一种改进的RBF网络结构及其参数的设计方法

针对神经网络在学习之后,模糊系统的原始结构被改变,或削弱了规则可解释性这一模糊系统突出特点的问题,给出了一种提取模糊If-then规则的径向基函数(RBF)神经网络结构。该神经网络结构具有能够同时清晰表达模糊控制系统输入空间划分和模糊规则可解释性的特点,克服了以往用神经网络提取模糊规则不能直观体现模糊语言规则可解释性的不足,并详细地讨论了此网络结构参数的设计方法。     

改进粒子群优化Takagi-Sugeno模糊径向基函数神经网络的非线性系统建模

针对复杂非线性系统建模的难点问题,提出了一种基于改进的粒子群优化算法（PSO)优化的T-S模糊径向基函数（RBF）神经网络的新型系统建模算法。该算法将T-S模糊模型良好的可解释性及RBF神经网络的自学习能力相结合,构成T-S模糊RBF神经网络用于系统建模,并采用动态调整惯性权重的改进的PSO算法结合递推最小二乘算法实现网络参数的优化调整。首先,利用所提算法进行了非线性多维函数的逼近仿真,仿真结果均方差（MSE）为0.00017,绝对值误差不大于0.04,逼近精度较高;又将该算法用于建立动态流量软测量模型,并进行了相关的实验研究,动态流量测量结果平均绝对误差小于0.15L/min,相对误差为1.97%,基本满足测量要求,并优于已有算法。上述仿真及实验研究结果表明,所提算法对于复杂非线性系统具有较高的建模精度和良好的自适应性。     

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     

基于在线减法聚类的RBF神经网络结构设计

以设计最小径向基函数（RBF）神经网络结构为着眼点,提出一种在线RBF网络结构设计算法.该算法将在线减法聚类能实时跟踪工况的特性与RBF网络参数学习过程相结合,使得网络既能在线适应实时对象的变化又能维持紧凑的结构,有效地解决了RBF神经网络结构自组织问题.该算法只调整欧氏距离距实时工况最近的核函数,大大提高了网络的学习速度.通过对典型非线性函数逼近和混沌时间序列预测的仿真,表明所提出的算法具有良好的动态特性响应能力和逼近能力.     

广义模糊推理与广义模糊RBF 神经网络

在提出广义模糊推理概念的基础上,提出并分析了广义模糊径向基(RBF)神经网络模型,给出了该网络的广义学习算法。仿真结果验证了广义模糊RBF神经网络模型具有良好的函数逼近能力,所提出的学习算法是可行和有效的。     

基于RBF神经网络的飞机发动机故障诊断研究

论述了径向基函数神经网络的基本网络结构和网络的学习及运行过程,结果表明:径向基神经网络具有极快的学习收敛速度。讨论了径向基神经网络在飞机发动机故障诊断中的应用,并对训练后的网络进行了仿真测试,仿真结果表明RBF网络有较高诊断正确率,且能满足实时诊断的要求。     

改进RBFNN求机械臂轨迹跟踪的研究

为了使机械臂准确跟踪目标轨迹,达到控制精度高、实时性好的目的,提出一种改进的径向基函数（RBF）模糊神经网络算法。该算法采用模糊遗传算法在线调整神经模糊控制器的参数,对其参数进行改进和优化,同时采用最近邻聚类算法对控制器的模糊规则库进行更新。仿真结果表明,该算法与传统的神经网络算法相比具有较好的性能,学习速度快,跟踪精度高,并具有良好的控制性能和自学习能力。     

改进的RBFNN在运动员竞技状态预测中的应用

提出了一种改进的径向基函数(RBF)神经网络,该神经网络以模糊系统模型为基础。首先利用减法聚类算法确定径向基函数的中心数,然后通过模糊C均值聚类算法优化基函数中心与宽度,最后依据样本数据的聚类结果设计RBF神经网络并进行训练。将该神经网络应用于网球队运动员的竞技状态的预测。仿真结果表明:该算法先进有效、具有较高的精度,用其建立的模型具有较强的实用性。     

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。     

一种结构自适应的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。在该模型中,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,分别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。     

