Smooth Decomposition Analysis and Order Reduction of Nonlinear Mechanical Systems Under Random Excitation

2012 ◽  
Author(s):  
Sergio Bellizzi ◽  
Rubens Sampaio
Keyword(s):  
Covariance Matrix ◽  
Decomposition Method ◽  
Equations Of Motion ◽  
Galerkin Approximation ◽  
Mechanical Systems ◽  
Decomposition Analysis ◽  
Original System ◽  
Random Excitation ◽  
Order Structure ◽  
Reduced Order

This paper presents a possible alternative procedure to the Karhunen-Loève approach to construct reduced order models which capture accurately the dynamics of nonlinear discrete mechanical systems under random excitation. This procedure combines the Smooth Decomposition method and the Petrov-Galerkin approximation. The smooth decomposition method is a multivariate-data analysis method characterizing coherent structures (the smooth modes) as the eigenvectors of the generalized eigenproblem defined from the covariance matrix of the displacement field and the covariance matrix of the velocity field. The Petrov-Galerkin approximation is used to project the dynamics in a subspace generated by a set of the smooth modes. The Petrov-Galerkin approximation preserves the second order structure of the equations of motion. The procedure is considered for a mechanical system including a strongly nonlinear end-attachment. The efficiency of the approach is analyzed comparing the power spectral density functions of the reduced-order model and of the original system.

Augmented Perpetual Manifolds and Perpetual Mechanical Systems-Part I: Definitions, Theorem and Corollary for Triggering Perpetual Manifolds, Application in Reduced Order Modeling and Particle-Wave Motion of Flexible Mechanical Systems

2021 ◽  
Author(s):  
Fotios Georgiades
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Mechanical Engineering ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Reduced Order ◽  
Rigid Body Motions ◽  
Definition Of ◽  
External Forces ◽  
Perpetual Points

Abstract Perpetual points in mechanical systems defined recently. Herein are used to seek specific types of solutions of N-degrees of freedom systems, and their significance in mechanics is discussed. In discrete linear mechanical systems, is proven, that the perpetual points are forming the perpetual manifolds and they are associated with rigid body motions, and these systems are called perpetual. The definition of perpetual manifolds herein is extended to the augmented perpetual manifolds. A theorem, defining the conditions of the external forces applied in an N-degrees of freedom system lead to a solution in the exact augmented perpetual manifold of rigid body motions, is proven. In this case, the motion by only one differential equation is described, therefore forms reduced-order modelling of the original equations of motion. Further on, a corollary is proven, that in the augmented perpetual manifolds for external harmonic force the system moves in dual mode as wave-particle. The developed theory is certified in three examples and the analytical solutions are in excellent agreement with the numerical simulations. The outcome of this research is significant in several sciences, in mathematics, in physics and in mechanical engineering. In mathematics, this theory is significant for deriving particular solutions of nonlinear systems of differential equations. In physics/mechanics, the existence of wave-particle motion of flexible mechanical systems is of substantial value. Finally in mechanical engineering, the theory in all mechanical structures can be applied, e.g. cars, aeroplanes, spaceships, boats etc. targeting only the rigid body motions.

Model Order Reduction of Transmission Line Model

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Transmission Line ◽  
Large Scale ◽  
Original System ◽  
Reduced Order Model ◽  
Benchmark Problems ◽  
Transmission Line Model ◽  
Order Model ◽  
Line Model ◽  
Reduced Order ◽  
Numerical Effort

Transmission Line model are an important role in the electrical power supply. Modeling of such system remains a challenge for simulations are necessary for designing and controlling modern power systems.In order to analyze the numerical approach for a benchmark collection Comprehensive of some needful real-world examples, which can be utilized to evaluate and compare mathematical approaches for model reduction. The approach is based on retaining the dominant modes of the system and truncation comparatively the less significant once.as the reduced order model has been derived from retaining the dominate modes of the large-scale stable system, the reduction preserves the stability. The strong demerit of the many MOR methods is that, the steady state values of the reduced order model does not match with the higher order systems. This drawback has been try to eliminated through the Different MOR method using sssMOR tools. This makes it possible for a new assessment of the error system Offered that the Observability Gramian of the original system has as soon as been thought about, an H∞ and H2 error bound can be calculated with minimal numerical effort for any minimized model attributable to The reduced order model (ROM) of a large-scale dynamical system is essential to effortlessness the study of the system utilizing approximation Algorithms. The response evaluation is considered in terms of response constraints and graphical assessments. the application of Approximation methods is offered for arising ROM of the large-scale LTI systems which consist of benchmark problems. The time response of approximated system, assessed by the proposed method, is also shown which is excellent matching of the response of original system when compared to the response of other existing approaches .

