Fuzzy system modeling using linear distance rules
Abstract
An approach of determining significant variables for multi-input systems is proposed by using a modified fuzzy rule form, called linear distance rules (LDR). By defining an index, we can know the influences of input signals on output and can determine significant variables from the index. We also propose a simple three-layered generalized neural network to realize the LDRs. Furthermore, this approach can be extended to decompose a multi-input–multi-output (MIMO) system into several simpler multi-input–single-output (MISO) systems.
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A T–S fuzzy model identification approach based on evolving MIT2-FCRM and WOS-ELM algorithm
2020, Engineering Applications of Artificial IntelligenceInter type-2 fuzzy model has been confirmed to be more effective in Takagi–Sugeno (T–S) fuzzy model identification compared to type-1 fuzzy model. It is indisputable that some algorithms based on inter type-2 fuzzy model have already been developed and shown remarkable modeling performance. To further improve the modeling accuracy, the optimization methods and the neural network are taken into consideration. In this paper, an evolving modified inter type-2 fuzzy c-regression model (MIT2-FCRM) algorithm based on gravitational search algorithm (GSA) and a consequent parameter identification method based on extreme learning machine algorithm with forgetting factor for processing online sequences (namely WOS-ELM) were proposed. Then a novel approach for T–S fuzzy modeling was presented, in which, the coefficients of the upper and lower hyperplanes were obtained by evolving MIT2-FCRM algorithm based on GSA, a hyper-plane-shaped membership function (MF) was utilized to identify the antecedent parameters of the T–S fuzzy model, and WOS-ELM was employed to identify the consequent parameters. The modeling results of six examples indicate that the proposed approach is superior to other studies in terms of identification accuracy, compact fuzzy rules and noise resistance ability.
Interval-valued membership function estimation for fuzzy modeling
2019, Fuzzy Sets and SystemsFuzzy modeling is an important topic in fuzzy sets theory and applications. A powerful method for constructing an interval-valued Takagi–Sugeno fuzzy model (IVFM), based on input–output data of the identified system, is presented. In this investigation, a Takagi–Sugeno fuzzy model is automatically generated in three steps: (1) Structure identification, (2) Envelope detection and (3) parameters identification. In the structure identification phase, a clustering method based on Gustafson–Kessel algorithm is used in order to detect the linear subsystems of the whole nonlinear system (local linearization). Then, an envelope detection algorithm (EDA) based on derivative concept is proposed to estimate both the upper and lower functions of the interval-valued membership function defined point-wise. In the parameter identification step, the least squares algorithm is applied to compute the best parameter values of the premises (Gaussians) and the Kalman Filter algorithm to compute the consequences (straight lines) parameters. The effectiveness of this approach is demonstrated on approximating some nonlinear static functions, real world data and dynamical systems.
Dynamic Type-2 Fuzzy Dependent Dirichlet Regression Mixture clustering model
2017, Applied Soft Computing JournalIn this paper, a new dynamic Interval Type-2 Fuzzy Dependent Dirichlet Piecewise Regression Mixture (IT2FDDPRM) clustering model is proposed. The model overcomes shortcomings of both Dependent Dirichlet Process Mixture (DDPM) technique and Interval Type-2 Fuzzy C-regression Clustering Model (IT2FCRM). DDPM method demonstrates that the probability of assigning data to a cluster including the maximum number of data among all clusters is higher, and it ignores the similarity of data to a cluster. However, the new IT2FDDPRM clustering technique supports assignment of data to a cluster which has the most similarity to them. It also allows the model to generate infinite number of clusters. Moreover, it has the capability of segmenting functions assigned to clusters. The model is validated using statistical tests, three validity functions, and mean square error of the model. The results of numerical experiments show that the proposed method has superior performance to other clustering techniques in literature.
Hydraulic turbine governing system identification using T-S fuzzy model optimized by chaotic gravitational search algorithm
2013, Engineering Applications of Artificial IntelligenceHydraulic turbine governing system (HTGS) is a complicated nonlinear system that controls the frequency and power output of hydroelectric generating unit (HGU). The modeling of HTGS is an important and difficult task, because some components, like hydraulic turbine and governor actuator, are with strong nonlinearity. In this paper, a novel Takagi–Sugeno (T–S) fuzzy model identification method based on chaotic gravitational search algorithm (CGSA) is proposed and applied in the modeling of HTGS. In the proposed method, fuzzy c-regression model clustering algorithm is used to partition the input space and identify the coarse antecedent membership function (MF) parameters at first. And then, a novel CGSA is proposed to search better MF parameters around the coarse results, in which chaotic search has been embedded in the iteration of basic GSA to search and replace the current best solution of GSA. The performance of the proposed fuzzy model identification method is validated by benchmark problems, and the results show that the accuracies of identified models have been improved significantly compared with the other existing models. Finally, the proposed approach has been applied to approximate the dynamic behaviors of HTGS of a HGU in a hydropower station of Jiangxi Province of China. The experimental results show that our approach can identify the HTGS satisfactorily with acceptable accuracy.
A type-2 fuzzy c-regression clustering algorithm for Takagi-Sugeno system identification and its application in the steel industry
2012, Information SciencesThis paper proposes a new type-2 fuzzy c-regression clustering algorithm for the structure identification phase of Takagi–Sugeno (T–S) systems. We present uncertainties with fuzzifier parameter “m”. In order to identify the parameters of interval type-2 fuzzy sets, two fuzzifiers “” and “” are used. Then, by utilizing these two fuzzifiers in a fuzzy c-regression clustering algorithm, the interval type-2 fuzzy membership functions are generated. The proposed model in this paper is an extended version of a type-1 FCRM algorithm [25], which is extended to an interval type-2 fuzzy model. The Gaussian Mixture model is used to create the partition matrix of the fuzzy c-regression clustering algorithm. Finally, in order to validate the proposed model, several numerical examples are presented. The model is tested on a real data set from a steel company in Canada. Our computational results show that our model is more effective for robustness and error reduction than type-1 NFCRM and the multiple-regression.
T-S fuzzy model identification based on a novel fuzzy c-regression model clustering algorithm
2009, Engineering Applications of Artificial IntelligenceThis 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.