Fuzzy C-regression Model Research Articles

Fuzzy double-ordered c-regression models based on fuzzy S-estimators

Among the most popular clustering methods is the fuzzy c-means one. Its generalization by application of hyperplane shaped prototypes of the clusters is known as the Fuzzy C-Regression Models (FCRM) method. Since this method is very sensitive to poor initialization and to the presence of noise and outliers in data, its numerous robust variants have been introduced, using also the ordering operation. In this paper, a new variation of the method has been introduced which uses ordering for the residuals of each model and ordering for residuals of each data pair, and additionally, uses a fuzzy S-regression estimator associated with M-scale to improve significantly the method robustness. Thus, the concept of a fuzzy S-regression estimator is also introduced. The new method is named as the Fuzzy Double Ordered C-Regression Models (FDOCRM) method. The method proposed is compared to a few other important reference ones. Large-scale simulations demonstrate its competitiveness and usefulness.

T-S fuzzy model identification based on an improved interval type-2 fuzzy c-regression model

Fuzzy clustering has been widely applied in T-S fuzzy model identification for nonlinear systems, however, tradition type-1 fuzzy clustering algorithms can’t deal with uncertainties in real world, an improved interval type-2 fuzzy c-regression model (IT2-FCRM) clustering is proposed for T-S fuzzy model identification in this paper. The improved IT2-FCRM adapts a new objective function, which makes the boundary of clustering more clearly and reduces the influence of outliers or noisy data on clustering results. The premise parameters of T-S fuzzy model are upper and lower hyperplanes obtained by improved IT2-FCRM, and the upper and lower hyperplanes are used to build hyper-plane-shaped type-2 Gaussian membership function. Compared with the hyper-sphere-shaped membership function of tradition IT2-FCRM, the hyper-plane-shaped membership function is more coincided with point to plane sample distance described by FCRM clustering. The simulation results of several benchmark problems and a real bed temperature in circulating fluidized bed plant show that the identification algorithm has higher accuracy.

Rule-based fuzzy neural networks realized with the aid of linear function Prototype-driven fuzzy clustering and layer Reconstruction-based network design strategy

In this study, we introduce novel fuzzy neural networks designed with the aid of linear function prototype-driven fuzzy clustering (LFPFC) and layer reconstruction-based network design strategy to deal with the regression problem. The LFPFC constitutes a new clustering technique inspired by the fuzzy c-regression model (FCRM) clustering unlike fuzzy c-means (FCM) clustering LFPFC represents the prototypes of clusters as linear functions, and this can lead to more reliable data analysis of complex regression problems. We propose two types of LFPFC such as an estimated output-based LFPFC and a distance-based LFPFC. The estimated output-based LFPFC uses the output estimated on a basis of the simple model instead of the target output to calculate the centroid of LFPFC. A centroid of distance-based LFPFC is computed through the Euclidean distance between input data and the centroid of the cluster. By using two kinds of LFPFC approaches, we propose three different types of fuzzy neural networks: i) the fuzzy neural networks through layer reconstruction-based network design strategy consists of two models. The first model serves as an estimate of the desired output and the estimated output is used in the LFPFC of the second model. ii) In the fuzzy neural networks applied to the basic architecture of distance-based LFPFC, the hidden layer using the membership function changes to basic distance-based LFPFC, and the partition matrix obtained from LFPFC is used as the output of the hidden layer. iii) in the fuzzy neural network with the advanced architecture of distance-based LFPFC, an additional auxiliary layer is considered between the hidden and output layers to estimate the membership function of output space through LFPFC. In the experiments, we evaluate the performance index of the proposed models using publicly available machine learning datasets. The superiority of the proposed fuzzy neural networks designed by using LFPFC is demonstrated through the comparative analysis with the diverse regression models offered in the Weka data mining software. By conducting the Friedman test we show that the proposed model exhibits visible competitiveness from the viewpoint of performance. In addition, a real-world Portland cement dataset is dealt with to demonstrate the superiority of the models designed with the aid of LFPFC and reinforced layer reconstruction-based network design strategy.

