR 200 Abstract The algebraic flux correction (AFC) paradigm is equipped with efficient solution strategies for implicit time-stepping schemes. It is shown that Newton-like techniques can be applied to the nonlinear systems of equations resulting from the application of high-resolution flux limiting schemes. To this end, the Jacobian matrix is approximated by means of first- or second-order finite differences. The edge-based formulation of AFC schemes can be exploited to devise an efficient assembly procedure for the Jacobian. Each matrix entry is constructed from a differential and an average contribution edge by edge. The perturbation of solution values affects the nodal correction factors at neighbouring vertices so that the stencil for each individual node needs to be extended. Two alternative strategies for constructing the corresponding sparsity pattern of the resulting Jacobian are proposed. For nonlinear governing equations, the contribution to the Newton matrix which is associated with the discrete transport operator is approximated by means of divided differences and assembled edge by edge. Numerical examples for both linear and nonlinear benchmark problems are presented to illustrate the superiority of Newton methods as compared to the standard defect correction approach. Copyright © 2007 John Wiley & Sons, Ltd. [source] A 3-D non-hydrostatic pressure model for small amplitude free surface flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2006J. W. Lee Abstract A three-dimensional, non-hydrostatic pressure, numerical model with k,, equations for small amplitude free surface flows is presented. By decomposing the pressure into hydrostatic and non-hydrostatic parts, the numerical model uses an integrated time step with two fractional steps. In the first fractional step the momentum equations are solved without the non-hydrostatic pressure term, using Newton's method in conjunction with the generalized minimal residual (GMRES) method so that most terms can be solved implicitly. This method only needs the product of a Jacobian matrix and a vector rather than the Jacobian matrix itself, limiting the amount of storage and significantly decreasing the overall computational time required. In the second step the pressure,Poisson equation is solved iteratively with a preconditioned linear GMRES method. It is shown that preconditioning reduces the central processing unit (CPU) time dramatically. In order to prevent pressure oscillations which may arise in collocated grid arrangements, transformed velocities are defined at cell faces by interpolating velocities at grid nodes. After the new pressure field is obtained, the intermediate velocities, which are calculated from the previous fractional step, are updated. The newly developed model is verified against analytical solutions, published results, and experimental data, with excellent agreement. Copyright © 2005 John Wiley & Sons, Ltd. [source] A natural redundancy-resolution for 3-D multi-joint reaching under the gravity effectJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 11 2005Masahiro Sekimoto A simple control method for 3-dimensional multi-joint reaching movements under redundancy of degrees of freedom (DOF) is proposed, which need neither introduce any performance index to solve inverse kinematics uniquely nor calculate pseudo-inverse of the Jacobian matrix of task coordinates with respect to joint coordinates. The proposed control signal is composed of linear superposition of three terms: (1) angular-velocity feedback for damping shaping, (2) task-space position error feedback with a single stiffness parameter, and (3) compensation for gravity force on the basis of estimates for uncertain parameters of the potential energy without calculation any inverse joint position to the target in task space. Through a theoretical analysis of the closed-loop dynamics and a variety of computer simulations by using a whole arm model with five DOFs, the importance of synergistic adjustments of damping factors as well as its relation to selection of the stiffness parameter is pointed out. It is shown that if damping factors are chosen synergistically corresponding to the inertia matrix at the initial time and the stiffness parameter then the endpoint converges asymptotically to the target position and reaches it smoothly without incurring any self-motion. © 2005 Wiley Periodicals, Inc. [source] Dynamics and Coupling Actuation of Elastic Underactuated ManipulatorsJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 3 2003Tie Shi Zhao This paper investigates the constraint and coupling characteristics of underactuated manipulators by proposing an elastic model of the manipulator and examining the second order constraint equation. A dynamic model and a coupling constraint equation are developed from a Jacobian matrix and the Newton-Euler formulation. The inertia matrix and the Christoffel tensor are analyzed and decomposed into the part concerning actuated joints and the part concerning passive joints. This decomposition is further extended to the dynamic coupling equation and generates an actuation coupling matrix and a dynamic coupling tensor. Two new dynamic coupling indices are hence identified. One is related to an actuation input and the other is related to centrifugal and Coriolis forces. The former reveals the dynamic coupling between the input and the acceleration of passive joints and gives the actuation effect on the passive joints. The latter reveals the dynamic coupling between the centrifugal and Coriolis forces and the acceleration of passive joints and provides the centrifugal and Coriolis effect on the acceleration of passive joints. The study reveals the coupling characteristics of an underactuated manipulator. This is then demonstrated in a three-link manipulator and extended to a serial manipulator with passive prismatic joint. © 2003 Wiley Periodicals, Inc. [source] A visual incompressible magneto-hydrodynamics solver with radiation, mass, and heat transferINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2009Necdet AslanArticle first published online: 8 JAN 200 Abstract A visual two-dimensional (2D) nonlinear magneto-hydrodynamics (MHD) code that is able to solve steady state or transient charged or neutral convection problems under the radiation, mass, and heat transfer effects is presented. The flows considered are incompressible and the divergence conditions on the velocity and magnetic fields are handled by similar relaxation schemes in the form of pseudo-iterations between the real time levels. The numerical method utilizes a matrix distribution scheme that runs on structured or unstructured triangular meshes. The time-dependent algorithm developed here utilizes a semi-implicit dual time stepping technique with multistage Runge-Kutta (RK) algorithm. It is possible for the user to choose different normalizations (natural, forced, Boussinesq, Prandtl, double-diffusive and radiation convection) automatically. The code is visual and runs interactively with the user. The graphics algorithms work multithreaded and allow the user to follow certain flow features (color graphs, vector graphs, one-dimensional profiles) during runs, see (Comput. Fluids 2007; 36:961,973) for details. With the code presented here nonlinear steady or time-dependent evolution of heated and stratified neutral and charged liquids, convection of mixture of neutral and charged gases, double-diffusive and salinity natural convection flows with internal heat generation/absorption and radiative heat transfer flows can be investigated. In addition, the numerical method (combining concentration, radiation, heat transfer, and MHD effects) takes the advantage of local time stepping and employs simplified residual jacobian matrix to increase pseudo-convergence rate. This code is currently being improved to simulate three-dimensional problems with parallel processing. Copyright © 2009 John Wiley & Sons, Ltd. [source] | |||||||||||||