design for self organizing fuzzy neural networks based on genetic algorithms a novel hybrid learning algorithm based on a genetic algorithm to design a growing fuzzy neural network named self organizing fuzzy neural network based on genetic algorithms sofnnga to implement takagi sugeno ts type fuzzy models is proposed in this paper a new adding method based on geometric growing criterion and the epsiv completeness of fuzzy rules is first used to generate the initial structure then a hybrid algorithm based on genetic algorithms backpropagation and recursive least squares estimation is used to adjust all parameters including the number of fuzzy rules this has two steps first the linear parameter matrix is adjusted and second the centers and widths of all membership functions are modified the ga is introduced to identify the least important neurons i e the least important fuzzy rules simulations are presented to illustrate the performance of the proposed algorithm

training anfis as an identifier with intelligent hybrid stable learning algorithm based on particle swarm optimization and extended kalman filter this paper proposes a novel hybrid learning algorithm with stable learning laws for adaptive network based fuzzy inference system anfis as a system identifier the proposed hybrid learning algorithm is based on the particle swarm optimization pso for training the antecedent part and the extended kalman filter ekf for training the conclusion part lyapunov stability theory is used to study the stability of the proposed algorithm comparison results of the proposed approach pso algorithm for training the antecedent part and recursive least squares rlss or ekf algorithm for training the conclusion part with the other classical approaches such as gradient descent resilient propagation quick propagation levenberg marquardt for training the antecedent part and rlss algorithm for training the conclusion part are provided moreover it is shown that applying pso a powerful optimizer to optimally train the parameters of the membership function on the antecedent part of the fuzzy rules in anfis system is a stable approach which results in an identifier with the best trained model stability constraints are obtained and different simulation results are given to validate the results also the stability of levenberg marquardt algorithms for anfis training is analyzed

a wavelet based approach for the identification of linear time varying dynamical systems a novel procedure is developed for the identification of linear discrete models of dynamical systems from noisy data of particular interest is the application of the methodology to time varying systems the procedure is based on a representation of the governing differential equations with respect to a wavelet basis and the formulation of an inverse algebraic problem in the associated subspace the effect of noisy data is considered and numerical simulations demonstrating the applicability of the method to single and multi degree of freedom dynamical systems are presented

a new fuzzy neural network with fast learning algorithm and guaranteed stability for manufacturing process control in this paper a new fuzzy neural network fnn is presented for manufacturing process control it is different from the conventional fnn in its structure learning algorithm and stability analysis method firstly it utilizes the input and output layer to on line fine tune scaling factors it can also use the hidden layers to realize the fuzzification fuzzy inference defuzzification and tune parameters such as membership functions fuzzy control rules dynamically secondly a new combining learning algorithm cl which combines the gradient based error back propagation algorithm ebp with similar newton sn algorithm is proposed in order to improve the convergence speed and release computational burden during the learning process lastly a convergence condition for determining the stability of fnn is established physical experiments for manufacturing process control are implemented to evaluate the effectiveness of the proposed scheme

successive identification of a fuzzy model and its applications to prediction of a complex system abstract a successive identification method of a fuzzy model is suggested the identification mechanism consists of two levels one is the supervisor level and the other is the adjustment level the supervisor level determines a policy of parameter adjustment using a set of fuzzy adjustment rules the adjustment rules are derived from the fuzzy implications of a fuzzy model and are extended to fuzzy adjustment rules by using an extended concept of zadeh s contrast intensification the adjustment level executes the policy of parameter adjustment determined with the fuzzy adjustment rules the parameter adjustment consists of premise parameter adjustment and consequent parameter adjustment both of them are realized by the weighted recursive least square algorithm finally it is shown from two examples that the method is very useful for modeling complex systems

identifying fuzzy models utilizing genetic programming abstract fuzzy models offer a convenient way to describe complex nonlinear systems moreover they permit the user to deal with uncertainty and vagueness due to these advantages fuzzy models are employed in various fields of applications e g control forecasting and pattern recognition nevertheless it has to be emphasized that the identification of a fuzzy model is a complex optimization task with many local minima genetic programming provides a way to solve such complex optimization problems in this work the use of genetic programming to identify the input variables the rule base and the involved membership functions of a fuzzy model is proposed for this purpose several new reproduction operators are introduced

