Binary nonlinearization of the super classical-Boussinesq hierarchy

The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.

SYMMETRY CONSTRAINT OF THE LEVI EQUATIONS BY BINARY NONLINEARIZATION

In this paper,the translation of the Lax pairs of the Levi equations is pre- sented.Then a symmetry constraint for the Levi equations is given by means of binary nonlinearization method. The spatial part and the temporal parts of the translated Lax pairs and its adjoint Lax pairs of the Levi equations are all constrainted as finite dimensional Liouville integrable Hamiltonian systems. Finally,the involutive solutions of the Levi equations are presented.

Bargmann Symmetry Constraint and Binary Nonlinearization of Super NLS-MKdV Hierarchy

An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.

AN EQUIVALENT NONLINEARIZATION METHOD FOR ANALYSINGRESPONSE OF NONLINEAR SYSTEMS TO RANDOM EXCITATIONS

In this paper, a new equivalent nonlinearization method is developed and used in analysing the response of nonlinear systems to Gaussian while noise excitation. Its basic idea and calculation method are expounded. With the help of the presented method, several kinds of usual nonlinear random vibration systems are analyzed. The numerical results show that the mean square responses of the proposed approach are much closer to the exact solutions or Monte Carlo solutions, than that obtained from equivalent linearization method.

Recent Progress in Reinforcement Learning and Adaptive Dynamic Programming for Advanced Control Applications

Reinforcement learning(RL) has roots in dynamic programming and it is called adaptive/approximate dynamic programming(ADP) within the control community. This paper reviews recent developments in ADP along with RL and its applications to various advanced control fields. First, the background of the development of ADP is described, emphasizing the significance of regulation and tracking control problems. Some effective offline and online algorithms for ADP/adaptive critic control are displayed, where the main results towards discrete-time systems and continuous-time systems are surveyed, respectively.Then, the research progress on adaptive critic control based on the event-triggered framework and under uncertain environment is discussed, respectively, where event-based design, robust stabilization, and game design are reviewed. Moreover, the extensions of ADP for addressing control problems under complex environment attract enormous attention. The ADP architecture is revisited under the perspective of data-driven and RL frameworks,showing how they promote ADP formulation significantly.Finally, several typical control applications with respect to RL and ADP are summarized, particularly in the fields of wastewater treatment processes and power systems, followed by some general prospects for future research. Overall, the comprehensive survey on ADP and RL for advanced control applications has d emonstrated its remarkable potential within the artificial intelligence era. In addition, it also plays a vital role in promoting environmental protection and industrial intelligence.

Characterization and identification towards dynamic-based electrical modeling of lithium-ion batteries

Lithium-ion batteries are widely recognized as a crucial enabling technology for the advancement of electric vehicles and energy storage systems in the grid.The design of battery state estimation and control algorithms in battery management systems is usually based on battery models,which interpret crucial battery dynamics through the utilization of mathematical functions.Therefore,the investigation of battery dynamics with the purpose of battery system identification has garnered considerable attention in the realm of battery research.Characterization methods in terms of linear and nonlinear response of lithium-ion batteries have emerged as a prominent area of study in this field.This review has undertaken an analysis and discussion of characterization methods,with a particular focus on the motivation of battery system identification.Specifically,this work encompasses the incorporation of frequency domain nonlinear characterization methods and dynamics-based battery electrical models.The aim of this study is to establish a connection between the characterization and identification of battery systems for researchers and engineers specialized in the field of batteries,with the intention of promoting the advancement of efficient battery technology for real-world applications.

Nonlinear phenomena in vibrations of embedded carbon nanotubes conveying viscous fluid

Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes(CNTs)are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems.Therefore,the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscousfluid and supported on a nonlinear elastic foundation.The proposed model is based on nonlocal Euler–Bernoulli beam theory.The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation,respectively.A detailed parametric study is reported into how the nonlocal parameter,foundation coefficients,fluid viscosity,and amplitude and frequency of the external force influence the nonlinear dynamics of the system.Subharmonic,quasi-periodic,and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories,frequency-response curves,bifurcation diagrams,phase portraits,power spectra,and Poincarémaps.Also,the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.

Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell:an experimental and numerical study

The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.

