Neuro-fuzzy system modeling based on automatic fuzzy clustering

A neuro-fuzzy system model based on automatic fuzzy dustering is proposed. A hybrid model identification algorithm is also developed to decide the model structure and model parameters. The algorithm mainly includes three parts：1） Automatic fuzzy C-means （AFCM）, which is applied to generate fuzzy rttles automatically, and then fix on the size of the neuro-fuzzy network, by which the complexity of system design is reducesd greatly at the price of the fitting capability; 2） R.ecursive least square estimation （RLSE）. It is used to update the parameters of Takagi-Sugeno model, which is employed to describe the behavior of the system;3） Gradient descent algorithm is also proposed for the fuzzy values according to the back propagation algorithm of neural network. Finally,modeling the dynamical equation of the two-link manipulator with the proposed approach is illustrated to validate the feasibility of the method.     

An approach to polynomial NARX/NARMAX systems identification in a closed-loop with variable structure control

Many physical processes have nonlinear behavior which can be well represented by a polynomial NARX or NARMAX model. The identification of such models has been widely explored in literature. The majority of these approaches are for the open-loop identification. However, for reasons such as safety and production restrictions, open-loop identification cannot always be done. In such cases, closed-loop identification is necessary. This paper presents a two-step approach to closed-loop identification of the polynomial NARX/NARMAX systems with variable structure control （VSC）. First, a genetic algorithm （GA） is used to maximize the similarity of VSC signal to white noise by tuning the switching function parameters. Second, the system is simulated again and its parameters are estimated by an algorithm of the least square （LS） family. Finally, simulation examples are given to show the validity of the proposed approach.     

一类欠驱动机械系统的动态及其稳定控制

Abstract The control of underactuated mechanical systems is very complex for the loss of its control inputs. The model of underactuated mechanical systems in a potential field is built with Lagrangian method and its structural properties are analyzed in detail. A stable control approach is proposed for the class of underactuated mechanical systems. This approach is applied to an unde ractuated double-pendulum-type overhead crane and the simulation results illustrate the correctness of dynamics analysis and validity of the proposed control algorithm.     

Interval analysis using least squares support vector fuzzy regression

A least squares support vector fuzzy regression model(LS-SVFR) is proposed to estimate uncertain and imprecise data by applying the fuzzy set principle to weight vectors.This model only requires a set of linear equations to obtain the weight vector and the bias term,which is different from the solution of a complicated quadratic programming problem in existing support vector fuzzy regression models.Besides,the proposed LS-SVFR is a model-free method in which the underlying model function doesn’t need to be predefined.Numerical examples and fault detection application are applied to demonstrate the effectiveness and applicability of the proposed model.     

Selective ensemble extreme learning machine modeling of effluent quality in wastewater treatment plants

Real-time and reliable measurements of the effluent quality are essential to improve operating efficiency and reduce energy consumption for the wastewater treatment process.Due to the low accuracy and unstable performance of the traditional effluent quality measurements,we propose a selective ensemble extreme learning machine modeling method to enhance the effluent quality predictions.Extreme learning machine algorithm is inserted into a selective ensemble frame as the component model since it runs much faster and provides better generalization performance than other popular learning algorithms.Ensemble extreme learning machine models overcome variations in different trials of simulations for single model.Selective ensemble based on genetic algorithm is used to further exclude some bad components from all the available ensembles in order to reduce the computation complexity and improve the generalization performance.The proposed method is verified with the data from an industrial wastewater treatment plant,located in Shenyang,China.Experimental results show that the proposed method has relatively stronger generalization and higher accuracy than partial least square,neural network partial least square,single extreme learning machine and ensemble extreme learning machine model.     

Universal triple I fuzzy reasoning algorithm of function model based on quotient space

Aiming at the deficiencies of analysis capacity from different levels and fuzzy treating method in product function modeling of conceptual design,the theory of quotient space and universal triple I fuzzy reasoning method are introduced,and then the function modeling algorithm based on the universal triple I fuzzy reasoning method is proposed.Firstly,the product function granular model based on the quotient space theory is built,with its function granular representation and computing rules defined at the same time.Secondly,in order to quickly achieve function granular model from function requirement,the function modeling method based on universal triple I fuzzy reasoning is put forward.Within the fuzzy reasoning of universal triple I method,the small-distance-activating method is proposed as the kernel of fuzzy reasoning;how to change function requirements to fuzzy ones,fuzzy computing methods,and strategy of fuzzy reasoning are respectively investigated as well;the function modeling algorithm based on the universal triple I fuzzy reasoning method is achieved.Lastly,the validity of the function granular model and function modeling algorithm is validated.Through our method,the reasonable function granular model can be quickly achieved from function requirements,and the fuzzy character of conceptual design can be well handled,which greatly improves conceptual design.     

