TSK Fuzzy Rules Research Articles

Direct adaptive control for nonlinear systems using a TSK fuzzy echo state network based on fractional-order learning algorithm

This paper presents a new Takagi-Sugeno-Kang fuzzy Echo State Neural Network (TSKFESN) structure to design a direct adaptive control for uncertain SISO nonlinear systems. The proposed TSKFESN structure is based on the echo state neural network framework containing multiple sub-reservoirs. Each sub-reservoir is weighted with a TSK fuzzy rule. The adaptive law of the TSKFESN-based direct adaptive controller is derived by using a fractional-order sliding mode learning algorithm. Moreover, the Lyapunov stability criterion is employed to verify the convergence of the fractional-order adaptive law of the controller parameters. The evaluation of the proposed direct adaptive control scheme is verified using two case studies, the regulation problem of a torsional pendulum and the speed control of a direct current (DC) machine as a real-time application. The simulation and the experimental results show the effectiveness of the proposed control scheme.

Deep fuzzy model for non-linear effective connectivity estimation in the intuition of consciousness correlates

The brain connectivity, as a promising technique to explore brain networks during resting-states or cognitive tasks, has been employed remarkably in recent years. The aim of this study is to propose a new approach to improve the Granger causality as one of the fundamental methods for calculation of brain effective connectivity. To this end, we utilized a deep fuzzy structure to model the multivariate autoregressive used in the Granger causality. The proposed model benefits from the hierarchical stacked structure where first – order TSK fuzzy rules are the cores of the network. In the first layer of the stacked structure, the antecedents of the fuzzy rules are extracted from the fuzzy clustering of the input space. For subsequent layers, due to the input perturbation which is caused by the previous layer output, a shuffling approach is adopted. To assess our proposed model, we applied it to two nonlinear synthetic time series and compared it with linear Granger. Results revealed that our model is superior in the detection of effective connectivity. We additionally exploit the pioneer model for one of the controversial concepts in cognitive neuroscience in recent years: the neural correlates of visual consciousness. We applied our method to detect connectivity networks of EEG in consciousness states. Our results demonstrated that the proposed nonlinear connectivity estimator was capable of detecting novel correlates: significant differences have been observed among different states of consciousness, not only in presence of attention, as the linear method detected it, but also in absence of attention.

Predicting Stock Trends Using Tsk-fuzzy Rule Based System

Stock investment is often regarded by investors as a green opportunity that is characterized by high rewards and its attendant risk. Consequently, investors are preoccupied with analysis and prediction of the future performance of stocks, and the direction and magnitude of future changes in the stock value. In this study, the Takagi-Sugueno-Kang - Fuzzy Rule Based System (TSK-FRBS) was used to analyzed the trend of stocks using historical data gathered over a period of five months between January and May 2015. The TSK-FRBS was implemented in R. The input data is split into training and testing data for experimentation, testing and further analysis. Predictive accuracy was evaluated using the root mean squared error (RMSE) and symmetric mean absolute percentage error (SMAPE). Final results showed consistency obtained from feeding the model with the data and hence provedthat patterns that allow for prediction can be deduced from the chaotic nature of the stock exchange market.

S-FRULER: Scalable fuzzy rule learning through evolution for regression

In genetic fuzzy systems (GFS) the size of the problem has a huge influence in the performance of the obtained models, since i) the fuzzy rule bases learned suffer from exponential rule explosion when the number of variables increases, and ii) the convergence time increments with the number of examples. In this paper we present S-FRULER, a scalable distributed version of FRULER which is a GFS that learns simple and linguistic TSK-1 knowledge bases for regression problems. S-FRULER obtains models with high accuracy and low complexity, whilst reducing the algorithm runtime. S-FRULER focuses on splitting the problem into smaller partitions and incorporates a feature selection process for reducing the number of variables used in each partition. Each partition is then solved independently using the FRULER algorithm. Afterwards, an aggregation function obtains the final linguistic TSK fuzzy rule base from the information generated in each partition. S-FRULER has been validated in terms of scalability, precision and complexity using 10 large-scale datasets and has been compared with three state of the art GFSs. Experimental results show that S-FRULER scales well while achieving simple models with a linguistic approach and a precision comparable with approximative models. Moreover, S-FRULER has been applied to a bioinformatics problem that was proposed as a benchmark for scalability of regression problems, obtaining good results in both accuracy and complexity.