Boil-Turbine System Identification Based on Robust Interval Type-2 Fuzzy C-Regression Model

The boil-turbine system is a multivariable and strong coupling system with the characteristics of nonlinearity, time-varying parameters, and large delay. The accurate model can effectively improve the performance of turbine–boiler coordinated control system. In this paper, the boil-turbine model is established by interval type-2 (IT2) T-S fuzzy model. The premise parameters of IT2 T-S fuzzy model are identified by robust IT2 fuzzy c-regression model (RIT2-FCRM) clustering algorithm. The RIT2-FCRM is based on interval type-2 fuzzy sets (IT2FS) and applies a robust objective function, this clustering algorithm can reduce the impacts of outliers and noise points. The effectiveness and practicability of RIT2-FCRM are demonstrated by the identification results of the boiler–turbine system.

Hysteresis Modeling of Piezoelectric Actuators Based on a T-S Fuzzy Model

Piezoelectric actuators (PEAs) have been widely used in aerospace, electronic communication and other high-accuracy manufacturing fields because of their high precision, low power consumption, fast response, and high resolution. However, piezoelectric actuators have very complicated hysteresis nonlinearity, which greatly affects their positioning and control accuracy. Particularly in the field of active vibration control, the control accuracy of piezoelectric actuators is easily affected by noise points. To address the problem, this paper proposes a hyperplane probability c-regression model (HPCRM) algorithm to establish its T-S fuzzy model of hysteresis nonlinearity. Firstly, an improved fuzzy c regression clustering algorithm is proposed to identify the antecedent parameters of T-S fuzzy model. This algorithm not only divides the fuzzy space better but also effectively avoids the influence of noise points generated by the external environment during data acquisition. Secondly, a new type of hyperplane membership function is introduced to solve the problem that the traditional Gaussian membership function does not match the hyperplane clustering algorithm. Finally, the accuracy of the modeling method is confirmed by several comparative experiments. Experimental results show that the proposed method is more precise than the traditional fuzzy c-regression models (FCRM) and probability c-regression models (PCRM) under the sine signals of 5 Hz–100 Hz.

An Approach Towards the Design of Interval Type-3 T–S Fuzzy System

This article providesa systematic approach for the design of an interval type-3 (IT3) Takagi–Sugeno (T–S) fuzzy logic system (FLS) using <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha $</tex-math></inline-formula> - plane representation. An IT3 FLS is designed with the baseline of the general type-2 (GT2) FLS in a similar manner as an IT2 FLS was designed from the baseline of type-1 FLS. Hence, IT3 FLS evolved as a successor of GT2 FLS, where secondary membership function is an interval type-2 fuzzy set (FS), and values of tertiary membership are unity over the footprint of uncertainty of secondary membership. This extra degree of freedom in IT3 FLS provides better modeling capability as compared to GT2 FLS in the presence of a high degree of uncertainty and vagueness. The proposed system will be more appealing while dealing with uncertain information or data, which is supposed to be generated from uncertain sources; i.e., there exist uncertainties even in the presence of uncertainty. The computations needed for the design of IT3 FLS are derived using IT2 FS and GT2 FS mathematics. The design algorithms adopted for the baseline IT2 T–S fuzzy system are as per the modified interval type-2 fuzzy c-regression model clustering algorithm and hyper-plane-shaped membership function. The proposed methodology is applied to several benchmark examples and obtained results are compared with recently developed fuzzy modeling methods having a comparable number of rule bases. The proposed IT3 T–S FLS shows good performance in terms of accuracy when data is corrupted by noise and uncertainties related to missing or unvarying data exist. The computational cost is linear with design parameters and by optimum choice of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha $</tex-math></inline-formula> -planes, it is still bearable considering advantages and nature of applications.

A composite framework coupling FCRM, LSSVM and improved hybrid IHHOMFO optimization for Takagi–Sugeno fuzzy model identification

This paper proposes a novel Takagi–Sugeno fuzzy model identification method by combining fuzzy c-regression model clustering (FCRM), least squares support vector machine (LSSVM) and intelligent optimization algorithm. Firstly, in order to improve the performance of FCRM for the complex nonlinear dataset, in this paper the method of FCRM based on LSSVM (FCRM-LSSVM) is proposed to discover the data structure and obtain the antecedent parameters. And then, a newly developed intelligent optimization algorithm by hybridizing Harris hawks optimization and moth-flame optimization algorithm (IHHOMFO) is proposed to further optimize the antecedent membership function parameters obtained by the FCRM-LSSVM. Finally, the proposed novel T-S fuzzy model identification combines FCRM, LSSVM and IHHOMFO for solving actual model identification problems. Experiments on five different datasets demonstrate that the proposed method is more efficient than conventional methods, such as T-S model identification based on fuzzy c-means (FCM), FCRM and FCRM-LSSVM, in standard measurement indexes. This study thus demonstrates that the proposed method is a credible and competitive fuzzy model identification method. The novel method contributes not only to the theoretical aspects of fuzzy model, but is also widely applicable in data mining, image recognition and prediction problems.

