brief paper least squares based iterative identification for a class of multirate systems this paper studies modeling and identification problems for multi input multirate systems with colored noises the state space models are derived for the systems with different input updating periods and furthermore the corresponding transfer functions are obtained to solve the difficulty of identification models with unmeasurable noises terms the least squares based iterative algorithm is presented by replacing the unmeasurable variables with their iterative estimates finally the simulation results indicate that the proposed iterative algorithm has advantages over the recursive algorithms

identification of arx models subject to missing data parameter estimation when the measurement information may be incomplete is discussed an arx model is used as a basic system representation the presentation covers both missing output and missing input first reconstruction of the missing values is discussed the reconstruction is based on a state space formulation of the system and is performed using kalman filtering or fixed interval smoothing formulas several approaches to the identification problem are presented including a new method based on the em expectation maximization algorithm the different approaches are tested and compared using monte carlo simulations the choice of method is always a tradeoff between estimation accuracy and computational complexity according to the simulations the gain in accuracy using the em method can be considerable if many data are missing

brief paper output prediction under scarce data operation control applications the problem of estimating the output in missing data situations is addressed in case a process model is present a simple algorithm is presented that uses the input output model difference equation replacing the unknown past values by estimates when necessary it is compared to state space approaches such as time varying kalman filtering the analysis of its convergence is carried out for the particular case of dual rate scarce sampling patterns the effects of disturbances are also studied the use of extended order models allows the design of the desired error dynamics applications such as parameter estimation and the control under scarce data operation are outlined

estimation of time series models in the presence of missing data abstract a method is proposed for the estimation of models for discrete time series in the presence of missing data some justification is given for the use of this method over alternatives the choice of estimator is likely to be governed by the pattern of missing data the nature of the time series model and computational considerations the method s performance in estimating simple models is studied by simulations and it is applied to a time series of pollution levels containing some missing observations

parameter estimation with scarce measurements in this paper the problems of parameter estimation are addressed for systems with scarce measurements a gradient based algorithm is derived to estimate the parameters of the input output representation with scarce measurements and the convergence properties of the parameter estimation and unavailable output estimation are established using the kronecker lemma and the deterministic version of the martingale convergence theorem finally an example is provided to demonstrate the effectiveness of the proposed algorithm

dual time frequency domain system identification in this paper we obtain the maximum likelihood estimate of the parameters of discrete time linear models by using a dual time frequency domain approach we propose a formulation that considers a reduced rank linear transformation of the available data such a transformation may correspond to different options selection of time domain data transformation to the frequency domain or selection of frequency domain data obtained from time domain samples we use the proposed approach to identify multivariate systems represented in state space form by using the expectation maximisation algorithm we illustrate the benefits of the approach via numerical examples

analysis and application of a novel fast algorithm for 2 d arma model parameter estimation abstract in this paper we analyze a novel algorithm for 2 d arma model parameter estimation in the presence of noise and then develop a fast and efficient blind image restoration algorithm we show that the novel algorithm can minimize a quadratic convex optimization problem and has a lower computational complexity than the conventional algorithms as a result the novel algorithm involves no convergence and local minimum issue moreover the proposed blind image restoration algorithm can overcome the local minimization problem computed results confirm that the novel algorithm can more quickly obtain more accurate estimates than the conventional algorithms in the presence of noise

identification of nonlinear membership function for failure of structural material and its application to structural optimization abstract the purpose of this paper is the identification and application of fuzzy membership function for material failure the concept of evolutionary damage in continuum damage mechanics is related with the decision of material failure in fuzzy set theory the failure phenomenon has a fuzzy nature and the internal state variable which indicates the degree of damage in continuum damage mechanics can be thought as a fuzzy membership function for failure in the structural design of machines such as automobiles airplanes and ships the results of the numerical analysis based on continuum damage mechanics which are verified by the uniaxial tensile test are introduced to obtain the evolution of the damage variable from which the fuzzy membership function for failure can be derived an exponential type fuzzy membership function is proposed to represent the fuzziness of material failure from the results of the numerical analysis in this study an elastoviscoplastic isotropic damage model of an isotropic hardening material is introduced and the three bar truss problem is revisited with the proposed fuzzy membership function which is applied to structural optimization

partially coupled stochastic gradient identification methods for non uniformly sampled systems this technical note addresses identification problems of non uniformly sampled systems for the input output representation of non uniform discrete time systems a partially coupled stochastic gradient c sg algorithm is proposed to estimate the model parameters with high computational efficiency compared with the standard stochastic gradient sg algorithm the analysis indicates that the partially c sg algorithm can give more accurate parameter estimates than the sg algorithm the parameter estimates obtained using the partially c sg algorithm converge to their true values as the data length approaches infinity

autoregressive spectral analysis when observations are missing a new missing data algorithm arfil gives good results in spectral estimation the log likelihood of a multivariate gaussian random variable can always be written as a sum of conditional log likelihoods for a complete set of autoregressive ar p data the best predictor in the likelihood requires only p previous observations if observations are missing the best ar predictor in the likelihood will in general include all previous observations using only those observations that fall within a finite time interval will approximate this likelihood the resulting non linear estimation algorithm requires no user provided starting values in various simulations the spectral accuracy of robust maximum likelihood methods was much better than the accuracy of other spectral estimates for randomly missing data

