Fuzzy systems modeling in practice

This paper proposes new algorithms based on the fuzzy c-regressing model algorithm for Takagi-Sugeno (T-S) fuzzy modeling of the complex nonlinear systems. A fuzzy c-regression state model (FCRSM) algorithm is a T-S fuzzy model in which the functional antecedent and the state-space-model-type consequent are considered with the available input-output data. The antecedent and consequent forms of the proposed FCRSM consists mainly of two advantages: one is that the FCRSM has low computation load due to only one input variable is considered in the antecedent part; another is that the unknown system can be modeled to not only the polynomial form but also the state-space form. Moreover, the FCRSM can be extended to FCRSM-ND and FCRSM-Free algorithms. An algorithm FCRSM-ND is presented to find the T-S fuzzy state-space model of the nonlinear system when the input-output data cannot be precollected and an assumed effective controller is available. In the practical applications, the mathematical model of controller may be hard to be obtained. In this case, an online tuning algorithm, FCRSM-FREE, is designed such that the parameters of a T-S fuzzy controller and the T-S fuzzy state model of an unknown system can be online tuned simultaneously. Four numerical simulations are given to demonstrate the effectiveness of the proposed approach.

Abstract. In this paper, possibilities of using fuzzy system models as a part of model-based fault diagnosis systems are discussed. Methods and experiences of using fuzzy system models at different stages of fault diagnosis systems are presented. In this study, fuzzy system models are used in fault detection and inverse fuzzy system models in fault localization. Inverse fuzzy models are discussed in the light of real-world applications. The mathematical theory is skipped entirely. Additionally we present some examples of using a fuzzy system model in an interface between a fault diagnosis system and a (human) operator. We also briefly discuss a total management of the life-cycle of mechatronic systems. We divide the life-cycle of a mechatronic system into four stages: design, development, installation (integration), and operation and maintenance. When a mechatronic device is being designed and built, it is difficult to analyze the behavior of the device before testing it in practice. It is common that many prototypes of the device are tested at different stages of the development process. The main idea of our approach is that a fuzzy model of a system is built as early as possible, and the model is used, for example, in analyzing the validity of design work done so far. The model is updated and used for different purposes throughout the development and installation process. Finally, the model is used as a part of fault diagnosis and control systems.Fault DiagnosisKnowledge Based SystemsFuzzy Modeling

Model identification for machine system design, design optimization, and manufacturing planning is an important method that has high prediction accuracy and could become an essential stage in practical applications. In this paper, an effective fuzzy model identification algorithm for mechanical system design is developed. First, a fuzzy c-regression model clustering algorithm, in which hyperplane-shaped cluster representatives are utilized to provide a mathematical tool to partition the input–output space reasonably, is introduced. Then, an enhanced cluster validity criterion, in which the structural information hidden in the clusters can be reflected in the index, is proposed to choose the optimal number of clusters. In the proposed architecture, an improved Takagi–Sugeno fuzzy model is proposed to describe the system. Two illustrative examples under various conditions are provided, and their performances are indicated in comparison with other published works. In comparison to these fuzzy works, the proposed fuzzy model identification requires fewer fuzzy rules and a shorter tuning time.

Hyper-plane-shaped clustering (HPSC) has been demonstrated to be more effective in Takagi–Sugeno (T–S) fuzzy model identification compared to hyper-sphere-shaped clustering. Although some HPSC algorithms, based on type-2 fuzzy theory, have already been developed and have been demonstrated to have outstanding performance in T–S fuzzy modeling, mismatching of the traditional hyper-sphere-shaped membership function and HPSC results will inevitably restrict the modeling performance. In this paper, a modified inter type-2 fuzzy c-regression model (IT2-FCRM) clustering and new hyper-plane-shaped Gaussian membership function were proposed for T–S fuzzy modeling. In the proposed approach, the coefficients of the upper and lower hyperplanes were deduced based on an IT2-FCRM algorithm. Then, a hyper-plane-shaped membership function was directly defined using the hyperplanes to identify the antecedent parameters of the T–S fuzzy model. The experimental results of several benchmark problems show that identification of T–S model accuracy was greatly promoted.

