Combined Iteration Method of Load Identification for a Complex Structure with Nonlinearity

2012 ◽  
Vol 466-467 ◽  
pp. 870-875
Author(s):  
Yu Hua Liu ◽  
Zhi Jun Li ◽  
Xue Feng Zhou ◽  
Wei Hou
Keyword(s):  
Finite Element ◽  
Iteration Method ◽  
Control Method ◽  
Nonlinear Dynamical Systems ◽  
Numerical Study ◽  
Complex Structure ◽  
Nonlinear Dynamical System ◽  
Load Identification ◽  
Combined System ◽  
Nonlinear Dynamical

A combined iteration method of load identification method is presented concerning one type of structure with nonlinearity. The proposed method realizes the load identification of the nonlinear dynamical system by combining and iterating the finite element method and the active control method. The finite element models of nonlinear dynamical systems are firstly contracted into the simplified model to make up the controlled plant. Then under the selected control law, the controller is designed to produce the system excitation, namely the identified load. The validity of the load is finally checked through the response of the nonlinear finite element model. For a conical shell-belting combined system, the numerical study regarding the load identification demonstrates the validity of combined iteration method, which can plays a guiding role in the load identification of vibration test respecting aerospace structures, such as missile, aerospacecraft, aerospaceplane, rocket and so on, making great contribution to the development of the aerospace industry.

scholarly journals Modeling of information channel by using of pseudorandom signals of nonlinear dynamical system

2020 ◽  
Vol 22 (4) ◽  
pp. 79-87
Author(s):  
I. K. Nasyrov ◽  
V. V. Andreev
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Detection Algorithm ◽  
Main Step ◽  
Operating Characteristics ◽  
Nonlinear Dynamical ◽  
Pseudorandom Signals ◽  
Chaotic Signals ◽  
Correlation Properties

Pseudorandom signals of nonlinear dynamical systems are studied and the possibility of their application in information systems analyzed. Continuous and discrete dynamical systems are considered: Lorenz System, Bernoulli and Henon maps. Since the parameters of dynamical systems (DS) are included in the equations linearly, the principal possibility of the state linear control of a nonlinear DS is shown. The correlation properties comparative analysis of these DSs signals is carried out.. Analysis of correlation characteristics has shown that the use of chaotic signals in communication and radar systems can significantly increase their resolution over the range and taking into account the specific properties of chaotic signals, it allows them to be hidden. The representation of nonlinear dynamical systems equations in the form of stochastic differential equations allowed us to obtain an expression for the likelihood functional, with the help of which many problems of optimal signal reception are solved. It is shown that the main step in processing the received message, which provides the maximum likelihood functionals, is to calculate the correlation integrals between the components and the systems under consideration. This made it possible to base the detection algorithm on the correlation reception between signal components. A correlation detection receiver was synthesized and the operating characteristics of the receiver were found.

The Generalized Shooting Arc-Length Method for Periodic Solutions and the Corresponding Periods of Nonlinear Dynamical Systems

2001 ◽  
Author(s):  
Dexin Li ◽  
Jianxue Xu
Keyword(s):  
Dynamical System ◽  
Periodic Solution ◽  
Periodic Orbit ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Optimization Method ◽  
Arc Length ◽  
Van Der Pol Equation ◽  
Van Der Pol ◽  
Nonlinear Dynamical

Abstract In this paper, a generalized shooting/arc-length method for determining periodic orbit and its period of nonlinear dynamical system is presented. At first, by changing the time scale the period value of periodic orbit of the nonlinear system is drawn into the governing equation of this system. Then, by using the period value as a parameter, the shooting/arc-length procedure is taken for seeking such a periodic solution and its period simultaneously. The value of increment changed in iteration procedure is selected by using optimization method. The procedure involves the detennining of periodic orbit and its period value of the system. Thereby, the periodic orbit and period value of the system can be sought out rapidly and precisely. At last, the validity of such method is verified by determining the periodic orbit and period value for van der pol equation and nonlinear rotor-bear system.

A New Method for Equilibria and Stability Analysis of Nonlinear Dynamical Systems

2014 ◽  
Vol 534 ◽  
pp. 131-136
Author(s):  
Long Cao ◽  
Yi Hua Cao
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Numerical Continuation ◽  
Vehicle Model ◽  
Nonlinear Dynamical ◽  
Novel Method ◽  
Linearized System ◽  
Continuation Algorithm

A novel method based on numerical continuation algorithm for equilibria and stability analysis of nonlinear dynamical system is introduced and applied to an aircraft vehicle model. Dynamical systems are usually modeled with differential equations, while their equilibria and stability analysis are pure algebraic problems. The newly-proposed method in this paper provides a way to solve the equilibrium equation and the eigenvalues of the locally linearized system simultaneously, which avoids QR iterations and can save much time.

COMPETITIVE MODES AND THEIR APPLICATION

2006 ◽  
Vol 16 (03) ◽  
pp. 497-522 ◽  
Author(s):  
WEIGUANG YAO ◽  
PEI YU ◽  
CHRISTOPHER ESSEX ◽  
MATT DAVISON
Keyword(s):  
Chaotic Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Point Of View ◽  
Frequency Function ◽  
Mode Competition ◽  
Integration Scheme ◽  
Nonlinear Dynamical ◽  
Competitive Modes ◽  
Definition Of

We investigate nonlinear dynamical systems from the mode competition point of view, and propose the necessary conditions for a system to be chaotic. We conjecture that a chaotic system has at least two competitive modes (CM's). For a general nonlinear dynamical system, we give a simple, dynamically motivated definition of mode suitable for this concept. Since for most chaotic systems it is difficult to obtain the form of a CM, we focus on the competition between the corresponding modulated frequency components of the CM's. Some direct applications result from the explicit form of the frequency functions. One application is to estimate parameter regimes which may lead to chaos. It is shown that chaos may be found by analyzing the frequency function of the CM's without applying a numerical integration scheme. Another application is to create new chaotic systems using custom-designed CM's. Several new chaotic systems are reported.