Multiple mixed state variable incremental integration for reconstructing extreme multistability in a novel memristive hyperchaotic jerk system with multiple cubic nonlinearity

Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting the incremental integration of the state variables into system parameters.However,this approach cannot solve memristive systems in the presence of nonlinear terms other than the memristor term.In addition,the converted state variables may suffer from a degree of divergence.To allow simpler mechanistic analysis and physical implementation of extreme multistability phenomena,this paper uses a multiple mixed state variable incremental integration(MMSVII)method,which successfully reconstructs a four-dimensional hyperchaotic jerk system with multiple cubic nonlinearities except for the memristor term in a three-dimensional model using a clever linear state variable mapping that eliminates the divergence of the state variables.Finally,the simulation circuit of the reduced-dimension system is constructed using Multisim simulation software and the simulation results are consistent with the MATLAB numerical simulation results.The results show that the method of MMSVII proposed in this paper is useful for analyzing extreme multistable systems with multiple higher-order nonlinear terms.

Experimental,Numerical,and Analytical Studies on the Bending of Mechanically Lined Pipe

Mechanically lined pipe(MLP)is often used for offshore oil and gas transport because of its low cost and corrosion resistance.During installation and operation,the pipe may undergo severe bending deformation,which causes the liner to separate from the outer pipe and buckles,affecting the stability of the whole line.In this paper,the buckling response of MLP subjected to bending is investigated to clarify its bending characteristics by employing both experiments,numerical simulation,as theoretical methods.Two types of MLPs were manufactured with GB 45 carbon steel(SLP)and Al 6061(ALP)used as the outer pipe material,respectively.The hydraulic expansion and bending experiments of small-scale MLPs are conducted.In addition to the ovalized shape of the cross-section for the SLP specimens,the copper liner was found to wrinkle on the compressive side.In contrast,the liner of ALP remains intact without developing any wrinkling and collapse mode.In addition,a dedicated numerical framework and theoretical models were also established.It was found both the manufacturing and bending responses of the MLP can be well reproduced,and the predicted maximum moment and critical curvatures are in good agreement with the experimental results.

Geometric Programming for Nonlinear Satellite Buffer Networks With Time Delays under L_(1)-Gain Performance

Dear Editor,This letter concerns the parameter tuning problem for nonlinear satellite buffer networks with communication delays, aiming to optimize their stability properties under L_(1)-gain. We first model the satellite buffer networks by a nonlinear time-delay positive system and propose a novel characterization under which the nonlinear system is asymptotically stable with a prescribed L_(1)-induced performance.

Nonreciprocal thermal metamaterials:Methods and applications

Nonreciprocity of thermal metamaterials has significant application prospects in isolation protection,unidirectional transmission,and energy harvesting.However,due to the inherent isotropic diffusion law of heat flow,it is extremely difficult to achieve nonreciprocity of heat transfer.This review presents the recent developments in thermal nonreciprocity and explores the fundamental theories,which underpin the design of nonreciprocal thermal metamaterials,i.e.,the Onsager reciprocity theorem.Next,three methods for achieving nonreciprocal metamaterials in the thermal field are elucidated,namely,nonlinearity,spatiotemporal modulation,and angular momentum bias,and the applications of nonreciprocal thermal metamaterials are outlined.We also discuss nonreciprocal thermal radiation.Moreover,the potential applications of nonreciprocity to other Laplacian physical fields are discussed.Finally,the prospects for advancing nonreciprocal thermal metamaterials are highlighted,including developments in device design and manufacturing techniques and machine learning-assisted material design.

Output Feedback Stabilization of High-Order Nonlinear Time-Delay Systems With Low-Order and High-Order Nonlinearities

Dear Editor,to This letter deals with the output feedback stabilization of a class of high-order nonlinear time-delay systems with more general low-order and high-order nonlinearities.By constructing reduced-order observer,based on homogeneous domination theory together with the adding a power integrator method,an output feedback controller is developed guarantee the equilibrium of the closed system globally uniformly asymptotically stable.

