基于小波神经网络的通用多变量非线性系统辨识算法和应用

在分析小波函数对L2(R)空间的逼近原理的基础上,给出了仅使用尺度函数的神经网络模型和网络学习方法,使得用于逼近低通系统的小波基函数大大减少,并给出逼近的理论依据.提出的小波神经网络模型的学习为线性LS参数估计问题,具有通用性和易用性,并具有线性系统中线性LS参数估计的优良性质,保证了在训练数据受噪声污染时的网络模型的推广能力.理论分析、仿真实验和实际应用结果都说明该辨识方法具有好的辨识精度和推广能力.     

T-S模糊广义系统的逼近性

本文研究T-S模糊广义系统的逼近性,给出了T-S模糊广义系统的逼近性定理.证明其可以以任意的精度逼近一类广泛存在的非线性广义系统.还将MISO(多输入单输出)情况推广到MIMO(多输入多输出)的情况.在逼近性定理的基础上,利用神经网络的方法对非线性广义系统建模,给出了神经网络的结构及学习算法.本文共提出了两种神经网路的训练策略,对各自的优点与不足给出了分析,最后用数值例子验证了算法的有效性.     

基于遗传算法的小波神经网络

介绍小波神经网络的基本原理.利用遗传算法来优化小波神经网络,达到提高逼近精度,简化网络结构,提高收敛速度的目的.通过实验将其与传统的小波神经网络进行比较,证实前者具有更优的网络结构,更高的逼近精度.     

基于小波模糊网络的非线性函数逼近方法的研究

针对非线性函数逼近问题，提出了一种新的融合策略——小波模糊网络;该网络将模糊模型引入小波网络，采用正交最小二乘法筛选小波，利用推广卡尔曼滤波算法调整网络非线性参数，避免陷入局部最优，提高学习速度，并采用最小二乘法修正权值，在不增加小波基函数的基础上提高网络的逼近精度；通过仿真，该网络的准确性和泛化能力都优于传统的小波神经网络，具有广泛的应用前景。     

基于小波神经网络的混沌时间序列分析与相空间重构

探讨了小波神经网络在混沌时间序列分析与相空间重构中的应用,通过混沌时间序列单步预测与多步预测的例子,比较了小波神经网络与MLP的逼近和收敛性能,对最近提出的一种多分辨率学习策略进行了改进,利用连续3次样条小和正交Daubechies小波代替Haar小波对时间序列做小波分解;用改进的学习算法训练网络并应用到混沌序列相空间重构中,实验结果表明,小波神经网络比MLP和ARMA模型具有更强大的逼近能力,因而十分适合应用于时间序列分析中;多分辨率学习算法可作为分析复杂混沌时间序列的一种重要工具。     

小波神经网络在图像配准中的应用

提出了一种基于小波网络的图像配准方法。将特征点定义进行了推广,提出了一种以特征区域定义和提取方法。使用Zernike矩表征区域的特征并进行特征区域的对应。因图像配准变换是复杂且难以预知的,利用小波神经网络具有良好的函数逼近性能,提出了具有局域特性的小波神经网络模型逼近图像的配准变换。实验表明这是一种有效的图像配准方法。     

一种小波神经网络的混沌加密算法研究

概括了小波神经网络的主要理论,将小波神经网络和混沌系统相结合,建立了一种混沌序列的生成模型,给出基于小波神经网络的混沌加密算法,最后对算法进行计算机仿真实验.结果表明小波神经网络具有更快的收敛速度和更准确的逼近能力,而基于小波神经网络的混沌加密算法具有很高的安全性.     

基于狼群算法的短时高速交通流量预测仿真

由于传统的短时高速交通流量预测算法的受到函数逼近能力影响,极易陷入局部极值的问题,提出基于狼群算法的短时高速交通流量预测算法。构造型前馈小波神经网络算法在多维空间内对短时高速交通流量预测,需通过构造型前馈小波神经网络算法分析随机相关多维样本逼近能力,利用改进狼群算法的全局寻优能力,提升算法搜索精度,并完成目标的搜索,根据搜索结果获取优质的函数逼近值最优解,提升构造型前馈小波神经网络算法函数的逼近能力,获取最佳短时高速交通流量预测值。仿真结果显示,上述算法的短时高速交通流量预测效果显著优于小波神经网络预测算法,且本文算法的预测精度较高,具有较高的稳定性。     

小波模糊神经网络在非线性函数逼近中的应用

将前馈神经网络与T-S模糊模型相融合构造了一种模糊神经网络,进一步利用小波变换的压缩特性与模糊神经网络相结合构造出一种小波模糊神经网络模型,并应用在非线性函数逼近上。通过仿真,结果表明小波模糊神经网络是最优的。     

