Identification and control of time-varying plants using type-2 fuzzy neural system

A fuzzy type-2 fault detection methodology to minimize false alarm rate in induction motor monitoring applications

Type-2 systems has been becoming the focus of research in the field of fuzzy logic in recent years. Comparing with type-1 systems, type-2 fuzzy systems are more complex and relatively more difficult to understand and implement. We developed an interactive graphical user interface (GUI) based toolbox, MFLS tool, for interval type-2 fuzzy logic system. This paper presents MFLS toolbox. Moreover, the versatility of the software is demonstrated via an prediction problem.

In this paper, an interval extension of the Gaussian mixture model called uncertain Gaussian mixture model (UGMM) is proposed and its transformation into the additive type-2 TSK fuzzy systems is presented. The conditions under which a UGMM becomes a corresponding type-2 TSK fuzzy system are derived theoretically. Furthermore, the mathematical equivalence between the conditional mean of a UGMM and the defuzzified output of a type-2 TSK fuzzy system is proved. Our results provide a new perspective for type-2 TSK fuzzy systems, i.e., interpreting them from a probabilistic viewpoint. Thus, instead of directly estimating the parameters of the fuzzy rules in a type-2 TSK fuzzy system, we can first estimate the parameters of the corresponding UGMM using any popular density estimation algorithm like the expectation maximization (EM) algorithm. Our experimental results clearly indicate that a type-2 fuzzy system trained in such a new way has higher approximation accuracy and stronger robustness than current type-2 fuzzy systems.

In this paper, the optimal designs of type-1 and interval type-2 fuzzy systems for the classification of the heart rate level are presented. The contribution of this work is a proposed approach for achieving the optimal design of interval type-2 fuzzy systems for the classification of the heart rate in patients. The fuzzy rule base was designed based on the knowledge of experts. Optimization of the membership functions of the fuzzy systems is done in order to improve the classification rate and provide a more accurate diagnosis, and for this goal the Bird Swarm Algorithm was used. Two different type-1 fuzzy systems are designed and optimized, the first one with trapezoidal membership functions and the second with Gaussian membership functions. Once the best type-1 fuzzy systems have been obtained, these are considered as a basis for designing the interval type-2 fuzzy systems, where the footprint of uncertainty was optimized to find the optimal representation of uncertainty. After performing different tests with patients and comparing the classification rate of each fuzzy system, it is concluded that fuzzy systems with Gaussian membership functions provide a better classification than those designed with trapezoidal membership functions. Additionally, tests were performed with the Crow Search Algorithm to carry out a performance comparison, with Bird Swarm Algorithm being the one with the best results.

A comparative study of type-2 fuzzy inference systems optimization as an integration method of Modular Neural Networks (MNNs) is presented [32]. The optimization method for type-2 fuzzy systems is based on the footprint of uncertainty (FOU) of the membership functions. We use different benchmark problems to test the optimization method for the fuzzy systems [34, 35]. First, we tested the methodology by manually incrementing the percentage in the FOU, later we apply a Genetic Algorithm to find the optimal type-2 fuzzy system. We show the comparative results obtained for the benchmark problems.

Studies on interval type-2 TSK fuzzy logic system is a hot topic in the current academic area. Parameter identification is very important for system design. Commonly used parameter identification methods are the least-square algorithm, BP algorithm, etc., few scholars use QPSO algorithm for parameter identification. In this paper, we propose a design of interval type-2 TSK fuzzy logic system based on quantum behaved particle swarm optimization (QPSO) intelligent algorithm. Firstly, by combining the A1–C1, A2–C0, A2–C1 interval type-2 TSK fuzzy logic system with neural network, the fuzzy neural network system is designed. Then, the QPSO intelligent algorithm was used to tune the fuzzy neural network system parameters, and the designed system model is applied to predict the Nasdaq Composite Index and International Gold Prices. Both QPSO algorithm and BP algorithm have been used to train the system model. By comparing QPSO algorithm and BP algorithm, the performance index and simulation results illustrated the proposed model is effective and feasible, which can achieve a better performance. Finally, compare the performance of the four fuzzy logic systems, it can be seen the effect of A2–C1 fuzzy logic system is better than that of the other three fuzzy logic systems.

This paper presents a rigorous mathematical development for the design of robust intelligent type-2 fuzzy control systems with regards to the disturbance rejection problem. The majority of the papers in the literature uses only type-1 fuzzy systems for the modeling of both plant ant controller. In the control structure presented in this paper, we use type-2 fuzzy systems, which are more generalized than their type-1 counterparts and particularly known for handling uncertainties. This work extends and generalizes the previous results for the design of robust intelligent control systems. The final robust criteria are given based on linear matrix inequalities (LMIs), and two examples are provided to demonstrate the developed methodologies. The simulation results also show the potential of type-2 fuzzy controllers in improving robustness compared to type-1. The mathematically-sound general framework proposed in this paper provides a systematic tool for the design of robust intelligent controllers, and hence it is expected to widen their applications.

