Subjects -> AERONAUTICS AND SPACE FLIGHT (Total: 124 journals)
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 Nonlinear DynamicsJournal Prestige (SJR): 1.468 Citation Impact (citeScore): 4Number of Followers: 20      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1573-269X - ISSN (Online) 0924-090X Published by Springer-Verlag  [2467 journals]
• Probing epileptic disorders with lightweight neural network and EEG's
intrinsic geometry

Abstract: Abstract The nonlinear dynamical systems can be stabilized on attractors in chaotic states, where the attractors depicted by dynamical trajectories may take on specific geometries. Electroencephalogram (EEG) signals are typically chaotic signals that have various nonlinear dynamic characteristics. Intrinsic geometry of EEG signals could contribute to tracking the recurrence of seizures and probing epileptic disorders, but it is ignored in most deep network-based seizure detection algorithms. Therefore, this paper presents an automatic detection framework called Recursive State-Space Neural Network (RSSNN) to infer the EEG geometry from single-channel signals and identify different epileptic patterns with a fast computational speed. RSSNN consists of a mathematical mapping module and a deep learning model. The former reconstructs EEG geometry in a high-dimensional state-space and maps it to a two-dimensional graph. The latter is a newly designed lightweight (0.68 MB) fully convolutional network that decodes geometry into brain states. We validated RSSNN on a public EEG dataset collected from epileptic patients with seizure and seizure-free conditions and healthy volunteers. A sliding window with a one-second length is utilized to verify the performance of RSSNN at the segment level. Moreover, the voting strategy is adopted to obtain the final prediction at the subject level. In the testing phase, RSSNN obtains an overall 99.79% accuracy at the EEG segment level and reaches 100% accuracy at the subject level. Notably, it takes less than 25 ms to predict one subject. This study proves the potential of EEG's intrinsic geometry as a seizure indicator for real-time monitoring by combining it with a lightweight neural network. It enriches the deep learning-based seizure prediction methodology in nonlinear dynamics.
PubDate: 2022-12-03

• Multiple bifurcation solitons, lumps and rogue waves solutions of a
generalized perturbed KdV equation

Abstract: Abstract The perturbed KdV equation has many applications in mechanics and sound propagation in fluids. The aim of this manuscript is to study novel crucial exact solutions of the generalized perturbed KdV equation. The Hirota bilinear technique is implemented to derive general form solution of the considered equation. The novel soliton solutions are studied by taking different dispersion coefficients. We analyse first- and second-order soliton solutions, multiple-bifurcated soliton solutions, first- and second-order lump and rogue wave solutions of the considered equations. We show the effect of the parameters on the evolution of soliton solutions of the considered equation. All the obtained results are simulated by using MATLAB-2020.
PubDate: 2022-12-03

• Novel command-filtered Nussbaum design for continuous-time nonlinear
dynamical systems with multiple unknown high-frequency gains

Abstract: Abstract Command filters (CFs) have been successfully developed to reduce computational complexity and eliminate the effect of filtering errors on control performance through a compensating mechanism. However, to deal with multiple unknown high-frequency gains, the CF design remains an open problem due to the gap between the compensating mechanism design and unknown high-frequency gains. This paper bridges this gap by developing two additional adaptive laws that can contribute to the compensating mechanism design in novel CFs while considering the effect of unknown high-frequency gains. In the novel Nussbaum design, the influences of filtering errors are taken into account by introducing compensating signals. In contrast to existing filter-based Nussbaum methods, the compensating signals developed in this paper can handle multiple unknown high-frequency gains on the basis of the additional adaptive laws. The effect of filtering errors on the tracking performance is analyzed within the Lyapunov stability framework, and it is shown that the boundedness of all signals in the closed-loop system with the presented design can be guaranteed. Simulation results validate the efficacy of the proposed command-filtered Nussbaum design scheme.
PubDate: 2022-12-02

• Analysis of nonlinear vibration control for a functionally graded material
plate by NiTiNOL-steel wire ropes

