Design Of Fuzzy System Research Articles

Intelligent modelling of continuous stirred tank reactor process

In this paper, we discuss the theory and design of the probabilistic fuzzy inference system, one that model and minimise the effects of rule uncertainties, i.e., existing randomness in many real world systems. This approach ascends from the combination of the concepts of degree of truth and probability of truth in a unique framework. This combination is carried out both in fuzzy sets and fuzzy rules, which leads to probabilistic fuzzy sets and probabilistic fuzzy rules. Using these probabilistic elements, an innovative probabilistic fuzzy logic system is obtained as a fuzzy probabilistic model of a complex non-deterministic system. We designed probabilistic fuzzy inference system for modelling the CSTR process, which shows dynamic nonlinearity and demonstrated its upgraded performance over the conventional fuzzy inference system.

Robust analysis and output feedback controller design of Takagi-Sugeno fuzzy systems via superstability conditions

The paper addresses an approach to the stability analysis and control design of continuoustime Takagi-Sugeno (T-S) fuzzy systems, based on the superstability conditions. The superstability conditions are the sufficient stability conditions, that are easy-to-use, because they are written as the restrictions on the elements of the matrices of linear subsystems of the T-S fuzzy model. Superstability is a useful property, allowing providing the given characteristics of the transient response. It is shown that the implementation of superstability conditions presents the general approach to the output superstabilization of the T-S fuzzy systems. Moreover the efficiency of superstability conditions for the robust analysis and stabilization of the T-S fuzzy systems with parametric uncertainties is exhibited below. An example of robust stabilization of the generalized chaotic system, shown in the work, proves the constructability of the offered approach.

A New Hybrid Modeling Method for Performance Digital Mock-Up of Hypersonic Vehicle

For the characteristics that a hypersonic vehicle has a large span of flight height and flight Mach number, and complicated flight environment, the model of which is highly nonlinear, unstable and multivariablecoupled, where using a single modelling approach is often difficult to achieve high modeling accuracy, hybrid modeling method is proposed to design its performance digital mock-up. The performance digital mock-up hybrid model are designed by using fuzzy set theory, neural networks and system identification method based on combination of the three fuzzy neural network identification method and technology. The simulation results show that high modeling accuracy of this modeling method is generally conventional neural network or fuzzy identification incomparable.

Subtractive Clustering Fuzzy Expert System for Engineering Applications

Abstract Performance of a fuzzy expert system is related with how good the membership functions are normalized, tuned for a problem statement and correlation of antecedents and consequents. This paper helps in tuning and designing the membership functions that are best suited for the problem statement by integrating subtractive clustering method for fuzzy expert system design. Subtractive clustering algorithm is used to generate the tuned membership functions automatically in accordance to the domain knowledge. The proposed integrated design of clustering based fuzzy expert system acts in improving the accuracy and leads to a precised decision making environment. A practical example for ageing assessment of transformer insulation oil has been included to illustrate the method much effectively; the discussed example has been validated practically in the laboratory and is found that the proposed method is efficient in decision making.

Research on RSSI–Based Localization System in the Wireless Sensor Network

Due to the rapid development in wireless sensor networks, the applications of the WSN have been extended to different environment and achieved a more diversified purpose. AS for the localization system, there are many related re- search achievements. A set of localization system is built through the system integration between the small-scale wireless hardware sensor and the wireless sensor platform, through the use of the RSSI and the integration of the fuzzy inference system. The blind nodes are experimented in the indoor environment so that the system's efficiency can be verified. The system is implemented in the 8 meters multiplying 8 meters indoor space which is divided into 16 sections. Then 4 anchor nodes are placed in the corners and the fuzzy identification system is built for the nodes' RSSI signal in the blocks. Later, the localization test is implemented in the random positions within the blocks. The experimental results show that the lo- calization system accuracy rate is more than 80% and can successfully reach the preliminary localization system.

