Online identification of evolving Takagi–Sugeno–Kang fuzzy models for crane systems

This paper suggests new evolving Takagi–Sugeno–Kang (TSK) fuzzy models dedicated to crane systems. A set of evolving TSK fuzzy models with different numbers of inputs are derived by the novel relatively simple and transparent implementation of an online identification algorithm. An input selection algorithm to guide modeling is proposed on the basis of ranking the inputs according to their important factors after the first step of the online identification algorithm. The online identification algorithm offers rule bases and parameters which continuously evolve by adding new rules with more summarization power and by modifying existing rules and parameters. The potentials of new data points are used with this regard. The algorithm is applied in the framework of the pendulum–crane system laboratory equipment. The evolving TSK fuzzy models are tested against the experimental data and a comparison with other TSK fuzzy models and modeling approaches is carried out. The comparison points out that the proposed evolving TSK fuzzy models are simple and consistent with both training data and testing data and that these models outperform other TSK fuzzy models.     

Hybrid robust approach for TSK fuzzy modeling with outliers

This study proposes a hybrid robust approach for constructing Takagi–Sugeno–Kang (TSK) fuzzy models with outliers. The approach consists of a robust fuzzy C-regression model (RFCRM) clustering algorithm in the coarse-tuning phase and an annealing robust back-propagation (ARBP) learning algorithm in the fine-tuning phase. The RFCRM clustering algorithm is modified from the fuzzy C-regression models (FCRM) clustering algorithm by incorporating a robust mechanism and considering input data distribution and robust similarity measure into the FCRM clustering algorithm. Due to the use of robust mechanisms and the consideration of input data distribution, the fuzzy subspaces and the parameters of functions in the consequent parts are simultaneously identified by the proposed RFCRM clustering algorithm and the obtained model will not be significantly affected by outliers. Furthermore, the robust similarity measure is used in the clustering process to reduce the redundant clusters. Consequently, the RFCRM clustering algorithm can generate a better initialization for the TSK fuzzy models in the coarse-tuning phase. Then, an ARBP algorithm is employed to obtain a more precise model in the fine-tuning phase. From our simulation results, it is clearly evident that the proposed robust TSK fuzzy model approach is superior to existing approaches in learning speed and in approximation accuracy.     

任务间共享和特有结构分解的多任务TSK模糊系统建模

现有的多任务Takagi-Sugeno-Kang (TSK) 模糊建模方法更注重利用任务间的相关性信息,而忽略了单个任务的特殊性。针对此问题,本文提出了一种考虑所有任务之间的共享结构和特有结构的TSK模糊系统多任务建模新方法。该方法将后件参数分解为共享参数和特有参数两个分量,既充分利用了任务间共享信息,又有效地保留了单个任务的特性。最后,本文利用增广拉格朗日乘子法(ALM)求解该最优化问题。实验结果表明,该方法比现有的模型获得了更好的表现。     

Identification of Lags in Nonlinear Autoregressive Time Series Using a Flexible Fuzzy Model

This work proposes a method to find the set of the most influential lags and the rule structure of a Takagi–Sugeno–Kang (TSK) fuzzy model for time series applications. The proposed method resembles the techniques that prioritize lags, evaluating the proximity of nearby samples in the input space using the closeness of the corresponding target values. Clusters of samples are generated, and the consistency of the mapping between the predicted variable and the set of candidate past values is evaluated. A TSK model is established, and possible redundancies in the rule base are avoided. The proposed method is evaluated using simulated and real data. Several simulation experiments were conducted for five synthetic nonlinear autoregressive processes, two nonlinear vector autoregressive processes and eight benchmark time series. The results show a competitive performance in the mean square error and a promising ability to find a proper set of lags for a given autoregressive process.     

竞争式Takagi-Sugeno模糊再励学习

针对连续空间的复杂学习任务,提出了一种竞争式Takagi-Sugeno模糊再励学习网络 (CTSFRLN),该网络结构集成了Takagi-Sugeno模糊推理系统和基于动作的评价值函数的再 励学习方法.文中相应提出了两种学习算法,即竞争式Takagi-Sugeno模糊Q-学习算法和竞争 式Takagi-Sugeno模糊优胜学习算法,其把CTSFRLN训练成为一种所谓的Takagi-Sugeno模 糊变结构控制器.以二级倒立摆控制系统为例,仿真研究表明所提出的学习算法在性能上优于 其它的再励学习算法.     

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.     

