Behavior Of Nonlinear Systems Research Articles

Assessing the Non-Linear Dynamics of a Hopf–Langford Type System

In this paper, the non-linear dynamical behavior of a 3D autonomous dissipative system of Hopf–Langford type is investigated. Through the help of a mode transformation (as the system’s energy is included) it is shown that the 3D nonlinear system can be separated of two coupled subsystems in the master (drive)-slave (response) synchronization type. After that, based on the computing first and second Lyapunov values for master system, we have attempted to give a general framework (from bifurcation theory point of view) for understanding the structural stability and bifurcation behavior of original system. Moreover, a family of exact solutions of the master system is obtained and discussed. The effect of synchronization on the dynamic behavior of original system is also studied by numerical simulations.

Features of business administration in the context of global chaordic business environment

The purpose of the article is to create professional guidelines for politicians, managers of organizations of various profiles and levels (national, regional and municipal), who have to take into account in their business practice the presence of uncertainty, turbulence and chaos in their business environment, including its international segment. It is known that administration as a bureaucratic method of management has long been widely used in routine, repetitive processes of business practice. But when the business process becomes more complicated, communications grow, the manager drowns in the flow of information, does not have time to make decisions, when the situation is unexpectedly and constantly changing, the efficiency of administration falls catastrophically and creates new more complex problems. Moreover, the higher the level of a manager, the more time they spend on the administration process, and the more in such cases it becomes a hindrance to development processes, causes them significant harm and becomes a catalyst for the strengthening or formation of new chaotic zones in the business environment. Numerous practical problems associated with attempts of managers to work constructively in chaos zones and effective management in conditions of increased uncertainty and turbulence in the business environment gradually began to form and make it possible to generalize significant experience in this area, called chaos management. The article systematizes the author’s many years of experience as an independent consultant on organizational and strategic development in Russian and foreign companies, which was associated with the search for effective solutions to improve the manageability of a business (company) in the face of constant turbulent changes in the market. The object of systematization is the administration processes for solving problems that arise in the business environment of modern companies, which the business community did not have to deal with so often and regularly early. The essence is that there is a tendency of the need for a significant rethinking of the approach to the work of modern managers-administrators, a revision of their work technologies and the structure of management functionality in a chaordic business environment. New skills of business thinking are required that are adequate to the principles of the theory of social chaos, which describes the features of the behavior of modern nonlinear systems (events), which at first glance seem random, unpredictable and disordered. Otherwise, the administrator will be "pulled" into the chaos zones and by his unprofessional actions will only expand and deepen them, stimulating the diffusion of the zones of instability and instability, i. e. the penetration of chaos into other areas (systems), where it can be claimed or borrowed, but for other purposes.

Nonparametric damage detection and localization model of framed civil structure based on local gravitation clustering analysis

Structural damage detection is still a stimulating problem due to the complicated non-linear behaviour of the structural system, incomplete sensed data, presence of noise in the data, and uncertainties in both experimental measurement and analytical model. This paper presents the application of a non-linear signal processing tool and artificial intelligence-based methodology for nonparametric damage detection to address the above stated issues. Local mean decomposition (LMD), as an adaptive signal processing technique, is exploited to extract multidimensional damage features over acquired non-linear non-stationary vibration signals. These features are classified into categories, which are then utilized to calculate a damage indicator. Classification of multidimensional feature space has been a challenging issue since its inception. To address this, local gravitation clustering (LGC), a self-evaluating, synergic clustering technique, is employed. The relevance and significance of the process corresponding to the problem have also been an important concern. The outcomes of the whole process prove its proficiency in damage identification. The efficiency of the process is then compared with existing clustering methods on several parameters. The proposed algorithm is also validated for operational and environmental conditions by considering finite cases analogues to physical ailments like temperature, ageing and live loads.

Understanding the Origin of Enhanced Piezoelectric Response in PVDF Matrices with Embedded ZnO Nanoparticles, from Polarizable Molecular Dynamics Simulations.