Identification of Circulating Fluidized Bed Boiler Bed Temperature Based on Hyper-Plane-Shaped Fuzzy C-Regression Model

Bed temperature in dense-phase zone is the key parameter of circulating fluidized bed (CFB) boiler for stable combustion and economic operation. It is difficult to establish an accurate bed temperature model as the complexity of circulating fluidized bed combustion system. T-S fuzzy model was widely applied in the system identification for it can approximate complex nonlinear system with high accuracy. Fuzzy c-regression model (FCRM) clustering based on hyper-plane-shaped distance has the advantages in describing T-S fuzzy model, and Gaussian function was adapted in antecedent membership function of T-S fuzzy model. However, Gaussian fuzzy membership function was more suitable for clustering algorithm using point to point distance, such as fuzzy c-means (FCM). In this paper, a hyper-plane-shaped FCRM clustering algorithm for T-S fuzzy model identification algorithm is proposed. The antecedent membership function of proposed identification algorithm is defined by a hyper-plane-shaped membership function and an improved fuzzy partition method is applied. To illustrate the efficiency of the proposed identification algorithm, the algorithm is applied in four nonlinear systems which shows higher identification accuracy and simplified identification process. At last, the algorithm is used in a circulating fluidized bed boiler bed temperature identification process, and gets better identification result.

부가정보를 이용한 조건부 Fuzzy C-Regression Model 클러스터링 알고리즘 기반 RBFNN 모델 설계

Fuzzy C-Regression Model(FCRM) 클러스터링은 Fuzzy C-Means(FCM) 클러스터링과는 다르게 각 클러스터의 중심을 직선으로 나타내는 방법이다. 데이터의 실제 출력값을 사용한다는 것이 FCRM 클러스터링의 약점으로 작용한다. 본 논문에서는, 실제 출력값을 사용하지 않기 위해 FCRM 클러스터링의 목적함수를 개선하였고, 개선된 FCRM 클러스터링에 부가정보가 추가된 조건부 FCRM 클러스터링 기반 방사형 기저함수 신경회로망(Radial Basis Function Neural Network, RBFNN) 모델을 설계한다. 조건부 FCRM 클러스터링의 부가정보는 데이터의 실제 출력과 FCRM 클러스터링 기반 RBFNN 모델의 출력 차이(오차)의 절댓값을 정규화한 값을 사용한다. 조건부 FCRM 클러스터링을 사용하여 구한 멤버쉽값 (소속정도)은 은닉층 노드의 출력값으로 이용된다. 은닉층과 출력층 사이의 연결가중치는 최소제곱 추정 (Least Square Estimation, LSE)을 사용하여 학습한다. 제안된 모델의 성능지수는 평균 제곱근 오차(Root Mean Squared Error, RMSE)를 적용하여 평가한다. 조건부 FCRM 클러스터링 기반 RBFNN 모델은 다양한 모델의 성능과 비교해서 우수성을 보여준다.

A T–S fuzzy model identification approach based on evolving MIT2-FCRM and WOS-ELM algorithm

Inter 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 Fuzzy c-Regression Models with Competitive Agglomeration for Symbolic Interval-Valued Data

In this study, a novel approach, interval fuzzy c-regression models with competitive agglomeration (IFCRMCA), is proposed to deal with the symbolic interval-valued data. The proposed IFCRMCA approach can identify the partition of the interval-valued data using both the distances to the cluster centers and the errors of interval regression models for each cluster. Due to the concepts of competitive agglomeration is used in the proposed approach, the pre-determination of the cluster number in the proposed IFCRMCA is not necessary. Various real experiments are carried on and the experimentally results shows that the proposed approaches are superior to the existing approaches.

