Fuzzy Modeling Framework Research Articles

Fuzzy Modeling Framework Using Sector Non-Linearity Techniques for Fixed-Wing Aircrafts

This paper presents a mathematical modeling approach utilizing a fuzzy modeling framework for fixed-wing aircraft systems with the goal of creating a highly desirable mathematical representation for model-based control design applications. The starting point is a mathematical model comprising fifteen non-linear ordinary differential equations representing the dynamic and kinematic behavior applicable to a wide range of fixed-wing aircraft systems. Here, the proposed mathematical modeling framework is applied to the AIRBUS A310 model developed by ONERA. The proposed fuzzy modeling framework takes advantage of sector non-linearity red techniques to recast all the non-linear terms from the original model to a set of combined fuzzy rules. The result of this fuzzification is a more suitable mathematical description from the control system design point of view. Therefore, the combination of this fuzzy model and the wide range of control techniques available in the literature for such kind of models, like parallel and non-parallel distributed compensation control laws using linear matrix inequality optimization, enables the development of control algorithms that guarantee stability conditions for a wide range of operations points, avoiding the classical gain scheduling schemes, where the stability issues can be extremely challenging.

A Parametric Family of Triangular Norms and Conorms with an Additive Generator in the Form of an Arctangent of a Linear Fractional Function

At present, fuzzy modeling has established itself as an effective tool for designing and developing systems for various purposes that are used to solve problems of control, diagnostics, forecasting, and decision making. One of the most important problems is the choice and justification of an appropriate functional representation of the main fuzzy operations. It is known that, in the class of rational functions, such operations can be represented by additive generators in the form of a linear fractional function, a logarithm of a linear fractional function, and an arctangent of a linear fractional function. The paper is devoted to the latter case. Restrictions on the parameters, under which the arctangent of a linear fractional function is an increasing or decreasing generator, are defined. For each case, a corresponding fuzzy operation (a triangular norm or a conorm) is constructed. The theoretical significance of the research results lies in the fact that the obtained parametric families enrich the theory of Archimedean triangular norms and conorms and provide additional opportunities for the functional representation of fuzzy operations in the framework of fuzzy modeling. In addition, in fact, we formed a scheme for study functions that can be considered additive generators and constructed the corresponding fuzzy operations.

Robust observer-based output-feedback control for epidemic models: Positive fuzzy model and separation principle approach

A feedback-type vaccination and treatment policy for a nonlinear susceptible–infected–recovered (SIR) epidemic model involving uncertainties and disturbances is designed by considering only the number of infected individuals. Specifically, an observer-based output-feedback (OBOF) controller design methodology in the Takagi–Sugeno fuzzy model framework is established. The designed controller exhibits L∞–L∞ disturbance attenuation performance, is robust against norm-bounded parametric uncertainties, and can preserve the closed-loop positivity. The primary contributions of the proposed design condition can be characterized as follows: (i) a novel structure of a fuzzy OBOF controller to ensure the closed-loop positivity; (ii) separate disturbance attenuation performances for the independent design of the controller and observer; (iii) The independent design conditions formulated as convex optimization problems in the presence of parametric uncertainties; (iv) the demonstration of the separation principle in the positive L∞–L∞ disturbance attenuation problem. Results of the case study pertaining to the SIR model demonstrate the efficacy of the proposed methodology.

Fuzzy Integral Sliding-Mode Control for Nonlinear Semi-Markovian Switching Systems With Application

The issue of sliding-mode control (SMC) design is studied for a class of nonlinear semi-Markovian switching systems (S-MSSs) via T–S fuzzy approach. Compared with previous literature, novel integral sliding-mode surfaces (ISMSs) are developed to depend on the designed controller gains and projection matrices. The aim of this work is to design an appropriate fuzzy SMC law under complex stochastic semi-Markovian switching process. For this purpose, the novel ISMSs are developed under the T–S fuzzy modeling framework. Then, based on the weak infinitesimal operator theory, sufficient conditions are given for stochastic stability criteria relying on the sojourn-time. Furthermore, an appropriate fuzzy SMC law is proposed to drive the state signals onto the predefined fuzzy manifold. Finally, an electric circuit model illustrates the effectiveness of the theoretical findings.