Optimization of interval type-2 fuzzy systems for image edge detection

This paper presents the optimization of a fuzzy edge detector based on the traditional Sobel technique combined with interval type-2 fuzzy logic. The goal of using interval type-2 fuzzy logic in edge detection methods is to provide them with the ability to handle uncertainty in processing real world images. However, the optimal design of fuzzy systems is a difficult task and for this reason the use of meta-heuristic optimization techniques is also considered in this paper. For the optimization of the fuzzy inference systems, the Cuckoo Search (CS) and Genetic Algorithms (GAs) are applied. Simulation results show that using an optimal interval type-2 fuzzy system in conjunction with the Sobel technique provides a powerful edge detection method that outperforms its type-1 counterparts and the pure original Sobel technique.

Joint Block Structure Sparse Representation for Multi-Input–Multi-Output (MIMO) T–S Fuzzy System Identification

Takagi-Sugeno (T-S) fuzzy system identification provides a reasonable framework for modeling and approximation by decomposition of a nonlinear system into a collection of local linear models. In this paper, we extend the multidimensional output fuzzy rule from the corresponding single-output fuzzy rule with the important difference in the variable definition of output, namely the output of each fuzzy rule is represented by a multidimensional vector instead of a scalar value. In this case, the consequent of the fuzzy rule with the multidimensional output variable share a common antecedent part. Different from the traditional methods that separate the multi-input-multi-output fuzzy system into a group of multi-input-single-output fuzzy models, in this paper, we take into account the block structure information in the T-S fuzzy system and cast the problem of multidimensional output fuzzy model identification as a joint structure sparse optimization problem, where the consequent parameters are estimated with a common block structured sparsity pattern over all dimensions of the output variable. Furthermore, we exploit a joint block sparse orthogonal-match-pursuit algorithm to reduce the number of fuzzy rules in terms of all dimensions of the output variable and prove the sufficient conditions in consideration of the multidimensional output together with the block structure in the T-S fuzzy model. This method is efficient and shows good performance in well-known benchmark datasets and real-world problems.

Self-generated fuzzy systems design using artificial bee colony optimization

In this paper, artificial bee colony (ABC) optimization based methodology is proposed for automatically extracting Takagi–Sugeno (TS) fuzzy systems with enhanced performance from data. The design procedure aims to find the structures and the parameters of the TS fuzzy systems simultaneously without knowing the rule number as a priori. In the proposed method, a fuzzy system is encoded into a food source with appropriate string representation so that the TS model is entirely specified. The encoded premise and consequent parameters of the fuzzy model evolve together through artificial bee colony optimization strategy simulating the global foraging behavior of honey bee swarm so that good solutions can be achieved. Simulations on benchmark modeling and tracking control problems are performed and compared with other existing methods. The experimental results indicate that the proposed ABC optimization based fuzzy systems design algorithms can successfully find accurate fuzzy models with appropriate number of rules. Moreover, the proposed approach outperforms the compared methods and can provide considerable improvements in tackling complex modeling and tracking control problems.

Similarity in fuzzy systems

This paper proposes to study the concept of similarity and its use in the design of fuzzy system. The concept of similarity relation is effectively used in fuzzification of crisp values. Similarity index is used in measuring approximate (graded) equality of fuzzy sets over a given universe of discourse. It is proposed to use such an index in modifying a fuzzy relation. Different similarity measures in the literature are elucidated, and a comparative study between different pairs of fuzzy sets is presented. One of these similarity measures has been used successfully in rule selection and modification of a fuzzy relation. In the process, a number of modification schemes based on different logic have been extensively studied for different reasoning mechanisms based on the same data and results are tabulated. A specificity-based approach to defuzzification is also presented, which is found to be suitable for similarity-based fuzzy systems. The results are illustrated with the behaviour of a direct current (DC) shunt motor.

