一种基于模糊径向基函数神经网络的自学习控制器

提出了一种新型的基于模糊径向基函数 (RBF)的神经网络学习控制器 ,并应用于电液伺服系统 .由于RBF网络和模糊推理系统具有函数等价性 ,采用模糊经验值方法选取网络中心值和基函数数目 .与一般的神经网络自学习控制器不同 ,以系统动态误差作为网络输入量 ,RBF神经网络控制器学习的是整个系统的动态逆过程 ,因而控制性能明显提高 .对电液位置伺服系统的仿真和实验结果表明 ,该控制方案可以有效提高系统的控制精度和自适应能力     

一种基于误差的径向基神经网络学习方法

提出了一种基于误差的径向基神经网络竞争学习法，它以网络的输出误差为度量，通过竞争调节神经元中心，RLS算法训练网络的权值，并利用IPL算法判断网络神经元的冗余性。仿真结果表明，该算法提高了网络的输出精度，简化了网络结构，其运算速度也较快。     

基于迁移学习的径向基函数神经网络学习

现实场景中存在很多小样本量数据集而且多有失真,传统神经网络在处理这类数据时泛化能力较差,不能达到预测数据或分类的目的。迁移学习可通过学习数据集A有用的知识对与其相关但不同正态分布的小样本数据集B进行辅助学习,因此提出了具有迁移学习能力的神经网络,以实现更好的分类或逼近效果。以基于ε-不敏感准则和结构风险的径向基神经网络（RBF）为基础构造了迁移径向基神经网络（T-RBF-NN）。通过加噪音数据集实验以及真实数据集实验验证加入迁移学习的神经网络在小样本情况下比传统神经网络具有更好的泛化性和鲁棒性。     

径向基神经网络的一种自适应混合学习算法

为设计具有良好逼近性能的径向基神经网络,提出一种两层结构的自适应混合学习算法.内层迭代过程综合了梯度下降法和智能优化方法的优点,采用基于衰减梯度信息的智能优化方法,对具有固定结构的网络进行参数训练;外层迭代根据内层迭代的效果,利用最优停止规则自适应地动态调节网络隐含层节点数,使算法以较大概率收敛至全局最优.设计了网络结构修正算子,实现对最终结果的进一步简化.最后,文章给出算法实现的具体步骤,并通过仿真实例验证了算法有效性和可行性.     

改进的径向基函数神经网络预测模型

在提高网络传输性能的研究中,径向基函数神经网络(RBF网络)的基函数个数、中心及宽度的确定一直是难解决的问题,为提高RBF网络泛化能力是当前一个重要的研究问题.分析了传统RBF网络工作原理及不足,提出了改进.采用梯度下降法训练径向基函数中心和宽度,提高网络泛化性能.改进最优停止训练算法,使算法效率提高,且避免过拟合现象,最终使RBF网络获得更优的泛化能力.用改进的RBF网络对iris及wine数据集建立预测模型,进行仿真.结果表明,梯度下降方法训练出更优的基函数参数,改进的最优停止训练方法缩短了训练时间、提高预测精度,网络泛化能力有明显提高.     

一种基于径向基神经网络的车牌字符识别方法

径向基函数神经网络具有局部逼近的能力和局部可调的特性,以车牌字符识别为例,构造了一种实用型的径向基神经网络,并与传统的BP神经网络作了对比.实验结果表明,在车牌字符识别中,径向基网络的识别能力、分类能力及识别速度等均优于BP网络.     

一种径向基函数神经网络的参数求解方法

为了求解径向基函数神经网络的权值,首先分析了传统基于训练误差的方法,发现该方法容易造成数据过拟合,原因在于训练误差是风险函数的下偏估计;因此,文中提出采用缺一交叉验证得分代替训练误差,来实现无偏估计风险函数;实验对摩托数据与玻璃数据进行拟合,证实了基于缺一交叉验证的方法优于传统基于训练误差的方法,且所得到的径向基函数网络能够较光滑地拟合数据,不会造成过拟合.     

径向基函数（RBF）神经网络的一种极大熵学习算法

RBF神经网络中心向量的确定是整个网络学习的关键,该文基于信息论中的极大熵原理构造了训练中心向量的极大熵聚类算法,由此给出了网络的极大熵学习算法。文中最后分别用一个时间序列预测和系统辨识问题验证了该学习算法的有效性,同RBF网络和多层感知机的误差回传算法相比,该算法不仅在学习精度和泛化推广能力上有一定程度的提高,而且学习时间有显著的降低。     

一种径向基函数神经网络生成模糊系统的方法研究

如何建立合适的模糊规则.是模糊系统设计的关键和难点。传统的方法是依靠统计分析或经验建立模糊规则库[lJ,不仅难度大,而且建立的模糊系统缺乏适应能力。人工神经网络(ANN)技术的发展为模糊规则的自动获取提供了一条新途径.许多学者研究ANN与模糊系统的融合问题,其主要目的就是利用ANN的学习能力和自适应能力,从样本中提取模糊规则.形成具有自适应能力的模糊系统。尽管利用多层前馈网获取模糊规则口     