Chaotic time series prediction via artificial neural square fuzzy inference system

The present article investigates the application of second order TSK (Takagi Sugeno Kang) fuzzy systems in predicting chaotic time series. A method has been introduced for training second order TSK fuzzy systems using ANFIS (Artificial Neural Fuzzy Inference System) training method. In a second order TSK system existence of nonlinear terms in the rules’ consequence prohibits use of current available ANFIS codes as is but the proposed method makes it possible to use ANFIS for a class of simplified second order TSK systems. The main impact of this method on the expert and intelligent systems is to provide a new way for modeling and predicting the future situation of more complex phenomena with a smaller decision rule base. The most significance of the proposed method is the simplicity and available code reuse property. As a case study the proposed method is used for the prediction of chaotic time series. Error comparison shows that the proposed method trains the second order TSK system more effectively.     

Relaxed fuzzy control synthesis of nonlinear networked systems under unreliable communication links

This paper proposes relaxed conditions for control synthesis of discrete-time Takagi–Sugeno fuzzy control systems under unreliable communication links. To widen the applicability of the fuzzy control approach under network environments, a novel fuzzy controller, which is homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the multi-steps-past normalized fuzzy weighting functions, is provided to make much more use of the information of the underlying system. Moreover, a new kind of slack variable approach is also developed and thus the algebraic properties of these multi-instant normalized fuzzy weighting functions are collected into some augmented matrices. As a result, the conservatism of control synthesis of discrete-time Takagi–Sugeno fuzzy control systems under unreliable communication links can be significantly reduced. Two illustrative examples are presented to demonstrate the effectiveness of the theoretical development.     

Improving the interpretability of TSK fuzzy models by combiningglobal learning and local learning

The fuzzy inference system proposed by Takagi, Sugeno, and Kang, known as the TSK model in fuzzy system literature, provides a powerful tool for modeling complex nonlinear systems. Unlike conventional modeling where a single model is used to describe the global behavior of a system, TSK modeling is essentially a multimodel approach in which simple submodels (typically linear models) are combined to describe the global behavior of the system. Most existing learning algorithms for identifying the TSK model are based on minimizing the square of the residual between the overall outputs of the real system and the identified model. Although these algorithms can generate a TSK model with good global performance (i.e., the model is capable of approximating the given system with arbitrary accuracy, provided that sufficient rules are used and sufficient training data are available), they cannot guarantee the resulting model to have a good local performance. Often, the submodels in the TSK model may exhibit an erratic local behavior, which is difficult to interpret. Since one of the important motivations of using the TSK model (also other fuzzy models) is to gain insights into the model, it is important to investigate the interpretability issue of the TSK model. We propose a new learning algorithm that integrates global learning and local learning in a single algorithmic framework. This algorithm uses the idea of local weighed regression and local approximation in nonparametric statistics, but remains the component of global fitting in the existing learning algorithms. The algorithm is capable of adjusting its parameters based on the user's preference, generating models with good tradeoff in terms of global fitting and local interpretation. We illustrate the performance of the proposed algorithm using a motorcycle crash modeling example     

Supervision of nonlinear adaptive controllers based on fuzzy models

A novel approach for the supervision of fuzzy model on-line adaptation is proposed. A nonlinear predictive controller is designed based on a Takagi–Sugeno fuzzy model. By adapting the fuzzy model on-line, high control performance can be achieved even with time-variant process behaviour and changing unmodelled disturbances. A local weighted recursive least-squares algorithm exploits the local linearity of Takagi–Sugeno fuzzy models. In order to cope with problems resulting from insufficient excitation, a supervisory level is introduced. It comprises a variable forgetting factor and an additional adaptation model which makes the on-line adaptation robust and reliable. The effectiveness and real-world applicability of the proposed approach are demonstrated by application to temperature control of a heat exchanger.     

Differences between t‐norms in fuzzy control

The application of conjunctive aggregation functions in fuzzy control systems with n inputs is discussed, and the effect of the choice of a continuous t‐norm in the inference phase for Takagi–Sugeno–Kang (TSK) systems is computed. A continuous t‐norm modeling AND connective in antecedent part of fuzzy rules can be reduced just to strict or nilpotent t‐norm. The isomorphism of strict (nilpotent) t‐norms enables simpler fitting of TSK fuzzy system parameters and reduces the computational complexity. Similar principle can also be used in the case of some noncommutative conjunctive aggregation functions modeling AND connective. The effect of the choice of a continuous t‐norm is then evaluated on well‐known case studies in fuzzy control, the Sinc function, and the urban traffic noise control system.     

