Model-Order Reduction by Simultaneous Realization of Eigenvalues and Mode Shapes (SREM)

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Fariborz Fariborzi ◽  
Ramin Bighamian ◽  
Hamid Reza Mirdamadi
Keyword(s):  
Cost Function ◽  
Degrees Of Freedom ◽  
Differential Evolution Algorithm ◽  
Order Reduction ◽  
Mode Shapes ◽  
System Response ◽  
Model Order ◽  
System Information ◽  
Distribution Vector ◽  
The Stability

In this paper, a unique technique “cost function” has been presented to simultaneously realize eigenvalues and mode shape vectors to attain a reduced model. Differential evolution algorithm has been utilized in order to numerically optimize the nonlinear cost function instead of the least squares solution of the characteristic equation of the system. The modal matrix is reduced by effective independence distribution vector (EIDV) method to remove the slave degrees of freedom and retain the master ones which have the most contribution in the system response. EIDV retains those degrees of freedom (DOFs) in such a way as to reserve the system information content, as much as possible. This procedure has been verified with some examples and good results have been obtained. It is shown that the algorithm has several advantages, e.g., the coupling between selected modes of full-order model will be attained to guarantee the stability of closed-loop system.

Stability of Ring-Type MEMS Gyroscopes Subjected to Stochastic Angular Speed Fluctuation

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Samuel F. Asokanthan ◽  
Soroush Arghavan ◽  
Mohamed Bognash
Keyword(s):  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Microelectromechanical Systems ◽  
Damping Ratio ◽  
Operating Conditions ◽  
System Stability ◽  
System Response ◽  
Ring Type ◽  
Mems Gyroscopes ◽  
The Stability

Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.

scholarly journals Stability-preserving model order reduction for linear stochastic Galerkin systems

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Roland Pulch
Keyword(s):  
Dynamical System ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Electric Circuit ◽  
Physical Parameters ◽  
Science And Engineering ◽  
Model Order ◽  
Linear Dynamical Systems ◽  
Stochastic Galerkin ◽  
The Stability

Abstract Mathematical modeling often yields linear dynamical systems in science and engineering. We change physical parameters of the system into random variables to perform an uncertainty quantification. The stochastic Galerkin method yields a larger linear dynamical system, whose solution represents an approximation of random processes. A model order reduction (MOR) of the Galerkin system is advantageous due to the high dimensionality. However, asymptotic stability may be lost in some MOR techniques. In Galerkin-type MOR methods, the stability can be guaranteed by a transformation to a dissipative form. Either the original dynamical system or the stochastic Galerkin system can be transformed. We investigate the two variants of this stability-preserving approach. Both techniques are feasible, while featuring different properties in numerical methods. Results of numerical computations are demonstrated for two test examples modeling a mechanical application and an electric circuit, respectively.

scholarly journals Mathematical Modelling Of Structures Using Model Order Reduction Technique

2019 ◽  
Vol 8 (10) ◽  
pp. 1700-1704
Keyword(s):  
Mathematical Model ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Simulation Software ◽  
Mode Shapes ◽  
Order System ◽  
Dynamic Simulations ◽  
Model Order ◽  
Fea Simulation ◽  
Virtual Domain

Today’s world is a world of simulation. Now a days, every product is first designed in virtual domain and then tested for actual implementation. To be able to perform such accurate virtual domain analysis, an accurate mathematical model is needed to be designed in first place. Specifically, in the field of dynamic analysis, so as to continuously monitor the system, the requirement a high-fidelity simulation models in all industries is rising rapidly and this has now become an important part of modern simulation strategies. FEA simulation software’s nowadays could provide very accurate results but they cannot be used directly for dynamic simulations where the environment is continuously changing (input forces, random vibrations etc.). Therefore, this paper deals with design of a mathematical model of a beam to overcome the above stated issue. The technique so used is Model Order Reduction. This method develops an efficient reduced model by reducing the degrees of freedom and also preserving a characteristic behavior of the system. The methodology deals with extracting the mass, and stiffness matrices from FEA simulation software, reducing their size (order), building a second order system using reduced sizes of mass and stiffness, analyzing mode shapes vectors and nodes for input force applications, and generating a state space model of the system.