Fuzzy logic control based on the Takagi–Sugeno inference method has been applied for the yeast alcoholic fermentation running in a continuous-time biochemical reactor in this paper. A type-1 fuzzy PID controller was designed to temperature control in a biochemical reactor. The fuzzy PID controller was also designed using type-2 fuzzy sets. The advantage of the fuzzy control is that it can be used very successfully for control of strongly non-linear processes and processes that are difficult to model because of complicated reaction kinetics. Obtained simulation results confirm this fact. The disadvantage of the fuzzy control design lies in the time-consuming tuning of controllers. The subtractive clustering method was used to identify the rule base. This approach was chosen to minimize the number of rules of the designed fuzzy logic controllers and to simplify the fuzzy controller design. Simulation results confirm that fuzzy PID controllers can assure better performance than conventional PID controllers. Yeast alcoholic fermentation is an exothermic process and the cooling is necessary to maintain the optimal temperature in the reactor. Fuzzy PID control reduces coolant consumption in comparison with conventional PID control and so it assures energy-efficient control of continuous-time alcoholic fermentation. Using type-2 fuzzy sets in the fuzzy PID controller design is very promising as the type-2 fuzzy controller offers even better results than the type-1 fuzzy controller.

This paper presents FPGA hardware implementation of a type-2 TSK fuzzy neural system for illuminant estimation, i.e., color temperature, based only on the contents of the image along with performing white balance for the image. The implementation is conducted on an FPGA development platform with Xilinx artix-7 XC7A200 chip. Experiments and comparative study are performed. It is shown that the proposed FPGA design can operate in real-time. For generic 1080p image, it can reach the frame rate of 51.598 frames per second at maximal operation frequency for illuminant estimation and white balance. This resolves the slow execution speed of the proposed algorithm on software platform. The results demonstrate major advancements of the proposed approach over previous and existing methods.

An interval type-2 fuzzy logic system (IT2FLS) can function well with uncertain data, with which a type-1 fuzzy logic system (T1FLS) is ineffective because its membership function rests upon crisp values. However, similar to T1FLSs, there are challenges associated with IT2FLSs in selecting parameters, which can significantly affect the accuracy of the classification results with their relatively high sensitivity. This paper discusses and proposes a hybrid model based on IT2FLS and particle swarm optimization (PSO) for prediction problems. The main objective of this paper is to find the optimal solution for the unknown fuzzy systems using labelled data for training the fuzzy system. The PSO technique was used to find the optimal parameters of the Gaussian membership functions which utilized for IT2FLSs. The authors tested two data sets for each of the two prediction problems, namely: burnt forest area prediction and wine quality prediction. The predictive results were compared with other predictive methods including random forest (RF), support vector machines (SVM), artificial neural network (ANN), adaptive neuro fuzzy inference system (ANFIS) and IT2FLS with parameters generated by using the fuzzy c-means algorithm (IT2FLS-FCM). Experiment results showed that the proposed method could significantly improve accuracy compared to several other predictive techniques.

A hybrid fuzzy neural architecture is proposed. The fuzzy neural system is a feedforward network that combines the basic notions of neural networks and fuzzy logic into a common structure. A back-propagation algorithm is used to train the FNS to perform the desired nonlinear mappings. Four simulation examples are presented where the fuzzy neural system is employed as a nonlinear identifier. Finally, comparisons between fuzzy neural systems, backpropagation neural networks and other fuzzy systems are given and discussed.

Classification is ubiquitous in real world applications. Classification problems deal with high amount of uncertainty. Cancer classification has become an important research problem in bio-medical systems. It is needed to distinguish between the relevant and irrelevant information. To segregate the data, many artificial soft computing techniques have been used. Soft computing finds many applications in the field of bio-medical sciences. In this paper, we present application of a type-2 fuzzy-neural evolutionary network IT2SuNFIS [1] in the area of classification. The performance of the network shows its potential to be used in the area of bioinformatics.

In an intelligent manufacturing context, the smooth operations of mechanical equipment in the production process of enterprises and timely fault diagnosis during operations have become increasingly important. However, the effect of traditional fault diagnosis depends on the feature extraction quality and experts’ empirical knowledge, which is inefficient and costly, and cannot match the needs of mechanical equipment fault diagnosis in intelligent manufacturing. The TSK fuzzy system has a strong approximation capability and the ability to interpret expert knowledge. The broad learning system (BLS) has strong feature extraction and fast computation capabilities. In this paper, we present a new model—the TSK fuzzy broad learning system (TSK-BLS). The model integrates the advantages of the BLS and the fuzzy system at the same time, which can be calculated quickly and accurately by pseudo-inverse and symmetry methods. On the other hand, the model is an embedded model-building mechanism, which extends the application scope of BLS theory. The model was tested on a bearing fault data set, provided by Case Western Reserve University, and the model’s fault diagnosis accuracy was as high as 0.9967. The results were compared with those of the convolutional neural network (CNN) and the BLS models, whose fault diagnosis accuracies are 0.6833 and 0.9133, respectively. Comparison showed that the proposed fault diagnosis model—TSK-BLS, achieved significant improvements.

Parallel Interval Type-2 Subsethood Neural Fuzzy Inference System

The main reason of the extensive usage of the fuzzy systems in many branches of science is their approximation ability. In this paper, an interval type-3 fuzzy system (IT3FS) is proposed. The uncertainty modeling capability of the proposed IT3FS is improved in contrast to type-1 and type-2 fuzzy systems (T1FS and T2FS). Because in the proposed IT3FS, the membership is defined as an interval type-2 fuzzy set, whereas in T1FS and T2FS, the membership is crisp value and type-1 fuzzy set, respectively. An online fractional-order learning algorithm is given to optimize the consequent parameters of the IT3FS. The stability of the learning algorithm is proved by utilizing the Lyapunov method. The validity of the proposed fuzzy system is illustrated by both simulation and the experimental studies. It is shown that the proposed fuzzy system and associated learning algorithm result in better approximation performance in comparison with the other well-known approaches.