Xianxia Zhang

A Three-Dimensional Fuzzy Control Methodology for a Class of Distributed Parameter Systems

The traditional fuzzy set is two-dimensional (2-D) with one dimension for the universe of discourse of the variable and the other for its membership degree. This 2-D fuzzy set is not able to handle the spatial information. The traditional fuzzy logic controller (FLC) developed from this 2-D fuzzy set should not be able to control the distributed parameter system that has the tempo-spatial nature. A three-dimensional (3-D) fuzzy set is defined to be made of a traditional fuzzy set and an extra dimension for spatial information. Based on concept of the 3-D fuzzy set, a new fuzzy control methodology is proposed to control the distributed parameter system. Similar to the traditional FLC, it still consists of fuzzification, rule inference, and defuzzification operations. Different to the traditional FLC, it uses multiple sensors to provide 3-D fuzzy inputs and possesses the inference mechanism with 3-D nature that can fuse these inputs into a so called ldquospatial membership function.rdquo Thus, a simple 2-D rule base can still be used for two obvious advantages. One is that rules will not increase as sensors increase for the spatial measurement; the other is that computation of this 3-D fuzzy inference can be significantly reduced for real world applications. Using only a few more sensors, the proposed FLC is able to process the distributed parameter system with little complexity increased from the traditional FLC. The 3-D FLC is successfully applied to a catalytic packed-bed reactor and compared with the traditional FLC. The results demonstrate its effectiveness to the nonlinear unknown distributed parameter process and its potential to a wide range of engineering applications.

Spatially Constrained Fuzzy-Clustering-Based Sensor Placement for Spatiotemporal Fuzzy-Control System

Many industrial processes are spatiotemporal dynamic systems. A three-dimensional fuzzy-logic controller (3-D FLC) has been recently developed to process the inherent capability of spatiotemporal dynamic systems. Sensor placement, which is always crucial to the control of spatiotemporal dynamic systems, is also critical to the design of the 3-D FLC. In this paper, a new sensor-placement strategy is developed. Its main feature is to position the sensor by utilizing the main characteristics of spatial distribution. The key technique is to use a spatial-constrained fuzzy c-means algorithm to extract the characteristics of spatial distribution. For an easy implementation, a systematic sensor-placement design scheme in four steps (i.e., data collection, dimension reduction, data clustering, and sensor locating) is developed. Finally, control of a catalytic packed-bed reactor is taken as an application to demonstrate the effectiveness of the proposed sensor-placement scheme.

SVR Learning-Based Spatiotemporal Fuzzy Logic Controller for Nonlinear Spatially Distributed Dynamic Systems

A data-driven 3-D fuzzy-logic controller (3-D FLC) design methodology based on support vector regression (SVR) learning is developed for nonlinear spatially distributed dynamic systems. Initially, the spatial information expression and processing as well as the fuzzy linguistic expression and rule inference of a 3-D FLC are integrated into spatial fuzzy basis functions (SFBFs), and then the 3-D FLC can be depicted by a three-layer network structure. By relating SFBFs of the 3-D FLC directly to spatial kernel functions of an SVR, an equivalence relationship of the 3-D FLC and the SVR is established, which means that the 3-D FLC can be designed with the help of the SVR learning. Subsequently, for an easy implementation, a systematic SVR learning-based 3-D FLC design scheme is formulated. In addition, the universal approximation capability of the proposed 3-D FLC is presented. Finally, the control of a nonlinear catalytic packed-bed reactor is considered as an application to demonstrate the effectiveness of the proposed 3-D FLC.

Data-driven based 3-D fuzzy logic controller design using nearest neighborhood clustering and linear support vector regression

Three-dimensional fuzzy logic controller (3-D FLC) is a novel FLC developed for spatially distributed parameter systems. In this study, we are concerned with data-based 3-D FLC design. A nearest neighborhood clustering algorithm is employed to extract fuzzy rules from input-output data pairs, and then an optimization algorithm based on geometric similarity measure is used to reduce the obtained rule base. The consequent parameters are estimated using linear support vector regression. Finally, a catalytic packed-bed reactor is taken as an application to demonstrate the effectiveness of the 3-D FLC.

Fuzzy clustering based spatiotemporal fuzzy logic controller design

Three-dimensional fuzzy logic controller (3-D FLC) is a novel FLC developed for spatially-distributed parameter systems. In this study, we concentrate on the data-driven based 3-D FLC design. Firstly, an initial rule-base of 3-D FLC is learned by fuzzy c-means algorithm from spatial-temporal data set. Then, the rule-base is reduced by using distance-based similarity measure to check similar fuzzy sets and similar rules. Finally, the parameters are refined by a gradient-descent approach. A catalytic packed-bed reactor is taken as an application to demonstrate the effectiveness of the proposed 3-D FLC design method.