The pervasive use of portable electronic devices, powered from rechargeable batteries, represents a significant portion of the electricity consumption in the world. A sustainable and alternative energy source for these devices would require unconventional power sources, such as harvesting kinetic/potential energy from mechanical vibrations, ultrasound waves, and biomechanical motion, to name a few. Piezoelectric materials transform mechanical deformation into electric fields or, conversely, external electric fields into mechanical motion. Therefore, accurate prediction of elastic and piezoelectric properties of materials, from the atomic structure and composition, is essential for studying and optimizing new piezogenerators. Here, we demonstrate the application of harmonic-covalent and reactive force fields (FF), Dreiding and ReaxFF, respectively, coupled to the polarizable charge equilibration (PQEq) model for predicting the elastic moduli and piezoelectric response of crystalline zinc oxide (ZnO) and polyvinylidene difluoride (PVDF). Furthermore, we parametrized the ReaxFF atomic interactions for Zn-F in order to characterize the interfacial effects in hybrid PVDF matrices with embedded ZnO nanoparticles (NPs). We capture the nonlinear piezoelectric behavior of the PVDF-ZnO system at different ZnO concentrations and the enhanced response that was recently observed experimentally, between 5 and 7 wt % ZnO concentrations. From our simulation results, we demonstrate that the origin of this enhancement is due to an increase in the total atomic stress distribution at the interface between the two materials. This result provides valuable insight into the design of new and improved piezoelectric nanogenerators and demonstrates the practical value of these first-principles based modeling methods in materials science.

Geometrically non-linear free and forced vibration of a shallow arch

The purpose of this present work is to investigate the geometrical non-linearity in free and forced vibration of a shallow arch elastically restrained at the ends. The non-linear governing equilibrium equation of the shallow arch is obtained after the Euler Bernoulli theory and the Von Karman geometrical non-linearity assumptions. After applying the ends conditions, the eigenvalues problem of the generalized trancendant equation have been determined iteratively using the Newton-Raphson algorithm. The kinetic and total strain energy have been discretized into a series of a finite spatial functions which are a combination of linear modes and basic function contribution coefficients. Using Hamilton’s principle energy and spectral analysis, the problem is reduced into a set of non-linear algebraic equations that solved numerically using an approximate explicit method developed previously the so-called second formulation. Considering a multimode approach, the effect of initial rise and concentrated force on non-linear behaviour of system has been illustrated in the backbone curves giving the non-linear amplitude-frequency dependence. The corresponding non-linear deflections and curvatures have been plotted for various vibration amplitudes.

Censored regression distributed functional link adaptive filtering algorithm over nonlinear networks

Wireless sensor network (WSN) is an important part of the Internet of Things (IoT) and has emerged in various new forms, such as smart home, smart city, and intelligent manufacturing system. Due to its high reliability, distributed estimation over nonlinear WSNs is one of the most active fields in recent years. In this paper, a novel distributed functional link least mean square (DFLMS) algorithm based on rblackthe diffusion strategy is proposed, in which the diffusion functional link network (DFLN) is used to model the nonlinear dynamic behavior of the distributed system. In particular, by using different orthogonal polynomials, we develop four types of DFLNs, i.e., trigonometric DFLN (TDFLN), Legendre DFLN (LDFLN), Chebyshev DFLN (CDFLN), and Hermite DFLN (HDFLN). However, the censored measurement caused by the range of sensors brings great challenges to the traditional distributed nonlinear estimation. To tackle this problem, a censored regression-distributed functional link adaptive filtering (CR-DFLAF) algorithm is further proposed. Compared with the DFLMS algorithm, the CR-DFLAF algorithm can compensate the estimated bias in the CR scenario at the price of slightly increased computational complexity. Simulations involving two distributed nonlinear networks verify the effectiveness of the proposed algorithms.

Switching dynamics of a non-autonomous FitzHugh-Nagumo circuit with piecewise-linear flux-controlled memristor

Memristor, as a nonlinear electronic component, has good switching characteristics, which makes it has excellent application in the field of artificial intelligence. The study for discontinuous dynamics of memristor-based neural network can best reflect the boundary effect of memristors and the complex nonlinear behaviors of system. In this paper, the non-autonomous FitzHugh-Nagumo neuronal circuit with piecewise memristor is investigated in flux-charge domain through the theory of switching flow. The sufficient and necessary conditions of switching motions, such as passable and grazing on the boundary, are developed to understand the switching mechanism. The switching bifurcation diagrams with changing the system parameters and initial conditions are studied to reveal the hidden extreme multistability and coexisting attractors. The parameter mappings and basins of attractor are also carried out to express the coexistences of periodic orbits and chaos with different mapping structures. The simulation results show that the switching and grazing motion are verified the effectiveness the analysis conditions.