Extracting Interpretable Fuzzy Rules from RBF Networks

Radial basis function networks and fuzzy rule systems are functionally equivalent under some mild conditions. Therefore, the learning algorithms developed in the field of artificial neural networks can be used to adapt the parameters of fuzzy systems. Unfortunately, after the neural network learning, the structure of the original fuzzy system is changed and interpretability, which is considered to be one of the most important features of fuzzy systems, is usually impaired. This Letter discusses the differences between RBF networks and interpretable fuzzy systems. Based on these discussions, a method for extracting interpretable fuzzy rules from RBF networks is suggested. Simulation examples are given to embody the idea of this paper.     

Neural and Neurofuzzy FELA Adaptive Robot Control Using Feedforward and Counterpropagation Networks

In this paper, the application of neural networks and neurofuzzy systems to the control of robotic manipulators is examined. Two main control structures are presented in a comparative manner. The first is a Counter Propagation Network-based Fuzzy Controller (CPN-FC) which is able to self-organize and correct on-line its rule base. The self-tuning capability of the fuzzy logic controller is attained by taking advantage of the structural equivalence between the fuzzy logic controller and a counterpropagation network. The second control structure is a more familiar neural adaptive controller based on a feedforward (MLP) network. The neural controller learns the inverse dynamics of the robot joints, and gradually eliminates the model uncertainties and disturbances. Both schemes cooperate with the computed torque control algorithm, and in that way the reduction of their complexity is achieved. The ability of adaptive fuzzy systems to compete with neural networks in difficult control problems is demonstrated. A sufficient set of numerical results is included.     

模糊神经网络技术综述

首先讨论了模糊神经网络协作体的产生和优越性，随后将模糊神经网络划分为狭义模糊神经网络、用模糊逻辑增强网络功能的神经网络和神经模糊系统，并分别介绍了各自的网络结构和学习算法，最后介绍了模糊神经网络的工业应用．     

基于HGA的模糊神经控制器设计及其应用

将神经网络与模糊控制相结合,实现了模糊控制器的自学习和自适应。给出一种基于递阶遗传算法的模糊神经网络优化算法,通过对每个染色体采用递阶编码,可以同时优化模糊神经网络结构和权值参数。将这种模糊神经网络控制器应用于镍氢电池的充电控制中,证明了算法的有效性。     

Hierarchical Fuzzy Systems for Function Approximation on Discrete Input Spaces With Application

This paper investigates the capabilities of hierarchical fuzzy systems to approximate functions on discrete input spaces. First, it is shown that any function on a discrete space has an arbitrary separable hierarchical structure and can be naturally approximated by hierarchical fuzzy systems. As a by-product of this result, a discrete version of Kolmogorov's theorem is obtained; second, it is proven that any function on a discrete space can be approximated to any degree of accuracy by hierarchical fuzzy systems with any desired separable hierarchical structure. That is, functions on discrete spaces can be approximated more simply and flexibly than those on continuous spaces; third, a hierarchical fuzzy system identification method is proposed in which human knowledge and numerical data are combined for system construction and identification. Finally, the proposed method is applied to the market condition performance modeling problem in site selection decision support and shows the better performance in both accuracy and interpretability than the regression and neural network approaches. In additions, the reason and mechanism why hierarchical fuzzy systems outperform regression and neural networks in this type of application are analyzed.      

RSPOP: rough set-based pseudo outer-product fuzzy rule identification algorithm

System modeling with neuro-fuzzy systems involves two contradictory requirements: interpretability verses accuracy. The pseudo outer-product (POP) rule identification algorithm used in the family of pseudo outer-product-based fuzzy neural networks (POPFNN) suffered from an exponential increase in the number of identified fuzzy rules and computational complexity arising from high-dimensional data. This decreases the interpretability of the POPFNN in linguistic fuzzy modeling. This article proposes a novel rough set-based pseudo outer-product (RSPOP) algorithm that integrates the sound concept of knowledge reduction from rough set theory with the POP algorithm. The proposed algorithm not only performs feature selection through the reduction of attributes but also extends the reduction to rules without redundant attributes. As many possible reducts exist in a given rule set, an objective measure is developed for POPFNN to correctly identify the reducts that improve the inferred consequence. Experimental results are presented using published data sets and real-world application involving highway traffic flow prediction to evaluate the effectiveness of using the proposed algorithm to identify fuzzy rules in the POPFNN using compositional rule of inference and singleton fuzzifier (POPFNN-CRI(S)) architecture. Results showed that the proposed rough set-based pseudo outer-product algorithm reduces computational complexity, improves the interpretability of neuro-fuzzy systems by identifying significantly fewer fuzzy rules, and improves the accuracy of the POPFNN.     

