The role of functional data analysis for instantaneous frequency estimation

This paper proposes a method for estimating the instantaneous frequency of a nonstationary signal; this method is based on a combination of empirical mode decomposition and functional data analysis. The proposed method incorporates a basis expansion technique for a functional data into time-varying phase derived by empirical mode decomposition and Hilbert transform, which provides a stable instantaneous frequency function. The superiority of the proposed method for instantaneous frequency estimation is demonstrated by various simulation studies. The analysis of multicomponent signals by the proposed method is also discussed. Furthermore, it is shown that the proposed method is highly effective for identifying groups (clusters) of nonstationary signals on the basis of the instantaneous frequency information.     

Solution of multivariable fuzzy equations

A method for the solution of multivariable fuzzy equations and inequalities is proposed. The proposed method is an extension of Sanchez' technique for a single fuzzy equation. A numerical example is given.     

Design and optimal tuning of nonlinear PI compensators

In this paper, linear time-invariant single-input single-output (SISO) systems that are stabilizable by linear proportional and integral (PI) compensators are considered. For such systems, a five-parameter nonlinear PI compensator is proposed. The parameters of the proposed compensator are tuned by solving an optimization problem. The optimization problem always has a solution.Additionally, a general nonlinear PI compensator is proposed and is approximated by easy-to-compute compensators, for instance, a six-parameter nonlinear PI compensator. The parameters of the approximate compensators are tuned to satisfy an optimality condition. The superiority of the proposed nonlinear PI compensators over linear PI compensators is discussed and is demonstrated for two feedback systems.     

RM approach for ranking of generalized trapezoidal fuzzy numbers

Ranking of fuzzy numbers play an important role in decision making, optimization and forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples, it is proved that ranking method proposed by Chen and Chen (Expert Systems with Applications 36 (3): 6833) is incorrect. The main aim of this paper is to propose a new approach for the ranking of generalized trapezoidal fuzzy numbers. The proposed ranking approach is based on rank and mode so it is named as an RM approach. The main advantage of the proposed approach is that the proposed approach provides the correct ordering of generalized and normal trapezoidal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets and Systems 118 (3): 375).     

A breadth-first search applied to the minimization of the open stacks

This paper presents a heuristic for the minimization of the open stacks problem (MOSP). The proposed heuristic is based on a simple breadth-first search in MOSP graphs and two new greedy rules to overcome errors. The performance of the proposed heuristic is compared with the best exact and heuristic methods available in the literature. The results show that in addition to the suggested heuristic having much shorter running times than the exact algorithm, the error gap between them is small for a substantial proportion of almost 4500 benchmark instances taken from the literature. The proposed heuristic also has a more robust behaviour than the best heuristic for the MOSP, although less accurate. The proposed heuristic therefore constitutes a viable and cost-effective alternative for solving or obtaining good upper bounds for the MOSP.     

A simple method of chaos control for a class of chaotic discrete-time systems

In this paper, a simple method is proposed for chaos control for a class of discrete-time chaotic systems. The proposed method is built upon the state feedback control and the characteristic of ergodicity of chaos. The feedback gain matrix of the controller is designed using a simple criterion, so that control parameters can be selected via the pole placement technique of linear control theory. The new controller has a feature that it only uses the state variable for control and does not require the target equilibrium point in the feedback path. Moreover, the proposed control method cannot only overcome the so-called “odd eigenvalues number limitation” of delayed feedback control, but also control the chaotic systems to the specified equilibrium points. The effectiveness of the proposed method is demonstrated by a two-dimensional discrete-time chaotic system.     

Effects of measurement error on a class of single-index varying coefficient regression models

This paper investigates the estimation in a class of single-index varying coefficient regression model when some covariates are contaminated with measurement errors. A bias-corrected least square procedure based on the observed data is proposed. By replacing the nonparametric single index part with a local linear approximation, an iterative algorithm for estimating the index parameter is proposed. More importantly, a special case is identified in which the naive procedure provides consistent estimates for the single index parameters. Large sample properties of the proposed estimators are established. The finite sample performance of the proposed estimators are evaluated by simulation studies.     