Analytical solution to incident angle quasi-phase-matching engineering for second harmonic generation in a periodic-poled lithium niobate crystal

Phase matching or quasi-phase matching(QPM)is of significant importance to the conversion efficiency of second harmonic generation(SHG)in artificial nonlinear crystals like lithium niobate(LN)crystal or microstructured nonlinear crystals like periodic-poled lithium niobate(PPLN)crystals.In this paper,we propose and show that the incident angle of pump laser light can be harnessed as an alternative versatile tool to engineer QPM for high-efficiency SHG in a PPLN crystal,in addition to conventional means of period adjusting or temperature tuning.A rigorous model is established and analytical solution of the nonlinear conversion efficiency under the small and large signal approximation theory is obtained at different incident angles.The variation of phase mismatching and walk-off length with incident angle or incident wavelength are also explored.Numerical simulations for a PPLN crystal with first order QPM structure are used to confirm our theoretical predictions based on the exact analytical solution of the general large-signal theory.The results show that the narrow-band tunable SHG output covers a range of 532 nm–552.8 nm at the ideal incident angle from 0°to 90°.This theoretical scheme,fully considering the reflection and transmission at the air-crystal interface,would offer an efficient theoretical system to evaluate the nonlinear frequency conversion and help to obtain the maximum SHG conversion efficiency by selecting an optimum incident wavelength and incident angle in a specially designed PPLN crystal,which would be very helpful for the design of tunable narrow-band pulse nanosecond,picosecond,and femtosecond laser devices via PPLN and other microstructured LN crystals.

Modeling Geometrically Nonlinear FG Plates: A Fast and Accurate Alternative to IGA Method Based on Deep Learning

Isogeometric analysis (IGA) is known to showadvanced features compared to traditional finite element approaches.Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functionalgrading (FG). However, the procedure is usually complex and often is time-consuming. We thus put forward adeep learning method to model the geometrically nonlinear bending behavior of FG plates, bypassing the complexIGA simulation process. A long bidirectional short-term memory (BLSTM) recurrent neural network is trainedusing the load and gradient index as inputs and the displacement responses as outputs. The nonlinear relationshipbetween the outputs and the inputs is constructed usingmachine learning so that the displacements can be directlyestimated by the deep learning network. To provide enough training data, we use S-FSDT Von-Karman IGA andobtain the displacement responses for different loads and gradient indexes. Results show that the recognition erroris low, and demonstrate the feasibility of deep learning technique as a fast and accurate alternative to IGA formodeling the geometrically nonlinear bending behavior of FG plates.

Dark Localized Waves in Shallow Waters:Analysis within an Extended Boussinesq System

We study dark localized waves within a nonlinear system based on the Boussinesq approximation,describing the dynamics of shallow water waves.Employing symbolic calculus,we apply the Hirota bilinear method to transform an extended Boussinesq system into a bilinear form,and then use the multiple rogue wave method to obtain its dark rational solutions.Exploring the first-and second-order dark solutions,we examine the conditions under which these localized solutions exist and their spatiotemporal distributions.Through the selection of various parameters and by utilizing different visualization techniques(intensity distributions and contour plots),we explore the dynamical properties of dark solutions found:in particular,the first-and second-order dark rogue waves.We also explore the methods of their control.The findings presented here not only deepen the understanding of physical phenomena described by the(1+1)-dimensional Boussinesq equation,but also expand avenues for further research.Our method can be extended to other nonlinear systems,to conceivably obtain higher-order dark rogue waves.

Dynamic performance and parameter optimization of a half-vehicle system coupled with an inerter-based X-structure nonlinear energy sink

