Fuzzy models within orthonormal basis function framework

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

Fuzzy systems modeling in practice

In hands-free telephone or video conference application, there exists an acoustic feedback coupling between the loudspeaker and microphone in an enclosed environment, which creates the acoustic echo. FIR filters are commonly used in acoustic echo cancellers because of their simple structure. However, in this paper, the Kautz and Laguerre filter structures are shown to be more efficient echo cancellers than the FIR filters, because they can describe accurately the acoustic echo system with fewer parameters. These filters are built from their respective orthonormal Kautz and Laguerre basis functions. The proposal is motivated by some theoretical and numerical results that the time-varying acoustic echo path is basically due to its time-varying zeros and not its time-invariant acoustical poles. Therefore, the poles of the Kautz and the Laguerre filters are estimated, and can be kept fixed or updated occasionally if required. The poles are estimated by a batch Gauss-Newton algorithm. Then, the coefficients of the Kautz and Laguerre filters can be estimated by most recursive algorithms that are suitable for linear regression models, e.g., the normalized LMS algorithm. Generally, it is shown that the proposed Kautz and Laguerre filters, as the filter structures in an acoustic echo canceller, have better convergence and tracking properties than the FIR and IIR filters.

One of the challenges research on model based fault detection and diagnosis of a system is finding the accurate models. In this paper, fuzzy logic based model using genetic algorithm for optimizing the membership function is used in the development of fault detection and diagnosis of a process control rig. The model is used to generate various residual signals, which relate to the faults of the system. These residual signals are used by artificial neural networks to classify the respective faults and finally to determine the faults of the system. Comparisons of the fault classification technique are done for two different models of the process control rig that are the conventional fuzzy model and the optimized fuzzy-GA model. The results show that the fuzzy-GA model gives more accurate fault classifications as compared to the conventional fuzzy logic model.

Enhancing the fuzzy set model for high quality document rankings

A new approach is presented to enhance fuzzy modeling using multidimensional fuzzy sets directly in the fuzzy model in place of decomposed fuzzy sets by projection. The antecedent fuzzy sets in the form of multivariable functions are represented in continuous form. This is accomplished by using a multi input and multi output neural network, which is in particular radial basis functions (RBF) network providing the required multivariable function approximation properties in a fuzzy model. The inputs of the network are fuzzy model inputs, outputs are the membership function values as to the multivariable fuzzy sets involved in the model. Thus, each output is restricted to one multivariable fuzzy set. The RBF network is trained according to the multidimensional fuzzy sets which are identified after fuzzy clustering of the data. Based on this, the linear model parameters are determined by the method of least squares in a straightforward manner. The transparency issues can be handled by means of projection process to have information about the shape and locations of the membership functions pertinent to each variable at the input. The accurate fuzzy modeling having been thus guaranteed the information on the linear model parameters are used to establish the multivariable fuzzy rules with their respective validity regions. The redundancy of the number of fuzzy sets can be circumvented by classical cluster merging algorithms available. In this approach, the fuzzy rules are determined from the local linear models, however in contrast with the conventional fuzzy modeling, the model outputs are determined by the multivariable fuzzy sets. To obtain regular sets, RBF network is trained by means of orthogonal least squares (OLS) method so that at the same time the convergence issues of general neural network training is eliminated.

Combining with ventilation requirements and safety regulation in coalmine, control strategy which aims at both safety and energy saving is established at length. Moreover, conventional double fuzzy control model is found to carry out two work mode, normal ventilation and gas discharging. Since four input signals affect output in different degree, three layers BP neural network is employed to compute weight. Based on conventional fuzzy model, self learning fuzzy model for partial fan is build to tackle with normal ventilation and gas discharging problem. Direct torque control style is applied to perform speed adjusting of partial fan. In order to testify the control strategy, an experiment platform including DSP and IPM is founded. The experiment results show that the control strategy is effective to fulfill the function of ventilation and gas discharge in heading laneway.

The goal of this paper is the approximation of a nonlinear, dynamic process. More specifically it is studied whether the nonlinear, dynamic process can be simplified by separating it in its linear dynamic and nonlinear static components. Focus of this work is the approximation of the dynamic proportion with orthonormal basis functions (OBFs). The approximation of the nonlinear static properties is not fixed to a specific technique, but we focus on Takagi-Sugeno fuzzy models. This approach contrasts with other publications like [10], [12], [15], where OBFs are used to model both the dynamic and nonlinear part of the process. By modeling NOBF models, the main task is the optimization of the OBF pole, because it is the hyper-parameter, which affects the model quality most. This contribution focuses on the loss functions used for the optimization of the OBF pole.The loss functions must fulfill several requirements: It has to have a unique minimum, must be computable without prior knowledge of the nonlinear component of the process, be smooth around minima and sufficiently fast to compute. We compare three approaches to approximate the loss function. The first approach is the true loss function, which is the squared error of the nonlinear model and acts as reference. The second approach incorporates the structure of local model networks [3]. Finally, we propose a new approach, which is model free and based on the gamma test. We further analyze for which type of systems the technique is suitable and compare the advantages and disadvantages of the respective approach.

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

Multi-scale fuzzy modeling of multivariable discrete-time nonlinear dynamical systems is approached analytically in this paper. The underlying idea of this approach is to introduce the idea of multi-scale fuzzy quantization. More globally supported membership functions are used at coarser scales to capture global characteristics of the unknown system, whereas more locally supported membership functions are used at finer scales to fill in the local features. Starting from the coarsest scale down to finer ones, a projection method is used to extract a partial fuzzy-model (in terms of fuzzy membership functions and fuzzy rules) from the residual of the system at each scale until the residual drops below a prescribed modeling error bound. The multi-scale fuzzy model is then obtained by assembling the partial fuzzy models together. To reach a near optimal fuzzy model, a rule reduction technique has also been developed to delete some fuzzy rules. An illustrative example is used to demonstrate the effectiveness of the scheme.

A fuzzy clustering approach is developed to select pole locations for Orthonormal Basis Functions (OBFs), used for identification of Linear Parameter Varying (LPV) systems. The identification approach is based on interpolation of locally identified Linear Time Invariant (LTI) models, using globally fixed OBFs. Selection of the optimal OBF structure, that guarantees the least worst-case local modelling error in an asymptotic sense, is accomplished through the fusion of the Kolmogorov n-width (KnW) theory and Fuzzy c-Means (FcM) clustering of observed sample system poles.

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.

Analysis of fuzzy operators for high quality information retrieval

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.