Based on the discrete T-S fuzzy system, this paper deals with investigating the trajectory tracking control of high-altitude long-endurance aircraft (HALE) under gust disturbance. Suitable operating points within the envelope range are selected to establish the T-S fuzzy model of highly flexible aircraft (HFA). In order to reduce the conservativeness of the closed-loop system, the continuous T-S fuzzy system is discretized to establish a discrete T-S fuzzy system model. Moreover, considering the tracking target and the robust performance, a Discrete Fuzzy Robust H∞ Control (DFRHC) strategy is proposed, which mainly includes two parts: the fuzzy feedforward control part for reference tracking control and the fuzzy feedback control part to provide robustness. Setting the flight speed and altitude as the tracking target, numerical simulations are performed to verify the control performance of DFRHC strategy based on the T-S fuzzy model. In the tracking control process, discrete gust and the influence of the saturation constraint of control actuator are considered. Simulation results show that the DFRHC strategy based on the T-S fuzzy model can achieve effective tracking control of HFA within the envelope.KeywordsHighly flexible aircraftDiscrete Fuzzy Robust H∞ ControlTrajectory tracking

This paper presents a novel fuzzy model identification method, which is based on Genetic Algorithms and Particle Swarm Optimization. The proposed method is compared to other existing strategies for identification of fuzzy systems and equivalent linear models. A wind turbine system is used to verify and validate the proposed strategy. For purposes of this work, it is assumed that the simulator of the plant represents the actual system that needs to be identified. Simulations are carried out in continuous time and data are acquired with fixed sample time to generate a black box model of the system, using different techniques of identification.

Traditionally, fuzzy logic has been viewed in the artificial intelligence (AI) community as an approach for managing uncertainty. In the 1990s, however, fuzzy logic has emerged as a paradigm for approximating a functional mapping. This complementary modern view about the technology offers new insights about the foundation of fuzzy logic, as well as new challenges regarding the identification of fuzzy models. In this paper, we first review some of the major milestones in the history of developing fuzzy logic technology. After a short summary of major concepts in fuzzy logic, we discuss a modern view about the foundation of two types of fuzzy rules. Finally, we review some of the research in addressing various challenges regarding automated identification of fuzzy rule-based models.

This paper presents a new evolutionary fuzzy system modeling strategy alternative to fuzzy rule bases, and does not entail if...then rule base structure. The new approach, which is based on improved fuzzy functions with genetic algorithms, is proposed to reduce complexity of earlier fuzzy system models and improve modeling accuracy. Structure identification of the new approach is based on a supervised improved fuzzy clustering (IFC) method with a dual optimization algorithm, which yields improved membership values. The merit of the proposed FSM is that uncertain information on natural grouping of data samples, i.e., membership values, is utilized as additional predictors while structuring fuzzy functions. Presented model is applied to desulphurization process of a steel company in Canada. It is shown that proposed approach is superior in comparison to earlier fuzzy, neuro-fuzzy, and non-fuzzy system models in terms of robustness and error reduction.

This paper develops a new adaptive feedback linearization based control scheme for T-S fuzzy systems in general non-canonical forms, which provides an effective control method to control non-canonical form nonlinear systems with large parameter uncertainties. Unlike commonly studied canonical form nonlinear systems whose T-S fuzzy approximation models have explicit relative degree structures which can be directly used to derive parametrized controllers for adaptation, non-canonical form nonlinear systems usually do not have explicit relative degrees as their T-S fuzzy system models are also in non-canonical forms. In order to achieve adaptive output tracking, the system dynamics of non-canonical form T-S fuzzy system models still needs to be parametrized. This paper extends the feedback linearization technique, commonly used for output tracking control of general nonlinear systems, to non-canonical form T-S fuzzy systems, and develops an adaptive feedback linearization based control method which guarantees closed-loop stability and asymptotic output tracking for T-S fuzzy system models. An illustrative example is presented with simulation results to demonstrate the control design procedure, and to verify the effectiveness of such a new design method.