Stabilization and tracking controller for a class of nonlinear discrete-time systems

In this paper, stabilization and tracking control problem for parametric strict feedback class of discrete time systems is addressed. Recursive design of control function based on contraction theory framework is proposed instead of traditional Lyapunov based method. Explicit structure of controller is derived for the addressed class of nonlinear discrete-time systems. Conditions for exponential stability of system states are derived in terms of controller parameters. At each stage of recursive procedure a specific structure of Jacobian matrix is ensured so as to satisfy conditions of stability. The closed loop dynamics in this case remains nonlinear in nature. The proposed algorithm establishes global stability results in quite a simple manner as it does not require formulation of error dynamics. Problem of stabilization and output tracking control in case of single link manipulator system with actuator dynamics is analyzed using the proposed strategy. The proposed results are further extended to stabilization of discrete time chaotic systems. Numerical simulations presented in the end show the effectiveness of the proposed approach.     

Criterion of adhesion strength in the presence of normal and shear stresses

A criterion of the short-time adhesion strength is proposed for the case where the interphase surface is subjected to the combined action of normal and shear stresses. The proposed criterion is based on the assumption that at the moment of adhesion failure a definite relation exists between τ_oct and σ_oct. The proposed criterion has been experimentally confirmed.     

Neural networks for a class of bi-level variational inequalities

In this paper, a class of bi-level variational inequalities for describing some practical equilibrium problems, which especially arise from engineering, management and economics, is presented, and a neural network approach for solving the bi-level variational inequalities is proposed. The energy function and neural dynamics of the proposed neural network are defined in this paper, and then the existence of the solution and the asymptotic stability of the neural network are shown. The simulation algorithm is presented and the performance of the proposed neural network approach is demonstrated by some numerical examples.     

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In this paper, a nonparametric method for reliability of the stress-strength model is proposed when the dependent stress variable and strength variable are subject to right censoring. The dependence between variables is measured by the common Farlie-Gumbel-Morgenstern copula function and Clayton copula function. Using the empirical process theory, consistency and asymptotic normality of the proposed estimator is established in this paper. The results of numerical simulation show that the proposed method performs well in the case of finite sample. The method proposed in this paper has a wide application prospect in practice.     

网络化马尔可夫跳变系统的鲁棒无源控制

针对基于网络的凸多面体不确定离散时间马尔可夫跳变系统,研究其鲁棒无源控制问题.在网络诱导时滞是时变且有界的情况下,基于李雅普诺夫稳定性理论,通过构造参数依赖的随机李雅普诺夫泛函和运用广义系统变换,提出了不依赖模态的无源控制器存在的时滞依赖充分条件.所设计的鲁棒无源控制器保证了相应的闭环系统是鲁棒随机稳定且具有指定耗散率.将鲁棒无源控制器设计问题转化为一组线性矩阵不等式的可解性问题.仿真算例证明了本文方法的有效性.     

一种求解救灾物资运输问题的改进解法

本文通过对B运输问题建立数学模型,提出了一种求解B运输问题的改进解法。改进解法首先通过最小元素法求出初始解,然后进行变量闭回路法调整,直到求出最优解,并给出了一个计算实例证明了解法的有效性。文章还对改进解法和另外两种现有的算法进行了综合的分析,由于改进解法计算过程中采用的变量闭回路法省略了求检验数的环节,使得新算法比两种现有的算法更简便。     

Testing for lack of dependence between functional variables

We introduce a test for the lack of dependence between two random variables valued into real Hilbert spaces. Here, we consider lack of dependence in the broader sense, that is, non-correlation. The test statistic is similar to the one proposed by Kokoszka et al. (2008) for testing for no effect in the linear functional model. The asymptotic distribution under the null hypothesis of this statistic is obtained as well as a consistency result for the proposed test. Applications to the case of functional variables are indicated and simulations show, in this context, the performance of the proposed method.     