A new approach for online T-S fuzzy identification and model predictive control of nonlinear systems

This paper proposes a new unsupervised fuzzy clustering algorithm (NUFCA) to construct a novel online evolving Takagi–Sugeno (T-S) fuzzy model identification method and an adaptive predictive process control methodology. The proposed system identification approach consists of two main steps: antecedent T-S fuzzy model parameters identification and consequent parameters identification. The NUFCA combines the K-nearest neighbour and fuzzy C-means methods into a fuzzy modelling method for partitioning of the input–output data and identifying the antecedent parameters of the fuzzy system; then the recursive least squares method is exploited to obtain initialization type consequent parameters and to construct a method for on-line fuzzy model identification. The integration of the proposed adaptive identification method with the generalized predictive control results in an effective adaptive predictive fuzzy control methodology. For better demonstration of the robustness and efficiency of the proposed methodology, it is applied to the identification of a model for the estimation of the flour concentration in the effluent of a real-world wastewater treatment plant (WWTP); and to control a simulated continuous stirred tank reactor (CSTR), and a real experimental setup composed of two coupled DC motors. The results show that the developed evolving T-S fuzzy model methodology can identify nonlinear systems satisfactorily and can be successfully used for a prediction model of the process for the generalized predictive controller. It is also shown that the algorithm is robust to changes in the initial parameters, and to unexpected disturbances.

Rule-Based Cooperative Continuous Ant Colony Optimization to Improve the Accuracy of Fuzzy System Design

This paper proposes a cooperative continuous ant colony optimization (CCACO) algorithm and applies it to address the accuracy-oriented fuzzy systems (FSs) design problems. All of the free parameters in a zero- or first-order Takagi-Sugeno-Kang (TSK) FS are optimized through CCACO. The CCACO algorithm performs optimization through multiple ant colonies, where each ant colony is only responsible for optimizing the free parameters in a single fuzzy rule. The ant colonies cooperate to design a complete FS, with a complete parameter solution vector (encoding a complete FS) that is formed by selecting a subsolution component (encoding a single fuzzy rule) from each colony. Subsolutions in each ant colony are evolved independently using a new continuous ant colony optimization algorithm. In the CCACO, solutions are updated via the techniques of pheromone-based tournament ant path selection, ant wandering operation, and best-ant-attraction refinement. The performance of the CCACO is verified through applications to fuzzy controller and predictor design problems. Comparisons with other population-based optimization algorithms verify the superiority of the CCACO.

Identification of Nonlinear System Based on Fuzzy Model with Enhanced Gradient Search

Theidentification and modeling theory of nonlinear systems has always been challengingto researchers. Fuzzy system due to its languagedescriptive way similar to human brain and deal with qualitative informationintelligently proves better choice for nonlinear system modeling over last fewdecades. The fuzzy system theory itself also has nonlinear characteristics thereforewhen establishing the fuzzy model of nonlinear system; it should be able towell describe the nonlinear characteristics. Takagi-Sugeno (TS) fuzzy systemsare not only suitable for modeling the nonlinear system due to combination ofthe good performance with the simple linear expressions, but also useful todesign the fuzzy controller. This paper proposed a new optimization algorithm namedas Enhanced Gradient Search (EGS) for identification of nonlinear system basedon TS fuzzy system. In proposed EGS, parameters of membership functions aretrained adaptively so as to calculate the gradient of cost function which isnecessary for minimizing the error. Using gradient information of costfunction, EGS applies in an innovative way such that it keeps and updates thebest search results at every training step during the optimization process. Theapplicability of EGS for TS fuzzy model shows splendid performance especially inmodeling of nonlinear system.

