Formal presentation of fuzzy systems with multiple sensor inputs

The paper addresses the problems of complexity in fuzzy rule based systems with multiple sensor inputs. The number of fuzzy rules in this case is an exponential function of the number of inputs. Some of the existing methods for rule base reductions are reviewed and their drawbacks summarized. As an alternative, a novel methodology for complexity management in fuzzy systems is presented which is based on formal presentation techniques such as integer tables. A Matlab example is shown illustrating the presentation of a fuzzy rule base with an integer table. Finally, some future research directions are outlined within the framework of the proposed methodology

Fuzzy modelling using a simplified rule base

Transparency and complexity are two major concerns of fuzzy rule-based systems. To improve accuracy and precision of the outputs, we need to increase the partitioning of the input space. However, this increases the number of rules exponentially, thereby increasing the complexity of the system and decreasing its transparency. The main factor behind these two issues is the conjunctive canonical form of the fuzzy rules. We present a novel method for replacing these rules with their singleton forms, and using aggregation operators to provide the mechanism for combining the crisp outputs

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use

Design and Rule Base Reduction of a Fuzzy Filter for the Estimation of Motor Currents

Fuzzy systems have been used extensively and successfully in control systems over the past few decades, but have been applied much less often to filtering problems. This is somewhat surprising in view of the dual relationship between control and estimation. This paper discusses and demonstrates the application of fuzzy filtering to motor winding current estimation in permanent magnet synchronous motors. Motor winding current estimation is an important problem because in order to implement effective closed-loop control, a good estimation of the current is needed. Motor winding currents are notoriously noisy because of electrical noise in the motor drive. We use a fuzzy system with correlation-product inference and centroid defuzzification for motor winding current estimation, With the assumption that the membership functions are triangular (but not necessarily symmetric), we then optimize the membership functions using gradient descent. Next we use singular value decomposition to reduce the rule base for the fuzzy filter. Rule base reduction can be important for fuzzy systems in those cases where the fuzzy system needs to be implemented in real time. This is especially true with regard to fuzzy filtering in a real time motor controller. The methods discussed in this paper are demonstrated on real motor winding currents that were collected with a digital oscilloscope. It is demonstrated that fuzzy techniques provide a feasible approach to motor current estimation, that gradient descent optimization improves the performance of the filter, and that rule base reduction results in a relatively small degradation of filter performance. (C) 2000 Elsevier Science Inc. All rights reserved

Design and Rule Base Reduction of a Fuzzy Filter for the Estimation of Motor Currents

Fuzzy systems have been used extensively and successfully in control systems over the past few decades, but have been applied much less often to filtering problems. This is somewhat surprising in view of the dual relationship between control and estimation. This paper discusses and demonstrates the application of fuzzy filtering to motor winding current estimation in permanent magnet synchronous motors. Motor winding current estimation is an important problem because in order to implement effective closed-loop control, a good estimation of the current is needed. Motor winding currents are notoriously noisy because of electrical noise in the motor drive. We use a fuzzy system with correlation-product inference and centroid defuzzification for motor winding current estimation, With the assumption that the membership functions are triangular (but not necessarily symmetric), we then optimize the membership functions using gradient descent. Next we use singular value decomposition to reduce the rule base for the fuzzy filter. Rule base reduction can be important for fuzzy systems in those cases where the fuzzy system needs to be implemented in real time. This is especially true with regard to fuzzy filtering in a real time motor controller. The methods discussed in this paper are demonstrated on real motor winding currents that were collected with a digital oscilloscope. It is demonstrated that fuzzy techniques provide a feasible approach to motor current estimation, that gradient descent optimization improves the performance of the filter, and that rule base reduction results in a relatively small degradation of filter performance. (C) 2000 Elsevier Science Inc. All rights reserved

Tradeoff between Approximation Accuracy and Complexity: HOSVD Based Complexity Reduction

Higher Order Singular Value Decomposition (HOSVD) based complexity reduction method is proposed in this paper to polytopic model approximation techniques. The main motivation is that the polytopic model has exponentially growing computational complexity with the improvement of its approximation property through, as usually practiced, increasing the density of local linear models. The reduction technique proposed here is capable of defining the contribution of each local linear model, which serves to remove the weakly contributing ones according to a given threshold. Reducing the number of local models leads directly to the complexity reduction. The proposed reduction can also be performed on TS fuzzy model approximation method. A detailed illustrative example of a non-linear dynamic model is also discussed. The main contribution of this paper is the multi-dimensional extension of the SVD reduction technique introduced in the preliminary work [1]. The advantage of this extension is that the HOSVD based technique of this paper can be applied to polytopic models varying in a multi-dimensional parameter space unlike the reduction method of [1] which is designed for one dimensional parameter space

A Review of Fault Diagnosing Methods in Power Transmission Systems

Transient stability is important in power systems. Disturbances like faults need to be segregated to restore transient stability. A comprehensive review of fault diagnosing methods in the power transmission system is presented in this paper. Typically, voltage and current samples are deployed for analysis. Three tasks/topics; fault detection, classification, and location are presented separately to convey a more logical and comprehensive understanding of the concepts. Feature extractions, transformations with dimensionality reduction methods are discussed. Fault classification and location techniques largely use artificial intelligence (AI) and signal processing methods. After the discussion of overall methods and concepts, advancements and future aspects are discussed. Generalized strengths and weaknesses of different AI and machine learning-based algorithms are assessed. A comparison of different fault detection, classification, and location methods is also presented considering features, inputs, complexity, system used and results. This paper may serve as a guideline for the researchers to understand different methods and techniques in this field