Abstract: Abstract Traditional nonlinear passive control for continuous structures often requires a non-negligible volume for installation and motion that indirectly changes the design of the original structure and degrades vibration attenuation. Functionally graded materials (FGMs) are typically used in aeronautics and astronautics and are constantly subjected to external excitations that cause significant undesirable vibration. To address this problem, the present work proposes a dynamic model of nonlinear forced vibration of a FGM rectangular plate coupled with NiTiNOL-steel wire ropes (NiTi-ST). NiTi-ST exerts on the FGM complex generalized recovery forces, which are investigated by using two methods: the Galerkin truncation method and the harmonic balanced method (HBM). The HBM coupled with arc-length continuation is used to predict the frequency response and closed detached response (CDR) of the coupling system. The results show that the NiTi-ST reduces the resonance frequency of the FGM plate. The linear damper term introduced by the NiTi-ST determines the level of vibration control. However, the appearance of a CDR could make the dynamic phenomenon more complicated. Furthermore, elimination of the CDR may improve the vibration suppression in the nonlinear system, making it more challenging and urgent to investigate the coupling system above.
PubDate: 2022-12-02

• Vibration characteristics of multi-dimensional isolator based on 4-PUU
parallel mechanism with joint clearance

Abstract: Abstract For isolating multi-dimensional vibration experienced by vehicle-mounted precise facility, a multi-dimensional vibration isolator based on parallel mechanism with joint clearance is designed and analyzed. The main thrust of this work is establishing kinematic and dynamic equations of the isolator and exploring vibration isolation capability with joint clearance. Firstly, type synthesis of the parallel mechanism with three translations and one rotation is performed. The kinematic and dynamic equations of the isolator with joint clearance are deduced. Subsequently, vibration isolation performance is simulated with different values of joint clearance under harmonic and stochastic excitations in time and frequency domain, respectively. The simulating results demonstrate the proposed isolator with joint clearance inhibit multi-dimensional vibration effectively. The first-order resonance peak is sensitive to the increment in joint clearance. Finally, the proposed multi-dimensional vibration isolator is fabricated. The vibration isolation experiment is conducted. Through experimental results, the isolator reduces multi-dimensional vibration effectively in time and frequency domain. The vibration isolation capability degenerates as the counterweight of moving platform increases.
PubDate: 2022-12-02

• Characterization of aeroelastic response and aerodynamic stiffness effect
of an airfoil in the presence of dynamic stall

Abstract: Abstract The response characteristics and aerodynamic stiffness characteristics of the self-excited aeroelastic system under the influence of dynamic stall are investigated adopting CFD (computational fluid dynamics) method. It is found that as velocity increases, the response type changes from asymmetric LCOs (limit cycle oscillations) to symmetric LCOs due to the effect of dynamic stall. Special stable fixed-point responses and low-amplitude LCOs are also found between the asymmetric and symmetric high-amplitude LCO state. The stability of the fixed point is analyzed by combining traditional linearization method and energy map. By observing the flow field variations, it is found that the occurrence of these special responses is related to the separation of the boundary layer of lower surface near the trailing edge, and its mechanism is completely different from the high-amplitude limit-cycle oscillation dominated by dynamic stall. Systems with small equilibrium angular position enter the symmetric limit-cycle state more quickly after the Hopf bifurcation and dynamic stall occur on both upper and lower surfaces of the airfoil, as the velocity increases. While in the case of systems with large equilibrium angular position, the minimum angle of attack of aeroelastic responses decreases slowly before reaching the negative angle that allows dynamic stall to occur on the lower surface, the system remains in the asymmetric limit-cycle state over a wide range of velocities. Thus, aerodynamic stiffness of system with large equilibrium angular position changes non-monotonically due to the varying aerodynamic moment characteristics at the minimum angle of attack of asymmetric LCOs. Furthermore, by increasing the initial angular velocity, we found that the system responses all become symmetric LCOs and therefore the aerodynamic stiffness increases monotonically with the flow velocity. As to the effect of structural stiffness, it is found that the variation of the LCO amplitude with the structural stiffness coefficients will show different trends at different free-stream velocities. Energy maps show that different parametric distributions of the energy transfer at different free-stream velocities contribute to this phenomenon. Aerodynamic stiffness maps based on equivalent linearization method are also established to explain the aerodynamic stiffness variation. Moreover, when entering the symmetric LCO state, the structural stiffness no longer has a significant effect on the aerodynamic stiffness of the system, as the LCO amplitude and the aerodynamic moment characteristics do not vary much, which results in constant dimensionless aerodynamic stiffness coefficient for this stage.
PubDate: 2022-12-02