recurrent neuro fuzzy networks for nonlinear process modeling a type of recurrent neuro fuzzy network is proposed in this paper to build long term prediction models for nonlinear processes the process operation is partitioned into several fuzzy operating regions within each region a local linear model is used to model the process the global model output is obtained through the centre of gravity defuzzification which is essentially the interpolation of local model outputs this modeling strategy utilizes both process knowledge and process input output data process knowledge is used to initially divide the process operation into several fuzzy operating regions and to set up the initial fuzzification layer weights process i o data are used to train the network network weights are such trained so that the long term prediction errors are minimized through training membership functions of fuzzy operating regions are refined and local models are learnt based on the recurrent neuro fuzzy network model a novel type of nonlinear model based long range predictive controller can be developed and it consists of several local linear model based predictive controllers local controllers are constructed based on the corresponding local linear models and their outputs are combined to form a global control action by using their membership functions this control strategy has the advantage that control actions can be calculated analytically avoiding the time consuming nonlinear programming procedures required in conventional nonlinear model based predictive control the techniques have been successfully applied to the modeling and control of a neutralization process

hybrid dirichlet mixture models for functional data summary in functional data analysis curves or surfaces are observed up to measurement error at a finite set of locations for say a sample of n individuals often the curves are homogeneous except perhaps for individual specific regions that provide heterogeneous behaviour e g damaged areas of irregular shape on an otherwise smooth surface motivated by applications with functional data of this nature we propose a bayesian mixture model with the aim of dimension reduction by representing the sample of n curves through a smaller set of canonical curves we propose a novel prior on the space of probability measures for a random curve which extends the popular dirichlet priors by allowing local clustering non homogeneous portions of a curve can be allocated to different clusters and the n individual curves can be represented as recombinations hybrids of a few canonical curves more precisely the prior proposed envisions a conceptual hidden factor with k levels that acts locally on each curve we discuss several models incorporating this prior and illustrate its performance with simulated and real data sets we examine theoretical properties of the proposed finite hybrid dirichlet mixtures specifically their behaviour as the number of the mixture components goes to 1 and their connection with dirichlet process mixtures

fuzzy identification using fuzzy neural networks with stable learning algorithms in general fuzzy neural networks cannot match nonlinear systems exactly unmodeled dynamic leads parameters drift and even instability problem according to system identification theory robust modification terms must be included in order to guarantee lyapunov stability this paper suggests new learning laws for mamdani and takagi sugeno kang type fuzzy neural networks based on input to state stability approach the new learning schemes employ a time varying learning rate that is determined from input output data and model structure stable learning algorithms for the premise and the consequence parts of fuzzy rules are proposed the calculation of the learning rate does not need any prior information such as estimation of the modeling error bounds this offer an advantage compared to other techniques using robust modification

extracting fuzzy rules for system modeling using a hybrid of genetic algorithms and kalman filter abstract this paper proposes a hybrid algorithm for extracting important fuzzy rules from a given rule base to construct a parsimonious fuzzy model with a high generalization ability this algorithm combines the advantages of genetic algorithms strong search capacity and kalman filter s fast convergence merit each random combination of the rules in the rule base is coded into a binary string and treated as a chromosome in genetic algorithms the binary string indicates the structure of a fuzzy model the parameters of the model are then estimated using the kalman filter in order to achieve a trade off between the accuracy and the complexity of a fuzzy model the schwarz rissanen criterion is used as an evaluation function in the hybrid algorithm the practical applicability of the proposed algorithm is examined by computer simulations on a human operator modeling problem and a nonlinear system modeling problem

learning and convergence analysis of neural type structured networks a class of feedforward neural networks structured networks has recently been introduced as a method for solving matrix algebra problems in an inherently parallel formulation a convergence analysis for the training of structured networks is presented since the learning techniques used in structured networks are also employed in the training of neural networks the issue of convergence is discussed not only from a numerical algebra perspective but also as a means of deriving insight into connectionist learning bounds on the learning rate are developed under which exponential convergence of the weights to their correct values is proved for a class of matrix algebra problems that includes linear equation solving matrix inversion and lyapunov equation solving for a special class of problems the orthogonalized back propagation algorithm an optimal recursive update law for minimizing a least squares cost functional is introduced it guarantees exact convergence in one epoch several learning issues are investigated

identification of linear time varying mdof dynamic systems from forced excitation using hilbert transform and emd method an algorithm is developed for the identification of linear time varying ltv multiple degrees of freedom systems it is based on the hilbert transform and the empirical mode decomposition with forced vibration response data the proposed identification algorithm is applied to single degree of freedom and multi degrees of freedom dynamic systems three ideal cases of ltv systems with smoothly varying abruptly varying and periodically varying stiffness and damping are studied to illustrate the capability of the algorithm to track the variations of the system simulation results demonstrate the effectiveness and the robustness of the proposed identification algorithm and the lack of complete orthogonality for any two intrinsic mode functions is one of the sources of error in the identification