A Novel Three-Dimensional Fuzzy Modeling Method for Nonlinear Distributed Parameter Systems

Data-based spatio-temporal modeling has rapidly developed over the past ten years. However, traditional spatio-temporal modeling methods will encounter some uncertainty caused by model reduction. In addition, the established model is complicated and short of linguistic interpretability. In this study, a novel three-dimensional (3-D) fuzzy modeling framework without model reduction is proposed and a new 3-D fuzzy modeling method based on clustering and support vector regression is developed. This method is based on a 3-D fuzzy system that naturally fuses time/space separation and time/space synthesis into a unified framework. Utilizing the machine learning algorithms (clustering and support vector regression), a 3-D fuzzy system is constructed for modeling an unknown nonlinear distributed parameter system. The advantages of the proposed modeling method over the traditional spatio-temporal modeling method are linguistic interpretability and no reliance on model reduction. The proposed modeling method consists of three steps. First, the nearest neighborhood clustering algorithm is used to learn initial structure model of antecedent sets of 3-D fuzzy rules. Then, similarity measure is used to simplify the initial structure via combining similar fuzzy sets and similar fuzzy rules. Finally, a support vector regression algorithm is applied to calculate spatial functions in the consequent sets of 3-D fuzzy rules. The simulation results demonstrate the effectiveness of the proposed modeling method.

Distributed Soft Fault Detection for Interval Type-2 Fuzzy-Model-Based Stochastic Systems With Wireless Sensor Networks

In this paper, a distributed filtering scheme is presented to deal with the fault detection problem of nonlinear stochastic systems with wireless sensor networks (WSNs). The nonlinear stochastic systems, which are of discrete-time form, are represented by interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy models. Each sensor of the WSN can receive measurements from itself and its neighboring sensors subject to a deterministic interconnection topology. Independent random variables obeying the Bernoulli distribution are formulated to characterize the randomly occurred packet losses between the WSN and the filter unit. To generate residual signals for evaluation functions of the fault detection mechanism, a novel type of IT2 T–S fuzzy distributed fault detection filter is proposed corresponding to each sensor node. Additionally, a fault reference model is adopted for improving the performance of the fault detection system. A new overall fault detection system is formulated in an IT2 T–S fuzzy model framework. Applying Lyapunov functional approach, we concentrate on the analysis of stability and performance of the resulting fault detection system. New techniques are utilized to handle the decoupling problem in design procedure. The desired parametric matrices of the fuzzy filters are designed subject to a developed criterion, which is a sufficient condition of the robust mean-square asymptotic stability for the overall fault detection system with a disturbance attenuation performance. Finally, a truck-trailer system with a four-node WSN is established for simulation validation. In simulations, the mincx function of the MatLab 2017a in Windows 10 OS is used to optimize the level of the disturbance attenuation performance, and to obtain the filter gains for the established system. By comparing the different time instants when the residual evaluation functions exceed their respective thresholds, simulation results successfully validate the effectiveness and applicability of the presented distributed fault detection scheme.

A New Fuzzy Modeling Framework for Integrated Risk Prognosis and Therapy of Bladder Cancer Patients

