Poincare Map Research Articles

Incipient fault detection and condition assessment in DFIGs based on external leakage flux sensing and modified multiscale poincare plots analysis

Abstract Although doubly fed induction generators (DFIG) are widely used, difficulties in early fault detection and severity assessment for inter-turn short-circuit (ITSC) faults are highly prominent. In this manuscript, a novel incipient fault detection and state assessment method based on external leakage flux sensing and modified multiscale poincare plots (MMSPP) is proposed. An external leakage flux sensor is placed on the axial-end position of the generator to monitor the presence and evolution of ITSC faults. Multiscale poincare mapping is a novel nonlinear tool that is further developed and modified using the normal cumulative distribution function and multiscale computing methods to capture the behavior evolution and changes in the generator’s external leakage flux signals. The healthy indicator is based on the analysis of elliptical orbit features extracted from MMSPP, established by support vector data description with parameter optimization. The effectiveness of the proposed method was implemented and verified under an experimental environment on a 100 kW DFIG platform to detect incipient inter-turn short circuits (mainly considering the two-turn ITSC) and evaluate the performance degradation (three- to eight-turn ITSC) with 0%, 50%, and 100% different load conditions. The experimental results showed the viability of the approach and fault indicator for incipient fault detection and condition assessment of the wind generator’s low inter-turn insulation faults and for relative quantification of ITSC fault severity.

On controlling, Vibration Performance and Energy Transfer of an Offshore Wind Turbine Tower System via PPF Controller

In this paper, we focus on the control, energy transfer, and vibration performance under multi mixed excitations for the offshore wind turbine tower (OWTT) system. For reducing the controlled system oscillations, the positive position feedback (PPF) controller is applied. The energy transfers occur in the system of wind turbine by adding the PPF controller to the system equations. With the help of the phase plane approach, frequency response equations, and Poincare maps, the bifurcation and stability at worst resonance cases are sought and investigated. The vibration behaviors are studied numerically at different parameters values for the wind turbine system. Additionally, the response and numerical outcomes are examined, also, the approach of multiple scales is used to establish the approximate solutions of the wind turbine-controlled system. Besides that, MAPLE and MATLAB algorithms are used to implement the numerical results and compare analytical solutions with numerical behavior. The results also be compared to previous research that has been published.

Symmetry and complexity: A Lie symmetry approach to bifurcation, chaos, stability and travelling wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili equation

This work delves into the investigation of the nonlinear dynamics pertaining to the (3+1)-dimensional Kadomtsev-Petviashvili equation, which describes the propagation of long-wave with dissipation and dispersion in nonlinear media. The research entails an exploration of symmetry reductions using Lie group analysis, an analysis of the dynamical system’s characteristics through bifurcation phase portraits, and a study of the perturbed dynamical system’s dynamic behavior through chaos theory. Chaotic behavior is identified using various tools for detecting chaos, including the Lyapunov exponent, 3D phase portrait, Poincare map, time series analysis, and an exploration of the presence of multistability in the autonomous system under different initial conditions. Additionally, the research applies the unified Riccati equation expansion method to solve the considered equation analytically and constructs the general solutions of solitary wave solutions such as trigonometric function solutions, periodic and singular soliton solutions. These solutions come with their associated constraint conditions and are demonstrated through visual representations in the form of 2D, 3D, and density plots with carefully selected parameters. Furthermore, the stability analysis of the considered equation is also discussed and shown graphically. The results of this work are relevant and have applications in describing the propagation of long-wave with dissipation and dispersion in nonlinear media.

Finite-time synchronization of fractional multi-wing chaotic system

The objective of this article is to obtain multi-wing chaotic attractors of fractional chaotic systems through computerized symbolic computation. By applying the Julia fractal technique, the different number wing attractors are constructed for proposed equations. Moreover, the dynamics of the multi-wing system are analyzed by phase diagram, Poincare mapping, etc Consequently, the system exhibits complex dynamics, and the motion states at different order can be known from the bifurcation diagram with the change of order. Additionally, aiming at multi- wing fractional chaotic system, the controllers are designed, and the finite time synchronization control of the proposed system is performed. The results prove that the proposed finite-time synchronization method has important research value in the field of engineering.