maximum likelihood estimation of gaussian models with missing data eight equivalent formulations in this paper we derive the maximum likelihood problem for missing data from a gaussian model we present in total eight different equivalent formulations of the resulting optimization problem four out of which are nonlinear least squares formulations among these formulations are also formulations based on the expectation maximization algorithm expressions for the derivatives needed in order to solve the optimization problems are presented we also present numerical comparisons for two of the formulations for an armax model

performance analysis of multi innovation gradient type identification methods it is well known that the stochastic gradient sg identification algorithm has poor convergence rate in order to improve the convergence rate we extend the sg algorithm from the viewpoint of innovation modification and present multi innovation gradient type identification algorithms including a multi innovation stochastic gradient misg algorithm and a multi innovation forgetting gradient mifg algorithm because the multi innovation gradient type algorithms use not only the current data but also the past data at each iteration parameter estimation accuracy can be improved finally the performance analysis and simulation results show that the proposed misg and mifg algorithms have faster convergence rates and better tracking performance than their corresponding sg algorithms

multi objective optimization of fuzzy structural systems it is recognized that there exists a vast amount of fuzzy information in both the objective and constraint functions of the optimum design of structures since most practical structural design problems involve several often conflicting objectives to be considered a multi objective fuzzy programming method is outlined in this work the fuzzy constraints define a fuzzy feasible domain in the design space and each of the fuzzy objective functions defines the optimum solution by a fuzzy set of points a method of solving a fuzzy multi objective structural optimization problem using ordinary single objective programming techniques is presented the computational approach is illustrated with two numerical examples

identification of continuous time arx models from irregularly sampled data the problem of estimating the parameters in a continuous time arx process from unevenly sampled data is studied a solution where the differentiation operator is replaced by a difference operator is suggested in the paper results are given for how the difference operator should be chosen in order to obtain consistent parameter estimates the proposed method is considerably faster than conventional methods such as the maximum likelihood method the crameacuter rao bound for estimation of the parameters is computed in the derivation the slepian bangs formula is used together with a state space framework resulting in a closed form expression for the crameacuter rao bound numerical studies indicate that the crameacuter rao bound is reached by the proposed method

parameter identification of systems with preload nonlinearities based on the finite impulse response model and negative gradient search abstract this paper considers identification problems of a class of nonlinear systems by introducing a switching function and the finite impulse response model we obtain the identification model of a preload nonlinear system and develop a stochastic gradient algorithm to the parameters of the system furthermore a stochastic gradient algorithm with a forgetting factor is given to improve the identification accuracy a simulation results indicate that the forgetting factor can improve the parameter estimation accuracy

lms like ar modeling in the case of missing observations this paper presents a new recursive algorithm for the time domain reconstruction and spectral estimation of uniformly sampled signals with missing observations an autoregressive ar modeling approach is adopted the ar parameters are estimated by optimizing a mean square error criterion the optimum is reached by means of a gradient method adapted to the nonperiodic sampling the time domain reconstruction is based on the signal prediction using the estimated model the power spectral density is obtained using the estimated ar parameters the development of the different steps of the algorithm is discussed in detail and several examples are presented to demonstrate the practical results that can be obtained the spectral estimates are compared with those obtained by known ar estimators applied to the same signals sampled periodically we note that this algorithm can also be used in the case of nonstationary signals

on periodic pulse interval analysis with outliers and missing observations analysis of periodic pulse trains based on time of arrival is considered with perhaps very many missing observations and contaminated data a period estimator is developed based on a modified euclidean algorithm this algorithm is a computationally simple robust method for estimating the greatest common divisor of a noisy contaminated data set the resulting estimate although it is not maximum likelihood is used as initialization in a three step algorithm that achieves the cramer rao bound crb for moderate noise levels as shown by comparing monte carlo results with the crbs this approach solves linear regression problems with missing observations and outliers comparisons with a periodogram approach based on a point process model are shown an extension using multiple independent data records is also developed that overcomes high levels of contamination

generalized method of moments estimation of location parameters application to blind phase acquisition in this paper we address the problem of location parameter estimation via a generalized method of moments gmm approach the general framework for the gmm estimation requires the minimization of a suitable generally nonconvex elliptic norm here we show that if the estimandum is a shift parameter for a suitable statistic of the observations a fast dft based computationally efficient procedure can be employed to perform the estimation besides we discuss the relation between the gmm estimation and the maximum likelihood ml estimation showing that the gmm estimation rule provides a closed form ml estimator for shift parameters when the observations are multinomially distributed as a case study we analyze a gmm blind phase offset estimator for general quadrature amplitude modulation constellations simulation results and theoretical performance analysis show that the gmm estimator outperforms selected state of the art estimators approaching the cramer rao lower bound for a wide range of signal to noise ratio values

brief paper robust filtering with stochastic nonlinearities and multiple missing measurements this paper is concerned with the filtering problem for a class of discrete time uncertain stochastic nonlinear time delay systems with both the probabilistic missing measurements and external stochastic disturbances the measurement missing phenomenon is assumed to occur in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval 01 such a probabilistic distribution could be any commonly used discrete distribution over the interval 01 the multiplicative stochastic disturbances are in the form of a scalar gaussian white noise with unit variance the purpose of the addressed filtering problem is to design a filter such that for the admissible random measurement missing stochastic disturbances norm bounded uncertainties as well as stochastic nonlinearities the error dynamics of the filtering process is exponentially mean square stable by using the linear matrix inequality lmi method sufficient conditions are established that ensure the exponential mean square stability of the filtering error and then the filter parameters are characterized by the solution to a set of lmis illustrative examples are exploited to show the effectiveness of the proposed design procedures