• Dissipative-based sampled-data control for T-S fuzzy wind turbine system
via fragmented-delayed state looped functional approach

Abstract: Abstract This study investigates thedissipative-based fuzzy sampled-data control scheme for variable-speed wind turbine system (WTS) by fragmented-delayed state looped functional framework. The main objective of this study is to stabilize the nonlinear variable-speed WTS and enhance its dynamic performance. To do this, initially, the proposed nonlinear variable-speed WTS is transformed into linear subsystems based on the Takagi–Sugeno (T-S) fuzzy approach. Then, the concept of coupling leakage time-varying delay is proposed to construct a more generalized T-S fuzzy model. After that, to minimize design conservatism, an improved fragmented- delayed state looped-Lyapunov functional is developed to fully utilize the advantages of the variable characteristics related to the actual sampling pattern. Besides, by applying the proposed new integral inequalities, some sufficient conditions are derived to ensure the addressed system is asymptotically stable under an optimizing performance index. Finally, numerical simulations are given to verify the effectiveness and feasibility of the proposed control scheme. The essential outcome of the proposed approach is that it can provide a superior dissipative performance index under the maximal sampling period.
PubDate: 2022-12-02

• Optimal Hilbert transform parameter identification of bistable structures

Abstract: Abstract Nonlinear bistable structures have received significant attention in the field of energy harvesting and vibration absorption. Obtaining their precise nonlinear restoring force is of significance to predict and enhance the system's performance. However, it is difficult to measure their nonlinear restoring force in experiments due to the distinct characteristic of snap-through. Moreover, the traditional Hilbert transform-based method may have insufficient identification accuracy or even be incapable because numerical integration or differentiation procedure is sensitive to noise disturbance. To address these issues, an optimal Hilbert transform parameter identification is proposed to precisely estimate the parameters in the bistable dynamic equation. The Hilbert transform interval estimation of mass, damping and nonlinear restoring force coefficients are derived for obtaining the reasonable range of identified parameters. Furthermore, an optimization fitness function is established to obtain the optimal value of nonlinear parameters in bistable structures. Numerical simulation of an asymmetric bistable dynamic equation shows that the proposed method exhibits an NMSE value of 2.52% for free vibration and 1.64% for forced periodic oscillation under 20 dB noise level. Besides, the damping effects on identification results are discussed. Experimental measurements of a magnetic coupled bistable cantilever beam under different conditions are performed to identify the nonlinear system parameters. Results indicate that the proposed method can effectively identify the nonlinear bistable structures with an average NMSE value of 8.23% for free vibration and 6.39% for forced periodic responses, respectively.
PubDate: 2022-12-02

• A reduced variational approach for searching cycles in high-dimensional
systems

Abstract: Abstract Searching recurrent patterns in complex systems with high-dimensional phase spaces is an important task in diverse fields. In the current work, an improved scheme is proposed to accelerate the recently designed variational approach for finding periodic orbits in systems with chaotic dynamics based on the existence of inertial manifold widely observed in various spatially extended systems, especially those with high dimensions. On the premise of keeping exponential convergence of the variational method, an effective loop evolution equation is derived to greatly reduce the storage and computation time. With repeated modification of local coordinates and evolution of the guess loop being carried out alternately, the rapid convergence and the stability of the reduction scheme are effectively achieved. The dimension of local coordinate subspaces is generally larger than the number of nonnegative Lyapunov exponents to ensure the exponential convergence. The proposed scheme is successfully demonstrated on several well-known examples and expected to supply a powerful tool in the exploration of high-dimensional nonlinear systems.
PubDate: 2022-12-02

• On multi-soliton solutions to a generalized inhomogeneous nonlinear
Schrödinger equation for the Heisenberg ferromagnetic spin chain