Dynamical analysis and finite-time synchronization of grid-scroll memristive chaotic system without equilibrium

The study of multi-scroll memristive chaotic system has attracted great interest due to their unique dynamics. In this paper, a novel five-dimensional chaotic system devoid of equilibria is constructed by introducing two memristors into a three-dimensional chaotic system, resulting in the emergence of a grid-scroll attractor. The evolution of the chaotic system is analyzed using techniques such as phase diagrams, Poincare maps, bifurcation diagrams, and Lyapunov exponents. The basin of attraction is delineated to investigate the coexisting attractors in the system. By manipulating the parameters, the partial amplitude of the system can be modulated. To experimentally confirm the existence of the proposed system, a circuit is meticulously designed and implemented. At last, an adaptive controller is designed, and it is observed from the simulation results that a synchronization state can be reached by the two chaotic systems within a finite time.

Study on vortex-induced multimodal coupled vibration of arch bridge suspenders

The objective of this paper was to investigate the 2-DOF suspender response under the condition of vortex-induced force and reveal the multimodal coupling mechanism. Firstly, an elastically mounted segmental model of suspender was established. Wind tunnel experiments were conducted to obtain the time history displacement signals in cross-flow and in-line directions, the empirical parameters were obtained by identify those signals. The nonlinear partial differential motion equation of suspender with two degrees of freedom was established based on Hamilton's principle, which considered the dynamic strain, bending stiffness and vortex-induced force of suspender. The Galerkin method was used to discretize the nonlinear partial differential equations into nonlinear motion governing equations, which considered the first three order modes. A numerical method was used to solve the motion governing equation, the time history displacement curve, phase diagram, amplitude spectrum and Poincare map of the multi-modal responses in the cross-flow and in-line directions were obtained. With the weak coupling effect of nonlinear stiffness and vortex-induced force, the cross-flow and in-line responses demonstrate period doubling bifurcation, quasi-periodic vibration, period doubling vibration, crises and transient chaotic phenomena. However, with the strong coupling effect, the crises and transient chaos in response amplitude disappear. More importantly, planar/non-planar multimodal internal resonance were found in this work. With the weak multimodal coupling effect in suspender response, the low-order modal response is dominant; as the multimodal coupling effect increases, the high-order modal response becomes predominant. In addition, the system energy not only transfers from high-order modal response to low-order modal response, but also the system energy transfer from low-order modal response to high-order modal response. These conclusions are useful for the design and practical engineering of suspenders, which have high theoretical research value in understanding the mechanism of multimodal coupling effects on suspender response.

The effect of climate change on the dynamics of a modified surface energy balance-mass balance model of Cryosphere under the frame of a non-local operator

One of the major causes of the intermittent nature of long-term climate changes is the interaction between the surface energy balance and the mass balance of the Cryosphere. In this paper, the pre-existing surface energy balance-mass balance model of the Cryosphere is modified by incorporating the radiative forcing of CO2 to observe the effect of global warming on the nature of the previous model. The modified model is generalized using Caputo’s non-local operator. The stability of the new model is analyzed at all the equilibrium points and also it is shown that there exists a unique and bounded solution for the modified system. Using bifurcation analysis and calculating the values of Lyapunov exponents for different fractional orders of the modified system, it is found that the system exhibits chaos for certain values of the radiating forcing of CO2 To observe and visualize the changes in the nature of the new model, the system is solved using the highly efficient 7th-order Runge–Kutta method. It is observed that with the inclusion of the radiative forcing of CO2, the nature of the system changes from asymptotically stable to chaotic as we decrease the order of the system. The Poincare map shows that the modified model even has characteristics of a strange attractor which is highly chaotic. The system becomes unstable when the value of the radiative forcing of CO2 is increased. As a result, the predictive power of the surface energy balance-mass balance model of the Cryosphere decreases. In addition to providing insights into the transition from stability to chaos in the Cryosphere model due to CO2 radiative forcing, this research offers a deeper understanding of the intricate interplay between climate dynamics and complex systems behavior.