Optimal fuzzy control system design for car-following behaviour based on the driver–vehicle unit online delays in a real traffic flow

Promoting safety and comfort in driving and reducing the traffic, the pollution and the energy consumption are the main purposes of using many control systems in different driving processes. Car following is the dominant and effective behaviour in traffic flow, the automatization of which is crucial to achieving the aforementioned goals. In this paper, a novel optimal fuzzy control system is designed so that the follower vehicle maintains a safe distance from the vehicle in front of it in a traffic queue with a reduction in the energy consumption. This controller is superior in that it considers the online delays in the reaction of the driver–vehicle unit in the design. The instantaneous delay is estimated using the stimulus–reaction idea based on a real car-following data set. Tuning the controller is achieved by using the linear quadratic regulator gains in the fuzzy scaling gains. Considering the reaction delay enables the controller to be used in an advanced driver assistance system to obtain simultaneously a higher degree of safety, greater energy saving and more freedom for the driver. Fewer errors and more optimality in the results demonstrated the better performance of the proposed control system in comparison with those of a real driver and other controllers.

Stable fuzzy logic control of a general class of chaotic systems

This paper proposes a new approach to the stable design of fuzzy logic control systems that deal with a general class of chaotic processes. The stable design is carried out on the basis of a stability analysis theorem, which employs Lyapunov's direct method and the separate stability analysis of each rule in the fuzzy logic controller (FLC). The stability analysis theorem offers sufficient conditions for the stability of a general class of chaotic processes controlled by Takagi---Sugeno---Kang FLCs. The approach suggested in this paper is advantageous because inserting a new rule requires the fulfillment of only one of the conditions of the stability analysis theorem. Two case studies concerning the fuzzy logic control of representative chaotic systems that belong to the general class of chaotic systems are included in order to illustrate our stable design approach. A set of simulation results is given to validate the theoretical results.

Automatic design of interpretable fuzzy predicate systems for clustering using self-organizing maps

In the area of pattern recognition, clustering algorithms are a family of unsupervised classifiers designed with the aim to discover unrevealed structures in the data. While this is a never ending research topic, many methods have been developed with good theoretical and practical properties. One of such methods is based on self organizing maps (SOM), which have been successfully used for data clustering, using a two levels clustering approach. Newer on the field, clustering systems based on fuzzy logic improve the performance of traditional approaches. In this paper we combine both approaches. Most of the previous works on fuzzy clustering are based on fuzzy inference systems, but we propose the design of a new clustering system in which we use predicate fuzzy logic to perform the clustering task, being automatically designed based on data. Given a datum, degrees of truth of fuzzy predicates associated with each cluster are computed using continuous membership functions defined over data features. The predicate with the maximum degree of truth determines the cluster to be assigned. Knowledge is discovered from data, obtained using the SOM generalization aptitude and taking advantage of the well-known SOM abilities to discover natural data grouping when compared with direct clustering. In addition, the proposed approach adds linguistic interpretability when membership functions are analyzed by a field expert. We also present how this approach can be used to deal with partitioned data. Results show that clustering accuracy obtained is high and it outperforms other methods in the majority of datasets tested.

Dynamic T‐S Fuzzy Systems Identification Based on Sparse Regularization

AbstractFuzzy system identification suffers from rules explosion, i.e., a large number of fuzzy rules are required for fuzzy systems with high dimension input variable. In this paper, a dynamic algorithm is proposed to address T‐S fuzzy system identification with both sparsity and dynamic clustering, named as dynamic sparse fuzzy inference systems (D‐sparseFIS). Due to two different estimation approaches of fuzzy rule consequence parameter, i.e., global estimation and local estimation, D‐sparseFIS.local and D‐sparseFIS.global methods are exploited with local least squares and global least squares estimation based on sparse regularization. Both two dynamic algorithms can guarantee a minimal number of fuzzy rules and nonzero consequence parameters are equipped in T‐S fuzzy system. Finally, some numerical experiments are presented to illustrate the effectiveness of the proposed algorithms.