Machine learning–based reduced-order modeling of hydrodynamic forces using pressure mode decomposition

2021 ◽  
pp. 095441002199986
Author(s):  
Hassan F Ahmed ◽  
Hamayun Farooq ◽  
Imran Akhtar ◽  
Zafar Bangash
Keyword(s):  
Machine Learning ◽  
Short Term Memory ◽  
Stokes Equations ◽  
Decomposition Analysis ◽  
Hydrodynamic Forces ◽  
Reduced Order Modeling ◽  
Navier Stokes ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Lift And Drag

In this article, we introduce a machine learning–based reduced-order modeling (ML-ROM) framework through the integration of proper orthogonal decomposition (POD) and deep neural networks (DNNs), in addition to long short-term memory (LSTM) networks. The DNN is utilized to upscale POD temporal coefficients and their respective spatial modes to account for the dynamics represented by the truncated modes. In the second part of the algorithm, temporal evolution of the POD coefficients is obtained by recursively predicting their future states using an LSTM network. The proposed model (ML-ROM) is tested for flow past a circular cylinder characterized by the Navier–Stokes equations. We perform pressure mode decomposition analysis on the flow data using both POD and ML-ROM to predict hydrodynamic forces and demonstrate the accuracy of the proposed strategy for modeling lift and drag coefficients.

A Very Simple Method to Calculate the (Positive) Largest Lyapunov Exponent Using Interval Extensions

2016 ◽  
Vol 26 (13) ◽  
pp. 1650226 ◽  
Author(s):  
Eduardo M. A. M. Mendes ◽  
Erivelton G. Nepomuceno
Keyword(s):  
Lyapunov Exponent ◽  
Lower Bound ◽  
Equations Of Motion ◽  
Original System ◽  
Glass System ◽  
Largest Lyapunov Exponent ◽  
Simple Method ◽  
Interval Extensions

In this letter, a very simple method to calculate the positive Largest Lyapunov Exponent (LLE) based on the concept of interval extensions and using the original equations of motion is presented. The exponent is estimated from the slope of the line derived from the lower bound error when considering two interval extensions of the original system. It is shown that the algorithm is robust, fast and easy to implement and can be considered as alternative to other algorithms available in the literature. The method has been successfully tested in five well-known systems: Logistic, Hénon, Lorenz and Rössler equations and the Mackey–Glass system.

scholarly journals Reduced order system identification for UAVs

2015 ◽  
Vol 119 (1218) ◽  
pp. 961-980 ◽  
Author(s):  
P-D. Jameson ◽  
A. K. Cooke
Keyword(s):  
System Identification ◽  
Equations Of Motion ◽  
Real Data ◽  
Flight Test ◽  
Rate Of Change ◽  
Order System ◽  
Parameter Estimates ◽  
Reduced Order Models ◽  
Test Scenario ◽  
Reduced Order

Abstract Reduced order models representing the dynamic behaviour of symmetric aircraft are well known and can be easily derived from the standard equations of motion. In flight testing, accurate measurements of the dependent variables which describe the linearised reduced order models for a particular flight condition are vital for successful system identification. However, not all the desired measurements such as the rate of change in vertical velocity (Ẇ) can be accurately measured in practice. In order to determine such variables two possible solutions exist: reconstruction or differentiation. This paper addresses the effect of both methods on the reliability of the parameter estimates. The methods are used in the estimation of the aerodynamic derivatives for the Aerosonde UAV from a recreated flight test scenario in Simulink. Subsequently, the methods are then applied and compared using real data obtained from flight tests of the Cranfield University Jetstream 31 (G-NFLA) research aircraft.

On the Properties of a Dynamic Model of Flexible Robot Manipulators

1998 ◽  
Vol 120 (1) ◽  
pp. 8-14 ◽  
Author(s):  
Marco A. Arteaga
Keyword(s):  
Dynamic Model ◽  
Structural Properties ◽  
Robot Manipulators ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Control Design ◽  
Flexible Manipulator ◽  
Robot Dynamics ◽  
Flexible Link ◽  
Flexible Robot

Control design of flexible robot manipulators can take advantage of the structural properties of the model used to describe the robot dynamics. Many of these properties are physical characteristics of mechanical systems whereas others arise from the method employed to model the flexible manipulator. In this paper, the modeling of flexible-link robot manipulators on the basis of the Lagrange’s equations of motion combined with the assumed modes method is briefly discussed. Several notable properties of the dynamic model are presented and their impact on control design is underlined.