identification and control of dynamic systems using recurrent fuzzy neural networks proposes a recurrent fuzzy neural network rfnn structure for identifying and controlling nonlinear dynamic systems the rfnn is inherently a recurrent multilayered connectionist network for realizing fuzzy inference using dynamic fuzzy rules temporal relations are embedded in the network by adding feedback connections in the second layer of the fuzzy neural network fnn the rfnn expands the basic ability of the fnn to cope with temporal problems in addition results for the fnn fuzzy inference engine universal approximation and convergence analysis are extended to the rfnn for the control problem we present the direct and indirect adaptive control approaches using the rfnn based on the lyapunov stability approach rigorous proofs are presented to guarantee the convergence of the rfnn by choosing appropriate learning rates finally the rfnn is applied in several simulations time series prediction identification and control of nonlinear systems the results confirm the effectiveness of the rfnn

maximum likelihood estimator of operational modal analysis for linear time varying structures in time frequency domain abstract this paper investigates the problem of modal parameter estimation of time varying structures under unknown excitation a time frequency domain maximum likelihood estimator of modal parameters for linear time varying structures is presented by adapting the frequency domain maximum likelihood estimator to the time frequency domain the proposed estimator is parametric that is the linear time varying structures are represented by a time dependent common denominator model to adapt the existing frequency domain estimator for time invariant structures to the time frequency methods for time varying cases an orthogonal polynomial and z domain mapping hybrid basis function is presented which has the advantageous numerical condition and with which it is convenient to calculate the modal parameters a series of numerical examples have evaluated and illustrated the performance of the proposed maximum likelihood estimator and a group of laboratory experiments has further validated the proposed estimator

fuzzy logic for digital phase locked loop filter design the problem of robust phase locked loop design has attracted attention for many years particularly since the advent of the global positioning system this paper proposes and demonstrates the use of a fuzzy pll to estimate the time varying phase of a sinusoidal signal it is shown via simulation results that fuzzy pll s offer performance comparable to analytically derived pll s e g kalman filters and h sub spl infin estimators when the phase exhibits high dynamics and high noise the fuzzy pll rules are optimized using a gradient descent method and a genetic algorithm

sequential adaptive fuzzy inference system safis for nonlinear system identification and prediction in this paper a sequential adaptive fuzzy inference system called safis is developed based on the functional equivalence between a radial basis function network and a fuzzy inference system fis in safis the concept of influence of a fuzzy rule is introduced and using this the fuzzy rules are added or removed based on the input data received so far if the input data do not warrant adding of fuzzy rules then only the parameters of the closest in a euclidean sense rule are updated using an extended kalman filter ekf scheme the performance of safis is compared with several existing algorithms on two nonlinear system identification benchmark problems and a chaotic time series prediction problem results indicate that safis produces similar or better accuracies with less number of rules compared to other algorithms

non stationary functional series tarma vibration modelling and analysis in a planar manipulator abstract the problem of non stationary stochastic vibration modelling and analysis is considered through a paradigm involving vibration analysis in a periodically varying manipulator a parametric functional series method based upon time dependent autoregressive moving average tarma models is applied for the first time within the vibration analysis context and comparisons with both pure tar and non parametric fourier based analysis are made these focus on achievable time dependent spectrum accuracy resolution and tracking as well as on estimated modal parameter accuracy the functional series tarma method is shown to lead unambiguously to a physically meaningful tarma 4 5 p 3 representation while the pure tar method leads to a tar 12 p 3 representation the tarma 4 5 p 3 model is shown to achieve superior spectral and modal parameter accuracy while avoiding the problem of estimated false modal modes of its tar 12 p 3 counterpart the tarma 4 5 p 3 model also attains lower parametric complexity and superior values of the model fit criteria the study demonstrates the facets and capabilities of the functional series tarma method for non stationary vibration analysis indicating that the tarma model s direct relationship with the underlying physical system constitutes an important asset of the method

training fuzzy systems with the extended kalman filter the generation of membership functions for fuzzy systems is a challenging problem we show that for mamdani type fuzzy systems with correlation product inference centroid defuzzification and triangular membership functions optimizing the membership functions can be viewed as an identification problem for a nonlinear dynamic system this identification problem can be solved with an extended kalman filter we describe the algorithm and compare it with gradient descent and with adaptive neuro fuzzy inference system anfis based optimization of fuzzy membership functions the methods discussed in this paper are illustrated on a fuzzy filter for motor winding current estimation and are compared with butterworth filtering we demonstrate that the kalman filter can be an effective tool for improving the performance of a fuzzy system