A fuzzy expert system design for forecasting return quantity in reverse logistics network

Purpose – The purpose of this study is to develop a fuzzy expert system to design robust forecast of return quantity in order to handle uncertainties from the return process in reverse logistic network. Design/methodology/approach – The most important factors which have impact on return of products are defined. Then the factors which have collinearity with others are eliminated by using dimension redundancy analysis. By training data of selected factors with fuzzy expert system, the return amounts of alternative cities are forecasted. Findings – The performance metrics of the proposed model are found as satisfactory. That means the result of this study indicates that fuzzy expert systems can be used as a supportive tool for forecasting return quantity of alternative areas. Research limitations/implications – In the future, the proposed model can be used for forecasting other uncertain parameters such as return quality and return time. Other fuzzy systems such as type-2 fuzzy sets can be used, or other exp...

An optimal design of interval type-2 fuzzy logic system with various experiments including magnetorheological fluid damper

This paper focuses on optimal design of an interval type-2 fuzzy logic system (IT-2FLS) to cope with uncertainty issue of training set and noisy data. Content of the solution is depicted based on the proposed algorithm to optimally design an IT-2FLS from a dataset, named OD-T2FLS. The major concept of the OD-T2FLS is a combination of a useful method of clustering data space to establish a type-1 fuzzy logic system (T-1FLS) and an appropriate way to transform the T-1FLS into an IT-2FLS as well as to optimally adjust parameters of the IT-2FLS. Firstly, an improved algorithm to establish an adaptive neuro-fuzzy inference system (ANFIS), named IM-ENFS, is presented. Based on the given dataset, clustering in the join input–output data space is realized to establish a cluster-data space. Using the IM-ENFS for this cluster-data space, together with the cluster-data space optimized, an ANFIS having a role as an optimal T1-FLS is also established. Parameters of the optimized T-1FLS are then used to build the initial structure of IT-2FLS. Subsequently, this IT-2FLS is optimally adjusted based on the well-known genetic algorithm. Finally, to demonstrate the effectiveness of the proposed OD-T2FLS, experiments including magnetorheological fluid damper are realized based on two different statuses of data sources, with and without noise.

Genetic Design of Optimal Type-1 and Type-2 Fuzzy Systems for Longitudinal Control of an Airplane

This paper presents the design of fuzzy systems for the longitudinal control of an F-14 airplane using genetic algorithms. The longitudinal control is carried out by controlling only the elevators of the airplane. To carry out such control it is necessary to use the stick, the rate of elevation and the angle of attack. These 3 variables are the inputs to the fuzzy inference system, which is of Mamdani type we obtain as the output value of the elevators. After designing the fuzzy inference system we turn to the simulation stage. Simulation results of the longitudinal control are obtained using a plant in Simulink and those results are compared against the PID controller. For optimizing the fuzzy logic control design we use a genetic algorithm. The main contribution of the paper is the optimal design of type-1 and type-2 fuzzy system for longitudinal control of the airplane.

A novel cost function based on decomposing least‐square support vector machine for Takagi–Sugeno fuzzy system identification

This study develops and illustrates a novel cost function which is the combination of these terms constituted of decomposing least square-support vector machine (LS-SVM) and error terms for the identification of Takagi-Sugeno (T-S) fuzzy system based only on measured data without any prior knowledge. The proposed method combines the advantages of fuzzy system theory and some ideas from LS-SVM. Firstly, Gustafson-Kessel clustering algorithm is applied to split training data into R clustering subsets. Likewise, LS-SVM is also decomposed into R terms and consequent parameters a k for T-S fuzzy system corresponding to these terms obtained by decomposing LS-SVM are combined with the error terms to form the new total cost function. Following that, this constrained optimisation problem based on the total cost function can be solved by applying the Lagrange technique. The resulting fuzzy system generated by this method has the following distinct features: (i) the obtained new cost function can be regarded as a structural risk instead of empirical risk; (ii) although incorporating LS-SVM concept into the cost function of T-S fuzzy model, it is shown that the computation process cannot only avoid the selection of kernel function, but also merely use the scalar product for original input space to further reduce the calculation greatly; and (iii) as seen in the proposed novel cost function, the approach can well guarantee the performance of both local-regression models and global model. Finally, the viability and superiority of the method are verified by simulation.