Ozone forecast models using nonlinear regression (NLR) have been successfully applied to daily ozone forecast for seven metro areas in Kentucky, including Ashland, Bowling Green, Covington, Lexington, Louisville, Owensboro, and Paducah. In this study, the updated 2005 NLR ozone forecast models for these metro areas were evaluated on both the calibration data sets and independent data sets. These NLR ozone forecast models explained at least 72% of the variance of the daily peak ozone. Using the models to predict the ozone concentrations during the 2005 ozone season, the metro area mean absolute errors (MAEs) of the model hindcasts ranged from 5.90 ppb to 7.20 ppb. For the model raw forecasts, the metro area MAEs ranged from 7.90 ppb to 9.80 ppb. Based on previously developed NLR ozone forecast models for those areas, Takagi-Sugeno fuzzy system models were developed for the seven metro areas. The fuzzy "c-means" clustering technique coupled with an optimal output predefuzzification approach (least square method) was used to train the Takagi-Sugeno fuzzy system. Two types of fuzzy models, basic fuzzy and NLR-fuzzy system models, were developed. The basic fuzzy and NLR-fuzzy models exhibited essentially equivalent performance to the existing NLR models on 2004 ozone season hindcasts and forecasts. Both types of fuzzy models had, on average, slightly lower metro area averaged MAEs than the NLR models. Among the seven Kentucky metro areas Ashland, Covington, and Louisville are currently designated nonattainment areas for both ground level O 3 and PM 2.5 . In this study, summer PM 2.5 forecast models were developed for providing daily average PM 2.5 forecasts for the seven metro areas. The performance of the PM 2.5 forecast models was generally not as good as that of the ozone forecast models. For the summer 2004 model hindcasts, the metro-area average MAE was 5.33ìg/m 3 . Exploratory research was conducted to find the relationship between the winter PM 2.5 concentrations and the meteorological parameters and other derived prediction parameters. Winter PM 2.5 forecast models were developed for seven selected metro areas in Kentucky. For the model fits, the MAE for the seven forecast models ranged from 3.23 ìg/m 3 to 4.61 ìg/m 3 (~26-28% NMAE). The fuzzy technique was also applied on PM 2.5 forecast models to seek more accurate PM 2.5 prediction. The NLR-fuzzy PM 2.5 had slightly better performance than the NLR models.

Fuzzy model identification is an effective tool for the approx- imation of uncertain nonlinear systems on the basis of measured data. The identification of a fuzzy model using input-output data can be divided into two tasks: structure identification, which determines the type and number of the rules and membership functions, and parameter identification. For both structural and parametric adjustment, prior knowledge plays an im- portant role. Hence, in this book the rules of the fuzzy system are designed based on the available a priori knowledge and the parameters of the mem- bership, and the consequent functions are adapted in a learning process based on the available input-output data. Hence, this chapter is devoted mainly to the parameter identification of the proposed fuzzy models, but certain structure identification tools are also discussed.

This chapter investigates the problem of stabilization of nonlinear discrete-time networked control systems (NCS) with event-triggering communication scheme in the presence of signal transmission delay. A Takagi–Sugeno (T–S) fuzzy model and parallel-distributed compensation (PDC) scheme are first employed to design a nonlinear fuzzy event-triggered controller for the stabilization of nonlinear discrete-time NCS. The idea of the event-triggering communication scheme (a soft computation algorithm) under consideration is that the current sensor data is transmitted only when the current sensor data and the previously transmitted one satisfy a certain state-dependent trigger condition. By taking the signal transmission delay into consideration and using delay system approach, a T–S fuzzy delay system model is established to describe the nonlinear discrete-time NCSs with event-triggering communication scheme. Attention is focused on the design of fuzzy event-triggered controller which ensures asymptotic stability of the closed-loop fuzzy systems. Linear matrix inequality- (LMI-) based conditions are formulated for the existence of admissible fuzzy event-triggered controller. If these conditions are feasible, a desired fuzzy event-triggered controller can be readily constructed. A nonlinear mass-spring-damper mechanical system is presented to demonstrate the effectiveness of the proposed method.

A new approach to fuzzy wavelet system modeling

In this chapter we consider the identification of a Takagi-Sugeno fuzzy model (TS fuzzy model) [2]. This type of fuzzy model is especially useful in the area of fuzzy model-based control [10]. The TS fuzzy model is a nonlinear system model represented by fuzzy rules of the type $$ {R^i}:If{x_1}isA_1^iand...and{x_m}isA_m^ithen{y^i} = a_0^i + a_1^i{x_1} + ... + a_m^i{x_m}$$ (1.1) where R i ( i = 1, 2, …,n denotes that the i-th fuzzy rule, x j (j = 1,2,…, m) are input variables and y i is an output. Furthermore, a j i are the parameters contained in the consequent (then-part) of the i-th rule, and the A 1 i ,A 2 i ,…,A m i are the linguistic values taken by the input variables in the antecedent (if-part) of the i-th rule. The meaning of these linguistic values is defined by corresponding membership functions. As shown in (1.1) and (1.2), this fuzzy model describes a nonlinear input-output relation.

This article addresses parameter convergence problem in identification of nonlinear dynamic systems using fuzzy models. We first establish persistent excitation conditions and then propose several detailed algorithms to generate input signals that guarantee the convergence of the parameter estimates in the fuzzy system models to the true values in identifications of second-order nonlinear moving-average and auto-regressive-moving-average systems. Numerical example is given to illustrate the ideas and results.