Dynamic phases induced by two-level system defects on driven qubits

Recent experimental evidences point to two-level defects, located in the oxides and on the interfaces of the Josephson junctions, as the major constituents of decoherence in superconducting qubits. How these defects affect the qubit evolution with the presence of external driving is less well understood since the semiclassical qubit-field coupling renders the Jaynes–Cummings model for qubit-defect coupling undiagonalizable. We analyze the decoherence dynamics in the continuous coherent state space induced by the driving and solve the master equation endowed with an extra decay-cladded driving term via a Fokker–Planck equation. The solutions for diffusion propagators as Gaussian distributions show four distinct dynamic phases: four types of convergence paths to limit cycles of varying radius by the distribution mean, which are determined by the competing external driving and the defect decays. The qubit trajectory resulted from these solutions is a super-Poissonian over displaced Fock states, which reduces to a Gibbs state of effective temperature decided by the defect at zero driving limit. Furthermore, the Poincare map shows the dependence of the rate of convergence on the initial state. In other words, the qubit evolution can serve as an indicator of the defect coupling strength through the variation of the driving strength as a parameter.

Bifurcation and Chaotic Behavior of Duffing System with Fractional-Order Derivative and Time Delay

In this paper, the abundant nonlinear dynamical behaviors of a fractional-order time-delayed Duffing system under harmonic excitation are studied. By constructing Melnikov function, the necessary conditions of chaotic motion in horseshoe shape are detected, and the chaos threshold curve is obtained by comparing the results obtained through the Melnikov theory and numerical iterative algorithm. The results show that the trend of change is the same, which confirms the accuracy of the chaos threshold curve. It could be found that when the excitation frequency ω is larger than a certain value, the Melnikov theory is not valid for these values. Furthermore, by numerical simulation, some numerical results are obtained, including phase portraits, the largest Lyapunov exponents, and the bifurcation diagrams, Poincare maps, time histories, and frequency spectrograms at some typical points. These numerical simulation results show that the system exhibits some new complex dynamical behaviors, including entry into the state of chaotic motion from single period to period-doubling bifurcation and chaotic motion and periodic motion alternating under the necessary condition of chaotic occurrence. In addition, the effects of time delay, fractional-order coefficient, fractional order, linear viscous damping coefficient, and linear stiffness coefficient on the chaotic threshold curve are discussed, respectively. Those results reveal that there exist abundant nonlinear dynamic behaviors in this fractional-order system, and by adjusting these parameters reasonably, the system could be transformed from chaotic motion to non-chaotic motion.

Numerical Simulation of the Coating Process of some Metals by Electrical Discharge Deposition

The paper deals with research on a hybrid technique of coating by Electrical Discharge Deposition (EDD) which has the advantage of lower costs than the other similar methods. This is due to the possibility of using a usual electrical discharge machine, with common tooling, aided by electromagnetic coils that increase the precision and the quality of deposed layers. Some metallic materials like W, Al, Ni, and Ti of high purity are used for EDD, which could be taken from available wires providers. Numerical simulation of the EDD process, using the metals mentioned above was achieved in Comsol Multiphysics. Two connected modules (physics) were used: Magnetic Fields that produced the magnetic force that actuated each of these four categories of ions and Charged Particle Tracing that highlighted the distribution of particles on different cut planes – Poincare maps. Based on these results provided by numerical simulation, it was possible to evaluate the ions behavior, in comparison to electrons, during EDD that is influenced by their atomic mass and the charge number.

Controlling subharmonic resonance and chaos by a fast forcing in a van der Pol–Duffing oscillator with parametrically excited damping

A periodically damped van der Pol oscillator is analysed with emphasis on the formation of sub harmonic resonance and the corresponding transition of its motion to the chaotic domain. The slow fast separation technique is used to analytically ascertain the domain of such resonances by the removal of secular terms. The same method is then used in conjunction of multiple scale technique to identify the existence of Hopf bifurcation and the generation of limit cycle. Furthermore the Hamiltonian nature of the system has been utilized in the Melnikov function to determine the threshold of the parameter values for the inset of chaos. Over and above the change in the hysteresis structure due to the periodic damping is explicitly determined. In the chaotic regime the characterization is done with the help of Lyapunov exponent, Poincare map and phase space attractor structure.