Terminal sliding mode control without singular for a class of uncertain system

An improved nonsingular terminal sliding mode method is proposed for a class of nonlinear systems with unmodeled dynamics. The proposed method can effectively avoid the singularity problem. The stability of the proposed procedure which could guarantee the robustness against uncertain unmodeled dynamic and external disturbances is proven by using the Lyapunov theory in finite time. An example is given to show the proposed improved terminal sliding mode control law without singular effectively. © 2016 Wiley Periodicals, Inc. Complexity 21: 566–572, 2016     

等腰三角形Mindlin板的自由振动分析

提出了一种新方法来对基于 Mindlin剪切变形理论的等腰三角形板进行自由振动分析 .此方法采用了一种新的基函数并利用 pb-2 Rayleigh-Ritz边界函数得到了一种新型的 Ritz方法 .这种方法的有效性通过收敛性和对比性分析得到了证实 .数值结果表明此方法相当精确有效 .     

Multiple nonlinear regressions derived with choice of free parameters

The common procedure of nonlinear approximation using linear multiple regressions developed in logarithmic space suffers from a number of inherent defects. Nonlinear approximation with choice of free parameters allows us to derive multiple regressions of varied structure, consisting of several members and an intercept. The calculations required for the proposed approximation are simple and can be implemented using standard statistical subprograms. More than 50 equations of the proposed type have been fitted for various purposes. The coefficient of determination is generally higher than 0.90. The application of the proposed method is demonstrated with two numerical examples and a number of equations derived for practical application in hydrology, geomorphology and water pollution studies. The proposed method can be used in any area of study where nonlinear multiple approximations are applicable.     

Improved 3D Surface Reconstruction via the Method of Fundamental Solutions

A new mathematical model of the modified bi-Helmholtz equation is proposed for the reconstruction of 3D implicit surfaces using the method of fundamental solutions. In the algorithm, we also show how to properly determine the parameter so that the spurious surface can be avoided. The main attraction of the proposed method is its simplicity. Four examples for the surface reconstruction are presented to validate the proposed numerical model.     

A Staged Continuous Tabu Search Algorithm for the Global Optimization and its Applications to the Design of Fiber Bragg Gratings

A novel staged continuous Tabu search (SCTS) algorithm is proposed for solving global optimization problems of multi-minima functions with multi-variables. The proposed method comprises three stages that are based on the continuous Tabu search (CTS) algorithm with different neighbor-search strategies, with each devoting to one task. The method searches for the global optimum thoroughly and efficiently over the space of solutions compared to a single process of CTS. The effectiveness of the proposed SCTS algorithm is evaluated using a set of benchmark multimodal functions whose global and local minima are known. The numerical test results obtained indicate that the proposed method is more efficient than an improved genetic algorithm published previously. The method is also applied to the optimization of fiber grating design for optical communication systems. Compared with two other well-known algorithms, namely, genetic algorithm (GA) and simulated annealing (SA), the proposed method performs better in the optimization of the fiber grating design.     

A novel scheme for the design of backstepping control for a class of nonlinear systems

A novel scheme is proposed for the design of backstepping control for a class of state-feedback nonlinear systems. In the design, the unknown nonlinear functions are approximated by the neural networks (NNs) identification models. The Lyapunov function of every subsystem consists of the tracking error and the estimation errors of NN weight parameters. The adaptive gains are dynamically determined in a structural way instead of keeping them constants, which can guarantee system stability and parameter estimation convergence. When the modeling errors are available, the indirect backstepping control is proposed, which can guarantee the functional approximation error will converge to a rather small neighborhood of the minimax functional approximation error. When the modeling errors are not available, the direct backstepping control is proposed, where only the tracking error is necessary. The simulation results show the effectiveness of the proposed schemes.