Nonlinear behavior of wireless power transfer systems: modeling, analysis, and experimental verification

Nonlinear behavior of wireless power transfer systems: modeling, analysis, and experimental verification

Effect of damage limit states on the seismic fragility of reinforced concrete frame-shear wall buildings

Assessment of the seismic vulnerability of frame-shear wall buildings can be performed by non-linear dynamic analysis and it needs detailed analytical modeling, structural performance measures and various earthquake intensities. The codal based design method can hardly be used for designing buildings of pre-defined target objectives whereas the Unified performance-based design (UPBD) method can be designed for buildings of pre-defined target objectives. In the current study, the UPBD method for frame-shear wall buildings has been applied for different performance levels (PL) i.e. Immediate occupancy (IO), Life safety (LS) and Collapse prevention (CP) with 1%, 2% and 3% drift in both the directions of the buildings. The nonlinear dynamic analysis of the reinforced concrete (RC) frame-shear wall buildings is performed considering spectrum compatible ground motions (SCGM) as per EC-8 demand spectrum at 0.45g level and type B soil condition. Vulnerability assessment of the frame-shear wall buildings is conducted by generating fragility curves and the probability failure of structure is checked based on different configurations and damage limit states of the structure. Finally, the outcome of the work gives a proper idea of the nonlinear behavior of the dual system so that optimum design could be acquired for achieving higher safety aspects.

Bayesian Model Selection in Nonlinear Subspace Identification

In nonlinear system identification, one of the main challenges is how to select a nonlinear model. The accuracy of nonlinear subspace identification depends on the accuracy of the nonlinear feedback force that the user chooses. Considering the uncertainties in the selection process of an appropriate nonlinear model, a novel Bayesian probability method calculation framework based on response data is established to improve the accuracy of nonlinear subspace identification. Three implementation steps are introduced: 1) establish the candidate model database; 2) the reconstructed signal can be calculated by nonlinear subspace identification; and 3) the posterior probability of each candidate model is estimated to get the optimal nonlinear model and determine the nonlinear coefficients of the nonlinearities. Two numerical simulations are investigated: a two-degree-of-freedom spring-mass system with nonlinear damping and a cantilever beam with nonlinear stiffness. The influence of the noise on the robustness of the algorithm is considered. The experimental investigation is eventually undertaken considering a device showing elastic and damping nonlinearities. The latter is represented by a friction model depending on both velocity and displacement. Results indicate that the proposed approach can effectively identify the nonlinear system behavior with high accuracy.

Frequency–energy plot and targeted energy transfer analysis of coupled bistable nonlinear energy sink with linear oscillator

The nonlinear energy sink (NES), which is proven to perform rapid and passive targeted energy transfer (TET), has been employed for vibration mitigation in many primary small- and large-scale structures. Recently, the feature of bistability, in which two nontrivial stable equilibria and one trivial unstable equilibrium exist, is utilized for passive TET in what is known as bistable NES (BNES). The BNES generates a nonlinear force that incorporates negative linear and multiple positive or negative nonlinear stiffness components. In this paper, the BNES is coupled to a linear oscillator (LO) where the dynamic behavior of the resulting LO-BNES system is studied through frequency–energy plots (FEPs), which are generated by analytical approximation using the complexification-averaging method and by numerical continuation techniques. The effect of the length and stiffness of the transverse coupling springs is found to affect the stability and topology of the branches and indicates the importance of the exact physical realization of the system. The rich nonlinear dynamical behavior of the LO-BNES system is also highlighted through the appearance of multiple symmetrical and unsymmetrical in- and out-of-phase backbone branches, especially at low energy levels. The superimposed wavelet frequency spectrums of the LO-BNES response on the FEP have verified the robustness of the TET mechanism where the role of the unsymmetrical NNM backbones in TET is clearly observed.

Nonlinear Dynamics and Motion Bifurcations of the Rotor Active Magnetic Bearings System with a New Control Scheme and Rub-Impact Force

This article is dedicated to investigating the nonlinear dynamical behaviors of the 8-pole rotor active magnetic bearing system. The rub and impact forces between the rotating disc and the pole-legs are included in the studied model for the first time. A new control scheme based on modifying the 8-pole positions has been introduced. The proposed control methodology is designed such that four poles only are located in the horizontal and vertical directions (i.e., in +X,+Y,−X,−Y directions), while the other four poles are inserted in a way such that each pole makes 45° with two of the axes +X,+Y,−X,−Y. The control currents in the horizontal and vertical poles are suggested to be proportional to both the velocity and displacement of the rotor in the horizontal and vertical directions, respectively, while the control currents in the inclined poles are proposed to be dependent on the combination of both the displacement and velocity of the rotor in the horizontal and vertical directions. Accordingly, the whole-system mathematical model is derived. The derived discontinuous dynamical system is analyzed employing perturbation methods, Poincare maps, bifurcation diagrams, whirling orbits, and frequency spectrum. The obtained results demonstrated that the controller proportional control gain can play a significant role in changing the vibratory behaviors of the system, where the proposed control method can behave either as a cartesian control strategy or as a radial control one depending on the magnitude of the proportional gain. In addition, it is found that the rotor system can vibrate with periodic, periodic-n, quasiperiodic, or chaotic motion when the rub and/or impact forces occur. Moreover, it is reported for the first time that the rotor-AMB can oscillate symmetrically in X and Y directions either in full annular rub mode or quasiperiodic partial rub mode depending on the impact stiffness coefficient and the dynamic friction coefficient.