Inspired by the demand of improving the riding comfort and meeting the lightweight design of the vehicle, an inerter-based X-structure nonlinear energy sink(IXNES) is proposed and applied in the half-vehicle system to enhance the dynamic performance. The X-structure is used as a mechanism to realize the nonlinear stiffness characteristic of the NES, which can realize the flexibility, adjustability, high efficiency, and easy operation of nonlinear stiffness, and is convenient to apply in the vehicle suspension, and the inerter is applied to replacing the mass of the NES based on the mass amplification characteristic. The dynamic model of the half-vehicle system coupled with the IX-NES is established with the Lagrange theory, and the harmonic balance method(HBM) and the pseudo-arc-length method(PALM) are used to obtain the dynamic response under road harmonic excitation. The corresponding dynamic performance under road harmonic and random excitation is evaluated by six performance indices, and compared with that of the original half-vehicle system to show the benefits of the IX-NES. Furthermore, the structural parameters of the IX-NES are optimized with the genetic algorithm. The results show that for road harmonic and random excitation, using the IX-NES can greatly reduce the resonance peaks and root mean square(RMS) values of the front and rear suspension deflections and the front and rear dynamic tire loads, while the resonance peaks and RMS values of the vehicle body vertical and pitching accelerations are slightly larger.When the structural parameters of the IX-NES are optimized, the vehicle body vertical and pitching accelerations of the half-vehicle system could reduce by 2.41% and 1.16%,respectively, and the other dynamic performance indices are within the reasonable ranges.Thus, the IX-NES combines the advantages of the inerter, X-structure, and NES, which improves the dynamic performance of the half-vehicle system and provides an effective option for vibration attenuation in the vehicle engineering.

Analysis and Design of Time-Delay Impulsive Systems Subject to Actuator Saturation

This paper investigates the exponential stability and performance analysis of nonlinear time-delay impulsive systems subject to actuator saturation. When continuous dynamics is unstable, under some conditions, it is shown that the system can be stabilized by a class of saturated delayed-impulses regardless of the length of input delays. Conversely, when the system is originally stable, it is shown that under some conditions, the system is robust with respect to sufficient small delayed-impulses. Moreover, the design problem of the controller with the goal of obtaining a maximized estimate of the domain of attraction is formulated via a convex optimization problem. Three examples are provided to demonstrate the validity of the main results.

Dynamic analysis of a novel multilink-spring mechanism for vibration isolation and energy harvesting

Due to technical limitations,existing vibration isolation and energy harvesting(VIEH)devices have poor performance at low frequency.This paper proposes a new multilink-spring mechanism(MLSM)that can be used to solve this problem.The VIEH performance of the MLSM under harmonic excitation and Gaussian white noise was analyzed.It was found that the MLSM has good vibration isolation performance for low-frequency isolation and the frequency band can be widened by adjusting parameters to achieve a higher energy harvesting power.By comparison with two special cases,the results show that the MLSM is basically the same as the other two oscillators in terms of vibration isolation but has better energy harvesting performance under multistable characteristics.The MLSM is expected to reduce the impact of vibration on high-precision sensitive equipment in some special sites such as subways and mines,and at the same time supply power to structural health monitoring devices.

Effects of connected automated vehicle on stability and energy consumption of heterogeneous traffic flow system

With the development of intelligent and interconnected traffic system,a convergence of traffic stream is anticipated in the foreseeable future,where both connected automated vehicle(CAV)and human driven vehicle(HDV)will coexist.In order to examine the effect of CAV on the overall stability and energy consumption of such a heterogeneous traffic system,we first take into account the interrelated perception of distance and speed by CAV to establish a macroscopic dynamic model through utilizing the full velocity difference(FVD)model.Subsequently,adopting the linear stability theory,we propose the linear stability condition for the model through using the small perturbation method,and the validity of the heterogeneous model is verified by comparing with the FVD model.Through nonlinear theoretical analysis,we further derive the KdV-Burgers equation,which captures the propagation characteristics of traffic density waves.Finally,by numerical simulation experiments through utilizing a macroscopic model of heterogeneous traffic flow,the effect of CAV permeability on the stability of density wave in heterogeneous traffic flow and the energy consumption of the traffic system is investigated.Subsequent analysis reveals emergent traffic phenomena.The experimental findings demonstrate that as CAV permeability increases,the ability to dampen the propagation of fluctuations in heterogeneous traffic flow gradually intensifies when giving system perturbation,leading to enhanced stability of the traffic system.Furthermore,higher initial traffic density renders the traffic system more susceptible to congestion,resulting in local clustering effect and stop-and-go traffic phenomenon.Remarkably,the total energy consumption of the heterogeneous traffic system exhibits a gradual decline with CAV permeability increasing.Further evidence has demonstrated the positive influence of CAV on heterogeneous traffic flow.This research contributes to providing theoretical guidance for future CAV applications,aiming to enhance urban road traffic efficiency and alleviate congestion.