Set-Membership Filtering Approach to Dynamic Event-Triggered Fault Estimation for a Class of Nonlinear Time-Varying Complex Networks

The present study addresses the problem of fault estimation for a specific class of nonlinear time-varying complex networks,utilizing an unknown-input-observer approach within the framework of dynamic event-triggered mechanism(DETM).In order to optimize communication resource utilization,the DETM is employed to determine whether the current measurement data should be transmitted to the estimator or not.To guarantee a satisfactory estimation performance for the fault signal,an unknown-input-observer-based estimator is constructed to decouple the estimation error dynamics from the influence of fault signals.The aim of this paper is to find the suitable estimator parameters under the effects of DETM such that both the state estimates and fault estimates are confined within two sets of closed ellipsoid domains.The techniques of recursive matrix inequality are applied to derive sufficient conditions for the existence of the desired estimator,ensuring that the specified performance requirements are met under certain conditions.Then,the estimator gains are derived by minimizing the ellipsoid domain in the sense of trace and a recursive estimator parameter design algorithm is then provided.Finally,a numerical example is conducted to demonstrate the effectiveness of the designed estimator.

Correlation between detrended fluctuation analysis and the Lempel-Ziv complexity in nonlinear time series analysis

We study the correlation between detrended fluctuation analysis（DFA） and the Lempel-Ziv complexity（LZC） in nonlinear time series analysis in this paper.Typical dynamic systems including a logistic map and a Duffing model are investigated.Moreover,the influence of Gaussian random noise on both the DFA and LZC are analyzed.The results show a high correlation between the DFA and LZC,which can quantify the non-stationarity and the nonlinearity of the time series,respectively.With the enhancement of the random component,the exponent α and the normalized complexity index C show increasing trends.In addition,C is found to be more sensitive to the fluctuation in the nonlinear time series than α.Finally,the correlation between the DFA and LZC is applied to the extraction of vibration signals for a reciprocating compressor gas valve,and an effective fault diagnosis result is obtained.

Multi-parameter Sensitivity Analysis and Application Research in the Robust Optimization Design for Complex Nonlinear System

The current research of complex nonlinear system robust optimization mainly focuses on the features of design parameters, such as probability density functions, boundary conditions, etc. After parameters study, high-dimensional curve or robust control design is used to find an accurate robust solution. However, there may exist complex interaction between parameters and practical engineering system. With the increase of the number of parameters, it is getting hard to determine high-dimensional curves and robust control methods, thus it＇s difficult to get the robust design solutions. In this paper, a method of global sensitivity analysis based on divided variables in groups is proposed. By making relevant variables in one group and keeping each other independent among sets of variables, global sensitivity analysis is conducted in grouped variables and the importance of parameters is evaluated by calculating the contribution value of each parameter to the total variance of system response. By ranking the importance of input parameters, relatively important parameters are chosen to conduct robust design analysis of the system. By applying this method to the robust optimization design of a real complex nonlinear system-a vehicle occupant restraint system with multi-parameter, good solution is gained and the response variance of the objective function is reduced to 0.01, which indicates that the robustness of the occupant restraint system is improved in a great degree and the method is effective and valuable for the robust design of complex nonlinear system. This research proposes a new method which can be used to obtain solutions for complex nonlinear system robust design.

Closed form soliton solutions of three nonlinear fractional models through proposed improved Kudryashov method

We introduce a new integral scheme namely improved Kudryashov method for solving any nonlinear fractional differential model.Specifically,we apply the approach to the nonlinear space-time fractional model leading the wave to spread in electrical transmission lines(s-tfETL),the time fractional complex Schrödinger(tfcS),and the space-time M-fractional Schrödinger-Hirota(s-tM-fSH)models to verify the effectiveness of the proposed approach.The implementing of the introduced new technique based on the models provides us with periodic envelope,exponentially changeable soliton envelope,rational rogue wave,periodic rogue wave,combo periodic-soliton,and combo rational-soliton solutions,which are much interesting phenomena in nonlinear sciences.Thus the results disclose that the proposed technique is very effective and straight-forward,and such solutions of the models are much more fruitful than those from the generalized Kudryashov and the modified Kudryashov methods.

The oblique derivative problem for nonlinear elliptic complex equations of second order in multiply connected unbounded domains

In this article,we discuss that an oblique derivative boundary value problem for nonlinear uniformly elliptic complex equation of second order with the boundary conditions in a multiply connected unbounded domain D.The above boundary value problem will be called Problem P.Under certain conditions,by using the priori estimates of solutions and Leray-Schauder fixed point theorem,we can obtain some results of the solvability for the above boundary value problem（0.1） and（0.2）.