Abstract: Abstract A generalized inhomogeneous higher-order nonlinear Schrödinger (GIHNLS) equation for the Heisenberg ferromagnetic spin chain system in (1+1)-dimensions under zero boundary condition at infinity is taken into account. The spectral analysis is first performed to generate a related matrix Riemann–Hilbert problem on the real axis. Then, through solving the resulting matrix Riemann–Hilbert problem by taking the jump matrix to be the identity matrix, the general bright multi-soliton solutions to the GIHNLS equation are attained. Furthermore, the one-, two-, and three-soliton solutions are written out and analyzed by figures.
PubDate: 2022-12-01

• Predicting impact scenarios of a rimless wheel: a geometrical approach

Abstract: Abstract The 2D motion of a rigid rimless wheel on an inclined plane has been widely studied as a first simple case of passive walker. Usually, it is modelled as a hybrid dynamical system alternating continuous smooth phases and discrete impact ones. As in other bipedal walkers, the related research is often devoted to the analysis of cyclic motions and assumes that the spoke-ground collision is a single-point one. This work focuses exclusively on the impact problem and explores the possibility of different transitions within the impact interval (single-point to double-point collisions, dynamic jamb, stick-slide transitions and sliding reversal) as a function of the spokes angular aperture, the wheel inertia, the wheel-ground friction coefficient, and the initial conditions. This analysis is done through an innovative geometrical approach based on the Percussion Centre.
PubDate: 2022-12-01

• Riemann–Hilbert approach and N-soliton solutions of the coupled
generalized Sasa–Satsuma equation

Abstract: Abstract We investigate the initial value problem for the coupled generalized Sasa–Satsuma equation. Firstly, based on the spectral analysis from Lax pair, we obtain desired analytic spectral functions, and a Riemann–Hilbert problem on the real line is formulated. Solving the special Riemann–Hilbert problem with reflectionless case, the N-soliton solutions of the coupled generalized Sasa–Satsuma equation are derived. In addition, by choosing suitable parameters, the structures of single-soliton solution and double-soliton solution are graphically presented.
PubDate: 2022-12-01

• Nonlinear dynamics of a bistable system impacting a sinusoidally vibrating
shaker

Abstract: Abstract Bistable systems have seen significant interest in recent years, in applications ranging from energy harvesting, impact mitigation, and aerospace, to precision sensing and metamaterials. However, most investigations of bistable systems consider only continuous external forcing. The literature on the topic of vibroimpact dynamics is vast, but is mostly limited to monostable systems. In this work, we advance the state of knowledge by considering the fundamental problem of a one degree-of-freedom bistable system subjected to vibroimpact forcing by a sinusoidally vibrating shaker. Using computational models, we find that by varying excitation amplitude and frequency, a rich nonlinear dynamic behavior can be observed. Some responses exhibit only intrawell dynamics, while others display interwell motion that may converge to a second equilibrium. Analytical equations are derived to estimate the amplitude threshold that corresponds to the excitation amplitude required to observe interwell motion. The influence of the excitation frequency on the nonlinear dynamics of the system includes the presence of a local minimum in the threshold which is linked to a nonlinear resonance of the system. Further, response types can be differentiated by aperiodic (including chaotic) and periodic responses that include responses of periods one through six. In addition to computational simulations, the existence and stability of periodic orbits are determined using a shooting method based on the response over a single cycle. Experimental work using a magnetic bistable pendulum qualitatively validates the theoretical findings.
PubDate: 2022-12-01

• Impact energy and the risk of injury to motorcar occupants in the
front-to-side vehicle collision

Abstract: Abstract The effects of a road accident where one vehicle hits its front on the side of another one are explored. In such cases, the impacted vehicle’s side is usually significantly deformed, which causes a risk of serious injury to vehicle occupants. An analysis of the front-to-side collision covers many nonlinear and highly complex processes, especially when it is based on the collision energy balance. For the analysis, a model of a front-to-side motorcar collision and a dummy representing the impacted vehicle’s driver was prepared. The model simulations carried out were supplemented with important experimental test results. The model validation and the drawing of conclusions from research results were based on crash test results. The shares of major components in the front-to-side collision energy balance were determined. The impact energy has been proposed as an alternative predicate of the road accident effects; as a measure of the effects, the risk of injury to vehicle occupant’s head and torso is considered. The model simulations were found to be in good conformity with experimental test results. The research results enabled determining the relation between the side impact energy and the risk of dummy’s head and torso injuries according to the Abbreviated Injury Scale. The relation obtained was approximated using the logit model. This relation helps to reconstruct road accidents and to improve the car side’s passive safety systems. A discussion of the results obtained has shown good consistence between the results of this work and other comparable research results.
PubDate: 2022-12-01