一种结构自适应径向基函数神经网络

提出了一种新的结构自适应的径向基函数(RBF)神经网络模型。在该网络中,自组织映射(SOM)神经网络作为聚类网络,采用无监督学习算法对输入样本进行自组织分类,并将分类中心及其对应的权值向量传递给RBF神经网络,作为径向基函数的中心和相应的权值向量;RBF神经网络作为基础网络,采用高斯函数实现输入层到隐层的非线性映射,输出层则采用有监督学习算法训练网络的权值,从而实现输入层到输出层的非线性映射。通过对字母数据集进行仿真,表明该网络具有较好的性能。     

Error-driven active learning in growing radial basis function networks for early robot learning

In this paper, we describe a new error-driven active learning approach to self-growing radial basis function networks for early robot learning. There are several mappings that need to be set up for an autonomous robot system for sensorimotor coordination and transformation of sensory information from one modality to another, and these mappings are usually highly nonlinear. Traditional passive learning approaches usually cause both large mapping errors and nonuniform mapping error distribution compared to active learning. A hierarchical clustering technique is introduced to group large mapping errors and these error clusters drive the system to actively explore details of these clusters. Higher level local growing radial basis function subnetworks are used to approximate the residual errors from previous mapping levels. Plastic radial basis function networks construct the substrate of the learning system and a simplified node-decoupled extended Kalman filter algorithm is presented to train these radial basis function networks. Experimental results are given to compare the performance among active learning with hierarchical adaptive RBF networks, passive learning with adaptive RBF networks and hierarchical mixtures of experts, as well as their robustness under noise conditions.     

梯度算法下RBF网的参数变化动态

分析神经网络学习过程中各参数的变化动态,对理解网络的动力学行为,改进网络的结构和性能等具有积极意义.本文讨论了用梯度算法优化误差平方和损失函数时RBF网隐节点参数的变化动态,即算法收敛后各隐节点参数的可能取值.主要结论包括:如果算法收敛后损失函数不为零,则各隐节点将位于样本输入的加权聚类中心;如果损失函数为零,则网络中的冗余隐节点将出现萎缩、衰减、外移或重合现象.进一步的试验发现,对结构过大的RBF网,冗余隐节点的萎缩、外移、衰减和重合是频繁出现的现象.     

Cooperative learning for radial basis function networks using particle swarm optimization

This paper presents a new evolutionary cooperative learning scheme, able to solve function approximation and classification problems with improved accuracy and generalization capabilities. The proposed method optimizes the construction of radial basis function (RBF) networks, based on a cooperative particle swarm optimization (CPSO) framework. It allows for using variable-width basis functions, which increase the flexibility of the produced models, while performing full network optimization by concurrently determining the rest of the RBF parameters, namely center locations, synaptic weights and network size. To avoid the excessive number of design variables, which hinders the optimization task, a compact representation scheme is introduced, using two distinct swarms. The first swarm applies the non-symmetric fuzzy means algorithm to calculate the network structure and RBF kernel center coordinates, while the second encodes the basis function widths by introducing a modified neighbor coverage heuristic. The two swarms work together in a cooperative way, by exchanging information towards discovering improved RBF network configurations, whereas a suitably tailored reset operation is incorporated to help avoid stagnation. The superiority of the proposed scheme is illustrated through implementation in a wide range of benchmark problems, and comparison with alternative approaches.     

MELM-GRBF: A modified version of the extreme learning machine for generalized radial basis function neural networks

In this paper, we propose a methodology for training a new model of artificial neural network called the generalized radial basis function (GRBF) neural network. This model is based on generalized Gaussian distribution, which parametrizes the Gaussian distribution by adding a new parameter τ. The generalized radial basis function allows different radial basis functions to be represented by updating the new parameter τ. For example, when GRBF takes a value of τ=2, it represents the standard Gaussian radial basis function. The model parameters are optimized through a modified version of the extreme learning machine (ELM) algorithm. In the methodology proposed (MELM-GRBF), the centers of each GRBF were taken randomly from the patterns of the training set and the radius and τ values were determined analytically, taking into account that the model must fulfil two constraints: locality and coverage. An thorough experimental study is presented to test its overall performance. Fifteen datasets were considered, including binary and multi-class problems, all of them taken from the UCI repository. The MELM-GRBF was compared to ELM with sigmoidal, hard-limit, triangular basis and radial basis functions in the hidden layer and to the ELM-RBF methodology proposed by Huang et al. (2004) [1]. The MELM-GRBF obtained better results in accuracy than the corresponding sigmoidal, hard-limit, triangular basis and radial basis functions for almost all datasets, producing the highest mean accuracy rank when compared with these other basis functions for all datasets.     