Robust T-S Fuzzy Model Identification Approach Based on FCRM Algorithm and L1-Norm Loss Function

The Takagi–Sugeno (T–S) fuzzy model identification is a very powerful tool for modelling of complicated nonlinear system. However, the traditional T-S fuzzy model typically uses the L2-norm loss function, which is very sensitive to outliers or noises. So an unreliable model may be obtained due to the presence of outliers or noises. In this paper, the outliers and noises robust T-S fuzzy model identification method based on the fuzzy c-regression model (FCRM) clustering and the L1-norm loss function is proposed. The hyper-plane-shaped clustering algorithm has been proved to be more effective than hyper-sphere-shaped clustering algorithm in T-S fuzzy model identification. Therefore the FCRM clustering algorithm is used in T-S fuzzy model identification for structure identification in the antecedent part. A mass of relevant researches have pointed out that the L1-norm loss function is more robust to outliers and noises than L2-norm loss function. In order to reduce the negative influence of outliers and noises, the L1-norm loss function is employed to enhance the robustness of T-S fuzzy model instead of the L2-norm loss function in the consequent part. Regression and classification applications have been used to demonstrate the validity of the proposed method. The experimental results show that the proposed method has significantly improved the modelling accuracy in dealing with data contaminated by outliers and noises compared with other algorithms.

Parameters identification and discharge capacity prediction of Nickel–Metal Hydride battery based on modified fuzzy c-regression models

The battery in the electric vehicles provides the electrical energy necessary to power all electrical and electronic components and main-drive electric motor. So, an accurate estimation of discharge capacity to predict the battery’s end of life is of paramount importance and critical for safe and efficient energy utilization, especially for battery management systems. The resistor–capacitor (RC) equivalent circuit model is commonly used in the literature to model battery. However, a battery is a chemical energy storage system, and then the RC model will therefore be extremely sensitive to the presence of vagueness of information due to that some parameters cannot be directly accessed using sensors. In this paper, we propose a new design methodology for estimating simultaneously the model and the discharge capacity of a Nickel–Metal Hydride (Ni–MH) battery. A modified fuzzy c-regression model algorithm is used to construct a prediction model for a small Ni–MH battery pack. Then, the model, so developed, is used to estimate the discharge capacity of the battery and to predict its remaining useful life. The validity of the proposed method is experimentally verified. According to experimental results, the proposed method can achieve satisfactory results with no more than a 2% error rate for the training and test data sets.

Adaptive Inverse Controller Design Based on the Fuzzy C-Regression Model (FCRM) and Back Propagation (BP) Algorithm

Establishing an accurate inverse model is a key problem in the design of adaptive inverse controllers. Most real objects have nonlinear characteristics, so mathematical expression of an inverse model cannot be obtained in most situation. A Takagi–Sugeno(T-S)fuzzy model can approximate real objects with high precision, and is often applied in the modeling of nonlinear systems. Since the consequent parameters of T-S fuzzy models are linear expressions, this paper firstly uses a fuzzy c-regression model (FCRM) clustering algorithm to establish inverse fuzzy model. As the least mean square (LMS) algorithm is only used to adjust consequent parameters of the T-S fuzzy model in the process of parameter adjustment, the premise parameters are fixed and unchanged in the process of adjustment. In this paper, the back propagation (BP) algorithm is applied to adjust the premise and consequent parameters of the T-S fuzzy model, simultaneously online. The simulation results show that the error between the system output controlled by proposed adaptive inverse controller and the desired output is smaller, also the system stability can be maintained when the system output has disturbances.

Modeling and state of health estimation of nickel–metal hydride battery using an EPSO-based fuzzy c-regression model

The prognostic and health management of the batteries continued to attract interest from automobile manufacturers as the key for lowering life-cycle costs, reducing unexpected power outages, and one of the most important and efficient ways for energy storage for electric vehicle applications. Indeed, an effective battery health monitoring depends on accurate estimation of state of health (SOH). However, the SOH cannot be directly measured by sensors in the battery management system. Moreover, the SOH estimation based on a standard resistor–capacitor (RC) battery model is not so accurate because a RC model is obtained with some approximations and without taking into account more detailed knowledge about the chemical reactions happening inside the battery. In this paper, a combined battery modeling and SOH estimation method over the lifespan of a nickel–metal hydride (Ni–MH) battery is proposed. First, a fuzzy c-regression model based on Euclidean particle swarm optimization is applied to modeling a Ni–MH battery. Second, the SOH monitoring is determined according to the discharge rate of the battery model. The performance of the proposed method has been analyzed through the modeling and the estimation of the SOH using a real data set of the Ni–MH battery.

Kernel Fuzzy c-Regression Based on Least Absolute Deviation with Modified Huber Function

The fuzzy c-regression models are useful for datasets with various correlations. To deal with nonlinear datasets, a kernel fuzzy c-regression (KFCR) method was previously proposed. However, this method is weak for outliers because its objective function is based on the least square principle. We introduce the least absolute deviation (LAD) method with a modified Huber function into the KFCR (LAD-KFCR) to overcome the abovementioned problem. We verify the usefulness of the proposed LAD-KFCR method through numerical examples.

