Hydraulic turbine governing system identification using T–S fuzzy model optimized by chaotic gravitational search algorithm

Hydraulic 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.     

Enhanced Fuzzy System Models With Improved Fuzzy Clustering Algorithm

Although traditional fuzzy models have proven to have high capacity of approximating the real-world systems, they have some challenges, such as computational complexity, optimization problems, subjectivity, etc. In order to solve some of these problems, this paper proposes a new fuzzy system modeling approach based on improved fuzzy functions to model systems with continuous output variable. The new modeling approach introduces three features: i) an improved fuzzy clustering (IFC) algorithm, ii) a new structure identification algorithm, and iii) a nonparametric inference engine. The IFC algorithm yields simultaneous estimates of parameters of c-regression models, together with fuzzy c-partitioning of the data, to calculate improved membership values with a new membership function. The structure identification of the new approach utilizes IFC, instead of standard fuzzy c-means clustering algorithm, to fuzzy partition the data, and it uses improved membership values as additional input variables along with the original scalar input variables for two different choices of regression methods: least squares estimation or support vector regression, to determine ldquofuzzy functionsrdquo for each cluster. With novel IFC, one could learn the system behavior more accurately compared to other FSM models. The nonparametric inference engine is a new approach, which uses the alike -nearest neighbor method for reasoning. Empirical comparisons indicate that the proposed approach yields comparable or better accuracy than fuzzy or neuro-fuzzy models based on fuzzy rules bases, as well as other soft computing methods.     

CLUSTERED BASED TAKAGI‐SUGENO NEURO‐FUZZY MODELING OF A MULTIVARIABLE NONLINEAR DYNAMIC SYSTEM

This research frame work investigates the application of a clustered based Neuro‐fuzzy system to nonlinear dynamic system modeling from a set of input‐output training patterns. It is concentrated on the modeling via Takagi‐Sugeno (T‐S) modeling technique and the employment of fuzzy clustering to generate suitable initial membership functions. Hence, such created initial memberships are then employed to construct suitable T‐S sub‐models. Furthermore, the T‐S fuzzy models have been validated and checked through the use of some standard model validation techniques (like the correlation functions). Compared to other well‐known approximation techniques such as artificial neural networks, fuzzy systems provide a more transparent representation of the system under study, which is mainly due to the possible linguistic interpretation in the form of rules. Such intelligent modeling scheme is very useful once making complicated systems linguistically transparent in terms of fuzzy if‐then rules. The developed T‐S Fuzzy modeling system has been then applied to model a nonlinear antenna dynamic system with two coupled inputs and outputs. Validation results have resulted in a very close antenna sub‐models of the original nonlinear antenna system. The suggested technique is very useful for development transparent linear control systems even for highly nonlinear dynamic systems.     

Structure and stability analysis of general Mamdani fuzzy dynamic models

Mamdani fuzzy models have always been used as black‐box models. Their structures in relation to the conventional model structures are unknown. Moreover, there exist no theoretical methods for rigorously judging model stability and validity. I attempt to provide solutions to these issues for a general class of fuzzy models. They use arbitrary continuous input fuzzy sets, arbitrary fuzzy rules, arbitrary inference methods, Zadeh or product fuzzy logic AND operator, singleton output fuzzy sets, and the centroid defuzzifier. I first show that the fuzzy models belong to the NARX (nonlinear autoregressive with the extra input) model structure, which is one of the most important and widely used structures in classical modeling. I then divide the NARX model structure into three nonlinear types and investigate how the settings of the fuzzy model components, especially input fuzzy sets, dictate the relations between the fuzzy models and these types. I have found that the fuzzy models become type‐2 models if and only if the input fuzzy sets are linear or piecewise linear (e.g., trapezoidal or triangular), becoming type 3 if and only if at least one input fuzzy set is nonlinear. I have also developed an algorithm to transfer type‐2 fuzzy models into type‐1 models as far as their input–output relationships are concerned, which have some important properties not shared by the type‐2 models. Furthermore, a necessary and sufficient condition has been derived for a part of the general fuzzy models to be linear ARX models. I have established a necessary and sufficient condition for judging local stability of type‐1 and type‐2 fuzzy models. It can be used for model validation and control system design. Three numeric examples are provided. Our new findings provide a theoretical foundation for Mamdani fuzzy modeling and make it more consistent with the conventional modeling theory. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 103–125, 2005.     