基于小波神经网络的流量混沌时间序列预测

在Takens提出的相空间重构模型基础上,应用小波变换对其进行改进,充分考虑噪声对重构结果的影响。将小波神经网络混沌时间序列预测方法引入网络流量预测中,介绍小波神经网络的基本构造和学习方法。实验表明,与RBF神经预测方法相比,小波神经网络预测方法的逼近效果更好、误差更小。     

A conservative method of wavelet neural network based meta-modeling in constrained approximate optimization

The paper aims at the development of the wavelet neural network (WNN) based conservative meta-model that satisfies the constraint feasibility of approximate optimal solution. The WNN based constraint-feasible meta-model is formulated via exterior penalty method to optimally determine interconnection weights and dilation and translation coefficients in the network. Using Ackley’s path function, the approximation performance of WNN is first tested in comparison with BPN. The proposed approach of constraint feasibility is then verified through a ten-bar planar truss problem. For constrained approximate optimization, the structural design of a composite rotor blade is explored to support the proposed strategies.     

Adaptive wavelet neural network control with hysteresis estimation for piezo-positioning mechanism

An adaptive wavelet neural network (AWNN) control with hysteresis estimation is proposed in this study to improve the control performance of a piezo-positioning mechanism, which is always severely deteriorated due to hysteresis effect. First, the control system configuration of the piezo-positioning mechanism is introduced. Then, a new hysteretic model by integrating a modified hysteresis friction force function is proposed to represent the dynamics of the overall piezo-positioning mechanism. According to this developed dynamics, an AWNN controller with hysteresis estimation is proposed. In the proposed AWNN controller, a wavelet neural network (WNN) with accurate approximation capability is employed to approximate the part of the unknown function in the proposed dynamics of the piezo-positioning mechanism, and a robust compensator is proposed to confront the lumped uncertainty that comprises the inevitable approximation errors due to finite number of wavelet basis functions and disturbances, optimal parameter vectors, and higher order terms in Taylor series. Moreover, adaptive learning algorithms for the online learning of the parameters of the WNN are derived based on the Lyapunov stability theorem. Finally, the command tracking performance and the robustness to external load disturbance of the proposed AWNN control system are illustrated by some experimental results.     

Intelligent transportation control system design using wavelet neural network and PID-type learning algorithms

In this paper, an intelligent transportation control system (ITCS) using wavelet neural network (WNN) and proportional-integral-derivative-type (PID-type) learning algorithms is developed to increase the safety and efficiency in transportation process. The proposed control system is composed of a neural controller and an auxiliary compensation controller. The neural controller acts as the main tracking controller, which is designed via a WNN to mimic the merits of an ideal total sliding-mode control (TSMC) law. The PID-type learning algorithms are derived from the Lyapunov stability theorem, which are utilized to adjust the parameters of WNN on-line for further assuring system stability and obtaining a fast convergence. Moreover, based on H_∞ control technique, the auxiliary compensation controller is developed to attenuate the effect of the approximation error between WNN and ideal TSMC law, so that the desired attenuation level can be achieved. Finally, to investigate the effectiveness of the proposed control strategy, it is applied to control a marine transportation system and a land transportation system. The simulation results demonstrate that the proposed WNN-based ITCS with PID-type learning algorithms can achieve favorable control performance than other control methods.     

参数可变系统时间序列短期预测方法

时间序列预测是一类非常重要的问题,但基本上局限于参数不可变问题的研究,而对实际问题中经常出现的更重要的参数可变系统的预测,由于构成几乎所有已有预测技术基础的Taken嵌入定理不再成立,所以这方面的研究成果极少.使用一种将(多)小波变换与反向传播神经网络相结合的新型网络结构--(多)小波神经网络,尝试对参数可变时间序列的预测.因为(多)小波神经网络的误差函数是一个凸函数,这在一定程度上可以避免经典神经网络容易陷入局部极小、收敛速度慢等问题.对著名的Ikeda参数可变系统的实验表明,多小波神经网络的预测性能较单小波神经网络要好,而单小波神经网络的性能较BP网要好.因此,该方法不失为时间可变系统预测的一种好的推荐.     

Indirect adaptive control of nonlinear dynamic systems using self recurrent wavelet neural networks via adaptive learning rates

This paper proposes an indirect adaptive control method using self recurrent wavelet neural networks (SRWNNs) for dynamic systems. The architecture of the SRWNN is a modified model of the wavelet neural network (WNN). However, unlike the WNN, since a mother wavelet layer of the SRWNN is composed of self-feedback neurons, the SRWNN can store the past information of wavelets. In the proposed control architecture, two SRWNNs are used as both an identifier and a controller. The SRWNN identifier approximates dynamic systems and provides the SRWNN controller with information about the system sensitivity. The gradient-descent method using adaptive learning rates (ALRs) is applied to train all weights of the SRWNN. The ALRs are derived from discrete Lyapunov stability theorem, which are applied to guarantee the convergence of the proposed control system. Finally, we perform some simulations to verify the effectiveness of the proposed control scheme.     