A novel recursive T-S fuzzy semantic modeling approach for discrete state-space systems

In this paper, we propose a novel recursive Takagi-Sugeno (T-S) fuzzy semantic modeling approach for discrete state-space system. According to the information learning theoretic (ILT), the correntropy can capture the higher moments of the error probability distribution to deal with non-Gaussian noise. Considering the advantages of fuzzy theory and correntropy, fuzzy correntropy is constructed and a novel kernel fuzzy C-regression model clustering based on fuzzy correntropy is proposed to solve the premise parameter identification problem of the T-S fuzzy model. To the identification of the consequent part parameters of the T-S fuzzy model, a modified extended forgetting factor recursive least squares (MEFRLS) estimator is presented. Moreover, to evaluate the performance of the proposed fuzzy model, the proposed T-S fuzzy model is applied to solve the problem of maneuvering target tracking by incorporating the target feature semantic information. Finally, the experiment results show the proposed algorithm can effectively track a maneuvering target, and its performance is better than the exist algorithms, such as interacting multiple model Kalman filter (IMMKF), interacting multiple model unscented Kalman filter (IMMUKF), the interacting multiple model particle filter (IMMPF) and interacting multiple model Rao-Blackwellized particle filter the (IMMRBPF).

Design of a robust interval-valued type-2 fuzzy c-regression model for a nonlinear system with noise and outliers

This paper presents the development of a novel interval-valued type-2 robust fuzzy c-regression model (IVT2RFCRM) clustering algorithm for identification of nonlinear systems taking into account the presence of noise and outliers in the associated dataset. On the one hand, the proposed method allows for the handling of the uncertainties of the FCRM due to its fixed fuzzier parameter m. In the other hand, the dataset is subject to various sources of uncertainty such as measurement uncertainty, fuzziness of information and environmental noise. As a result, obtaining a high-quality approximation of real processes is often a difficult task. In this paper, the structure of the proposed clustering algorithm is given and its parameter update rule is derived. First, the modified objective functions use a kernel measure of error to deal with the noisy data. Then, a credibility function is integrated into the clustering process in order to reduce the effect of outliers. Finally, the effectiveness of the proposed algorithm is evaluated by comparing the obtained results with others reported in the literature and also through the simulation results of a real liquid level process.

A T–S Fuzzy Model Identification Approach Based on a Modified Inter Type-2 FRCM Algorithm

Hyper-plane-shaped clustering (HPSC) has been demonstrated to be more effective in Takagi–Sugeno (T–S) fuzzy model identification compared to hyper-sphere-shaped clustering. Although some HPSC algorithms, based on type-2 fuzzy theory, have already been developed and have been demonstrated to have outstanding performance in T–S fuzzy modeling, mismatching of the traditional hyper-sphere-shaped membership function and HPSC results will inevitably restrict the modeling performance. In this paper, a modified inter type-2 fuzzy c-regression model (IT2-FCRM) clustering and new hyper-plane-shaped Gaussian membership function were proposed for T–S fuzzy modeling. In the proposed approach, the coefficients of the upper and lower hyperplanes were deduced based on an IT2-FCRM algorithm. Then, a hyper-plane-shaped membership function was directly defined using the hyperplanes to identify the antecedent parameters of the T–S fuzzy model. The experimental results of several benchmark problems show that identification of T–S model accuracy was greatly promoted.

A New Fuzzy Time Series Model Based on Fuzzy C-Regression Model

This study proposes a new fuzzy time series model based on Fuzzy C-Regression Model clustering algorithm (FCRMF). There are two major superiorities of FCRMF in comparison with existing fuzzy time series model based on fuzzy clustering. The first one is that FCRMF partitions data set by taking into account the relationship between the classical time series and lagged values, and thus, it gives the more realistic clustering results. The second one is that FCRMF produces different forecasting values for each data point, while the other fuzzy time series methods produce same forecasting values for many data points. In order to validate the forecasting performance of proposed method and compare it to the other fuzzy time series methods based on fuzzy clustering, six simulation studies and two real-time examples are carried out. According to goodness-of-fit measures, it is observed that FCRMF provides the best forecasting results, especially in cases when time series are not stationary. When considering that fuzzy time series was proposed especially for cases that time series do not satisfy statistical assumptions such as the stationary, this is very important advantage.