optimal design of laminated composite plates in a fuzzy environment the present study focuses on a fuzzy optimization approach to the optimal design of simply supported laminated composite plates the goal is minimum weight design of the composite plates the design constraints are the magnitude of center displacement and lamina failure criteria a procedure of two level optimization in a fuzzy environment is presented and this procedure is applied to the design of laminated composite plates to consider the influences of fiber direction and thickness of each lamina separately it is shown that the membership function in the case of failure can be deduced from continuum damage mechanics the membership function for failure criteria is the function of the internal state variable for degree of damage in the continuum damage mechanics the modified weibull membership function is chosen to be used as a simple case of damage progression the finite element method is used to calculate the displacement of the plate and the stresses of each lamina the fuzzy optimization formulation as a max min problem is transformed into a classical one this classical optimization problem is solved using the augmented lagrange multiplier method with the quasi newton method two examples are solved to demonstrate the procedure from the results it is shown that optimal design of laminated composite plates is more useful in a fuzzy environment and the modified weibull membership function characterizes the fuzziness of failure nomenclature bi upper limit of the inequality constraint d fuzzy decision f x objective function f x fuzzy goal

robust h control for a class of nonlinear discrete time delay stochastic systems with missing measurements this paper is concerned with the problem of robust h output feedback control for a class of uncertain discrete time delayed nonlinear stochastic systems with missing measurements the parameter uncertainties enter into all the system matrices the time varying delay is unknown with given low and upper bounds the nonlinearities satisfy the sector conditions and the missing measurements are described by a binary switching sequence that obeys a conditional probability distribution the problem addressed is the design of an output feedback controller such that for all admissible uncertainties the resulting closed loop system is exponentially stable in the mean square for the zero disturbance input and also achieves a prescribed h performance level by using the lyapunov method and stochastic analysis techniques sufficient conditions are first derived to guarantee the existence of the desired controllers and then the controller parameters are characterized in terms of linear matrix inequalities lmis a numerical example is exploited to show the usefulness of the results obtained

parameter estimation of dual rate stochastic systems by using an output error method in this note a new gradient based recursive algorithm for estimating parameters of dual rate sampled data systems is presented the basic idea is by using an output error method to identify the single rate models and the unknown noise free outputs true outputs directly from dual rate input output data further convergence properties of the proposed algorithm in parameter and output estimation are analyzed and the result is illustrated and tested with an experimental water level system

reduced dimension blind space time 2 d rake receivers for ds cdma communication systems blind space time rake receivers for classical ds cdma that cancel strong multiuser access interference while optimally combining the desired user s multipath are presented the delay spread is assumed to be fraction of a symbol interval as in the is 95 cdma standard the post correlation symbol interval is segmented into that which encompasses the rake fingers and that away from the rake fingers the signal plus interference and interference alone space time correlation matrices are estimated during the former and latter respectively reduced dimension space time rake receivers are investigated for alleviation of the computational burden of computing the largest generalized eigenvector of the resulting matrix pencil theoretical analysis and supporting simulations reveal that if the space and time compressing transformations are designed judiciously reduced dimension two dimensional 2 d rake receivers offer faster convergence at the expense of only a slight loss in asymptotic signal to interference plus noise ratio sinr relative to the full dimension space time rake receiver applications to the is 95 uplink are also presented along with supporting simulations

hierarchical estimation algorithms for multivariable systems using measurement information abstract with the development of industry information technology many modelling methods have been focusing on the estimation problems of multivariable systems especially for the multivariable systems with output error autoregressive noises from input output measurement information since such a system includes both a parameter vector and a parameter matrix the conventional methods cannot be applied to parameter estimation and modelling in order to solve this difficulty a hierarchical least squares based iterative identification algorithm and a hierarchical generalized least squares identification algorithm are proposed the basic idea is to decompose the system into two fictitious subsystems to estimate the parameters of each subsystem and to coordinate the associated items between the two subsystems the simulation results indicate that the proposed algorithm is effective

lattice algorithm for adaptive stable identification and robust reconstruction of nonstationary ar processes with missing observations this paper deals with the problem of adaptive reconstruction and identification of nonstationary ar processes with randomly missing observations existent methods use a direct realization of the filter therefore the estimated parameters may not correspond to a stable all pole filter in addition when the probability of missing a sample is high existent methods may converge slowly or even fail to converge we propose at our knowledge the first algorithm based on the lattice structure for online processing of signals with missing samples it is an extension of the rlsl algorithm to the case of missing observations using a kalman filter for the prediction of missing samples the estimated parameters guarantee the stability of the corresponding all pole filter in addition it is robust to high probabilities of missing a sample it offers a fast parameter tracking even for high probabilities of missing a sample it is compared to the kalman pseudolinear rls algorithm an already proposed algorithm using a direct realization of the filter the proposed algorithm shows better performance in reconstruction of audio signals