A structure identification method of submodels for hierarchical fuzzy modeling using the multiple objective genetic algorithm

Fuzzy models describe nonlinear input‐output relationships with linguistic fuzzy rules. A hierarchical fuzzy modeling is promising for identification of fuzzy models of target systems that have many input variables. In the identification, (1) determination of a hierarchical structure of submodels, (2) selection of input variables of each submodel, (3) division of input and output space, (4) tuning of membership functions, and (5) determination of fuzzy inference method are carried out. This article presents a hierarchical fuzzy modeling method with an uneven division method of input space of each submodel. For selecting input variables of submodels, the multiple objective genetic algorithm (MOGA) is utilized. MOGA finds multiple models with different input variables and different numbers of fuzzy rules as compromising solutions. A human designer can choose desirable ones from these candidates. The proposed method is applied to acquisition of fuzzy rules from cyclists' pedaling data. In spite of a small number of data, the obtained model was able to give detailed suggestions to each cyclist. © 2002 Wiley Periodicals, Inc.     

Experiences of system identification applied to ship steering

Different system identification methods have been applied to determine ship steering dynamics from full-scale experiments. The techniques used include output error, maximum likelihood and more general prediction error methods. Different model structures have been investigated ranging from input-output models in difference equation form to the equations of motion in their natural form. Effects of disturbances, errors and dynamics in sensors and actuators have been considered. Programs for interactive system identification have been used extensively. The experiments have been performed both under open loop and closed loop conditions. Both linear and nonlinear models have been considered. The paper summarizes the experiences obtained from applying system identification methods to many different ships. The results have been applied both to investigate steering properties and to design autopilots for ship steering. Insight into ship steering dynamics and identification methodology has been obtained.     

Identification of nonlinear systems by Takagi–Sugeno fuzzy logic grey box modeling for real-time control

Identification of nonlinear systems by fuzzy models has been successfully applied in many applications. Fuzzy models are capable of approximating any real continuous function to a chosen accuracy. An algorithm for real-time identification of nonlinear systems using Takagi–Sugeno's fuzzy models is presented in this paper. A Takagi–Sugeno fuzzy system is trained incrementally each time step and is used to predict one-step ahead system output. Ability of the proposed identifier to capture the nonlinear behavior of a synchronous machine is illustrated. Effectiveness of the proposed identification technique is demonstrated by simulation and experimental studies on a power system.     

Nonlinear system identification of large-scale smart pavement systems

This paper proposes a novel model for predicting complex behavior of smart pavements under a variety of environmental conditions. The mathematical model is developed through an adaptive neuro fuzzy inference system (ANFIS). To evaluate the effectiveness of the ANFIS model, the temperature fluctuations at different locations in smart pavement systems equipped with pipe network systems under solar radiations is investigated. To develop the smart pavement ANFIS model, various sets of input and output field experimental data are collected from large-scale experimental test beds. The solar radiation and the inlet water flow are used as input signals for training complex behavior of the smart pavement ANFIS model, while the temperature fluctuation of the smart pavement system is used for the output signal. The trained model is validated using 20 different data sets that are not used for the training process. It is demonstrated from the simulation that the ANFIS identification approach is effective in modeling complex behavior of the pavement–fluid system under a variety of environmental conditions. Comparison with high fidelity data proves the viability of the proposed approach in pavement health monitoring setting, as well as automatic control systems.     

催化裂化过程稳态优化控制研究

催化裂化装置是一个高度非线性、时变、长时延、强耦合、分布参数和不确定性的复杂 系统.在研究其过程机理的基础上,定义了一种模糊神经网络用以建模,用自相关函数检验法检 验模型的正确性,再用改进的Frank-Wolfe算法进行稳态优化计算,并以一炼油厂催化裂化装 置为对象进行试验,研究其辨识、建模和稳态优化控制.这种模糊神经网络具有隐层数多、隐层 结点数多、泛化能力和逼近能力强、收敛速度快的优点,更突出的特点还在于可由输出端对输入 求导,为稳态优化计算提供了极大方便,它与改进的Frank-Wolfe算法相结合用于解决非线性 复杂生产过程的建模和稳态优化控制问题是可行的.     

