Several Results on the Number of Zeroes of Nonlinear Mappings on Bounded Regions

With homotopy methods, this paper discusses the existence and the number of zeroes of nonlinear mappings on bounded regions and extends some classical theorems.

Condition Monitoring of Turbines Using Nonlinear Mapping Method

Aiming at the non-linear nature of the signals generated from turbines, curvilinear component analysis (CCA), a novel nonlinear projection method that favors local topology conservation is presented for turbines conditions monitoring. This is accomplished in two steps. Time domain features are extracted from raw vibration signals, and then they are projected into a two-dimensional output space by using CCA method and form regions indicative of specific conditions, which helps classify and identify turbine states visually. Therefore, the variation of turbine conditions can be observed clearly with the trajectory of image points for the feature data in the two-dimensional space, and the occurrence and development of failures can be monitored in time. Key words condition monitoring - turbines - nonlinear mapping - curvilinear component analysis CLC number TP 17 - TH 17 Foundation item: Supported by the National Key Basic Research Special Found of China (2003CB716207) and the National Natural Science Foundation of China (50375047)Biography: Liao Guang-lan (1974-), male, Ph. D. candidate, research direction: fault diagnosis, pattern recognition and neural networks.

A Chaotic Block Encryption Scheme Based on the Piecewise Nonlinear Map

In order to improve communication security, proposed a chaotic block cryptographic scheme based on the coupled piecewise nonlinear map. Using the coupled chaotic systems to generate random binary sequences, a key-dependent shill approach permated the plain-text block and then using the classical chaotic masking technique encrypted the plain-text block. Simulation results show that the proposed algorithm has excellent cryptographic properties such as diffusion and confusion properties and it can resist the know plaintext attacks and chosen plain-text attacks.

Seismic-inversion method for nonlinear mapping multilevel well–seismic matching based on bidirectional long short-term memory networks

In this paper,the recurrent neural network structure of a bidirectional long shortterm memory network(Bi-LSTM)with special memory cells that store information is used to characterize the deep features of the variation pattern between logging and seismic data.A mapping relationship model between high-frequency logging data and low-frequency seismic data is established via nonlinear mapping.The seismic waveform is infinitely approximated using the logging curve in the low-frequency band to obtain a nonlinear mapping model of this scale,which then stepwise approach the logging curve in the high-frequency band.Finally,a seismic-inversion method of nonlinear mapping multilevel well–seismic matching based on the Bi-LSTM network is developed.The characteristic of this method is that by applying the multilevel well–seismic matching process,the seismic data are stepwise matched to the scale range that is consistent with the logging curve.Further,the matching operator at each level can be stably obtained to effectively overcome the problems that occur in the well–seismic matching process,such as the inconsistency in the scale of two types of data,accuracy in extracting the seismic wavelet of the well-side seismic traces,and multiplicity of solutions.Model test and practical application demonstrate that this method improves the vertical resolution of inversion results,and at the same time,the boundary and the lateral characteristics of the sand body are well maintained to improve the accuracy of thin-layer sand body prediction and achieve an improved practical application effect.

Controlling and synchronizing spatiotemporal chaos of the coupled Bragg acousto-optical bistable map system using nonlinear feedback

In this paper we present the control and synchronization of a coupled Bragg acousto-optic bistable map system using nonlinear feedback technology. This nonlinear feedback technology is useful to control a temporally chaotic system as well as a spatiotemporally chaotic system. It can be extended to synchronize the spatiotemporal chaos. It can work in a wide range of the controlled and synchronized signals, so it can decrease the sensitivity down to a noise level. The synchronization can be obtained by the analysis of the largest conditional Lyapunov exponent spectrum, and easily implemented in practical systems just by adjusting the coupled strength without any pre-knowledge of the dynamic system required.

Block and parallel modelling of broad domain nonlinear continuous mapping based on NN

The necessity of the use of the block and parallel modeling of the nonlinear continuous mappings with NN is firstly expounded quantitatively. Then, a practical approach for the block and parallel modeling of the nonlinear continuous mappings with NN is proposed. Finally, an example indicating that the method raised in this paper can be realized by suitable existed software is given. The results of the experiment of the model discussed on the 3-D Mexican straw hat indicate that the block and parallel modeling based on NN is more precise and faster in computation than the direct ones and it is obviously a concrete example and the development of the large-scale general model established by Tu Xuyan.

THE MAPPING RELATION AMONG SOLUTION OF SOME NONLINEAR EQUATIONS

Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of any one equation is known, so are the other two.

Algorithm of solutions for generalized nonlinear implicit quasivariational inclusions with fuzzy mappings

A class of generalized implicit quasivariational inclusions with fuzzy mappings in Hilbert space is discussed in this paper which proves an existence theorem of the solutions and proposes a new iterative algorithm and the convergence of the iterative sequence generated by the new algorithm. These results extend and improve some recent corresponding achievements.

