Solving nonlinear Volterra–Fredholm integro-differential equations using He's variational iteration method

In this paper, a nonlinear Volterra–Fredholm integro-differential equation is solved by using He's variational iteration method. The approximate solution of this equation is calculated in the form of a sequence where its components are computed easily. The accuracy of the proposed numerical scheme is examined by comparing with the modified Adomian decomposition method. The existence and uniqueness of the solution and convergence of the proposed method are proved.     

Levy变异ABC算法优化二阶Volterra核的鲁棒人脸识别

针对人脸识别中由于人脸表情、姿态、尺度、光照和其他环境参数变化而影响识别性能的问题,提出了一种随机优化算法。首先,将原始图像划分成特定空间子块,并使用二阶Volterra核寻找非线性函数映射;然后,使用人工蜂群算法获取最优Volterra核,从而在特征空间内最大化类间距离并最小化类内距离;最后,利用投票策略和最近邻分类器完成人脸的分类。在两个通用人脸数据集Yale A和扩展Yale B上对该算法进行了评估,并将其与其他统计学习算法和几种最新提出的方法进行了比较。实验结果表明了Levy变异人工蜂群算法优化Volterra核的有效性,识别效果明显优于许多现有算法。     

Nonlinear MPC based on a Volterra series model for greenhouse temperature control using natural ventilation

Suitable environmental conditions are a fundamental issue in greenhouse crop growth and can be achieved by advanced climate control strategies. In different climatic zones, natural ventilation is used to regulate both the greenhouse temperature and humidity. In mild climates, the greatest problem faced by far in greenhouse climate control is cooling, which, for dynamical reasons, leads to natural ventilation as a standard tool. This work addresses the design of a nonlinear model predictive control (NMPC) strategy for greenhouse temperature control using natural ventilation. The NMPC strategy is based on a second-order Volterra series model identified from experimental input/output data of a greenhouse. These models, representing the simple and logical extension of convolution models, can be used to approximate the nonlinear dynamic effect of the ventilation and other environmental conditions on the greenhouse temperature. The developed NMPC is applied to a greenhouse and the control performance of the proposed strategy will be illustrated by means of experimental results.     

Non-linear generalised minimum variance control state space design for a second-order Volterra series model

This paper presents a non-linear generalised minimum variance (NGMV) controller for a second-order Volterra series model with a general linear additive disturbance. The Volterra series models provide a natural extension of a linear convolution model with the nonlinearity considered in an additive term. The design procedure is entirely carried out in the state space framework, which facilitates the application of other analysis and design methods in this framework. First, the non-linear minimum variance (NMV) controller is introduced and then by changing the cost function, NGMV controller is defined as an extended version of the linear cases. The cost function is used in the simplest form and can be easily extended to the general case. Simulation results show the effectiveness of the proposed non-linear method.     

Unsharp masking using quadratic filter for the enhancement of fingerprints in noisy background

The paper summarizes the design and implementation of a quadratic edge detection filter based on Volterra series. The filter is employed in an unsharp masking scheme for enhancing fingerprints in a dark and noisy background. The proposed filter can account for much of the polynomial nonlinearities inherent in the input image and can replace the conventional edge detectors like Laplacian, LoG, etc. The application of the new filter is in forensic investigation where enhancement and identification of latent fingerprints are key issues. The enhancement of images by the proposed method is superior to that with unsharp masking scheme employing conventional filters in terms of the visual quality, the noise performance and the computational complexity, making it an ideal candidate for latent fingerprint enhancement.     

Nonlinear influence in the frequency domain: Alternating series

The nonlinear influence on system output spectrum is studied for a class of nonlinear systems which have Volterra series expansion. It is shown that under certain conditions the system output spectrum can be expressed in an alternating series with respect to some model parameters which define system nonlinearities. The magnitude of the system output spectrum can therefore be suppressed by exploiting the properties of alternating series. Sufficient (and necessary) conditions in which the output spectrum can be cast into an alternating series are studied. These results reveal a novel frequency-domain insight into the nonlinear influence on a system, and provide a new method for the analysis and design of nonlinear systems in the frequency domain. Examples are given to illustrate the results.     

Approximate solution of fractional integro-differential equations by Taylor expansion method

In this paper, Taylor expansion approach is presented for solving (approximately) a class of linear fractional integro-differential equations including those of Fredholm and of Volterra types. By means of the mth-order Taylor expansion of the unknown function at an arbitrary point, the linear fractional integro-differential equation can be converted approximately to a system of equations for the unknown function itself and its m derivatives under initial conditions. This method gives a simple and closed form solution for a linear fractional integro-differential equation. In addition, illustrative examples are presented to demonstrate the efficiency and accuracy of the proposed method.     

Volterra神经网络水文模型及应用研究

本文在对Volterra泛函模型与ANN模型进行一致性研究的基础上,提出了基于Volterra泛函结构的神经网络水文模型(VNNH)。VNNH模型吸取了Volterra模型和ANN模型的优点,克服了它们的不足之处。VNNH模型设计了一种多项式的激活函数,克服了Volterra模型求解高阶核函数的困难。并利用自组织神经网络算法确定VNNH模型隐含层神经元的数目;根据Volterra模型的结构由流域的单位线确定VNNH模型的初始权值。将VNNH模型应用于两个实际流域的洪水模拟和预测中,取得了较为满意的结果。     

非线性逆系统的一种求解方法

基于沃尔特拉级数理论和多维拉普拉斯变换,给出了非线性逆系统的一种求解方法,得出了一些有意义的重要结果,并给出计算实例.借助于所给出的方法可以十分有效地解决数字信号处理、通信等技术中的非线性逆系统问题.     

A cumulant based algorithm for the identification of input-output quadratic systems

The identification of a special class of polynomial models is pursued in this paper. In particular a parameter estimation algorithm is developed for the identification of an input-output quadratic model excited by a zero mean white Gaussian input and with the output corrupted by additive measurement noise. Input-output crosscumulants up to the fifth order are employed and the identification problem of the unknown model parameters is reduced to the solution of successive triangular linear systems of equations that are solved at each step of the algorithm. Simulation studies are carried out and the proposed methodology is compared with two least squares type identification algorithms, the output error method and a combination of the instrumental variables and the output error approach. The proposed cumulant based algorithm and the output error method are tested with real data produced by a robotic manipulator.