Multibody Dynamics of a Floating Wind Turbine Considering the Flexibility Between Nacelle and Tower

2018 ◽  
Vol 18 (06) ◽  
pp. 1850085 ◽  
Author(s):  
Vahid Jahangiri ◽  
Mir Mohammad Ettefagh
Keyword(s):  
Wind Turbine ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Equations Of Motion ◽  
System Response ◽  
Floating Wind Turbine ◽  
Conservation Of Momentum ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
6 Degrees Of Freedom

Stability and dynamic modeling of the floating wind turbine (FWT) is a crucial challenge in designing of the type of structures. In this paper, the tension leg platform (TLP) type FWT is modeled as a multibody system considering the flexibility between the nacelle and tower. The flexibility of the FWT is modeled as a torsional spring and damper. It has 6 degrees of freedom (DOFs) related to the large-amplitude translation and rotation of the tower and 4 DOFs related to the relative rotation between the rotor-nacelle assembly and the tower. First, the nonlinear equations of motion are derived by the theory of momentum cloud based on the conservation of momentum. Then, the equations of motion are solved and the system is simulated in MATLAB. Moreover, the effect of flexibility between the nacelle and tower is investigated via the dynamic response. The stability of the system in three different environmental conditions is studied. Finally, the spring and damping coefficients for the system response to get near to instability are determined, by which the critical region is defined. The simulation results demonstrate the importance of the flexibility between the nacelle and tower on the overall behavior of the system and its stability.

scholarly journals A comparison of second-order model order reduction methods for an artificial fishtail

2019 ◽  
Vol 67 (8) ◽  
pp. 648-667 ◽  
Author(s):  
Jens Saak ◽  
Dirk Siebelts ◽  
Steffen W. R. Werner
Keyword(s):  
Model Order Reduction ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Order Reduction ◽  
Second Order ◽  
Scale Model ◽  
Order Model ◽  
Model Order ◽  
Reduction Methods ◽  
Second Order Model

Abstract In order to apply control theory in small autonomous vehicles, mathematical models with small numbers of states are required for using the limited computational power in embedded programming. In this paper, we consider an artificial fishtail as an example for a complex mechanical system with a second-order large-scale model, which is derived by using the finite element method. To meet the above limitations, the several hundreds of thousands of degrees of freedom need to be reduced to merely a handful of surrogate degrees of freedom. We seek to achieve this task by various second-order model order reduction methods. All methods are applied on the fishtail’s matrices and their results are evaluated and compared in the frequency domain as well as in the time domain.

Discussion of “Dynamic Modeling and Projection-Based Reduction Methods for Bladed Disks With Nonlinear Frictional and Intermittent Contact Interfaces” (Mitra, M., Epureanu, B. I., 2018, ASME Appl. Mech. Rev., 71(5), p. 050803)

2019 ◽  
Vol 71 (5) ◽  
Author(s):  
Jörg Wallaschek ◽  
Sebastian Willeke ◽  
Lars Panning-von Scheidt
Keyword(s):  
Model Order Reduction ◽  
Degrees Of Freedom ◽  
Turbine Blades ◽  
Computational Cost ◽  
Order Reduction ◽  
Bladed Disks ◽  
Model Order ◽  
Advantages And Disadvantages ◽  
Reduction Methods ◽  
Intermittent Contact