A class of type-2 fuzzy neural networks for nonlinear dynamical system identification

This paper presents the ability of the interval type-2 Takagi–Sugeno–Kang fuzzy neural networks (IT2-TSK-FNN) for nonlinear dynamical system identification. The proposed IT2-TSK-FNN has seven layers. The first two layers consist of type-2 fuzzy neurons with uncertainty in the mean of Gaussian membership functions. Third layer is rule layer. Type-reduction is done in fourth layer. In the fifth, sixth, and seventh layers, consequent left–right firing points, two end points, and output are evaluated, respectively. In this paper, gradient descent with adaptive learning rate backpropagation is used in learning phase. IT2-TSK-FNN is used for the identification of three nonlinear systems, and then results are compared with adaptive-network-based fuzzy inference system (ANFIS).     

An evolving recurrent interval type-2 intuitionistic fuzzy neural network for online learning and time series prediction

The prediction of time series has both the theoretical value and practical significance in reality. However, since the high nonlinear and noises in the time series, it is still an open problem to tackle with the uncertainties and fuzziness in the forecasting process. In this article, an evolving recurrent interval type-2 intuitionistic fuzzy neural network (eRIT2IFNN) is proposed for time series prediction and regression problems. The eRIT2IFNN employs interval type-2 intuitionistic fuzzy sets to enhance the modeling of uncertainties by intuitionistic evaluation and noise tolerance of the system. In the eRIT2IFNN, the antecedent part of each fuzzy rule is defined using intuitionistic interval type-2 fuzzy sets, and the consequent realizes the Takagi–Sugeno–Kang type fuzzy inference mechanism. In order to utilize the prior knowledge including intuitionistic information, a local internal feedback is established by feeding the rule firing strength of each rule to itself eRIT2IFNN is fully adaptive to the evolving of sequence data by online learning of structure and parameters. A modified density-based clustering is implemented for the structure learning, where both densities and membership degrees are involved to determine the fuzzy rules. Performance of eRIT2IFNN is evaluated using a set of benchmark problems and compared with existing fuzzy inference systems. Moreover, the eRIT2IFNN is tested for identification of dynamics under both noise-free and noisy environments. Finally, a group of practical financial price-tracking problems including high-frequency data of financial future, commodity future and precious metal are used for the evaluation of the proposed inference system.     

Evolving Takagi–Sugeno fuzzy model based on switching to neighboring models

In this paper, we propose a new online identification approach for evolving Takagi–Sugeno (TS) fuzzy models. Here, for a TS model, a certain number of models as neighboring models are defined and then the TS model switches to one of them at each stage of evolving. We define neighboring models for an in-progress (current) TS model as its fairly evolved versions, which are different with it just in two fuzzy rules. To generate neighboring models for the current model, we apply specially designed split and merge operations. By each split operation, a fuzzy rule is replaced with two rules; while by each merge operation, two fuzzy rules combine to one rule. Among neighboring models, the one with the minimum sum of squared errors – on certain time intervals – replaces the current model.To reduce the computational load of the proposed evolving TS model, straightforward relations between outputs of neighboring models and that of current model are established. Also, to reduce the number of rules, we define and use first-order TS fuzzy models whose generated local linear models can be localized in flexible fuzzy subspaces. To demonstrate the improved performance of the proposed identification approach, the efficiency of the evolving TS model is studied in prediction of monthly sunspot number and forecast of daily electrical power consumption. The prediction and modeling results are compared with that of some important existing evolving fuzzy systems.     

Incremental modeling with rough and fine tuning method

In this paper, we propose a new learning approach for designing an incremental model that has a cascade learning structure combined with a rough and fine tuning method for the learning scheme. Recently, various fuzzy logic-based modeling methods, with fuzzy if-then type rules, have been proposed in an attempt to obtain good approximations and generalization performances. In contrast to these various modeling methods, the new proposed incremental modeling scheme presented here is combined with a rough and fine tuning scheme, to learn and construct the best architecture for the model. A compensation idea is introduced in the fine tuning stage to solve the over-fitting problem caused from testing data. For this purpose, a construct of an extreme learning machine (ELM) is used as a global model, and this is compensated through a conditional fuzzy C-means (CFCM)-based fuzzy inference system (FIS) with a Takagi–Sugeno–Kang (TSK)-type method, which captures the remaining localized nonlinearities of the model. The experimental results, obtained by the proposed model have proved to show better performances in comparison with previous works.     