This paper presents a new fuzzy modeling approach for analyzing censored survival data and finding risk groups of patients diagnosed with bladder cancer. The proposed framework involves a new procedure for integrating the frameworks of interval type-2 fuzzy logic and Cox modeling intrinsically. The output of this synergistic framework is a score/prognostics index which is indicative of the patient's level of mortality risk. A threshold value is selected whereby patients with risk scores that are greater than this threshold are classed as high-risk patients and vice versa. Unlike in the case of black-box type modeling approaches, the paper shows that interpretability and transparency are maintained using the proposed fuzzy modeling framework. Two datasets are used to test the modeling accuracy of the elicited models. The first is an artificial dataset which has similar characteristics as in a typical survival data. The second relates to real-life bladder cancer data from which one requires a model that identifies the low-risk and high-risk patients and then recommends risk management decisions based on, predicted risk level, patient history and characteristics, disease pathology, and event times. The performance of the proposed framework is compared with the traditional Cox model, logistic regression as well as a nonlinear survival data modeling technique based on neural networks. This is the first time an attempt has been made to exploit the transparency advantages of fuzzy models and the principled statistical framework of the Cox model in order to identify risk groups and recommend risk management decisions from complex survival datasets. In both the artificial data and real data, the proposed modeling framework, although minimalistic, shows better generalization performances than the previously reported models against which the results were compared.

Vibration Control Design for a Plate Structure with Electrorheological ATVA Using Interval Type-2 Fuzzy System

This study presents vibration control using actively tunable vibration absorbers (ATVA) to suppress vibration of a thin plate. The ATVA is made of a sandwich hollow structure embedded with electrorheological fluid (ERF). ERF is considered to be one of the most important smart fluids and it is suitable to be embedded in a smart structure due to its controllable rheological property. ERF’s apparent viscosity can be controlled in response to the electric field and the change is reversible in 10 microseconds. Therefore, the physical properties of the ERF-embedded smart structure, such as the stiffness and damping coefficient, can be changed in response to the applied electric field. A mathematical model is difficult to be obtained to describe the exact characteristics of the ERF embedded ATVA because of the nonlinearity of ERF’s viscosity. Therefore, a fuzzy modeling and experimental validations of ERF-based ATVA from stationary random vibrations of thin plates are presented in this study. Because Type-2 fuzzy sets generalize Type-1 fuzzy sets so that more modeling uncertainties can be handled, a semi-active vibration controller is proposed based on Type-2 fuzzy sets. To investigate the different performances by using different types of fuzzy controllers, the experimental measurements employing both type-1 fuzzy and interval type-2 fuzzy controllers are implemented by the Compact RIO embedded system. The fuzzy modeling framework and solution methods presented in this work can be used for design, performance analysis, and optimization of ATVA from varying harmonic vibration of thin plates.

Fuzzy modeling of holding capacity of offshore suction caisson anchors

SummaryA fuzzy algorithm, the Takagi–Sugeno model, is implemented to develop a fuzzy inference system for predicting the holding capacity of suction caisson foundations for offshore platforms. The premise parameters of the fuzzy model are optimized by using a subtractive clustering algorithm. The consequent parameters are optimally determined via a weighted least square estimation. The input variables used for training the fuzzy model include the aspect ratio of the caisson, the undrained shear strength of the clay, and the angle that the chain force forms with the horizontal. The output of the proposed fuzzy model is the capacity of the suction caisson anchor. To demonstrate the effectiveness of the fuzzy modeling framework, the results of extensive finite element analyses are investigated. Comparisons of the trained fuzzy model with the data demonstrate that the proposed modeling framework is an effective method to estimate the holding capacity of offshore suction caisson systems. Moreover, the performance of the fuzzy model is robust against higher levels of input data uncertainties. Copyright © 2017 John Wiley & Sons, Ltd.

Exploiting Mobile Ad Hoc Networking and Knowledge Generation to Achieve Ambient Intelligence

Ambient Intelligence (AmI) joins together the fields of ubiquitous computing and communications, context awareness, and intelligent user interfaces. Energy, fault-tolerance, and mobility are newly added dimensions of AmI. Within the context of AmI the concept of mobile ad hoc networks (MANETs) for “anytime and anywhere” is likely to play larger roles in the future in which people are surrounded and supported by small context-aware, cooperative, and nonobtrusive devices that will aid our everyday life. The connection between knowledge generation and communication ad hoc networking is symbiotic—knowledge generation utilizes ad hoc networking to perform their communication needs, and MANETs will utilize the knowledge generation to enhance their network services. The contribution of the present study is a distributed evolving fuzzy modeling framework (EFMF) to observe and categorize relationships and activities in the user and application level and based on that social context to take intelligent decisions about MANETs service management. EFMF employs unsupervised online one-pass fuzzy clustering method to recognize nodes' mobility context from social scenario traces and ubiquitously learn “friends” and “strangers” indirectly and anonymously.