Synchronizing spatiotemporal chaos in the coupled map lattices using nonlinear feedback functions

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Solution of Nonlinear Advection-Diffusion Equations via Linear Fractional Map Type Nonlinear QCA

Linear fractional map type (LFMT) nonlinear QCA (NLQCA), one of the simplest reversible NLQCA is studied analytically as well as numerically. Linear advection equation or Time Dependent Schrödinger Equation (TDSE) is obtained from the continuum limit of linear QCA. Similarly it is found that some nonlinear advection-diffusion equations including inviscid Burgers equation and porous-medium equation are obtained from LFMT NLQCA.

多策略融合的改进黑猩猩优化算法

针对黑猩猩优化算法存在迭代速度慢、精度不高及初始化分布不均匀等问题,提出一种融合多策略的改进黑猩猩优化算法。采用改进的Sine混沌映射初始化种群,解决种群边界聚集分布问题,引入考虑线性权重系数、自适应加速因子的粒子群思想,配合改进的非线性收敛因子平衡算法的全局搜索能力,加快算法收敛,提高收敛精度。引入自适应水波因子改进麻雀精英突变和Bernoulli混沌映射策略,提高个体跳出局部最优的能力。利用22个基准测试函数进行迭代分析求解和Wilcoxon秩和统计检验,得出所提算法迭代速度更快、精度更高、跳出局部最优能力更强。将所提算法应用到工程实例中,进一步验证算法处理现实优化问题的优越性。

Isomap的最优嵌入维数的估计算法

等距特征映射(Isomap)是一种新颖、高效的非线性降维技术,它的一个突出优点是只有两个参数需要设定,即邻域参数和嵌入维数。我们提出了一种新的估计Isomap的最优嵌入维数的算法,该算法使用执行Isomap过程本身所产生的数据来估计流形的最优嵌入维数,同时能确定邻域参数的最优值。通过与常用的残差估计方法的实例对比,说明这种算法对人造数据集和真实数据集都很有效,而且能更加合理、更加客观地估计出流形的最优嵌入维数。

基于L-ISOMAP降维的快速模糊聚类算法

模糊C-均值聚类算法是非监督模式识别中广泛应用的算法之一。但是,FCM算法在迭代过程中需要大量的计算,尤其当特征向量维数较高时,使用聚类分堆训练,不仅效率低下,还有可能导致"维数灾难"。针对该问题,分析模糊C-均值聚类算法在高维特征分析过程中,聚类中心的求解问题是一个np-hard问题,为了提高模糊C-均值聚类算法在高维特征分析中的实时性与有效性,结合界标等距映射(L-ISOMAP)算法,提出了改进算法FCM-LI,先对样本初步分析,利用聚类结果及样本数据相关性,使用界标等距映射(L-ISOMAP)算法降维,在此基础上进一步分析,获得最终分析结果。通过实验证明,FCM-LI算法在高维数据分析过程中的有效性与实时性。

LLE与ISOMAP降维的对比研究

局部线性嵌套和等距流形映射是两个基本的非线性降维方式,各自的优点和不足在人脸识别上值得做出深入的对比研究。因此对比测试这两种降维方式在不同参数下的执行效率,分析和总结这两种降维方式的适用特点和范围,选择局部线性嵌套和主成分分析,通过应用于人脸识别中,并总结人脸识别的识别率。

The homotopic mapping method for sea-air oscillator model of interdecadal climate fluctuations

The E1 Nifio/La Nifia Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, a coupled system of sea-air oscillator model is studied. The aim is to create an asymptotic solving method of nonlinear equation for the ENSO model. And based on a class of oscillators of ENSO model, employing the method of homotopic mapping, the approximate solution of corresponding problem is studied. It is proven from the results that the homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for ENSO model.

Bifurcation and chaos analysis for aeroelastic airfoil with freeplay structural nonlinearity in pitch

The dynamics character of a two degree-of-freedom aeroelastic airfoil with combined freeplay and cubic stiffness nonlinearities in pitch submitted to supersonic and hypersonic flow has been gaining significant attention. The Poincare mapping method and Floquet theory are adopted to analyse the limit cycle oscillation flutter and chaotic motion of this system. The result shows that the limit cycle oscillation flutter can be accurately predicted by the Floquet multiplier. The phase trajectories of both the pitch and plunge motion are obtained and the results show that the plunge motion is much more complex than the pitch motion. It is also proved that initial conditions have important influences on the dynamics character of the airfoil system. In a certain range of airspeed and with the same system parameters, the stable limit cycle oscillation, chaotic and multi-periodic motions can be detected under different initial conditions. The figure of the Poincare section also approves the previous conclusion.