Combined learning and pruning for recurrent radial basis function networks based on recursive least square algorithms

This paper discusses a way to combine training and pruning for the construction of a recurrent radial basis function network (RRBFN) based on recursive least square (RLS) learning. In our approach, a RRBFN is first trained using the proposed RLS algorithms. Afterwards, the error covariance matrix which is directly obtained from the RLS computations is used to remove some unimportant radial basis function (RBF) nodes. We propose two algorithms: (1) a “global” version which is suitable for low dimensional input space situation, and (2) a “local” version which can be applied in situations when the input dimension is large. In both cases, it is shown that the error covariance matrix, obtained from the RLS algorithms, can be used as a means for pruning the trained RRBFN. Simulation examples are presented to illustrate the proposed approaches.     

机械臂的自适应径向基函数神经网络双二次泛函最优控制

针对非线性机械臂系统中难以权衡控制能量与控制误差比重的最优控制问题,本文提出一种基于自适应径向基函数(RBF)神经网络二阶段叠加优化的双二次泛函最优求解模型,实现在非线性机械臂控制系统中用不大的控制能量来保持较小的控制误差的综合最优控制.在本文所提模型中,首先设计一种线性误差函数,作用于非线性控制方程,并采用自适应RBF网络逼近非线性控制方程中存在的不确定项,构成闭环反馈系统,实现对非线性系统的最优控制;其次,将待求参数复合成双二次泛函的解域,并设计一种新型的类递归神经网络求解该带约束条件的双二次型模型,实现模型求解的快速收敛并得其解.通过理论分析及数值仿真实例验证了所提模型能有效提高非线性系统的控制精度、稳定性、鲁棒性及自适应性,从而实现非线性系统的综合最优控制.     

On stability analysis via Lyapunov exponents calculated based on radial basis function networks

The concept of Lyapunov exponents is a powerful tool for analysing the stability of nonlinear dynamic systems, especially when the mathematical models of the systems are available. For real world systems, such models are often unknown. Estimating Lyapunov exponents using a time series has the advantage in that no mathematical model is required. However the time-series-based methods are believed to be reliable only for estimating positive exponents. Furthermore, when nonlinear mapping is applied for deriving the neighbourhood-to-neighbourhood matrices, the loads of mathematical deduction and programming increase significantly, which makes it unfeasible to nonlinear systems with high dimensions. In contrary, the model-based methods are constructive and reliable for calculating both positive and non-positive exponents. The use of the system Jacobians is the key to the advantage of the model-based methods. In this article, a novel approach is proposed, where the system Jacobians are derived based on system approximation using the radial basis function network. The proposed method inherits the advantage of the model-based methods, yet no mathematical model is required. Two case studies are presented to demonstrate the efficacy of the proposed method. We believe that the work can contribute to the stability analysis of nonlinear systems of which the dynamics are either difficult to model due to complexities or unknown.     

基于变结构径向基函数网络的船舶运动预测PID控制

针对船舶在海上运动的大时滞和动态时变等特点,提出基于一种变结构径向基函数(RBF)神经网络的预测PID控制器.通过建立反映系统动态变化的滑动数据窗口,在线序贯学习窗口内的数据,动态调整隐层节点与隐层至输出层的连接权值,得到结构可自适应变化的RBF网络.将该变结构RBF网络用于预测PID控制器中系统状态的在线多步预测,通过得到的预测模型灵敏度信息在线调整PID控制器参数以控制系统的输出.将该控制器用于船舶航向跟踪控制的仿真实验,结果表明该控制器具有良好的的适应性和鲁棒性.     

Modelling of a magneto-rheological damper by evolving radial basis function networks

This paper presents an approach to approximate the forward and inverse dynamic behaviours of a magneto-rheological (MR) damper using evolving radial basis function (RBF) networks. Due to the highly nonlinear characteristics of MR dampers, modelling of MR dampers becomes a very important problem to their applications. In this paper, an alternative representation of the MR damper in terms of evolving RBF networks, which have a structure of four input neurons and one output neuron to emulate the forward and inverse dynamic behaviours of an MR damper, respectively, is developed by combining the genetic algorithms (GAs) to search for the network centres with other standard learning algorithms. Training and validating of the evolving RBF network models are achieved by using the data generated from the numerical simulation of the nonlinear differential equations proposed for the MR damper. It is shown by the validation tests that the evolving RBF networks can represent both forward and inverse dynamic behaviours of the MR damper satisfactorily.     

Speech recognition using pulse-coupled neural networks with a radial basis function

We have developed a novel pulse-coupled neural network (PCNN) for speech recognition. One of the advantages of the PCNN is in its biologically based neural dynamic structure using feedback connections. To recall the memorized pattern, a radial basis function (RBF) is incorporated into the proposed PCNN. Simulation results show that the PCNN with a RBF can be useful for phoneme recognition. This work was presented in part at the 7th International Symposium on Artificial Life and Robotics, Oita, Japan, January 16–18, 2002