Adaptive force–environment estimator for manipulators based on adaptive wavelet neural network

This study focuses on the accurate tracking control and sensorless estimation of external force disturbances on robot manipulators. The proposed approach is based on an adaptive Wavelet Neural Network (WNN), named Adaptive Force-Environment Estimator (WNN-AFEE). Unlike disturbance observers, WNN_AFEE does not require the inverse of the Jacobian transpose for computing the force, thus, it has no computational problem near singular points. In this scheme, WNN estimates the external force disturbance to attenuate its effects on the control system performance by estimating the environment model. A Lyapunov based design is presented to determine adaptive laws for tuning WNN parameters. Another advantage of the proposed approach is that it can estimate the force even when there are some parametric uncertainties in the robot model, because an additional adaptive law is designed to estimate the robot parameters. In a theorem, the stability of the closed loop system is proved and a general condition is presented for identifying the force and robot parameters. Some suggestions are provided for improving the estimation and control performance. Then, a WNN-AFEE is designed for a planar manipulator as an example, and some simulations are performed for different conditions. WNN_AFEE results are compared attentively with the results of an adaptive force estimator and a disturbance estimator. These comparisons show the efficiency of the proposed controller in dealing with different conditions.     

Development of PI training algorithms for neuro-wavelet control on the synchronization of uncertain chaotic systems

This paper investigates a neuro-wavelet control (NWC) system to address the problem of synchronization control of uncertain chaotic systems. In this NWC system, a wavelet neural network (WNN) controller is the principal tracking controller designed to mimic the perfect control law and an auxiliary compensation controller is used to recover the residual approximation error so that the favorable synchronization can be achieved. Moreover, the proportional-integral (PI) training algorithms of the control system are derived from the Lyapunov stability theorem, which are utilized to update the adjustable parameters of WNN controller on-line for further assuring system stability and obtaining a fast convergence. In addition, to relax the requirement of unknown uncertainty bound, a bound estimation law is derived to estimate the uncertainty bound. Finally, some numerical simulations are presented to illustrate the effectiveness of the proposed control strategy. The simulation results demonstrate that the proposed NWC with PI training algorithms can synchronize the chaotic systems more accurately than the other control strategies.     

SSUKF-WNN算法及其在飞行器气动力建模中的应用

针对传统小波网络算法的不足,提出一种基于改进无迹Kalman滤波(UKF)的小波网络算法.该算法使用一种基于简化球形分布Sigma点的UKF(SSUKF)来训练小波网络的参数,以提高小波网络的学习性能和训练质量.飞行器气动力建模算例表明,相对于BP算法和EKF算法,SSUKF算法训练的小波网络收敛速度更快,估计精度更高,计算量更小.同时也为飞行器的气动力建模提供了一种有效可行的手段.     

小波神经网络模型的改进方法

为了改善小波神经网络(WNN)在处理复杂非线性问题的性能,针对量子粒子群优化(QPSO)算法易早熟、后期多样性差、搜索精度不高的缺点,提出一种同时引入加权系数、引入Cauchy随机数、改进收缩扩张系数和引入自然选择的改进量子粒子群优化算法,将其代替梯度下降法,训练小波基系数和网络权值,再将优化后的参数组合输入小波神经网络,以实现算法的耦合。通过对3个UCI标准数据集的仿真实验表明,与WNN、PSO-WNN、QPSO-WNN算法相比,改进的量子粒子群小波神经网络(MQPSO-WNN)算法的运行时间减少了11%~43%,而计算相对误差较之降低了8%~57%。因此,改进的量子粒子群小波神经网络模型能够更迅速、更精确地逼近最优值。     

Wavelet reduced order observer based adaptive tracking control for a class of uncertain nonlinear systems using reinforcement learning

This Paper investigates the mean to design the reduced order observer and observer based controllers for a class of uncertain nonlinear system using reinforcement learning. A new design approach of wavelet based adaptive reduced order observer is proposed. The proposed wavelet adaptive reduced order observer performs the task of identification of unknown system dynamics in addition to the reconstruction of states of the system. Reinforcement learning is used via two wavelet neural networks (WNN), critic WNN and action WNN, which are combined to form an adaptive WNN controller. The “strategic” utility function is approximated by the critic WNN and is minimized by the action WNN. Owing to their superior learning capabilities, wavelet networks are employed in this work for the purpose of identification of unknown system dynamics. Using the feedback control, based on reconstructed states, the behavior of closed loop system is investigated. By Lyapunov approach, the uniformly ultimate boundedness of the closed-loop tracking error is verified. A numerical example is provided to verify the effectiveness of theoretical development.