On qualitative behaviors of nonlinear singular systems with multiple constant delays

This paper deals with some qualitative properties of a class of nonlinear singular systems with multiple constant delays. Via the Lyapunov-Krasovskii functional (LKF) method and integral inequalities, we obtain some new sufficient conditions which guarantee that the considered systems are regular, impulse-free and exponentially stable. Two numerical examples are given to illustrate the applicability of the obtained results using MATLAB software. By this work, we extend and improve some results of the past literature.

Nonlinear dynamics of controlled release mechanism under boundary friction

Friction bounds the lower performance in control applications. Effective product modeling of controlling mechanisms and capturing the nonlinearity imposed by friction always attract the attention of researchers. Present work intends to capture the nonlinear dynamic behavior of a mechanical system with control release operation under boundary friction. The system used for this purpose is a second-order mechanical system comprising of rotary inertia element (lever), linear element (targeted mass), and spring element. The mechanical system chosen bears a resemblance to actual systems with control release like actuators, hydraulically operated copy turning machine, flight control mechanism, and robotics. The system dynamics have been captured under the light of two friction models viz. LuGre model and Dahl model. The performance of the system under these two friction models is ascertained for different times taken by the mass to settle, post and pre-zero-crossing time taken by target mass, maximum amplitude, time-period, and amplitude decay. The present work is capable of providing guidelines to simulate systems with control release under friction.

Amplitude modulation control method for bursting dynamics under time-delayed feedback

Time-delayed feedback control is one of the important active control methods for complex dynamical behaviors in nonlinear systems. Yet its relationship and effectiveness on multiple time scale dynamics need to be further explored. As a purpose to gain insight into such complexity, we investigate the effectiveness of amplitude modulation in controlling (suppressing or enhancing) bursting oscillations in a classical mechanical oscillator with time-delayed feedback. It is shown how the presence of delay can change the amplitude of the singular cycle oscillations, or suppress them altogether. The results are compared to the conventional periodic perturbation method. In many cases, the amplitudes of periodic solutions under delayed feedback are easier to satisfy the technical requirements. If the delayed feedback is added, stable periodic bursting can be easily accomplished. Therefore, we demonstrate that an effective vibration modulation for bursting dynamics is possible if appropriate time delay and feedback gains are chosen.

Physical-stochastic continuous-time identification of a forced Duffing oscillator

Despite the simplicity of the Duffing oscillator, its dynamical behaviour is extremely rich. Hence, the Duffing equations are used to describe the dynamic behaviour of many real-world nonlinear systems for a wide range of frequency bands and amplitude of the excitation signal in basic sciences and engineering. For example, the Duffing oscillator has been successfully used to model a variety of physical processes such as stiffening springs, beam buckling, nonlinear electronic circuits, superconducting Josephson parametric amplifiers, and ionisation waves in plasmas etc. Therefore, the identification of the Duffing oscillator model/parameters directly from the measured input–output data is a topic of active research in many scientific fields In this paper, we use the concept of stochastic differential equations (SDEs) to identify a model of the Duffing oscillator. SDE-based grey-box models allow us to capture the underlying mathematical structure describing the physics of the system (e.g. the original Duffing equations) using the drift term and explicitly handling of model uncertainty (or the process noise) using the diffusion term whereas the measurement uncertainty is modelled using the measurement noise term respectively. In this paper, we propose a slight variation of the maximum likelihood estimation framework used for the identification of SDEs based grey-box models yielding improved performance for long-term predictions. The proposed framework is combined with an iterative residual analysis to develop a grey-box model of the forced Duffing oscillator. The benchmark data from the so-called Brussels “Silverbox system”, which is an electrical circuit mimicking the forced Duffing oscillator dynamics is used for the identification purpose. Finally, the identified model performance (the simulation errors) is compared with the existing results available in the literature.