fuzzy goal programming approach for water quality management in a river basin abstract two fuzzy goal programming fgp approaches are applied to water quality management in a river basin for solving multiobjective optimization problems involving vague and imprecise information several fgp models including equal weight and unequal weight nonpreemptive priority and preemptive priority are proposed to assist water quality management involving multiple conflicting goals optimal water quality management involves obtaining optimal analysis of assimilative capacity also referred to as allowable pollution loading and treatment cost of wastewater based on models and standards of water quality as well as an equitable removal of wastewater in a river basin two fgp schemes that are capable of maximizing achieved membership function and minimizing the deviation from a set of preferred target assimilative capacity and treatment cost are considered moreover methodologies using two fuzzy decision theories in fgp approaches i e max min operator and compensatory operator are also proposed those methodologies are illustrated in a case study of multiobjective water quality management in the tou chen river basin taiwan the case study demonstrates the capability of the two fgp approaches based on variable fuzzy decision theories to work suitably in water quality management in a river basin

a method using fuzzy mathematics to solve the vectormaximum problem in this paper a new solution of the vectormaximum problem will be defined in terms of fuzzy mathematics and may be called the fuzzy solution it will overcome difficulties which appear if otherwise solved by nonfuzzy mathematics in this paper the relation between this solution and the important concepts of vecormaximum problem the efficient and weak efficient solutions will be shown

observable state space realizations for multivariable systems this paper derives two canonical state space forms i e the observer canonical form and the observability canonical form from multiple input multiple output systems described by difference equations the state space model is expressed by the first order difference equation and is equivalent to the input output representation more specifically by setting the different state variables the difference equations or the input output representations can be transformed into two observable canonical forms and the canonical state space model can be also transformed into the difference equations finally two examples are given

modifications of the euclidean algorithm for isolating periodicities from a sparse set of noisy measurements modifications of the euclidean algorithm are presented for determining the period from a sparse set of noisy measurements the elements of the set are the noisy occurrence times of a periodic event with perhaps very many missing measurements this problem arises in radar pulse repetition interval pri analysis in bit synchronization in communications and in other scenarios the proposed algorithms are computationally straightforward and converge quickly a robust version is developed that is stable despite the presence of arbitrary outliers the euclidean algorithm approach is justified by a theorem that shows that for a set of randomly chosen positive integers the probability that they do not all share a common prime factor approaches one quickly as the cardinality of the set increases in the noise free case this implies that the algorithm produces the correct answer with only 10 data samples independent of the percentage of missing measurements in the case of noisy data simulation results show for example good estimation of the period from 100 data samples with 50 of the measurements missing and 25 of the data samples being arbitrary outliers

parameter estimation of cyclostationary am time series with application to missing observations time series with systematic misses occur often in practice and can be modeled as amplitude modulated arma processes with this as a motivating application modeling of cyclostationary amplitude modulated time series is addressed in the paper assuming that the modulating sequence is almost periodic parameter estimation algorithms are developed based on second and higher order cumulants of the resulting cyclostationary observations which may be corrupted by any additive stationary noise of unknown covariance if unknown the modulating sequence can be recovered even in the presence of additive perhaps nonstationary and colored gaussian or any symmetrically distributed noise if the arma process is nongaussian cyclic cumulants of order greater than three can identify non causal and non minimum phase models from partial noisy data simulation experiments corroborate the theoretical results

optimal input design for identifying parameters and orders of mimo systems with initial values along with the development of modern industrial systems the identification issues for multi input multi output mimo systems have attracted much attention initial values of systems have an influence both on the input and output which directly reduces the accuracy of estimated model parameters to solve the identification problem for mimo systems with initial values this paper proposes a simple and efficient identification method containing the optimal input design the multi dimensional inverse m sequences are used as the input signals which both basically meet the requirements of optimal input design and have a reference value in the practical applications based on the optimal input design we can eliminate the influence of initial values generated by the system and develop an identification algorithm for multi input multi output stochastic systems by means of finite impulse response fir models finally the identification procedure is to discuss the pade approximation method to produce the parameter estimates and further to use the loss functions to determine the orders of mimo systems the simulation results show that the proposed method is quite efficient

brief paper structure detection and parameter estimation for narx models in a unified em framework in this paper we consider structure detection and parameter estimation of the nonlinear auto regressive with exogenous inputs narx model using the em expectation maximisation algorithm the parameter estimation step uses particle smoothing to obtain the necessary expectations in the e step and the parameters are then estimated in closed form in the m step the model structure detection is performed using an f test which makes use of the parameter information matrix inverse of the covariance matrix obtained from an augmentation of the em algorithm the steps for obtaining the information matrix are robust guaranteeing a positive semi definite information matrix to use in the structure detection step for the case of unknown model orders a method is proposed using the stochastic complexity sc information criterion for selecting between candidate models the sc is composed of the information matrix representing model complexity and a likelihood estimate representing model accuracy which are both generated as byproducts of the augmented em algorithm numerical results demonstrate that the em approach performs well in comparison to a standard alternative based on orthogonal least squares and also avoids the need to estimate a noise model for the case of measurement noise corrupted output signals