Multiscale fuzzy system identification

One of the biggest challenges in constructing empirical models is the presence of measurement errors in the data. These errors (or noise) can have a drastic effect on the accuracy and prediction of estimated models, and thus need to be removed for improved models accuracy. Multiscale representation of data has shown great noise-removal ability when used in data filtering. In this paper, this advantage of multiscale representation is exploited to improve the accuracy of the nonlinear Takagi–Sugeno (TS) fuzzy models by developing a multiscale fuzzy (MSF) system identification algorithm. The developed algorithm relies on constructing multiple TS fuzzy models at multiple scales using the scaled signal approximations of the input–output data, and then selecting the optimum multiscale model that maximizes the signal-to-noise ratio of the model prediction. The developed algorithm is shown to outperform the time domain fuzzy model, NARMAX model, and fuzzy model estimated from pre-filtered data using an Exponentially weighted Moving Average (EWMA) filter through a simulated shell and tube heat exchanger modeling example. The reason for this improvement is that the developed MSF modeling algorithm improves the model accuracy by integrating modeling and data filtering using a filter bank, from which the optimum filter (for modeling purposes) is selected.     

一种基于T-S模型的快速自适应建模方法

在分析Takagi-Sugeno模型的网格法（即ANFIS方法），聚类法和模糊树法的基础上，提出一种新的改进的建模方法，它划分的空间的个数与分布和采样数据的特征密切相关，具有自适应能力。应用国际标准例题进行仿真，说明了该方法的有效性。     

Fuzzy modeling of high-dimensional systems: complexity reductionand interpretability improvement

Fuzzy modeling of high-dimensional systems is a challenging topic. This paper proposes an effective approach to data-based fuzzy modeling of high-dimensional systems. An initial fuzzy rule system is generated based on the conclusion that optimal fuzzy rules cover extrema. Redundant rules are removed based on a fuzzy similarity measure. Then, the structure and parameters of the fuzzy system are optimized using a genetic algorithm and the gradient method. During optimization, rules that have a very low firing strength are deleted. Finally, interpretability of the fuzzy system is improved by fine training the fuzzy rules with regularization. The resulting fuzzy system generated by this method has the following distinct features: (1) the fuzzy system is quite simplified; (2) the fuzzy system is interpretable; and (3) the dependencies between the inputs and the output are clearly shown. This method has successfully been applied to a system that has 11 inputs and one output with 20 000 training data and 80 000 test data     

Predictive human operator model to be utilized as a controller using linear,neuro-fuzzy and fuzzy-ARX modeling techniques

Modeling human operator's behavior as a controller in a closed-loop control system recently finds applications in areas such as training of inexperienced operators by expert operator's model or developing warning systems for drivers by observing the driver model parameter variations. In this research, first, an experimental setup has been developed for collecting data from human operators as they controlled a nonlinear system. Appropriate reference signals and scenarios were designed according to the system identification and human operator modeling theory, to collect data from subjects. Different modeling schemes, namely ARX models as linear approach, and adaptive-network-based fuzzy inference system (ANFIS) as intelligent modeling approach have been evaluated. A hybrid modeling method, fuzzy-ARX (F-ARX) model, has been developed and its performance was found to be better in terms of predicting human operator's control actions as well as replacing the operator as a stand-alone controller. It has been concluded that F-ARX models can be a good alternative for modeling the human operator.     

Recurrent neuro-fuzzy networks for nonlinear process modeling

A type of recurrent neuro-fuzzy network is proposed in this paper to build long-term prediction models for nonlinear processes. The process operation is partitioned into several fuzzy operating regions. Within each region, a local linear model is used to model the process. The global model output is obtained through the centre of gravity defuzzification which is essentially the interpolation of local model outputs. This modeling strategy utilizes both process knowledge and process input/output data. Process knowledge is used to initially divide the process operation into several fuzzy operating regions and to set up the initial fuzzification layer weights. Process I/O data are used to train the network. Network weights are such trained so that the long-term prediction errors are minimized. Through training, membership functions of fuzzy operating regions are refined and local models are learnt. Based on the recurrent neuro-fuzzy network model, a novel type of nonlinear model-based long range predictive controller can be developed and it consists of several local linear model-based predictive controllers. Local controllers are constructed based on the corresponding local linear models and their outputs are combined to form a global control action by using their membership functions. This control strategy has the advantage that control actions can be calculated analytically avoiding the time consuming nonlinear programming procedures required in conventional nonlinear model-based predictive control. The techniques have been successfully applied to the modeling and control of a neutralization process.     

