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.

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.

Nonlinear Hilbert Boundary Value Problem of Negative Index for Nonlinear Elliptic Complex Equation

This paper deals with a nonlinear boundary value problem for a complex equation W_z = H(Z,W,W_z),Z ∈G : |Z|<1 with boundary eondition of the form I.l-i Re[Z-W(Z)] = ψ(Z,W(Z)) + Re[λ_0+sum from k=1 to |n|-1(λ_k + iλ_k)Z^k],Z∈Γ:|z|=1 k--1 in which the index is negative. By establishing a priori estimate and using the imbdding method combined with the the Newton interation procedure, it is proved that the above problem is solvable and the solution is unique in C^l+a(g) ,O<a<].

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.

A Novel Evolutionary-Fuzzy Control Algorithm for Complex Systems

This paper presents an adaptive fuzzy control scheme based on modified genetic algorithm. In the control scheme, genetic algorithm is used to optimze the nonlinear quantization functions of the controller and some key parameters of the adaptive control algorithm. Simulation results show that this control scheme has satisfactory performance in MIMO systems, chaotic systems and delay systems.

A weak condition for secant method to solve systems of nonlinear equations

In this paper, a new weak condition for the convergence of secant method to solve the systems of nonlinear equations is proposed. A convergence ball with the center x0 is replaced by that with xl, the first approximation generated by the secant method with the initial data x-1 and x0. Under the bounded conditions of the divided difference, a convergence theorem is obtained and two examples to illustrate the weakness of convergence conditions are provided. Moreover, the secant method is applied to a system of nonlinear equations to demonstrate the viability and effectiveness of the results in the paper.

Fractional-Order Modeling and Dynamical Analysis of a Francis Hydro-Turbine Governing System with Complex Penstocks

This paper investigates the stability of the Francis hydro-turbine governing system with complex penstocks in the grid-connected mode. Firstly, a novel fractional-order nonlinear mathematical model of a Francis hydro-turbine governing system with complex penstocks is built from an engineering application perspective. This model is described by state-space equations and is composed of the Francis hydro-turbine model, the fractional-order complex penstocks model, the third-order generator model, and the hydraulic speed governing system model. Based on stability theory for a fractional-order nonlinear system, this study discovers a basic law of the bifurcation points of the above system with a change in the fractional-order a. Secondly, the stable region of the governing system is investigated in detail,and nonlinear dynamical behaviors of the system are identified and studied exhaustively via bifurcation diagrams, time waveforms, phase orbits, Poincare maps, power spectrums and spectrograms. Results of these numerical experiments provide a theoretical reference for further studies of the stability of hydropower stations.

基于强化学习的柴油机调速算法研究

为了更好地调节柴油机转速,提出一种强化学习–比例积分微分(proportional integral derivative, PID)控制器,并应用到了柴油机转速控制中。基于连续动作空间的柔性动作–评价(soft actor-critic, SAC)算法,结合连续型PID控制器,设计了一种强化学习–PID控制器,可代替传统PID控制的转速环。优化设计了基于演员–评论家(actor-critic)框架的输入输出和奖励函数以匹配柴油机特性,采用随机动作增加寻优效率,形成SAC-PID控制柴油机转速的网络交互结构,达到快速调整转速,减小稳定时间的效果。构建了以柴油机D6114为原型机的MATLAB/Simulink平均值模型,并利用试验数据验证了仿真模型的有效性。利用平均值模型,仿真验证了该控制算法效果。经过仿真验证本算法使柴油机转速响应曲线超调量更小,响应时间更快,鲁棒性更强,SAC-PID控制负载瞬态调速率和稳定时间均已达到1级精度指标。仿真对比验证了SAC算法的联合控制效果,结果表明其较其他算法更佳。

基于综合贡献率的舰船装备体系寿命评估

为了更科学地预测装备寿命,提升装备的作战效益,从装备对体系的“综合贡献率”视角出发,探究了舰船装备“体系寿命”的评估方法。首先,基于作战环理论和非线性结构方程模型,引入二次交互项,构建舰船装备体系作战能力的指标体系,建立了体系作战效能的评估模型;然后,运用阈值法建立了舰船装备体系的复杂网络模型,基于拓扑特征统计值,构建了舰船装备体系网络结构特征的指标体系,将层次分析法与熵权法相结合来计算指标权重;最后,提出了舰船装备体系综合贡献率、体系寿命的定义和数学模型,并以航母编队体系对抗为算例,通过实验仿真数据,验证了模型和方法的可行性和有效性。

Inter-well internal resonance analysis of rectangular asymmetric cross-ply bistable composite laminated cantilever shell under transverse foundation excitation

The chaotic dynamic snap-through and complex nonlinear vibrations are investigated in a rectangular asymmetric cross-ply bistable composite laminated cantilever shell,in cases of 1:2 inter-well internal resonance and primary resonance.The transverse foundation excitation is applied to the fixed end of the structure,and the other end is in a free state.The first-order approximate multiple scales method is employed to perform the perturbation analysis on the dimensionless two-degree-of-freedom ordinary differential motion control equation.The four-dimensional averaged equations are derived in both polar and rectangular coordinate forms.Deriving from the obtained frequency-amplitude and force-amplitude response curves,a detailed analysis is conducted to examine the impacts of excitation amplitude,damping coefficient,and tuning parameter on the nonlinear internal resonance characteristics of the system.The nonlinear softening characteristic is exhibited in the upper stable-state,while the lower stable-state demonstrates the softening and linearity characteristics.Numerical simulation is carried out using the fourth-order Runge-Kutta method,and a series of nonlinear response curves are plotted.Increasing the excitation amplitude further elucidates the global bifurcation and chaotic dynamic snap-through characteristics of the bistable cantilever shell.