Feedforward control of a class of hybrid systems using an inverse model

Abstract In this paper we describe the design of a control algorithm for MISO systems, which can be modelled as hybrid fuzzy models. Hybrid fuzzy models present a convenient approach to modelling nonlinear hybrid systems. We discuss the formulation of a hybrid fuzzy model, its structure and the identification procedure. This is followed by a derivation of the inverse model and its implementation in the control algorithm. The control scheme we are discussing splits the control algorithm in two parts: the feedforward part and the feedback part. In the paper, we deal with the feedforward part of the control algorithm, which is based on an inverse of a hybrid fuzzy model. Next, a batch-reactor process is introduced. The modelling of the batch reactor is tackled and the results of the simulation experiments using the proposed control algorithm are presented. The experiments involved controlling the temperature of a batch reactor using two on/off input valves and a continuous mixing valve. The main advantage of the proposed approach is that the feedforward part of the control algorithm can bring the system close to the desired adjusted feasible trajectory, which avoids the need for a very complex feedback part of the algorithm. Therefore, the control algorithm presents a low computational burden, particularly comparing to the standard model predictive control algorithms. These usually require a considerable computational effort, which often thwarts their implementation on real industrial systems. Nevertheless, we show that using the proposed control approach the hybrid fuzzy model framework presents a convenient option for modelling complex systems for control purposes in practice.

The development of fuzzy radial basis function neural networks based on the concept of information ambiguity

There is a remarkably rich landscape of fuzzy clustering and ensuing design procedures of information granules. In a nutshell, fuzzy clustering (and clustering, in general) leads to direction-free constructs meaning that there is no clear distinction between input and output variables. In the framework of fuzzy modeling, information granules are used in the development of input–output mapping and from this perspective it becomes beneficial to consider the aspect of directionality in the construction of information granules (fuzzy sets) in the input space. Conditional fuzzy C-means clustering comes as one of the algorithmically viable alternatives using which we construct fuzzy sets over the input space in presence of supervision coming in the form of structure of data distributed over the output space. In this paper, presented is a new clustering method in which we use the ambiguity index to express the boundaries of the clusters. The design is illustrated with the aid of several numeric examples that provide a detailed insight into the performance of the fuzzy models formed in this manner and also highlight several crucial design issues.

Cognitive Robotics and Multiagency in a Fuzzy Modeling Framework

Fuzzy algebraic structures are a useful and flexible tool for modeling cognitive agents and their societies. In this article we propose a fuzzy algebraic framework where the valuating sets are other than the unit interval (lattices, partially ordered sets or relational structures) . This provides for a flexible organization of the information gathered by the agent (via interactions with the environment and/or other agents) and enables its selected use when different drives are active. Agents (Petitagé, ANNA, POPSICLE and Izbushka), which are instantiations of our model, are also given in order to illustrate the use of this framework, as well as its possible extensions.