stability analysis and stabilization of fuzzy state space models abstract a new stability test method for linguistic fuzzy state space models is proposed in this paper this method allows the determination of stability of fuzzy models by applying the lyapunov function to each rule a gradient based algorithm is suggested to simplify the stability tests using this algorithm the lyapunov equation can be updated towards the direction where the stability can be determined more correctly an additional gradient based stabilizing algorithm is also derived which allows a systematic approach to find stabilizing controls by updating the lyapunov equations towards the direction where unstable eigenvalues are decreased examples demonstrate the convenience of the stability test and the two suggested gradient based algorithms

the poles and zeros of a linear time varying system abstract for linear time varying discrete time and continuous time systems a notion of poles and zeros is developed in terms of factorizations of operator polynomials with time varying coefficients in the discrete time case it is shown that the poles can be computed by solving a nonlinear recursion with time varying coefficients in the continuous time case the poles can be calculated by solving a nonlinear differential equation with time varying coefficients the theory is applied to the study of the zero input response and asymptotic stability it is shown that if a time varying analogue of the vandermonde matrix is invertible the zero input response can be decomposed into a sum of modes associated with the poles stability is then studied in terms of the components of the modal decomposition

extension of modal analysis to linear time varying systems linear time varying ltv systems have been often dealt with on a case by case basis many well developed concepts and analytic methods of linear time invariant lti systems cannot be applied to ltv systems for example the conventional definition of modal parameters is invalid for ltv systems the first part of this paper explores the possibility of extending the modal concept of ltv systems the discrete time state space model is used to represent ltv systems by analogy to lti systems the pseudo modal parameters are defined using the eigenvalues of the discrete time state transition matrix the paper shows that the pseudo modal parameters preserve certain properties of the conventional modal parameters defined for lti systems the second part of the paper extends a previously developed algorithm to identify the pseudo modal parameters using forced responses and forcing inputs for a general ltv system the input and output hankel matrices formed by an ensemble of data satisfy a matrix facotrization relation the key step of the method is to modify the output matrix in such a way that the range space of the observability matrix can be extracted a robotic manipulator with varying inertia links is used as an example the first part of the numerical simulation illustrates the applications of the pseudo modal parameters the second part of the simulation tests the identification algorithm under different conditions several practical issues are addressed

a recurrent self organizing neural fuzzy inference network a recurrent self organizing neural fuzzy inference network rsonfin is proposed the rsonfin is inherently a recurrent multilayered connectionist network for realizing the basic elements and functions of dynamic fuzzy inference and may be considered to be constructed from a series of dynamic fuzzy rules the temporal relations embedded in the network are built by adding some feedback connections representing the memory elements to a feedforward neural fuzzy network each weight as well as node in the rsonfin has its own meaning and represents a special element in a fuzzy rule there are no hidden nodes initially in the rsonfin they are created online via concurrent structure identification and parameter identification the structure learning together with the parameter learning forms a fast learning algorithm for building a small yet powerful dynamic neural fuzzy network two major characteristics of the rsonfin can thus be seen 1 the recurrent property of the rsonfin makes it suitable for dealing with temporal problems and 2 no predetermination like the number of hidden nodes must be given since the rsonfin can find its optimal structure and parameters automatically and quickly moreover to reduce the number of fuzzy rules generated a flexible input partition method the aligned clustering based algorithm is proposed various simulations on temporal problems are done and performance comparisons with some existing recurrent networks are also made efficiency of the rsonfin is verified from these results

implementation of evolutionary fuzzy systems evolutionary fuzzy systems are discussed in which the membership function shapes and types and the fuzzy rule set including the number of rules inside it are evolved using a genetic evolutionary algorithm in addition the genetic parameters operators of the evolutionary algorithm are adapted via a fuzzy system benefits of the methodology are illustrated in the process of classifying the iris data set possible extensions of the methods are summarized

the fuzzy kalman filter state estimation using possibilistic techniques a new method to implement fuzzy kalman filters is introduced the combination of possibilistic techniques and the extended kalman filter has special application in fields where inaccurate information is involved the novelty of this article comes from the fact that by using possibility distributions instead of gaussian distributions a fuzzy description of the expected state and observation is sufficient to obtain a good estimation some characteristics of this approach are that uncertainty does not need to be symmetric and that a wide region of possible values for the expectations is allowed to implement the algorithm this approach also contributes a method to propagate uncertainty through the process model and the observation model based on trapezoidal possibility distributions finally several examples of a real mobile robot moving through a localization process while using qualitative landmarks are shown