Abstract Mitra and Epureanu have written a very good and complete overview on nonlinear vibrations of turbine blades. Nonlinearities due to friction and contact mechanics are the main focus. Questions related to modeling and model reduction are particularly addressed. This paper begins with an investigation of the vibration behavior of cyclic linear structures, in which a variety of considerations about the occurrence of standing and propagating waves play an important role. Subsequently, several methods of model-order reduction are presented, where cyclic sectors of tuned bladed disks are assumed. The classification of the linear vibration modes according to their nodal diameters (NDs) is explained in detail. Large models with a high number of degrees-of-freedom (DOF) occurring in the field of turbomachinery dynamics lead to very high computational cost. In this context, the authors consider model-order reduction with projection-based methods to be of particular interest. They give an overview of modern projection-based methods and compare them with regard to their respective advantages and disadvantages in the context of bladed disks with nonlinear friction and intermittent contact.

scholarly journals Switched Systems Reduction Framework Based on Convex Combination of Generalized Gramians

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Hamid Reza Shaker ◽  
Rafael Wisniewski
Keyword(s):  
Switched Systems ◽  
Convex Combination ◽  
Order Reduction ◽  
Galerkin Projection ◽  
Model Order ◽  
Linear Dynamical Systems ◽  
Reduction Methods ◽  
The Stability ◽  
Classical Reduction ◽  
General Method

A general method for model-order reduction of switched linear dynamical systems is presented. The proposed technique uses convex generalized gramian which is a convex combination of the generalized gramians. It is shown that different classical reduction methods can be developed into the generalized gramian framework for model reduction of linear systems and further for the reduction of switched systems by construction of the convex generalized gramian. Balanced reduction within specified frequency bound is taken as an example which is developed within this framework. In order to avoid numerical instability and also to increase the numerical efficiency, convex generalized gramian-based Petrov-Galerkin projection is constructed instead of the similarity transform approach for reduction. It is proven that the method preserves the stability of the original switched system at least for stabilizing switching signal and it is also less conservative than the method which is based on the common generalized gramian. Some discussions on the coefficient of the vertices of the convex variables are presented. The performance of the proposed method is illustrated by numerical examples.

scholarly journals MixedLpEstimators Variety for Model Order Reduction in Control Oriented System Identification

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Christophe Corbier ◽  
Jean-Claude Carmona
Keyword(s):  
Model Order Reduction ◽  
Degrees Of Freedom ◽  
Linear Models ◽  
Order Reduction ◽  
Model Complexity ◽  
Model Order ◽  
New Family ◽  
Systems Identification ◽  
Consistency Properties ◽  
Oriented System

A new family of MLE typeLpestimators for model order reduction in dynamical systems identification is presented in this paper. A family ofLpdistributions proposed in this work combinesLp2(1<p2<2) andLp1(0<p1<1) distributions which are quantified by four parameters. The main purpose is to show that these parameters add degrees of freedom (DOF) in the estimation criterion and reduce the estimated model complexity. Convergence consistency properties of the estimator are analysed and the model order reduction is established. Experimental results are presented and discussed on a real vibration complex dynamical system and pseudo-linear models are considered.

scholarly journals Is model-order reduction viable for the broadband finite-element analysis of electrically large antenna arrays?

2015 ◽  
Vol 13 ◽  
pp. 31-39 ◽  
Author(s):  
O. Floch ◽  
A. Sommer ◽  
O. Farle ◽  
R. Dyczij-Edlinger
Keyword(s):  
Finite Element ◽  
Antenna Arrays ◽  
Model Order Reduction ◽  
Numerical Study ◽  
Order Reduction ◽  
Order System ◽  
System Response ◽  
Element Analysis ◽  
Model Order ◽  
Frequency Sweeps

Abstract. Model-order reduction provides an efficient way of computing frequency sweeps for finite-element models, because the dimension of the reduced-order system depends on the complexity of the frequency response rather than the size of the original model. For electrically large domains, however, the applicability of such methods is unclear because the system response may be very complicated. This paper provides a numerical study of the effects of bandwidth, electrical size, and scan angle on the size and convergence of the ROM, by considering linear antenna arrays. A mathematical model is proposed and validated against numerical experiments.

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