Spatial Oscillations of a Pipeline with Vibrating Supports

Spatial oscillations of a section of a pipeline with a liquid contained in it during the translational vibrational movements of the supports are investigated. Oscillations of both supports occur with equal amplitudes, frequencies and phases. Pipe deformations associated with the exit of its axis from the bending plane are assumed to be small. The interactions of internal constant pressure and changes in the curvature of the axial line, longitudinal and circumferential deformations of the pipe are taken into account. Its flexural-rotational vibrations are described by a system of two non-linear differential equations. By applying the Bubnov-Galerkin method, this system is reduced to the Cauchy problem, which is then solved numerically by the Runge-Kutta method. In the case of small bending and angular motions of the pipe, a comparison of the analytical and numerical solutions is given. An analysis is given of periodic and non-periodic oscillations of steel, titanium and composite pipes, for which, in particular, frequency spectra and Poincare mappings are constructed.

Effect of internal excitation induced by non-uniform contact of roller bearings on nonlinear vibration and stability of rotor system under combined loads

The misalignment of roller bearing rings will results in moment load, together with the unbalance and external loads, forming the combined dynamic loads. The complex combined load can cause non-uniform contact of rollers and rings, which reduces the bearing’s life and significantly affect the vibration of rotor systems. This paper mainly studies the roller bearing internal contact performances under combined loads and the influence of internal excitation on the nonlinear vibration of rotor systems. First, the “slices” method is used to establish the mechanical model of roller bearings, which considers the radial clearance and nonlinear Hertz contact. The obtained time-varying bearing nonlinear support reaction is introduced into the rotor concentrated mass model, and a roller bearing–rotor system dynamic model is proposed. Further, the system’s complex nonlinear vibrations, such as bifurcation and chaos, are analyzed by spectrum, orbits, bifurcation, and Poincare map. The roller bearing contact performances and stability under the influence of ring tilt angle, rotational speed, and unbalance, are analyzed by contact load statistical features. Finally, based on a rolling bearing–rotor test rig, the vibration experiment considering the combined load was performed, and the experiment results are compared with simulation results to verify the proposed model and conclusions.

Financial model with chaotic analysis

Recently, it was proposed to use a brand-new set of nonlinear ordinary differential equations. The system aims to represent chaotic financial activities. Such a system was taken into consideration for various analyses in this paper. For each of the three axes, we first evaluated the nullcline points and then gave the formula for the associated Poincare mapping. With various differential operators, we have analyzed the existence and uniqueness of systems of solutions. We have numerically solved the model using the well-known Nystrom in the case of the classical model and the Midpoint in the case of fractional derivatives.

Vibro-impact analysis and characterization of pipeline conveying fluids with multi-segmented motion-limiting constraints

Previous studies of the cantilevered pipeline conveying fluid system have included motion-limiting constraints in the form of trilinear springs. While this is desirable in experimental scenarios, it may not be representative of real-world applications. Therefore, this study focuses on multi-segmented motion-limiting constraints. As this type of motion-limiting constraint has not been investigated with a cantilevered pipeline system, a wide variety of outer and inner constraint stiffness and constraint gap sizes are investigated in this study to gain a comprehensive understanding of how the multi-segmented constraints affect the dynamics of the cantilevered pipeline. In this effort, bifurcation diagrams, phase portraits, Poincare maps, time histories, and power spectra are used to investigate the dynamics of the system, and the fluid flow speeds where dynamic characteristics are considered. In general, it is found that critical flow speeds like when the pipe sticks in the constraints are reduced as the constraint stiffnesses are increased. Additionally, the sticking flow speed occurred at lower flow speeds as the gap sizes of the inner and outer constraints decrease, and a larger constraint offset results in a smaller inner gap size leading to critical behaviors occurring at earlier flow speeds.