多尺度PCA在传感器故障诊断中的应用研究

A multiscale principal component analysis method is proposed for sensor fault detection and identification. After decomposition of sensor signal by wavelet transform, the coarse-scale coef-ficients from the sensors with strong correlation are employed to establish the principal component analysis model. A moving window is designed to monitor data from each sensor using the model.For the purpose of sensor fault detection and identification, the data in the window is decomposed with wavelet transform to acquire the coarse-scale coefficients firstly, and the square prediction error is used to detect the failure. Then the sensor validity index is introduced to identify faulty sensor,which provides a quantitative identifying index rather than qualitative contrast given by the approach with contribution. Finally, the applicability and effectiveness of the proposed method is illustrated by sensors of industrial boiler.     

Intelligent non-linear modelling of an industrial winding process using recurrent local linear neuro-fuzzy networks

This study deals with the neuro-fuzzy (NF) modelling of a real industrial winding process in which the acquired NF model can be exploited to improve control performance and achieve a robust fault-tolerant system. A new simulator model is proposed for a winding process using non-linear identification based on a recurrent local linear neuro-fuzzy (RLLNF) network trained by local linear model tree (LOLIMOT), which is an incremental tree-based learning algorithm. The proposed NF models are compared with other known intelligent identifiers, namely multilayer perceptron (MLP) and radial basis function (RBF). Comparison of our proposed non-linear models and associated models obtained through the least square error (LSE) technique (the optimal modelling method for linear systems) confirms that the winding process is a non-linear system. Experimental results show the effectiveness of our proposed NF modelling approach.     

Intelligent non-linear modelling of an industrial winding process using recurrent local linear neuro-fuzzy networks

This study deals with the neuro-fuzzy (NF) modelling of a real industrial winding process in which the acquired NF model can be exploited to improve control performance and achieve a robust fault-tolerant system. A new simulator model is proposed for a winding process using non-linear identification based on a recurrent local linear neuro-fuzzy (RLLNF) network trained by local linear model tree (LOLIMOT), which is an incremental tree-based learning algorithm. The proposed NF models are compared with other known intelligent identifiers, namely multilayer perceptron (MLP) and radial basis function (RBF). Comparison of our proposed non-linear models and associated models obtained through the least square error (LSE) technique (the optimal modelling method for linear systems) confirms that the winding process is a non-linear system. Experimental results show the effectiveness of our proposed NF modelling approach.     

基于聚类和SVD算法的解释性模糊建模方法

提出了一种基于减法聚类算法构造解释性模糊模型的方法。首先指出模糊模型解释性的重要地位,分析影响解释性的主要因素;然后利用减法聚类算法辨识初始模糊模型,SVD算法和集合非冗余度约简初始模糊模型,从而提高其解释性;最后采用约束优化算法整体优化模型,提高其精度。PH值中和过程的模糊建模验证了该方法的有效性。     

基于聚类和遗传算法的解释性模糊模型设计

提出了一种基于模糊聚类和遗传算法构建解释性模糊模型的设计方法。定义了模糊模型的精确性指标,给出了模糊模型解释性的必要条件。然后利用模糊聚类算法和最小二乘法辨识初始的模糊模型;采用多目标遗传算法优化模糊模型;为提高模型的解释性,在遗传算法中利用基于相似性的模糊集合和模糊规则的简化方法对模型进行约简。采用该方法对Mackey-Glass系统进行建模,仿真结果验证了该方法的有效性。     

基于多目标遗传算法的TS模糊模型设计

提出一种利用遗传算法进行TS模糊模型的优化设计方法。首先定义了TS模糊模型的精确性指标,给出模糊模型解释性的必要条件。然后利用模糊聚类算法和最小二乘法辨识初始的模糊模型;利用多目标遗传算法优化模糊模型;为提高模型的解释性,在遗传算法中利用基于相似性的模糊集合和模糊规则简化方法对模型进行约简。最后利用该方法进行一类二阶合成非线性动态系统的建模,仿真结果验证了该方法的有效性。     

基于协同进化算法的TS模糊模型设计

提出一种基于协同进化算法的TS模糊模型设计方法．该方法由以下两步组成：（1）采用模糊聚类算法辨识初始的模糊模型；（2）利用协同进化算法对所获得的初始模糊模型进行结构和参数的优化．协同进化算法由两类种群组成：规则前件种群和隶属函数参数种群；其适应度函数同时考虑模型的精确性和解释性，采用两种群合作计算的策略；为提高模型的解释性，在协同进化算法中利用基于相似性的模型简化方法对模型进行约简．最后，利用该方法对Mackey-Glass系统进行辨识，仿真结果验证了方法的有效性．     