솔더링 시스템의 온도 제어를 위한 퍼지 PI 제어기 설계

This paper proposes controller design algorithms for a ceramic soldering iron temperature control system, and reports their effectiveness in a control experiment. Because the responses of the ceramic soldering iron temperature to the control input are non-linear and very slow, precise modeling and controller design is difficult. In this study, the temperature characteristics of a ceramic soldering iron are represented by TSK fuzzy models consisting of TSK fuzzy rules. In the fuzzy rules, the premise variable is the control input and the consequences are the transfer functions. The transfer functions in the fuzzy model were obtained from the step input responses. As the responses of the ceramic soldering iron temperature are very slow, it is difficult to obtain the complete step input responses. This paper proposes a genetic algorithm to obtain the transfer functions from an incomplete step input responses, and showed its effectiveness in examples. This paper also reports a fuzzy controller design method from the TSK fuzzy model and examples. The proposed methods were applied to the temperature control experiments of ceramic iron. The TSK fuzzy model consisted of 7 TSK fuzzy rules, and the consequences were PI controllers. The experimental results of the proposed fuzzy PI controller were superior to the linear controller and were as good as in previous studies using a fuzzy PID controller.

Time series forecasting with a neuro-fuzzy modeling scheme

Time series forecasting concerns the prediction of future values based on the observations previously taken at equally spaced time points. Statistical methods have been extensively applied in the forecasting community for the past decades. Recently, machine learning techniques have drawn attention and useful forecasting systems based on these techniques have been developed. In this paper, we propose an approach based on neuro-fuzzy modeling for time series prediction. Given a predicting sequence, the local context of the sequence is located in the series of the observed data. Proper lags of relevant variables are selected and training patterns are extracted. Based on the extracted training patterns, a set of TSK fuzzy rules are constructed and the parameters involved in the rules are refined by a hybrid learning algorithm. The refined fuzzy rules are then used for prediction. Our approach has several advantages. It can produce adaptive forecasting models. It works for univariate and multivariate prediction. It also works for one-step as well as multi-step prediction. Several experiments are conducted to demonstrate the effectiveness of the proposed approach.

퍼지 PID 제어기에 의한 리워크 시스템의 온도제어

BGA 또는 SMD 형태를 갖는 반도체 칩을 인쇄회로 기판에 장착/제거 등의 수리작업에 사용되는 리워크 시스템은 작업 대상물의 손상을 줄이기 위해 열풍 토출구의 온도를 정밀하게 제어할 필요가 있다. 본 논문에서는 비선형 시스템인 리워크 시스템의 열풍 온도 제어를 위해 TSK 퍼지 규칙으로 구성되는 퍼지 PID 제어기 설계 방법을 제시한다. 먼저 제안하 는 제어기의 설계 알고리즘을 제시하고, 리워크 시스템에 적용하여 제어기를 설계하는 과정을 보인다. 제안한 제어기의 성능 을 확인하기 위하여 온도 제어를 실험한 결과, 제안 방법의 최소자승오차는 9.44로서 일반적으로 사용하는 PID 제어기를 사용한 경우의 오차인 15.88보다 설정온도에 잘 수렴함을 보였다.

Adaptive multi-controller TSK Fuzzy Structure for Control of Nonlinear MIMO Dynamic Plant

In the paper an adaptive multi-controller control system utilizing a TSK fuzzy rules for a MIMO nonlinear dynamic plant is presented. The problems under study are exemplified by synthesis of a position and yaw angle control system for a drillship described by a 3DOF nonlinear mathematical model of low-frequency motions made by the drillship over the drilling point. In the proposed control system use is made of a set of linear modal controllers that create a multi-controller structure from which a group of controllers appropriate to given operation conditions is chosen and used to calculate, by using TSK fuzzy rules, control signals. The final part of the paper includes simulation results of system operation with an adaptive controller of (stepwise) varying parameters along with conclusions and final remarks.