A Novel Three-dimensional Fuzzy Controller for the Distributed Parameter System

A three-dimensional fuzzy logic controller (3-D FLC) is presented for the control of distributed parameter system (DPS). Different to the traditional FLC, the 3-D FLC deals with three-dimensional fuzzy set (3-D fuzzy set), i.e. the traditional fuzzy set plus spatial dimension. The proposed FLC still consists of defuzzification, rule inference, and defuzzification. Different to the traditional FLC, the 3-D FLC can fuse information measured from space domain into a spatial membership function, and then rules will not increase as sensors increase for spatial measurement. Therefore, the 3-D FLC has the capability to handle spatial information. Application of the 3-D FLC is presented for a catalytic packed-bed reactor to show the effectiveness of the new fuzzy controller design, and comparisons with the traditional fuzzy controller are also given

Online Support Vector Machine: A Survey

Support Vector Machine (SVM) is one of the fastest growing methods of machine learning due to its good generalization ability and good convergence performance; it has been successfully applied in various fields, such as text classification, statistics, pattern recognition, and image processing. However, for real-time data collection systems, the traditional SVM methods could not perform well. In particular, they cannot well cope with the increasing new samples. In this paper, we give a survey on online SVM. Firstly, the description of SVM is introduced, then the brief summary of online SVM is given, and finally the research and development of online SVM are presented.

Analytical model of three-dimensional fuzzy logic controller for spatio-temporal processes

A novel three-dimensional fuzzy logic controller (3D FLC) is presented for controlling the spatio-temporal systems, with the help of three-dimensional (3D) fuzzy sets and inference logic. The analytical model of the 3D FLC is derived to disclose its working principle and guide the control design. The derived model show that the 3D FLC has a global sliding mode structure over the spatial domain, which explains why the 3D FLC is able to process spatial information more effectively with a few more sensors. Based on its sliding mode feature, the 3D fuzzy logic control system can be analyzed and designed in the sense of Lyapunov stability. Finally, a catalytic reactor is presented as an example to validate the effectiveness of 3D FLC.

Space-decomposition based 3D fuzzy control design for nonlinear spatially distributed systems with multiple control sources using multiple single-output SVR learning

We decompose complex spatially distributed systems with multiple control.Sources into multiple sub-systems with one control source.Space-decomposition based 3D fuzzy control scheme is proposed.A data-driven multiple 3D FLC design method is developed.Multiple single-output SVRs with spatial kernel functions are presented to cope with a multi-output spatio-temporal data set. Three-dimensional fuzzy logic controller (3D FLC) is a recently developed FLC integrating space information expression and processing for nonlinear spatially distributed dynamical systems (SDDSs). Like a traditional FLC, expert knowledge can help design a 3D FLC. Nevertheless, there are some situations where expert knowledge cannot be formulated into precise words; whats worse, it might not be explicitly expressed in words. In contrast, spatio-temporal data sets containing control laws are usually available. In this study, a data-driven based 3D FLC design method using multiple single-output support vector regressions (SVRs) is proposed for SDDSs with multiple control sources. Firstly, in terms of the locally spatial influence feature of control sources on the space domain, a complex SDDS is decomposed into multiple SDDSs with one control source and a space-decomposition based 3D fuzzy control scheme is proposed. Secondly, multiple single-output SVRs with -insensitive cost function are used to learn and design multiple 3D FLCs from spatio-temporal data sets. Thirdly, a five-step design scheme is proposed, including space decomposition, data collection, spatial support-vector learning, 3D fuzzy rule construction, and 3D fuzzy controller integration. Finally, the proposed method is applied to a packed-bed reactor and simulation results were used to verify its effectiveness.

Support Vector Regression Based 3-D Fuzzy Logic Controller Design for spatially distributed systems

Abstract This paper presents a data-driven based 3-D FLC design methodology using support vector regression (SVR) learning. The key technique is to relate spatial fuzzy basis functions of a 3-D FLC to kernel functions of a SVR and construct an equivalence relationship of a 3-D FLC and a SVR. Therefore, a 3-D FLC can be established using the learned results of a SVR. Utilizing the concept of reference function, 3-D membership functions can be generated through location transformation. Thus, we can have more choice for 3-D membership functions. The proposed method was applied to a catalytic packed-bed reactor and simulation results have verified its effectiveness.