Experimental field study of floater motion effects on a main bearing in a full-scale spar floating wind turbine

In this paper we present a full-scale experimental field study of the effects of floater motion on a main bearing in a 6 MW turbine on a spar-type floating substructure. Floating wind turbines are necessary to access the full offshore wind power potential, but the characteristics of their operation leave a gap with respect to the rapidly developing empirical knowledge on operation of bottom-fixed turbines. Larger wind turbines are one of the most important contributions to reducing cost of energy, but challenge established drivetrain layouts, component size envelopes and analysis methods. We have used fibre optic strain sensor arrays to measure circumferential strain in the stationary ring in a main bearing. Strain data have been analysed in the time domain and the frequency domain and compared with data on environmental loads, floating turbine motion and turbine operation. The results show that the contribution to fluctuating strain from in-plane bending strain is two orders of magnitude larger than that from membrane strain. The fluctuating in-plane bending strain is the result of cyclic differences between blade bending moments, both in and out of the rotor plane, and is driven by wind loads and turbine rotation. The fluctuating membrane strain appears to be the result of both axial load from thrust, because of the bearing and roller geometry, and radial loads on the rotating bearing ring from total out-of-plane bending moments in the three blades. The membrane strain shows a contribution from slow-varying wind forces and floating turbine pitch motion. However, as the total fluctuating strain is dominated by the intrinsic effects of blade bending moments in these turbines, the relative effect of floater motion is very small. Mostly relevant for the intrinsic membrane strain, sum and difference frequencies appear in the measured responses as the result of nonlinear system behaviour. This is an important result with respect to turbine modelling and simulation, where global structural analyses and local drivetrain analyses are frequently decoupled.

A review of non-probabilistic machine learning-based state of health estimation techniques for Lithium-ion battery

Lithium-ion batteries are used in a wide range of applications including energy storage systems, electric transportations, and portable electronic devices. Accurately obtaining the batteries’ state of health (SOH) is critical to prolong the service life of the battery and ensure the safe and reliable operation of the system. Machine learning (ML) technology has attracted increasing attention due to its competitiveness in studying the behavior of complex nonlinear systems. With the development of big data and cloud computing, ML technology has a big potential in battery SOH estimation. In this paper, the five most studied types of ML algorithms for battery SOH estimation are systematically reviewed. The basic principle of each algorithm is rigorously derived followed by flow charts with a unified form, and the advantages and applicability of different methods are compared from a theoretical perspective. Then, the ML-based SOH estimation methods are comprehensively compared from following three aspects: the estimation performance of various algorithms under five performance metrics, the publication trend obtained by counting the publications in the past ten years, and the training modes considering the feature extraction and selection methods. According to the comparison results, it can be concluded that amongst these methods, support vector machine and artificial neural network algorithms are still research hotspots. Deep learning has great potential in estimating battery SOH under complex aging conditions especially when big data is available. Moreover, the ensemble learning method provides an emerging alternative trading-off between data size and accuracy. Finally, the outlooks of the research on future ML-based battery SOH estimation methods are closed, hoping to provide some inspiration when applying ML methods to battery SOH estimation.

Unexpected Scaling of Peak Acceleration for a Yielding Mass-Spring System Subjected to a Triangular Base Acceleration Pulse

Abstract The use of bounding scenarios is a common practice that greatly simplifies the design and qualification of structures. However, this approach implicitly assumes that the quantities of interest increase monotonically with the input to the structure, which is not necessarily true for nonlinear structures. This paper surveys the literature for observations of nonmonotonic behavior of nonlinear systems and finds such observations in both the earthquake engineering and applied mechanics literature. Numerical simulations of a single degree-of-freedom mass-spring system with an elastic–plastic spring subjected to a triangular base acceleration pulse are then presented, and it is shown that the relative acceleration of this system scales nonmonotonically with the input magnitude in some cases. The equation of motion for this system is solved symbolically and an approximate expression for the relative acceleration is developed, which qualitatively agrees with the nonmonotonic behavior seen in the numerical results. The nonmonotonicity is investigated and found to be a result of dynamics excited by the discontinuous derivative of the base acceleration pulse, the magnitude of which scales nonmonotonically with the input magnitude due to the fact that the first yield of the spring occurs earlier as the input magnitude is increased. The relevance of this finding within the context of defining bounding scenarios is discussed, and it is recommended that modeling be used to perform a survey of the full range of possible inputs prior to defining bounding scenarios.

Nonlinear behaviors analysis of high-speed rotor system supported by aerostatic bearings

In the paper, the dynamic model of aerostatic bearing-rotor system combining rotor motion equation and transient Reynolds equation is established to study influences of rotational speed, unbalance, rotor mass and supply pressure on the nonlinear behaviors of rotor system. The results reveal abundant nonlinear phenomenon consisting of 3 T-periodic, 5 T-periodic and quasi-periodic motions. Furthermore, chosen proper unbalance, smaller rotor mass and larger supple pressure can control the nonlinear vibration and improve the system stability. The results provide a theoretical basis for a simple and feasible method to control the nonlinear vibration of rotor system by adjusting supply pressure.