identification of linear time varying systems abstract this paper is concerned with the identification of linear time varying systems the discrete time state space model of freely vibrating systems is used as an identification model the focus is placed on identifying successive discrete transition matrices that have the same eigenvalues as the original transition matrices first a typical subspace based method is presented to illustrate the extraction of the observability range space using the singular value decomposition svd of a general hankel matrix then the identification of varying transition matrices is approached by using an ensemble of response sequences for arbitrarily varying systems a series of the hankel matrices are formed by an ensemble set of responses which are obtained through multiple experiments on the system with the same time varying behaviour the varying transition matrix at each moment is estimated through the svd of two successive hankel matrices the proposed algorithm is applied to two special cases that require only a single response series i e periodically varying systems and slowly varying systems the use of the eigenvalues of the transition matrices is discussed and the pseudomodal parameters are defined finally a two link manipulator subjected to a varying end force is used as an example to illustrate the tracking capability and performance of the proposed algorithm

fuzzy kalman filtering the classical kalman filtering kf algorithm has recently been extended to interval linear systems with interval parameters under the same statistical assumptions on noise where the new algorithm is called interval kalman filtering ikf scheme the ikf algorithm has the same structure and preserves the same optimality as the classical kf scheme but provides interval valued estimates if the interval system has confidence description about the distribution of its interval values we can further incorporate the ikf scheme with fuzzy logic inference so as to develop a new filtering algorithm called fuzzy kalman filtering fkf algorithm this algorithm preserves the same recursive mechanism of the kf and ikf but produces a scalar valued rather than an interval valued estimate at each iteration of the filtering process to compare the fkf to the ikf computer simulation is included which shows that the fkf is also robust against system parameter variations

stability analysis of discrete tsk type ii iii systems we propose a new approach for the stability analysis of discrete sugeno types ii and iii fuzzy systems the approach does not require the existence of a common lyapunov function we introduce the concept of fuzzy positive definite and fuzzy negative definite functions this new concept is used to replace classical positive and negative definite functions in arguments similar to those of traditional lyapunov stability theory we obtain the equivalent fuzzy system for a cascade of two type ii iii fuzzy systems we use the cascade of a system and a fuzzy lyapunov function candidate to derive new conditions for stability and asymptotic stability for discrete type ii and type iii fuzzy systems to demonstrate the new approach we apply it to numerical examples where no common lyapunov function exists

automatic design of hierarchical takagi sugeno type fuzzy systems using evolutionary algorithms this paper presents an automatic way of evolving hierarchical takagi sugeno fuzzy systems ts fs the hierarchical structure is evolved using probabilistic incremental program evolution pipe with specific instructions the fine tuning of the if then rule s parameters encoded in the structure is accomplished using evolutionary programming ep the proposed method interleaves both pipe and ep optimizations starting with random structures and rules parameters it first tries to improve the hierarchical structure and then as soon as an improved structure is found it further fine tunes the rules parameters it then goes back to improve the structure and the rules parameters this loop continues until a satisfactory solution hierarchical ts fs model is found or a time limit is reached the proposed hierarchical ts fs is evaluated using some well known benchmark applications namely identification of nonlinear systems prediction of the mackey glass chaotic time series and some classification problems when compared to other neural networks and fuzzy systems the developed hierarchical ts fs exhibits competing results with high accuracy and smaller size of hierarchical architecture

moving kriging shape function modeling of vector tarma models for modal identification of linear time varying structural systems abstract this work proposes a moving kriging mk shape function modeling method for modal identification of linear time varying ltv structural systems based on vector time dependent autoregressive moving average vtarma models it aims to avoid the functional subspaces selection of the conventional functional series vtarma fs vtarma models instead of the common basis functions it constructs the time varying coefficients on the time nodes with the mk shape functions in a compact support domain the merit of the mk shape function is to determine its shape parameters upon vector random vibration signals adaptively model identification is effectively dealt with through an optimization scheme that decomposes the identification problem into two subproblems estimating model parameters via two stage least squares 2sls method and estimating shape function parameters via a discrete continuous variable hybrid optimization in addition the model order selection is achieved by the optimization scheme this method has been validated by a monte carlo study of simulation case and further by an experimental test case and the performance and potential advantages are illustrated