• An efficient analytical approach to assess root cause of nonlinear
electric vehicle gear whine

Abstract: Abstract Noise, vibration, and harshness (NVH) issues pose considerable challenges for electric vehicle powertrain engineers. Gear vibrations generate an intrusive gear whine noise, with significant impact on the sound quality of electric powertrains. Dynamic transmission error (DTE) is the most quantitative indicator for gear NVH. Backlash, time variable meshing stiffness and damping contribute to DTE. Hence, a better understanding of these excitation sources is essential. A gear tribodynamics model is developed using potential energy method to estimate time variable meshing stiffness (TVMS). A fully analytical time-efficient model is proposed for lubricated contact stiffness based on transitions in the regimes of lubrication. The model accounts for the combined effects of surface elasticity and lubricant stiffness. Film thickness and damping coefficients are transiently updated at each instant during meshing cycle. The predictions from this model are compared with measured results from the literature and predicted results from Hertz contact model. The lubricated contact model successfully shows the contribution of the lubricant stiffness to TVMS and its variations with elasticity and viscosity parameters during meshing cycle. Gear harmonic and super-harmonic resonances are accurately estimated in terms of amplitude, frequencies and stiffness softening nonlinearities. Time history responses and phase-displacement diagrams show good agreement with the gear dynamics response at the main harmonic and second super-harmonic frequencies. The proposed model has a reasonable accuracy, significantly better than those from Hertzian contact models, and is considerably time efficient in comparison to numerical EHL solvers.
PubDate: 2022-12-01

• Observer-based prescribed performance tracking control for MEMS Gyroscope
subject to input saturation

Abstract: Abstract In this work, a fixed-time prescribed performance output feedback tracking control scheme is presented for Micro-Electro-Mechanical Systems (MEMS) gyroscope subjected to uncertain system parameters. To obtain the state information of MEMS gyroscope, a state observation system with neural network approximation technique is firstly constructed such that the observation error can converge to a small residual set, and the size of the residual set can be adjusted by the observer gain. On the basis of obtaining the estimated state, a novel preassigned time performance function and a dynamic auxiliary system with hyperbolic tangent function are introduced into the design of closed-loop system. By using the error coordinate transformation and backstepping design process, an anti-saturation control law is devised based on the Lyapunov stability analysis method. The proposed controller can ensure that all signals in the whole closed-loop system are bounded, and meanwhile the tracking errors are driven to a preassigned set in a fixed time. In the end, simulation results verify the effectiveness of the proposed method.
PubDate: 2022-12-01

• The impact of vaccination on the modeling of COVID-19 dynamics: a
fractional order model

Abstract: Abstract The coronavirus disease 2019 (COVID-19) is a recent outbreak of respiratory infections that have affected millions of humans all around the world. Initially, the major intervention strategies used to combat the infection were the basic public health measure, nevertheless, vaccination is an effective strategy and has been used to control the incidence of many infectious diseases. Currently, few safe and effective vaccines have been approved to control the inadvertent transmission of COVID-19. In this paper, the modeling approach is adopted to investigate the impact of currently available anti-COVID vaccines on the dynamics of COVID-19. A new fractional-order epidemic model by incorporating the vaccination class is presented. The fractional derivative is considered in the well-known Caputo sense. Initially, the proposed vaccine model for the dynamics of COVID-19 is developed via integer-order differential equations and then the Caputo-type derivative is applied to extend the model to a fractional case. By applying the least square method, the model is fitted to the reported cases in Pakistan and some of the parameters involved in the models are estimated from the actual data. The threshold quantity $$({\mathcal {R}}_0)$$ is computed by the Next-generation method. A detailed analysis of the fractional model, such as positivity of model solution, equilibrium points, and stabilities on both disease-free and endemic states are discussed comprehensively. An efficient iterative method is utilized for the numerical solution of the proposed model and the model is then simulated in the light of vaccination. The impact of important influential parameters on the pandemic dynamics is shown graphically. Moreover, the impact of different intervention scenarios on the disease incidence is depicted and it is found that the reduction in the effective contact rate (up to 30%) and enhancement in vaccination rate (up to 50%) to the current baseline values significantly reduced the disease new infected cases.
PubDate: 2022-12-01