maximum likelihood parameter estimation of bilinear systems this paper addresses the problem of estimating the parameters in a multivariable bilinear model on the basis of observed input output data the main contribution is to develop analyze and empirically study new techniques for computing a maximum likelihood based solution in particular the emphasis here is on developing practical methods that are illustrated to be numerically reliable robust to choice of initialization point and numerically efficient in terms of how computation and memory requirements scale relative to problem size this results in new methods that can be reliably deployed on systems of nontrivial state input and output dimension underlying these developments is a new approach in this context of employing the expectation maximization method as a means for robust and gradient free computation of the maximum likelihood solution

estimation prediction and interpolation for arima models with missing data abstract we show how to define and then compute efficiently the marginal likelihood of an arima model with missing observations the computation is carried out by using the univariate version of the modified kalman filter introduced by ansley and kohn 1985a which allows a partially diffuse initial state vector we also show how to predict and interpolate missing observations and obtain the mean squared error of the estimate

bifurcation diagrams for feedback families of linear systems abstract the purpose of this note is to give a proof of the theorem on the form of bifurcation diagrams for generic feedback families of linear systems announced in 1 the main result stated as theorem 3 1 provides explicit algebraic description of the diagrams

hierarchical least squares based iterative estimation algorithm for multivariable box jenkins like systems using the auxiliary model abstract this paper presents a hierarchical least squares iterative algorithm to estimate the parameters of multivariable box jenkins like systems by combining the hierarchical identification principle and the auxiliary model identification idea the key is to decompose a multivariable systems into two subsystems by using the hierarchical identification principle as there exist the unmeasurable noise free outputs and noise terms in the information vector the solution is using the auxiliary model identification idea to replace the unmeasurable variables with the outputs of the auxiliary model and the estimated residuals a numerical example is given to show the performance of the proposed algorithm

novel parameter estimation of autoregressive signals in the presence of noise this paper proposes a new method for estimating the parameters of an autoregressive ar signal from observations corrupted by white noise the feature of the new method is that the observation noise variance estimate is converted into the only solution of a nonlinear equation to yield unbiased estimate of the ar parameters moreover a convergent newton iterative algorithm with a deterministic initial point is presented for efficient implementation of the proposed new estimation method as a result the proposed new method can minimize the error of estimating the variance of the observation noise since more accurate estimates of this observation noise variance can be attained at earlier stages the proposed method can achieve a good performance in estimating the ar signal parameters numerical results demonstrate that the proposed new algorithm is more effective in terms of accuracy and robustness against noise than conventional algorithms

maximum likelihood stochastic gradient estimation for hammerstein systems with colored noise based on the key term separation technique this paper considers the identification problems of hammerstein finite impulse response moving average fir ma systems using the maximum likelihood principle and stochastic gradient method based on the key term separation technique in order to improve the convergence rate a maximum likelihood multi innovation stochastic gradient algorithm is presented the simulation results show that the proposed algorithms can effectively estimate the parameters of the hammerstein fir ma systems

a parametric representation of additive value functions this paper introduces a new parameter for measuring deterministic preference tradeoffs between pairs of attributes in terms of this parameter necessary and sufficient conditions for a value function to be additive are established when additivity conditions are satisfied a set of these parameters is shown to characterize the value function uniquely up to a set of scaling constants implications for assessment for transforming a nonadditive representation into an additive one and for multiattribute utility functions are presented

robust maximum likelihood estimation of multivariable dynamic systems this paper examines the problem of estimating linear time invariant state space system models in particular it addresses the parametrization and numerical robustness concerns that arise in the multivariable case these difficulties are well recognised in the literature resulting for example in extensive study of subspace based techniques as well as recent interest in data driven local co ordinate approaches to gradient search solutions the paper here proposes a different strategy that employs the expectation maximisation em technique the consequence is an algorithm that is iterative with associated likelihood values that are locally convergent to stationary points of the gaussian likelihood function furthermore theoretical and empirical evidence presented here establishes additional attractive properties such as numerical robustness avoidance of difficult parametrization choices the ability to naturally and easily estimate non zero initial conditions and moderate computational cost moreover since the methods here are maximum likelihood based they have associated known and asymptotically optimal statistical properties

generalized hybrid method for fuzzy multiobjective optimization of engineering systems a generalized hybrid approach is presented for the multiobjective optimization of engineering systems in the presence of objectives and constraints that are partly fuzzy and partly crisp the methodology is based on both fuzzy set and dempster shafer theories to capture the features of incomplete imprecise uncertain or vague information that is often present in real world engineering systems the original partly fuzzy multiobjective optimization problem is first defuzzified into a crisp generalized multiobjective optimization problem using fuzzy set theory the resulting multiobjective problem is then transformed into an equivalent single objective optimization problem using a modified dempster shafer theory the computational details of the approach are illustrated with a structural design example

arma spectral estimation of time series with missing observations the problem of estimating the power spectral density of stationary time series when the measurements are not contiguous is considered a new autoregressive moving average arma method is proposed for this problem based on nonlinear optimization of a weighted squared error criterion the method can handle either regularly or randomly missing observations as a special case the method can handle the problem of missing sample covariances the computational complexity is modest compared to exact maximum likelihood estimation of the same parameters the performance of the algorithm is illustrated by some numerical examples and is shown to be statistically efficient in these cases