scholarly journals Lagrange and practical stability criteria for dynamical systems with nonlinear perturbations

2012 ◽  
Vol 22 (1) ◽  
pp. 43-58
Author(s):  
Assen Krumov
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Computer Control ◽  
Nonlinear Dynamical System ◽  
Sufficient Conditions ◽  
Practical Stability ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Nonlinear Operators ◽  
Nonlinear Dynamical

Lagrange and practical stability criteria for dynamical systems with nonlinear perturbationsIn the paper two classes of nonlinear dynamical system with perturbations are considered. The sufficient conditions for robust Lagrange and practical stability are proven with theorems, applying the theory of nonlinear operators of the functional analysis. The presented criteria give also the bounds of the analyzed dynamical processes. Three examples comparing the numerical computer solutions and the analytical investigation of the stability of the systems are given. The method can be applied to analytical and computer modeling of nonlinear dynamical systems, synthesis of computer control and optimization.

scholarly journals Constrained attractor selection using deep reinforcement learning

2020 ◽  
pp. 107754632093014
Author(s):  
Xue-She Wang ◽  
James D Turner ◽  
Brian P Mann
Keyword(s):  
Reinforcement Learning ◽  
Gradient Method ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Learning Approaches ◽  
Multiple Attractors ◽  
Nonlinear Dynamical ◽  
Cross Entropy Method ◽  
Policy Gradient ◽  
Attractor Selection

This study describes an approach for attractor selection (or multistability control) in nonlinear dynamical systems with constrained actuation. Attractor selection is obtained using two different deep reinforcement learning methods: (1) the cross-entropy method and (2) the deep deterministic policy gradient method. The framework and algorithms for applying these control methods are presented. Experiments were performed on a Duffing oscillator, as it is a classic nonlinear dynamical system with multiple attractors. Both methods achieve attractor selection under various control constraints. Although these methods have nearly identical success rates, the deep deterministic policy gradient method has the advantages of a high learning rate, low performance variance, and a smooth control approach. This study demonstrates the ability of two reinforcement learning approaches to achieve constrained attractor selection.

DESIGNING HOPF BIFURCATIONS INTO NONLINEAR DISCRETE-TIME SYSTEMS VIA FEEDBACK CONTROL

2004 ◽  
Vol 14 (07) ◽  
pp. 2283-2293 ◽  
Author(s):  
GUILIN WEN ◽  
DAOLIN XU
Keyword(s):  
Feedback Control ◽  
Center Manifold ◽  
Control Method ◽  
Nonlinear Dynamical Systems ◽  
Critical Conditions ◽  
Hopf Bifurcations ◽  
Control Law ◽  
Nonlinear Dynamical ◽  
Weak Resonance ◽  
Time Systems

Hopf bifurcations lead to limit circles that exhibit oscillatory behaviors in nonlinear dynamical systems. Building a specified limit circle into nonlinear systems by control enables us to achieve preferred dynamical performance in the systems. This paper reports a general control method for generating a variety of specified Hopf bifurcations at a desired parameter location. The proposed control law is applicable to nonresonance, weak resonance, strong resonance, or degenerate cases. It allows us to flexibly operate and manipulate the control of Hopf bifurcations. The discrete washout filters are used for the feedback controller. The feedback control gains are derived from the critical conditions and stability conditions of Hopf bifurcations by means of the center manifold method and normal form technique. Numerical experiments indicate that the control method is effective.

Singularities in the complex time plane and exactly solvable dynamical systems

1994 ◽  
Vol 72 (3-4) ◽  
pp. 147-151 ◽  
Author(s):  
W.-H. Steeb ◽  
Assia Fatykhova
Keyword(s):  
Differential Equation ◽  
Quantum Mechanics ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Numerical Study ◽  
Complex Time ◽  
Nonlinear Dynamical ◽  
Singularity Structure ◽  
Exactly Solvable ◽  
Solvable Dynamical Systems

A powerful tool in the study of nonlinear dynamical systems is the investigation of the singularity structure in the complex time plane. In most cases the singularity structure can only be found numerically. Here we give two models that can be solved exactly, i.e., we can give the singularities in the complex time plane. The two models play a central role in quantum mechanics. Then we compare them with the numerical study of the nonlinear differential equation.

scholarly journals Nonlinear Network Dynamics with Consensus–Dissensus Bifurcation

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Karel Devriendt ◽  
Renaud Lambiotte
Keyword(s):  
Dynamical System ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Global Bifurcation ◽  
Basins Of Attraction ◽  
Complete Graphs ◽  
Stationary States ◽  
Qualitative Properties ◽  
Nonlinear Dynamical ◽  
Tree Graphs

AbstractWe study a nonlinear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and the dominating behaviour of a general class of nonlinear dynamical systems. The equilibrium behaviour of the system exhibits a global bifurcation with respect to the system parameter, with a transition from a single constant stationary state to a large range of possible stationary states. Our main result classifies the stability of (a subset of) these stationary states in terms of the effective resistances of the underlying graph; this classification clearly discerns the influence of the specific topology in which the local pitchfork systems are interconnected. We further describe exact solutions for graphs with external equitable partitions and characterize the basins of attraction on tree graphs. Our technical analysis is supplemented by a study of the system on a number of prototypical networks: tree graphs, complete graphs and barbell graphs. We describe a number of qualitative properties of the dynamics on these networks, with promising modelling consequences.

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