A REDUCED ORDER MODEL BASED ON BLOCK ARNOLDI METHOD FOR AEROELASTIC SYSTEM

2014 ◽  
Vol 06 (06) ◽  
pp. 1450069 ◽  
Author(s):  
QIANG ZHOU ◽  
GANG CHEN ◽  
YUEMING LI
Keyword(s):  
Original System ◽  
Reduced Order Model ◽  
System Stability ◽  
Arnoldi Method ◽  
Order Model ◽  
Aeroelastic System ◽  
Reduced Order ◽  
Block Arnoldi ◽  
Flutter Boundary ◽  
Linearized Model

A reduced-order model (ROM) based on block Arnoldi algorithm to quickly predict flutter boundary of aeroelastic system is investigated. First, a mass–damper–spring dynamic system is tested, which shows that the low dimension system produced by the block Arnoldi method can keep a good dynamic property with the original system in low and high frequencies. Then a two-degree of freedom transonic nonlinear aerofoil aeroelastic system is used to validate the suitability of the block Arnoldi method in flutter prediction analysis. In the aerofoil case, the ROM based on a linearized model is obtained through a high-fidelity nonlinear computational fluid dynamics (CFD) calculation. The order of the reduced model is only 8 while it still has nearly the same accuracy as the full 9600-order model. Compared with the proper orthogonal decomposition (POD) method, the results show that, without snapshots the block Arnoldi/ROM has a unique superiority by maintaining the system stability aspect. The flutter boundary of the aeroelastic system predicted by the block Arnoldi/ROM agrees well with the CFD and reference results. The Arnoldi/ROM provides an efficient and convenient tool to quick analyze the system stability of nonlinear transonic aeroelastic systems.

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

scholarly journals CONSTRUCTION OF EQUATIONS OF MOTION OF MULTIBODY SYSTEMS AND COMPUTER MODELING

2018 ◽  
pp. 74-81
Author(s):  
Darina Hroncová
Keyword(s):  
Mathematical Model ◽  
Computer Modeling ◽  
Computer Model ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Ideal Gas ◽  
Material Point ◽  
Operating Conditions ◽  
Contact Friction ◽  
Knowledge Process

Urgency of the research. Computer models mean new quality in the knowledge process. Using a computer model, the properties of the subject under investigation can be tested under different operating conditions. By experimenting with a com-puter model, we learn about the modelled object. We can test different machine variants without having to produce and edit prototypes. Target setting. The development of computer technology has expanded the possibility of solving mathematical models and allowed to gradually automate the calculation of mathematical model equations. It is necessary to insert appropriate inputs of the mathematical model and monitor and evaluate the output results through the computer output device The target was to describe the mathematical apparatus required for mathematical modeling and subsequently to compile a model for computer modeling. Actual scientific researches and issues analysis. When formulating a mathematical model for a computer, the laws and the theory we use are always valid under more or less idealized conditions, and operate with fictitious concepts such as, material point, ideal gas, intangible spring, and the like. However, with these simplifications, we describe a realistic phenomenon where the initial assumptions are only met to a certain extent. In order for the results not to be different from the modeled reality, it is to be assumed that a good computer model arises gradually, by verifying and modifying it, which is one of the advantages of MSC Adams. Uninvestigated parts of general matters defining. The question of building a real manipulator model. Based on the above simulation, it is possible to build a real model. The research objective. Using MSC Adams to simulate multiple body systems and verify its suitability for simulating ma-nipulator and robot models. In various versions of the assembled model we can monitor its behavior under different operating conditions. The statement of basic materials. In computer simulation, MSC Adams-View is used to simulate mechanical systems. It has an interactive environment for automated dynamic analysis of parameterized mechanical systems with an arbitrary struc-ture of rigid and flexible bodies with geometric or force joints, in which act gravity, inertia, experimentally designed contact, friction, aerodynamic, hydrodynamic or electromechanical forces and have integrated control, hydraulic, pneumatic or elec-tromechanical circuits. Conclusions. Working with a mathematical model on a computer opens space for specific synthesis of empirical and ana-lytical method of scientific knowledge. Working with the computer model carries the characteristic features of classical experi-mentation. It represents a qualitatively new way of solving tasks that can not be experimented with on a real object. The result is the equivalence of the computer model and the object being investigated with the features and expressions chosen as essen-tial, with accuracy sufficient to the exact purpose.

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