Fuzzy wavelet neural network based on fuzzy clustering and gradient techniques for time series prediction

This paper presents the development of fuzzy wavelet neural network system for time series prediction that combines the advantages of fuzzy systems and wavelet neural network. The structure of fuzzy wavelet neural network (FWNN) is proposed, and its learning algorithm is derived. The proposed network is constructed on the base of a set of TSK fuzzy rules that includes a wavelet function in the consequent part of each rule. A fuzzy c-means clustering algorithm is implemented to generate the rules, that is the structure of FWNN prediction model, automatically, and the gradient-learning algorithm is used for parameter identification. The use of fuzzy c-means clustering algorithm with the gradient algorithm allows to improve convergence of learning algorithm. FWNN is used for modeling and prediction of complex time series and prediction of foreign-exchange rates. Exchange rates are dynamic process that changes every day and have high-order nonlinearity. The statistical data for the last 2 years are used for the development of FWNN prediction model. Effectiveness of the proposed system is evaluated with the results obtained from the simulation of FWNN-based systems and with the comparative simulation results of previous related models.

Artificial Neural Networks are Zero-Order TSK Fuzzy Systems

In this paper, the functional equivalence between the action of a multilayered feed-forward artificial neural network (NN) and the performance of a system based on zero-order TSK fuzzy rules is proven. The resulting zero-order TSK fuzzy systems have the two following features: (A) the product t-norm is used to add IF-part fuzzy propositions of the obtained rules and (B) their inputs are the same as the initial neural networkNN ones. This fact makes us gain an understanding of the ANN-embedded knowledge. Besides, it allows us to simplify the architecture of a network through the reduction of fuzzy propositions in its equivalent zero-order TSK system. These advantages are the result of applying fuzzy system area properties on the neural networkNN area. They are illustrated with several examples.

Smooth transition autoregressive models and fuzzy rule-based systems: Functional equivalence and consequences

In this work we will explore the theoretical connections existing between fuzzy rule-based systems (FRBS) applied on univariate time series and two statistical reference tools, the autoregressive (AR) models and the smooth transition autoregressive (STAR) model. We will show that a TSK fuzzy rule happens to be a localised AR model and that a STAR model can hence be interpreted as a restricted FRBS. Several consequences derive from this fact, and we will explore some of them, including a statistical inference-based procedure to incrementally build FRBS or the linguistic interpretation of STAR models. Finally an econometric example is given to illustrate the core idea.

A nonlinear adaptive fuzzy approximator technique with its application to prediction of non-stationary EEG dynamics and estimation of single-sweep evoked potentials

In this paper, we apply a fast training paradigm to the optimization of fuzzy approximator and a nonlinear adaptive fuzzy approximator (NAFA) is constructed. Using TSK fuzzy rules, the structured knowledge along with numerical information are parameterized and utilized in the NAFA, which can be easily configured as a multi-layer network when its transparency is desired. We propose a fast training paradigm, which is actually a combination of Kalman filtering and LMS adaptation, to optimize the linear and nonlinear parameters of the NAFA separately. The NAFA is characterized by concise representation of structured knowledge, fast learning capability, as well as universal approximation property. The NAFA is applied to forecast the non-stationary EEG time-series and to estimate single-sweep evoked potentials (EPs). The corresponding simulation results are given. It is concluded that the NAFA technique can provide efficient nonlinear separation of single-sweep EPs, which allows for quantitative examination of the cross-trial variability of clinical EPs.

Evolving TSK Fuzzy Rules For ClassificationTasks By Genetic Algorithms

This paper presents a method for classification based on a genetic algorithm to evolve a Takagi-Sugeno-Kang fuzzy rule bases. It is shown how a fuzzy rule base is generated from a numerical database and how its best subset is found by the genetic algorithm. The method not only produces rule base subsets with very good performance but also reveals itself as a feature selector. Analyses are realized on the results obtained from several classification problems approached by the method and by a decision tree based algorithm.