SBR系统中的模糊神经网络控制器设计

将模糊控制与神经网络相结合,设计4层模糊神经网络控制器,分析其结构及算法。利用神经网络的自学习能力,在线动态调整模糊变量的隶属函数,优化控制规则,并对曝气池中溶解氧浓度与活性污泥浓度进行控制。通过Matlab对溶解氧的控制进行数字仿真实验,结果表明,具有学习能力的模糊神经网络控制可在污水处理系统的应用中获得更优的性能。     

Falcon: neural fuzzy control and decision systems using FKP and PFKP clustering algorithms.

Neural fuzzy networks proposed in the literature can be broadly classified into two groups. The first group is essentially fuzzy systems with self-tuning capabilities and requires an initial rule base to be specified prior to training. The second group of neural fuzzy networks, on the other hand, is able to automatically formulate the fuzzy rules from the numerical training data. Examples are the Falcon-ART, and the POPFNN family of networks. A cluster analysis is first performed on the training data and the fuzzy rules are subsequently derived through the proper connections of these computed clusters. This correspondence proposes two new networks: Falcon-FKP and Falcon-PFKP. They are extensions of the Falcon-ART network, and aimed to overcome the shortcomings faced by the Falcon-ART network itself, i.e., poor classification ability when the classes of input data are very similar to each other, termination of training cycle depends heavily on a preset error parameter, the fuzzy rule base of the Falcon-ART network may not be consistent Nauck, there is no control over the number of fuzzy rules generated, and learning efficiency may deteriorate by using complementarily coded training data. These deficiencies are essentially inherent to the fuzzy ART, clustering technique employed by the Falcon-ART network. Hence, two clustering techniques--Fuzzy Kohonen Partitioning (FKP) and its pseudo variant PFKP, are synthesized with the basic Falcon structure to compute the fuzzy sets and to automatically derive the fuzzy rules from the training data. The resultant neural fuzzy networks are Falcon-FKP and Falcon-PFKP, respectively. These two proposed networks have a lean and efficient training algorithm and consistent fuzzy rule bases. Extensive simulations are conducted using the two networks and their performances are encouraging when benchmarked against other neural and neural fuzzy systems.     

Knowledge-based parameter identification of TSK fuzzy models

Linear/1st order Takagi–Sugeno–Kang (TSK) fuzzy models are widely used to identify static nonlinear systems from a set of input–output pairs. The synergetic integration of TSK fuzzy models with artificial neural networks (ANN) has led to the emergence of hybrid neuro-fuzzy models that can have excellent adaptability and interpretability at the same time. One drawback of these hybrid models is that they tend to have more black-box characteristics of ANN than the transparency of fuzzy systems. If the quality of training data is questionable then it may lead to a fuzzy model with poor interpretability. In an attempt to remediate this problem, we propose a parameter identification technique for TSK models that relies on a-priori available qualitative domain knowledge. The technique is devised for rule-centered TSK models in which the consequent polynomial can be interpreted as the 1st order Taylor series approximation of the underlying nonlinear function that is being modeled. The resulting neuro-fuzzy model is named as a-priori knowledge-based fuzzy model (APKFM). We have shown that besides being reasonably accurate, APKFM has excellent interpretability and extrapolation capability. The effectiveness of APKFM is shown using two examples of static systems. In the first example, a toy nonlinear function is chosen for approximation by an APKFM. In the second example, a real world problem pertaining to the maintenance cost estimation of electricity distribution networks is addressed.