Constraint-Based Fuzzy Models for an Environment with Heterogeneous Information-Granules

A novel framework for fuzzy modeling and model-based control design is described. Based on the theory of fuzzy constraint processing, the fuzzy model can be viewed as a generalized Takagi-Sugeno (TS) fuzzy model with fuzzy functional consequences. It uses multivariate antecedent membership functions obtained by granular-prototype fuzzy clustering methods and consequent fuzzy equations obtained by fuzzy regression techniques. Constrained optimization is used to estimate the consequent parameters, where the constraints are based on control-relevant a priori knowledge about the modeled process. The fuzzy-constraint-based approach provides the following features. 1) The knowledge base of a constraint-based fuzzy model can incorporate information with various types of fuzzy predicates. Consequently, it is easy to provide a fusion of different types of knowledge. The knowledge can be from data-driven approaches and/or from control-relevant physical models. 2) A corresponding inference mechanism for the proposed model can deal with heterogeneous information granules. 3) Both numerical and linguistic inputs can be accepted for predicting new outputs.The proposed techniques are demonstrated by means of two examples: a nonlinear function-fitting problem and the well-known Box-Jenkins gas furnace process. The first example shows that the proposed model uses fewer fuzzy predicates achieving similar results with the traditional rule-based approach, while the second shows the performance can be significantly improved when the control-relevant constraints are considered.

Support Vector Learning Mechanism for Fuzzy Rule-Based Modeling: A New Approach

This paper describes a fuzzy modeling framework based on support vector machine, a rule-based framework that explicitly characterizes the representation in fuzzy inference procedure. The support vector learning mechanism provides an architecture to extract support vectors for generating fuzzy IF-THEN rules from the training data set, and a method to describe the fuzzy system in terms of kernel functions. Thus, it has the inherent advantage that the model does not have to determine the number of rules in advance, and the overall fuzzy inference system can be represented as series expansion of fuzzy basis functions. The performance of the proposed approach is compared to other fuzzy rule-based modeling methods using four data sets.

ADAPTIVE FUZZY MODEL BASED PREDICTIVE CONTROL OF AN EXOTHERMIC BATCH CHEMICAL REACTOR*

An adaptive fuzzy model based predictive control (AFMBPC) approach is presented to track the desired temperature trajectories in an exothermic batch chemical reactor. The AFMBPC incorporates an adaptive fuzzy modeling framework into a model based predictive control scheme to derive analytical controller output. This approach has the flexibility to cope with different fuzzy model structures whose choice also lead to improve the controller performance. In this approach, adaptation of fuzzy models using dynamic process information is carried out to build a predictive controller, thus eliminating the determination of a predefined fixed fuzzy model based on various sets of known input-output relations. The performance of the AFMBPC is evaluated by comparing to a fixed fuzzy model based predictive controller (FFMBPC) and a conventional PID controller. The results show the better suitability of AFMBPC for the control of highly nonlinear and time varying batch chemical reactors.

Fuzzy modeling with multivariate membership functions: gray-box identification and control design

A novel framework for fuzzy modeling and model-based control design is described. The fuzzy model is of the Takagi-Sugeno (TS) type with constant consequents. It uses multivariate antecedent membership functions obtained by Delaunay triangulation of their characteristic points. The number and position of these points are determined by an iterative insertion algorithm. Constrained optimization is used to estimate the consequent parameters, where the constraints are based on control-relevant a priori knowledge about the modeled process. Finally, methods for control design through linearization and inversion of this model are developed. The proposed techniques are demonstrated by means of two benchmark examples: identification of the well-known Box-Jenkins gas furnace and inverse model-based control of a pH process. The obtained results are compared with results from the literature.

Dynamic fuzzy model based predictive controller for a biochemical reactor

The kinetics of bioreactions often involve some uncertainties and the dynamics of the process vary during the course of fermentation. For such processes, conventional control schemes may not provide satisfactory control performance and demands extra effort to design advanced control schemes. In this study, a dynamic fuzzy model based predictive controller (DFMBPC) is presented for the control of a biochemical reactor. The DFMBPC incorporates an adaptive fuzzy modeling framework into a model based predictive control scheme to derive analytical controller output. The DFMBPC has the flexibility to opt with various types of fuzzy models whose choice also lead to improve the control performance. The performance of DFMBPC is evaluated by comparing with a fuzzy model based predictive controller (FMBPC) with no model adaptation and a conventional PI controller. The results show that DFMBPC provides better performance for tracking setpoint changes and rejecting unmeasured disturbances in the biochemical reactor.