a complete characterization of orbit closures of controllable singular systems under restricted system equivalence in this paper properties of the orbit space of controllable generalized state space systems modulo restricted system equivalence are derived in particular it is shown that this space is a smooth quasiprojective variety of dimension nm then the possible degenerations of controllable systems under transformations of restricted system equivalence are characterized and it is proved that every noncontrollable system can be approximated by a family of controllable systems that belong to a single equivalence class in the single input case this class is uniquely determined whereas in the multivariable case a noncontrollable system may lie in the boundary of finitely or even infinitely many equivalence classes

multi innovation stochastic gradient algorithm for multiple input single output systems using the auxiliary model in order to reduce computational burden and improve the convergence rate of identification algorithms an auxiliary model based multi innovation stochastic gradient am misg algorithm is derived for the multiple input single output systems by means of the auxiliary model identification idea and multi innovation identification theory the basic idea is to replace the unknown outputs of the fictitious subsystems in the information vector with the outputs of the auxiliary models and to present an auxiliary model based stochastic gradient algorithm and then to derive the am misg algorithm by expanding the scalar innovation to innovation vector and introducing the innovation length the simulation example shows that the proposed algorithms work quite well

a fuzzy goal programming approach to multi objective optimization problem with priorities abstract in goal programming problem the general equilibrium and optimization are often two conflicting factors this paper proposes a generalized varying domain optimization method for fuzzy goal programming fgp incorporating multiple priorities according to the three possible styles of the objective function the varying domain optimization method and its generalization are proposed this method can generate the results consistent with the decision maker dm s expectation that the goal with higher priority may have higher level of satisfaction using this new method it is a simple process to balance between the equilibrium and optimization and the result is the consequence of a synthetic decision between them in contrast to the previous method the proposed method can make that the higher priority achieving the higher satisfactory degree to get the global solution of the nonlinear nonconvex programming problem resulting from the original problem and the varying domain optimization method the co evolutionary genetic algorithms gas called genocopiii is used instead of the sqp method in this way the dm can get the optimum of the optimization problem we demonstrate the power of this proposed method by illustrative examples

two stage least squares based iterative identification algorithm for controlled autoregressive moving average carma systems a two stage least squares based iterative two stage lsi identification algorithm is derived for controlled autoregressive moving average carma systems the basic idea is to decompose a carma system into two subsystems and to identify each subsystem respectively because the dimensions of the involved covariance matrices in each subsystem become small the proposed algorithm has a high computational efficiency the simulation results indicate that the proposed algorithm is effective

fuzzy goal programming with different importance and priorities abstract this paper formulates fuzzy goal programming fgp incorporating different importance and preemptive priorities by using an additive model to maximize the sum of achievement degrees of all fuzzy goals in contrast to previous works the proposed approach allows the decision maker to determine a desirable achievement degree for each fuzzy goal to reflect explicitly the relative importance of these goals this approach can generate a set of achievement degrees consistent with the decision maker s expectations even though the relative importance of the goals may change furthermore in this paper we incorporate the decision maker s preemptive priority structure into a single formulation the resulting solutions satisfy both the preemptive priority structure and have the maximum achievement degrees in sum the proposed approaches effectiveness and computational superiority over the existing approaches are demonstrated and compared with examples from the literature

system parameter estimation with input output noisy data and missing measurements an investigation is undertaken to examine the parameter estimation problem of linear systems when some of the measurements are unavailable i e missing data and the probability of occurrence of missing data is unknown a priori the system input and output data are also assumed to be corrupted by measurement noise and the knowledge of the noise distribution is unknown under the unknown noise distribution and missing measurements a consistent parameter estimation algorithm which is based on an l sub p norm iterative estimation algorithm iteratively reweighted least squares irls is proposed to estimate the system parameters we show that if the probability of missing measurement is less than one half the parameter estimates via the proposed estimation algorithm will converge to the true parameters as the number of data tends to infinity finally several simulation results are presented to illustrate the performance of the proposed l sub p norm iterative estimation algorithm simulation results indicate that under input output missing data and noise environment the proposed parameter estimation algorithm is an efficient approach toward the system parameter estimation problem

a multi innovation generalized extended stochastic gradient algorithm for output nonlinear autoregressive moving average systems this paper proposes a generalized extended stochastic gradient gesg algorithm for estimating the parameters of a class of wiener nonlinear autoregressive moving average systems using the gradient search in order to improve the convergence rates of the gesg algorithm a multi innovation gesg algorithm is derived the simulation results indicate that the proposed algorithms can effectively estimate the parameters of a class of output nonlinear systems

reconstruction of continuous time systems from their non uniformly sampled discrete time systems a continuous time system cannot be recovered solely from its uniformly sampled discrete time model through the zero order hold discretization or step invariant transformation but our studies indicate that it can be recovered uniquely from its non uniformly sampled discrete time model in this paper we discuss some related issues of non uniformly sampled systems including model derivation controllability and observability computation of single rate models with different sampling periods reconstruction of continuous time systems and parameter identification of non uniformly sampled discrete time systems a numerical example is also given for illustration

the second order moments of the sample covariances for time series with missing observations the estimation of the covariances of a stationary time series with missing observations is considered general formulas for the asymptotic second order moments of the sample covariances of such a time series are given for either random or deterministic patterns of misses closed form expressions are derived for the random bernoulli pattern and for the deterministic periodic pattern of missing observations and are explicitly evaluated for autoregressive moving average time series these results are useful for constructing and analyzing parameter or spectrum estimation algorithms based on the sample covariances for a stationary time series with missing observations