• Equiprobable symbolization pattern entropy for time series complexity
measurement

Abstract: Abstract In order to effectively mine the structural features in time series and simplify the complexity of time series analysis, equiprobable symbolization pattern entropy (EPSPE) is proposed in this paper. The original time series are implemented through symbolic processing according to an equal probability distribution. Then, the sliding window technique is used to obtain a finite number of different symbolic patterns, and the pattern pairs are determined by calculating the conversion between the symbolic patterns. Next, the conversion frequency between symbolized patterns is counted to calculate the probability of the pattern pairs, thus estimating the complexity measurement of complex signals. Finally, we conduct extensive experiments based on the Logistic system under different parameters and the natural wind field. The experimental results show our EPSPE of the Logistic system increases from 5 to 7.5 as the parameters increase, which makes the distinction of periodic and complex time series with varying degrees intuitive. Meanwhile, it can more concisely reflect the structural characteristics and interrelationships between time series from the natural wind field (8.8–10 for outdoor and 7.8–8.3 for indoor). In contrast, the results of several state-of-the-art schemes are irregular and cannot distinguish the complexity of periodic time series as well as accurately predict the spatial deployment relationship of nine 2D ultrasonic anemometers.
PubDate: 2022-12-01

• Quasiperiodic and chaotic behaviours in time evolution of pulsar spin

Abstract: Abstract In this article, dynamical behaviour of pulsar spin-down is analysed with the presence of time-dependent external torques. The model incorporates nonlinear superfluidity of the core of pulsar. The spin-down rate of the crust becomes perturbed whenever a glitch occurs. An abrupt increase appears in the pulsar spin-down rate for a short period of time. Although there are several mechanisms proposed to understand those glitches, the exact mechanism is still unknown. The fluctuations in pulsar spin-down cannot be predicted either from time series analysis or governing equations for rotational dynamics. Long-term irregularities in pulsar spin-down give clues about some spiking activity or intermittency in the governing dynamics, which immediately enforce one to think about chaotic dynamics that may this trigger glitch behaviour. With this motivation behind, we modified an existing model known as vortex creep model to figure out the stochasticity in the dynamics of the system. The new model exhibits very interesting dynamical features. First of all, it is able to demonstrate glitch-like behaviour for suitable parameters. With the applied modification in the equations of motion, the system is showing different dynamical regimes from periodicity to quasiperiodicity and also chaotic dynamics become obvious for special parameter settings. The rich dynamical feature of the system is shown with the aid of nonlinear tools such as phase portraits, bifurcation diagrams, Lyapunov exponents and Poincaré sections.
PubDate: 2022-12-01

• Dynamics study of constant diastolic interval and constant TR control for
cardiac alternans based on a two-dimensional cellular automata model

Abstract: Abstract As a precursor for cardiac arrhythmias such as atrial and ventricular fibrillations, which could cause sudden cardiac death, cardiac alternans is essentially an unstable heart rhythm with alternating long and short action potential durations (APD) of cardiac myocytes that usually occurs under fast pacing conditions. In this paper, the constant TR control method based on a global pseudo-electrocardiogram (ECG) is studied and compared with the local constant diastolic interval (DI) control method using a 2-dimensional (2-D) cellular automata model (CAM), aiming at preventing or eliminating cardiac alternans before arrhythmias. The results show that both the constant TR and constant DI control methods are effective in stabling the alternans to a smaller basic cycle length (BCL). Also, the efficacy of the two control approaches depends on the “decrease step” Δ in the downsweep protocol, and a smaller Δ could significantly improve their performance. In addition, constant TR control is generally superior to constant DI control in alternans prevention when a relatively large Δ is adopted.
PubDate: 2022-12-01

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