基于干扰观测器的复杂非线性系统优化控制方法

为了提高具有未知干扰的复杂非线性系统的控制性能和运行性能,提出了一种基于干扰观测器的复杂非线性系统优化控制方法(IOCM).该方法设计了一个基于模糊神经网络的模型逼近器来捕捉系统的非线性动力学,并利用干扰观测器来描述系统的未知干扰,以获得更准确的系统预测模型.然后,在多目标模型预测控制的框架下,提出了一种具有协同成本函数和多梯度算法的优化控制结构,以综合求解设定点和控制律.采用城市污水处理过程基准仿真平台(BSM1)验证所提方法的有效性.实验结果表明:暴雨天气条件下平均出水水质(EQ)为6711 mg/L、平均运行能耗(EC)为3805 kW·h;对比其他分步实现的优化控制方法,IOCM具有较好的鲁棒性,能够提高非线性系统的优化控制性能.

基于合理边界的更高速动车组多专业设计优化

考虑到非光滑与大位移两大非线性影响,作为大型复杂非线性系统的更高速动车组多专业设计优化需回归到合理的轮轨匹配边界条件。文章结合国内外高铁运维实践特殊性,以德国ICE3系列转向架为基础,提出更高速动车组转向架自适应改进方案,并针对该方案下的车体不稳定问题提出半主动车减振技术;通过构建三车组列车多体动力学仿真模型,验证了仅凭半主动车间减振技术即可解决车体不稳定问题;在不同工况下,验证更高速动车组转向架对轨道线路的适应性。结果表明:钢轨专业具备实施低锥度均匀磨耗策略的能力;车辆专业可改善对中央凹陷踏面磨耗的自清理能力;客运专业通过最优交路规划,有条件满足经济镟修要求。

Comparing dynamical systems concepts and techniques for biomechanical analysis

Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.

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.

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.

COMPLEX INNER PRODUCT AVERAGING METHOD FOR CALCULATING NORMAL FORM OF ODE

This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.

1970s中期全球气温关联网络结构特征的变化研究

气温关联网络结构特征分析是当前气候系统复杂网络研究领域的热点科学问题,相关研究成果对于深入认识气候系统的复杂性和内部相互作用等具有重要的科学意义.为深入探究气温关联网络结构的时间演化特征,本研究尝试构建偏冷态和偏暖态对应的气温关联网络,揭示1970s中期气温关联网络结构的变化及其可能成因.研究结果表明,气温关联网络连通性在1970s中期由偏冷态强于偏暖态转变为偏暖态强于偏冷态,且这种变化在赤道中东太平洋等低纬度大洋关键区域尤为显著.1970s中期之后,偏冷态对应的热带大西洋、印度洋等关键区域的气温距平由负相位调整为正相位,造成其与赤道中东太平洋区域之间的气温协方差为负值的概率显著增加,相关系数减小,网络联通性显著减小;偏暖态则对应关键区域气温距平维持正位相为主,气温协方差为正值概率高,相关系数略增大,网络连通性略有所增加.此消彼长,造成1970s中期之后气温关联网络结构特征出现偏暖态网络连通度强弱对比的反转.去除全球增暖对应的线性趋势后,偏冷态和偏暖态之间的网络连通度差异明显减小,1976年前由13.1%下降到-1.7%,1976年后由-37.0%下降到-8.2%.因此,全球增暖趋势通过改变全球不同区域的气温距平正负位相,进而造成网络连通度强弱对比的反转,即全球增暖不仅简单表现为气温的总体上升,更会引起气候系统内部网络结构特征的调整.

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.

基于BP神经网络辨识的预测滤波PID控制

针对复杂非线性系统采用常规PID控制性能不好的问题,通过BP神经网络构建系统输出量的辨识器,在目标函数中加入优化参数的增量约束项,提出可克服算法病态的牛顿法,并用其在线学习BP神经网络的连接权,根据增量式预测滤波PID控制,推导了PID控制参数应满足的线性不等式约束条件,将PID控制参数的优化归结为线性不等式约束的最优化问题。综上研究提出基于BP神经网络辨识的在线优化参数预测滤波PID控制。仿真研究说明,因算法具有在线优化PID控制参数和预测控制性能,故提出的智能PID控制算法与常规PID控制相比,具有更优的性能。