combined parameter and output estimation of dual rate systems using an auxiliary model for a dual rate sampled data system an auxiliary model based identification algorithm for combined parameter and output estimation is proposed the basic idea is to use an auxiliary model to estimate the unknown noise free output true output of the system and directly to identify the parameters of the underlying fast single rate model from the dual rate input output data it is shown that the parameter estimation error consistently converges to zero under generalized or weak persistent excitation conditions and unbounded noise variance and that the output estimates uniformly converge to the true outputs an example is included

a canonical parameterization of the kronecker form of a matrix pencil abstract the kronecker form is the classical canonical form for matrix pencils under strict equivalence transformation consider a matrix pencil whose entries are smooth functions of a parameter vector the kronecker form of the parameterized pencil will in general be a discontinuous function of the parameters for a linear time invariant control system these discontinuities correspond to a change in the finite and infinite invariant zero structure since many control strategies require knowledge of or place restrictions on the zero structure these points of discontinuity are of considerable interest in this paper a general approach to the study of such points is developed in the framework of singularity theory we derive a miniversal parameterization of a given pencil that is a parameterized family of pencils that i includes the given pencil ii is locally equivalent to any other family up to a change of parameters and iii uses the fewest number of parameters to achieve this property all nearby zero structures can be obtained by varying parameter values in the miniversal parameterization from all miniversal parameterizations one having a particularly uncluttered representation is selected as canonical however some restrictions on the finite elementary divisors are then required

brief recursive identification under scarce measurements convergence analysis in this paper the problem of recursive identification under scarce data operation is addressed the control action is assumed to be updated at a fixed rate while the output is assumed to be measured synchronously with the input update but with an irregular availability pattern under these conditions the use of pseudo linear recursive algorithms is studied the main result is the convergence analysis for the case of regular but scarce data availability the existence of wrong attractors is demonstrated and a local stability condition of the identification algorithm is derived

optimal arma parameter estimation based on the sample covariances for data with missing observations the problem of spectral estimation through the autoregressive moving average arma modeling of stationary processes with missing observations is considered a class of estimators based on the sample covariances is presented and an asymptotically optimal estimator in this class is proposed the proposed algorithm is based on a nonlinear least squares fit of the sample covariances computed from the data to the true covariances of the assumed arma model the statistical properties of the algorithm are explored and used to show that it is asymptotically optimal in the sense of achieving the smallest possible asymptotic variance the performance of the algorithm is illustrated by some numerical examples

fuzzy goal programming with nested priorities abstract this paper proposes a new approach to formulating fuzzy priorities in a goal programming problem the proposed methodology remedies certain shortcomings of the composite membership function approach discussed in previous works 7 10 the principal advantage of the proposed method is that it leads to a formulation in which tradeoffs between goals more closely reflect the decision maker s intentions than in other noninteractive approaches 8 9 10 14 in some of which a fixed hierarchy of goals is assumed

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

exact likelihood of vector autoregressive moving average process with missing or aggregated data summary this note points out that by using the kalman filter with nonconstant coefficients we can compute the exact likelihood of an autoregressive moving average process observed with noise when some of our observations are either missing or aggregated

nonlinear membership functions in multiobjective fuzzy optimization of mechanical and structural systems an application of fuzzy mathematical programming techniques to multiple objective design problems is presented two examples dealing with the multiobjective design of mechanical and structural systems are considered the concept of a pareto optimal and fuzzy pareto optimal solution is discussed and it is shown that the resulting formulation yields pareto optimal solutions the fundamental assumption in fuzzy mathematical programming applications involving the use of linear membership functions is critically examined several nonlinear shapes for the membership functions of the fuzzy sets are proposed consistent with varying perceptions of the designer and are analyzed to determine their impact on the overall design process these shapes correspond to what we define as the coefficient of membership satiation it is seen that optimum designs for both examples are strongly influenced by the sign of the membership satiation coefficient

self tuning control based on multi innovation stochastic gradient parameter estimation abstract this paper uses the multi innovation stochastic gradient misg algorithm to estimate the parameters of discrete time systems and presents an misg based self tuning control scheme furthermore we prove that the parameter estimation error converges to zero under persistent excitation and the parameter estimation based control algorithm can asymptotically achieve virtually optimal control and ensure that the closed loop systems are stable and globally convergent the simulation example is included

the burg algorithm for segments in many applications the duration of an uninterrupted measurement of a time series is limited however it is often possible to obtain several separate segments of data the estimation of an autoregressive model from this type of data is discussed a straightforward approach is to take the average of models estimated from each segment separately in this way the variance of the estimated parameters is reduced however averaging does not reduce the bias in the estimate with the burg algorithm for segments both the variance and the bias in the estimated parameters are reduced by fitting a single model to all segments simultaneously as a result the model estimated with the burg algorithm for segments is more accurate than models obtained with averaging the new weighted burg algorithm for segments allows combining segments of different amplitudes