Dynamic modeling and analysis of high-speed aerostatic journal bearing-rotor system with recess

To analyze the dynamic properties of high-speed aerostatic journal bearing with recess, a bidirectional fluid-structure coupling dynamic model is established. The mathematical model is established by coupling the governing equation of the transient air film flow, the flow balance equation, and the rotor motion equation. Based on the trajectory of rotor axis, trajectory of rotor center, Poincare map, time response of rotor, frequency spectrum, mass flow rate, and bifurcation diagram, the influences of operating parameters on the coupling system are analyzed theoretically and experimentally. The results indicate that the system has abundant nonlinear behavior, and the instability parameters of the system are determined. This study provides guidance for the theoretical design and practical operation of this type of system.

Research on high-speed bounding gait analysis and control of quadruped robot

In order to improve the performance of the quadruped robot, the impact of high-speed gait is an important target to measure the performance of the robot. This paper elaborates the research methods of high-speed gait movement of quadrupeds, and a multi-rigid-body dynamics modelling method is presented. According to the analysis of high-speed bounding gait, the dynamic modelling of quadruped motion system is calculated. The motion planning for a rigid-torso quadruped robot based on Poincare Map is presented, and the high-speed bounding gait motion control strategy is established. The simulation experiments have been carried out, and the results have demonstrated the effectiveness of the motion planning model and high-speed bounding method.

The dynamic regimes and the energy harvesting of the energy harvester based on the bistable piezoelectric composite laminate

The dynamic regimes and the energy harvesting of the bistable energy harvester based on the bistable piezoelectric composite laminate are elaborated here. To identify the all-around dynamic regimes and assess the bistable energy harvesting performance, the forward frequency sweep, the reverse frequency sweep and the resistance sweep are conducted. The peak-to-peak frequency–amplitude response curves on the displacement and the voltage output are graphically presented. The single-well vibration, the limit cycle oscillations, the intermittency between the limit cycle oscillations and the chaotic snapthrough, the intermittency between the multiple periods snapthrough and the chaotic snapthrough, the multiple periods snapthrough and the chaotic snapthrough are elaborated by the Time history diagram, the Phase diagram and the Poincare map. The dynamic regimes are graphically presented delivering the stability zone for the dynamic responses and the optimal region for the energy harvesting. The RMS power output and the Max voltage output are checked to be the value judgements. Due to the softening nonlinear effect and the hysteresis, the conspicuous biases between the forward and reverse frequency sweeps are found to exist illustrating that the limit cycle oscillations expand the bandwidth of the double-well regimes during the reverse frequency sweep. From the perspective of the energy harvesting capacity, the limit cycle oscillations are demonstrated to be optimal, the double-well responses generally outperform the single-well responses concerning the off-resonance and the single-well responses concerning the primary resonance around the reduced modal frequency may outperform the double-well responses except the limit cycle oscillations. The load resistance is crucial to the power generation performance and needs optimizing with the change of the external excitation. The load resistance, the external excitation amplitude and frequency are interrelated and can be optimized simultaneously for the maximum power generation efficiency.

Influence of inter and subharmonics on the chaotic behavior of the stator current waveform in an induction motor

This article presents the results of research on the influence of the distorted induction motor supply voltage on two selected indicators (phase trajectories and Poincare maps) of chaotic behavior observed in the stator current of an induction motor. The tests were carried out with the use of the proprietary engine model realized in the ANSYS Electronics Desktop environment.

Natural Exponential and Three-Dimensional Chaotic System.

Existing chaotic system exhibits unpredictability and nonrepeatability in a deterministic nonlinear architecture, presented as a combination of definiteness and stochasticity. However, traditional two-dimensional chaotic systems cannot provide sufficient information in the dynamic motion and usually feature low sensitivity to initial system input, which makes them computationally prohibitive in accurate time series prediction and weak periodic component detection. Here, a natural exponential and three-dimensional chaotic system with higher sensitivity to initial system input conditions showing astonishing extensibility in time series prediction and image processing is proposed. The chaotic performance evaluated theoretically and experimentally by Poincare mapping, bifurcation diagram, phase space reconstruction, Lyapunov exponent, and correlation dimension provides a new perspective of nonlinear physical modeling and validation. The complexity, robustness, and consistency are studied by recursive and entropy analysis and comparison. The method improves the efficiency of time series prediction, nonlinear dynamics-related problem solving and expands the potential scope of multi-dimensional chaotic systems.