Data-based multiple-model prediction of the production rate for hematite ore beneficiation process

The prediction of the production rate of the hematite ore beneficiation process is important to plant-wide optimization. This paper presents a data-based multi-model approach to predict the production rate with multiple operating modes. The inputs of the predictive model are the performance indices of each unit process, and the output is the global production index (the production rate) of the hematite ore beneficiation process. The multiple models are developed by integrating the fuzzy clustering algorithm and machine learning algorithm. A global model, Takagi–Sugeno–Kang fuzzy model, and multiple neural network model were compared using the data obtained from a practical industrial process, and the effectiveness of the proposed algorithm was proven.     

Efficient stock price prediction using a Self Evolving Recurrent Neuro-Fuzzy Inference System optimized through a Modified Differential Harmony Search Technique

This paper proposes a new Self Evolving Recurrent Neuro-Fuzzy Inference System (SERNFIS) for efficient prediction of highly fluctuating and irregular financial time series data like stock market indices over varying time frames. The network is modeled including the first order Takagi Sugeno Kang (TSK) type fuzzy if then rules with two types of feedback loops. The recurrent structure in the proposed model comes from locally feeding the firing strength of the fuzzy rule back to itself and by including a few time delay components at the output layer. The novelty of the model is based on the fact that the internal temporal feedback loops and time delayed output feedback loops are used for further enhancing the prediction capability of traditional neuro-fuzzy system in handling more dynamic financial time series data. Another recurrent functional link artificial neural network (RCEFLANN) model is also presented for a comparative study. In the second part of the paper a modified differential harmony search (MDHS) technique is proposed for estimating the parameters of the model including the antecedent, consequent and feedback loop parameters. Experimental results obtained by implementing the model on two different stock market indices demonstrate the effectiveness of the proposed model compared to existing models for stock price prediction.     

Local and global optimization for Takagi–Sugeno fuzzy system by memetic genetic programming

This work presents a method to incorporate standard neuro-fuzzy learning for Takagi–Sugeno fuzzy systems that evolve under a grammar driven genetic programming (GP) framework. This is made possible by introducing heteroglossia in the functional GP nodes, enabling them to switch behavior according to the selected learning stage. A context-free grammar supports the expression of arbitrarily sized and composed fuzzy systems and guides the evolution. Recursive least squares and backpropagation gradient descent algorithms are used as local search methods. A second generation memetic approach combines the genetic programming with the local search procedures. Based on our experimental results, a discussion is included regarding the competitiveness of the proposed methodology and its properties. The contributions of the paper are: (i) introduction of an approach which enables the application of local search learning for intelligent systems evolved by genetic programming, (ii) presentation of a model for memetic learning of Takagi–Sugeno fuzzy systems, (iii) experimental results evaluating model variants and comparison with state-of-the-art models in benchmarking and real-world problems, (iv) application of the proposed model in control.     

ReNFFor: a recurrent neurofuzzy forecaster for telecommunications data

In this work, a dynamic neurofuzzy system for forecasting outgoing telephone calls in a University Campus is proposed. The system comprises modified Takagi–Sugeno–Kang fuzzy rules, where the rules’ consequent parts are small neural networks with unit internal recurrence. The characteristics of the proposed forecaster, which is entitled recurrent neurofuzzy forecaster, are depicted via a comparative analysis with a series of well-known forecasting models.     

Local identification of prototypes for genetic learning of accurate TSK fuzzy rule‐based systems

This work presents the use of local fuzzy prototypes as a new idea to obtain accurate local semantics‐based Takagi–Sugeno–Kang (TSK) rules. This allow us to start from prototypes considering the interaction between input and output variables and taking into account the fuzzy nature of the TSK rules. To do so, a two‐stage evolutionary algorithm based on MOGUL (a methodology to obtain Genetic Fuzzy Rule‐Based Systems under the Iterative Rule Learning approach) has been developed to consider the interaction between input and output variables. The first stage performs a local identification of prototypes to obtain a set of initial local semantics‐based TSK rules, following the Iterative Rule Learning approach and based on an evolutionary generation process within MOGUL (taking as a base some initial linguistic fuzzy partitions). Because this generation method induces competition among the fuzzy rules, a postprocessing stage to improve the global system performance is needed. Two different processes are considered at this stage, a genetic niching‐based selection process to remove redundant rules and a genetic tuning process to refine the fuzzy model parameters. The proposal has been tested with two real‐world problems, achieving good results. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 909–941, 2007.