A New Framework for Fuzzy Modeling Using Genetic Algorithm

This paper presents a new framework for fuzzy modeling using genetic algorithm. A model of actual object in the real world should satisfy various criteria, such as precision, generality, noise immunity, etc. It has been difficult for the fuzzy modeling to allocate proper weights on these criteria. The framework introduced in this paper consists of a model generation block and a model-testing block. The model generation block generates candidates of fuzzy model under criteria with higher importance, and the model-testing block tests the candidates under notso-important criteria. This division of criteria can put emphasis on the criteria in the generation block and less on those in the testing block. Simulations are done to show the effectiveness of the proposed framework.

Rule Extraction from Data

Rule extraction from data is one of the key technologies for solving the bottlenecks in artificial intelligence. Artificial neural networks are well suited for representing any knowledge in given data. Extraction of logical/fuzzy rules from the trained artificial neural network is of great importance to researchers in the fields of artificial intelligence and soft computing. Fuzzy rule sets are capable of approximating any nonlinear mapping relationships. Extraction of rules from data has been discussed in terms of fuzzy modeling, fuzzy clustering, and classification with fuzzy rule sets. This special issue entitled"Rule Extraction from Data" is aimed at providing the readers with good insights into the advanced studies in the field of rule extraction from data using neural networks/fuzzy rule sets. I invited seven research papers best suited for the theme of this special issue. All the papers were reviewed rigorously by two reviewers each. The first paper proposes an interesting rule extraction method from data using neural networks. Ishikawa presents a combination of learning with an immediate critic and a structural learning with forgetting. This method is capable of generating skeletal networks for logical rule extraction from data with correct and wrong answers. The proposed method is applied to rule extraction from lense data. The second paper presents a new methodology for logical rule extraction based on transformation of MLP (multilayered perceptron) to a logical network. Duck et al. applied their C-MLP2LN to the Iris benchmark classification problem as well as real-world medical data with very good results. In the third paper, Geczy and Usui propose fuzzy rule extraction from trained artificial neural networks. The proposed algorithm is implied from their theoretical study, not from heuristics. Their study enables to initially consider derivation of crisp rules from trained artificial neural network, and in case of conflict, application of fuzzy rules. The proposed algorithm is experimentally demonstrated with the Iris benchmark classification problem. The fourth paper presents a new framework for fuzzy modeling using genetic algorithm. The authors have broken new ground of fuzzy rule extraction from neural networks. For the fuzzy modeling, they have proposed a particular type of neural networks containing nodes representing membership functions. In this fourth paper, the authors discuss input variable selection for the fuzzy modeling under multiple criteria with different importance. A target system with a strong nonlinearity is used for demonstrating the proposed method. Kasabov, et al. present, in the fifth paper, a method for extraction of fuzzy rules that have different level of abstraction depending on several modifiable thresholds. Explanation quality becomes better with higher threshold values. They apply the proposed method to the Iris benchmark classification problem and to a real world problem. J. Yen and W. Gillespie address interpretability issue of Takagi-Sugeno-Kang model, one of the most popular fuzzy mdoels, in the fifth paper. They propose a new approach of fuzzy modeling that ensures not only a high approximation of the input-output relationship in the data, but also good insights about the local behavior of the model. The proposed method is applied to fuzzy modeling of sinc function and Mackey-Glass chaotic time series data. The last paper discusses fuzzy rule extraction from numerical data for high-dimensional classification problems. H.Ishibuchi, et al. have been pioneering methods for classification of data using fuzzy rules and genetic algorithm. In this last paper, they introduced a new criterion, simplicity of each rule, together with the conventional ones, compactness of rule base and classification ability, for high-dimensional problem. The Iris data is used for demonstrating their new classification method. They applied it also to wine data and credit data. I hope that the readers will be encouraged to explore the frontier to establish a new paradigm in the field of knowledge representation and rule extraction.