Analysis on the Performance of the SLIP Runner with Nonlinear Spring Leg

The spring-loaded inverted pendulum(SLIP) has been widely studied in both animals and robots.Generally,the majority of the relevant theoretical studies deal with elastic leg,the linear leg length-force relationship of which is obviously conflict with the biological observations.A planar spring-mass model with a nonlinear spring leg is presented to explore the intrinsic mechanism of legged locomotion with elastic component.The leg model is formulated via decoupling the stiffness coefficient and exponent of the leg compression in order that the unified stiffness can be scaled as convex,concave as well as linear profile.The apex return map of the SLIP runner is established to investigate dynamical behavior of the fixed point.The basin of attraction and Floquet Multiplier are introduced to evaluate the self-stability and initial state sensitivity of the SLIP model with different stiffness profiles.The numerical results show that larger stiffness exponent can increase top speed of stable running and also can enlarge the size of attraction domain of the fixed point.In addition,the parameter variation is conducted to detect the effect of parameter dependency,and demonstrates that on the fixed energy level and stiffness profile,the faster running speed with larger convergence rate of the stable fixed point under small local perturbation can be achieved via decreasing the angle of attack and increasing the stiffness coefficient.The perturbation recovery test is implemented to judge the ability of the model resisting large external disturbance.The result shows that the convex stiffness performs best in enhancing the robustness of SLIP runner negotiating irregular terrain.This research sheds light on the running performance of the SLIP runner with nonlinear leg spring from a theoretical perspective,and also guides the design and control of the bio-inspired legged robot.

Nonlinear Dimensionality Reduction and Data Visualization:A Review

Dimensionality reduction and data visualization are useful and important processes in pattern recognition. Many techniques have been developed in the recent years. The self-organizing map （SOM） can be an efficient method for this purpose. This paper reviews recent advances in this area and related approaches such as multidimensional scaling （MDS）, nonlinear PC A, principal manifolds, as well as the connections of the SOM and its recent variant, the visualization induced SOM （ViSOM）, with these approaches. The SOM is shown to produce a quantized, qualitative scaling and while the ViSOM a quantitative or metric scaling and approximates principal curve/surface. The SOM can also be regarded as a generalized MDS to relate two metric spaces by forming a topological mapping between them. The relationships among various recently proposed techniques such as ViSOM, Isomap, LLE, and eigenmap are discussed and compared.

New Finite Difference Mapped WENO Schemes with Increasingly High Order of Accuracy

In this paper,a new type of finite difference mapped weighted essentially non-oscillatory(MWENO)schemes with unequal-sized stencils,such as the seventh-order and ninthorder versions,is constructed for solving hyperbolic conservation laws.For the purpose of designing increasingly high-order finite difference WENO schemes,the equal-sized stencils are becoming more and more wider.The more we use wider candidate stencils,the bigger the probability of discontinuities lies in all stencils.Therefore,one innovation of these new WENO schemes is to introduce a new splitting stencil methodology to divide some fourpoint or five-point stencils into several smaller three-point stencils.By the usage of this new methodology in high-order spatial reconstruction procedure,we get different degree polynomials defined on these unequal-sized stencils,and calculate the linear weights,smoothness indicators,and nonlinear weights as specified in Jiang and Shu(J.Comput.Phys.126:202228,1996).Since the difference between the nonlinear weights and the linear weights is too big to keep the optimal order of accuracy in smooth regions,another crucial innovation is to present the new mapping functions which are used to obtain the mapped nonlinear weights and decrease the difference quantity between the mapped nonlinear weights and the linear weights,so as to keep the optimal order of accuracy in smooth regions.These new MWENO schemes can also be applied to compute some extreme examples,such as the double rarefaction wave problem,the Sedov blast wave problem,and the Leblanc problem with a normal CFL number.Extensive numerical results are provided to illustrate the good performance of the new finite difference MWENO schemes.

Mapping equivalent approach to analysis and realization of memristor-based dynamical circuit

A novel mapping equivalent approach is proposed in this paper, which can be used for analyzing and realizing a memristor-based dynamical circuit equivalently by a nonlinear dynamical circuit with the same topologies and circuit parameters. A memristor-based chaotic circuit and the corresponding Chua＇s chaotic circuit with two output differentiators are taken as examples to illustrate this approach. Equivalent dynamical analysis and realization of the memristor-based chaotic circuit are performed by using Chua＇s chaotic circuit. The results indicate that the outputs of memristor-based chaotic circuit and the corresponding outputs of Chua＇s chaotic circuit have identical dynamics. The proposed approach verified by numerical simulations and experimental observations is useful in designing and analyzing memristor-based dynamical circuits.