Nonlinear modeling and adaptive fuzzy control of MCFC stack

To improve availability and performance of fuel cells, the operating temperature of molten carbonate fuel cells (MCFC) stack should be controlled within a specified range. However, the most existing models of MCFC are not ready to be applied in synthesis. In this paper, a radial basis function neural networks identification model of MCFC stack is developed based on the input–output sampled data. A novel adaptive fuzzy control procedure for the temperature of MCFC stack is also developed. The parameters of the fuzzy control system are regulated by back-propagation algorithm, and the rule database of the fuzzy system is also adaptively adjusted by the nearest-neighbor-clustering algorithm. Finally using the neural networks model of MCFC stack, the simulation results of the control algorithm are presented. The results show the effectiveness of the proposed modeling and design procedures for MCFC stack based on neural networks identification and the novel adaptive fuzzy control.     

C-R模糊模型在连续搅拌反应釜中的应用

针对化工生产过程中强非线性对象的动态建模问题,本文提出了具有代表性的连续搅拌反应釜的非机理模糊建模方法。从系统的输入输出数据出发,根据辨识精度将系统空间划分为个子空间,然后由隶属函数将子空间模型联接成全局模型来表征系统的整体非线性特性。仿真结果表明,该模型输出能够很好地跟踪系统的参考输出,效果明显。     

Deterministic approach to robust adaptive learning of fuzzy models

This study is concerned with the adaptive learning of an interpretable Sugeno-type fuzzy inference system, in a deterministic framework, in the presence of data uncertainties and modeling errors. The authors explore the use of H/sup /spl infin// estimation theory and least squares estimation for online learning of membership functions and consequent parameters without making any assumption and requiring a priori knowledge of upper bounds, statistics, and distribution of data uncertainties and modeling errors. The issues of data uncertainties, modeling errors, and time variations have been considered mathematically in a sensible way. The proposed robust approach to the adaptive learning of fuzzy models has been illustrated through the examples of adaptive system identification, time-series prediction, and estimation of an uncertain process.     

Fuzzy functions based ARX model and new fuzzy basis function models for nonlinear system identification

In this study, auto regressive with exogenous input (ARX) modeling is improved with fuzzy functions concept (FF-ARX). Fuzzy function with least squares estimation (FF-LSE) method has been recently developed and widely used with a small improvement with respect to least squares estimation method (LSE). FF-LSE is structured with only inputs and their membership values. This proposed model aims to increase the capability of the FF-LSE by widening the regression matrix with lagged input–output values. In addition, by using same idea, we proposed also two new fuzzy basis function models. In the first, basis of the fuzzy system and lagged input–output values are structured together in the regression matrix and named as “L-FBF”. Secondly, instead of using basis function, the membership values of the lagged input–output values are used in the regression matrix by using Gaussian membership functions, called “M-FBF”. Therefore, the power of the fuzzy basis function is also enhanced. For the corresponding models, antecedent part parameters for the input vectors are determined with fuzzy c-means (FCM) clustering algorithm. The consequent parameters of the all models are estimated with the LSE. The proposed models are utilized and compared for the identification of nonlinear benchmark problems.     

Neuro-fuzzy methods for nonlinear system identification

Most processes in industry are characterized by nonlinear and time-varying behavior. Nonlinear system identification is becoming an important tool which can be used to improve control performance and achieve robust fault-tolerant behavior. Among the different nonlinear identification techniques, methods based on neuro-fuzzy models are gradually becoming established not only in the academia but also in industrial applications. Neuro-fuzzy modeling can be regarded as a gray-box technique on the boundary between neural networks and qualitative fuzzy models. The tools for building neuro-fuzzy models are based on combinations of algorithms from the fields of neural networks, pattern recognition and regression analysis. In this paper, an overview of neuro-fuzzy modeling methods for nonlinear system identification is given, with an emphasis on the tradeoff between accuracy and interpretability.