基于Pareto协同进化算法的TS模糊模型设计

提出一种可同时构造多个精确性和解释性较好折中的TS模糊模型的设计方法．该方法由以下两步组成：1）采用模糊聚类算法辨识初始模型;2）利用Pareto协同进化算法对所获得的初始模型进行结构和参数优化．Pareto协同进化算法由规则前件种群和隶属函数种群组成,其目标函数同时考虑模型的精确性和解释性,采用一种新的基于非支配排序的多种群合作策略．利用该方法对一类合成非线性动态系统进行建模,仿真结果验证了该方法的有效性．     

基于正交最小二乘估计的非线性系统模糊辨识

提出了一种基于正交最小二乘的模糊模型结构和参数辨识方法．首先，基于正交最小二乘方法分析模糊模型的模糊关系矩阵．通过分析正交向量在模型中贡献的大小，确定模糊模型的结构，即确定模糊模型的规则数、规则．另外，再次通过正交最小二乘方法确定模糊模型的结论参数，实现模糊模型结构和参数的优化．为了证明该方法的有效性，采用该文方法对Box-Jenkins煤气炉数据系统进行建模研究，仿真结果表明该文方法能够对非线性系统进行辨识．     

遗传算法在模糊模型参数辨识中的应用

介绍了T-S模糊模型的建模过程,在现有T-S模糊模型参数辨识方法的基础上,提出了一种先应用最小二乘法对结论参数进行粗略辨识,以确定参数的大致范围之后,再应用遗传算法对前提参数和结论参数同时优化的参数辨识方法,通过MATLAB对本算法进行了仿真,并对非线性函数进行了逼近实验,所取得的结果令人满意。     

Parameter identification of PWARX models using fuzzy distance weighted least squares method

PieceWise AutoRegressive eXogenous (PWARX) models represent one of the broad classes of the hybrid dynamical systems (HDS). Among many classes of HDS, PWARX model used as an attractive modeling structure due to its equivalence to other classes. This paper presents a novel fuzzy distance weight matrix based parameter identification method for PWARX model. In the first phase of the proposed method estimation for the number of affine submodels present in the HDS is proposed using fuzzy clustering validation based algorithm. For the given set of input–output data points generated by predefined PWARX model fuzzy c-means (FCM) clustering procedure is used to classify the data set according to its affine submodels. The fuzzy distance weight matrix based weighted least squares (WLS) algorithm is proposed to identify the parameters for each PWARX submodel, which minimizes the effect of noise and classification error. In the final phase, fuzzy validity function based model selection method is applied to validate the identified PWARX model. The effectiveness of the proposed method is demonstrated using three benchmark examples. Simulation experiments show validation of the proposed method.     

T–S fuzzy model identification based on a novel fuzzy c-regression model clustering algorithm

This paper proposes a novel approach for identification of Takagi–Sugeno (T–S) fuzzy model, which is based on a new fuzzy c-regression model (FCRM) clustering algorithm. The clustering prototype in fuzzy space partition is hyper-plane, so FCRM clustering technique is more suitable to be applied in premise parameters identification of T–S fuzzy model. A new FCRM clustering algorithm (NFCRMA) is presented, which is deduced from the fuzzy clustering objective function of FCRM with Lagrange multiplier rule, possessing integrative and concise structure. The proposed approach consists mainly of two steps: premise parameter identification and consequent parameter identification. The NFCRMA is utilized to partition the input–output data and identify the premise parameters, which can discover the real structure of the training data; on the other hand, orthogonal least square is exploited to identify the consequent parameters. Finally, some examples are given to verify the validity of the proposed modeling approach, and the results show the new approach is very efficient and of high accuracy.     

Context adaptation of fuzzy systems through a multi-objective evolutionary approach based on a novel interpretability index

Context adaptation (CA) based on evolutionary algorithms is certainly a promising approach to the development of fuzzy rule-based systems (FRBSs). In CA, a context-free model is instantiated to a context-adapted FRBS so as to increase accuracy. A typical requirement in CA is that the context-adapted system maintains the same interpretability as the context-free model, a challenging constraint given that accuracy and interpretability are often conflicting objectives. Furthermore, interpretability is difficult to quantify because of its very nature of being a qualitative concept. In this paper, we first introduce a novel index based on fuzzy ordering relations in order to provide a measure of interpretability. Then, we use the proposed index and the mean square error as goals of a multi-objective evolutionary algorithm aimed at generating a set of Pareto-optimum context-adapted Mamdani-type FRBSs with different trade-offs between accuracy and interpretability. CA is obtained through the use of specifically designed operators that adjust the universe of the input and output variables, and modify the core, the support and the shape of fuzzy sets characterizing the partitions of these universes. Finally, we show results obtained by using our approach on synthetic and real data sets.