Nonlinear Dynamics in a Nonextensive Complex Plasma with Viscous Electron Fluids

Cylindrical and spherical dust-electron-acoustic （DEA） shock waves and double layers in an unmagnetized, col- lisionless, complex or dusty plasma system are carried out. The plasma system is assumed to be composed of inertial and viscous cold electron fluids, nonextensive distributed hot electrons, Maxwellian ions, and negatively charged stationary dust grains. The standard reductive perturbation technique is used to derive the nonlinear dynamical equations, that is, the nonplanar Burgers equation and the nonplanar further Burgers equation. They are also numerically analyzed to investigate the basic features of shock waves and double layers （DLs）. It is observed that the roles of the viscous cold electron fluids, nonextensivity of hot electrons, and other plasma parameters in this investigation have significantly modified the basic features （such as, polarity, amplitude and width） of the nonplanar DEA shock waves and DLs. It is also observed that the strength of the shock is maximal for the spherical geometry, intermediate for cylindrical geometry, while it is minimal for the planar geometry. The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear phenomena associated with the nonplanar DEA waves in both space and laboratory plasmas.

Theoretical convergence analysis of complex Gaussian kernel LMS algorithm

With the vigorous expansion of nonlinear adaptive filtering with real-valued kernel functions,its counterpart complex kernel adaptive filtering algorithms were also sequentially proposed to solve the complex-valued nonlinear problems arising in almost all real-world applications.This paper firstly presents two schemes of the complex Gaussian kernel-based adaptive filtering algorithms to illustrate their respective characteristics.Then the theoretical convergence behavior of the complex Gaussian kernel least mean square（LMS） algorithm is studied by using the fixed dictionary strategy.The simulation results demonstrate that the theoretical curves predicted by the derived analytical models consistently coincide with the Monte Carlo simulation results in both transient and steady-state stages for two introduced complex Gaussian kernel LMS algonthms using non-circular complex data.The analytical models are able to be regard as a theoretical tool evaluating ability and allow to compare with mean square error（MSE） performance among of complex kernel LMS（KLMS） methods according to the specified kernel bandwidth and the length of dictionary.

Application of complex nonlinear modes to determine dry whip motion in a rubbing rotor system

Dry whip motion is an instability of rubbing rotor system and may cause catastrophic failures of rotating machinery.Up to now,the related mechanisms of the dry whip is still not well understood.This paper aims to build the relationship between the complex nonlinear modes and the dry whip motion,and propose an effective method to predict the response characteristics and existence boundary of the dry whip through complex nonlinear modes.For the first time,the paper discusses how to use the complex nonlinear modes to predict the dry whip systematically,and as a consequence,the mechanism of the relationship between the complex nonlinear mode and the dry whip is revealed.The results show that the Backward Whirl(BW)mode motion of the rubbing rotor system dominates the response characteristics and the existence boundary of dry whip.The whirl amplitude and whirl frequency of dry whip are equal to the modal amplitude and modal frequency of the BW mode at the jump up point where the modal damping is equal to zero.The existence boundary corresponds to the critical rotation speed where the minimum of the modal damping of the BW mode motion is exactly equal to zero.Moreover,the proposed nonlinear modal method in this article is very effective for the prediction of dry whip of the more complicated practical rotor system,which has been verified by applying the predicted method into a rubbing rotor test rig.

Traveling wave solutions to some nonlinear fractional partial differential equations through the rational(G'/G)-expansion method

In this article,the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regu-larized long wave(SRLW)equation are successfully examined by the recently established rational(G/G)-expansion method.The suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex transform.Consequently,the theories of the ordinary differential equations are implemented effectively.Three types closed form traveling wave solutions,such as hyper-bolic function,trigonometric function and rational,are constructed by using the suggested method in the sense of conformable fractional derivative.The obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a channel.It is observed that the performance of the rational(G/G)-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.

Dynamic Transmissibility of a Complex Nonlinear Coupling Isolator

A mathematical model was developed for a complex nonlinear coupling isolator for attenuating vibration which coupled quadratic damping, viscous damping, Coulomb damping, and nonlinear spring forces. The approximate analytical solution for the dynamic transmissibility of the isolator was deduced by combining Fourier transforms and the harmonic balance method with deterministic excitation. The mathematical characteristics of the dynamic transmissibility were analyzed to illustrate the dynamic performance of the isolator. The analytical results show multiple solutions, especially the low-frequency attenuation characteristics below the resonance frequency. The results provide a theoretical basis for the design of nonlinear isolators.

Bis(4,4′-dimethyl-2,2′-bipyridine)ruthenium(II) Complexes Containing 2-Arylimidazo-phenanthroline: Syntheses, Characterization and Third-order Nonlinear Optical Properties

Four novel mononuclear ruthenium(II) complexes [Ru-(dmb) 2L] 2+ [dmb=4,4′-dimethyl-2,2′-bipyridine, L=imid-azo-[4,5-f]phenanthroline (IP), 2-phenylimidazo-phenanthroline (PIP), 2-(4′-hydroxyphenyl)imidazo-phenanthroline (HOP), 2-(4′-dimethylami- nophenyl)imidazo-phenanthroline (DMNP)] were synthesized and characterized by ES-MS, 1H NMR, UV-vis and electrochemistry. The nonlinear optical properties of the ruthenium(II) complexes were investigated by Z-scan techniques with 12 ns laser pulse at 540 nm, and all of them exhibit both nonlinear optical (NLO) absorption and self-defocusing effect. The corresponding effective NLO susceptibility |χ 3| of the complexes is in the range of 2.68×10 -12-4.57×10 -12 esu.