bounds on the accuracy of gaussian arma parameter estimation methods based on sample covariances the asymptotic accuracy of gaussian arma parameter estimation methods based on a fixed number of sample covariances is considered several key results are briefly reviewed including i a general asymptotic expression for the error covariance of the arma parameter estimates ii the fact that this error covariance is always greater than a certain lower bound iii the fact that this lower bound is strictly greater than the cramer rao bound iv an explicit arma estimation technique that asymptotically achieves the bound the key result of this note is a proof that this lower bound approaches the cramer rao bound as the number of sample covariances tends to infinity

miniversal deformations of linear systems under the full group action abstract we consider the equivalence relation in the space of time invariant linear dynamical systems of the form x ax bu y cx du under the full group action of state feedback output injection transformations as in the case of the reduction of a matrix to its jordan canonical form the reduction of a quadruple a b c d defining a system as above to its canonical reduced form is an unstable operation following v i arnold s techniques the starting point for the study of local perturbations is to obtain a miniversal deformation of a differentiable family of quadruples in this paper a real miniversal deformation and some applications are shown

a method for solving fuzzy goal programming problems based on minmax approach abstract narasimhan incorporated fuzzy set theory within goal programming formulation in 1980 since then numerous research has been carried out in this field one of the well known models for solving fuzzy goal programming problems was proposed by hannan in 1981 in this paper the conventional minmax approach in goal programming is applied to solve fuzzy goal programming problems it is proved that the proposed model is an extension to hannan model that deals with unbalanced triangular linear membership functions in addition it is shown that the new model is equivalent to a model proposed in 1991 by yang et al moreover a weighted model of the new approach is introduced and is compared with kim and whang s model presented in 1998 a numerical example is given to demonstrate the validity and strengths of the new models

estimation of multicomponent polynomial phase signals with missing observations in contrast to the assumption of perfect observations by a number of developed methods for the analysis of nonstationary signals missing observations do occur in practice which lead to performance degradation we consider the parameter estimation problem of multicomponent polynomial phase signals pps when there are randomly missing observations the derivation shows that the cramer rao bound for the missing observations case can be readily obtained from the result of perfect observations then we propose an expectation maximization based method to estimate the pps parameters simulation results show that the proposed method approaches the cramer rao bound at moderate to high signal to noise ratios whilst standard techniques fail when there is a fair amount of missing observations

hierarchical least squares identification for linear siso systems with dual rate sampled data this technical note studies identification problems for dual rate sampled data linear systems with noises a hierarchical least squares hls identification algorithm is presented to estimate the parameters of the dual rate armax models the basic idea is to decompose the identification model of a dual rate system into several sub identification models with smaller dimensions and fewer parameters the proposed algorithm is more computationally efficient than the recursive least squares rls algorithm since the rls algorithm requires computing the covariance matrix of large sizes while the hls algorithm deals with the covariance matrix of small sizes compared with our previous work a detailed study of the hls algorithm is conducted in this technical note the performance analysis and simulation results confirm that the estimation accuracy of the proposed algorithm are close to that of the rls algorithm but the proposed algorithm retains much less computational burden

skew symmetric matrix pencils codimension counts and the solution of a pair of matrix equations the homogeneous system of matrix equations x t a ax xb b t bx 0 0 where a b is a pair of skew symmetric matrices of the same size is considered we establish the general solution

optimization of actively controlled structures using goal programming techniques the problem of design of actively controlled structures subject to restrictions on the damping parameters of the closed loop system is formulated and solved as a multiobjective optimization problem the purpose of control is to effectively suppress structural vibrations due to initial excitation the cross sectional areas of the members are treated as design variables the structural weight and the controlled system energy are considered as objective functions for minimization the goal programming approach is used for the solution of the multiobjective optimization problems the procedure is illustrated through numerical simulations using two bar and twelve bar truss structures

variance constrained filtering for uncertain stochastic systems with missing measurements in this note we consider a new filtering problem for linear uncertain discrete time stochastic systems with missing measurements the parameter uncertainties are allowed to be norm bounded and enter into the state matrix the system measurements may be unavailable i e missing data at any sample time and the probability of the occurrence of missing data is assumed to be known the purpose of this problem is to design a linear filter such that for all admissible parameter uncertainties and all possible incomplete observations the error state of the filtering process is mean square bounded and the steady state variance of the estimation error of each state is not more than the individual prescribed upper bound it is shown that the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic riccati like inequalities or linear matrix inequalities the explicit expression of the desired robust filters is parameterized and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach

fuzzy finite element approach for the analysis of imprecisely defined systems many engineering systems are too complex to be defined in precise mathematical terms they often contain information and features that are vague imprecise qualitative linguistic or incomplete the traditional deterministic and probabilistic techniques are not adequate to analyze such systems this paper aims at developing a fuzzy finite element approach for the analysis of imprecisely defined systems the development of the methodology starts from the basic concepts of fuzzy numbers of fuzzy arithmetic and implements suitably defined fuzzy calculus concepts such as differentiation and integration for the derivation manipulation and solution of the finite element equations simple stress analysis problems involving vaguely defined geometry material properties external loads and boundary conditions are solved to establish and to illustrate the new procedure the approach developed is applicable to systems that are described in linguistic terms as well as those that are described by incomplete information if complete data are known the method handles the information similar to that of a probabilistic approach the present approach represents a unique methodology that enables us to handle certain types of imprecisely known data more realistically compared with the existing procedures

convergence of stochastic gradient estimation algorithm for multivariable arx like systems this paper studies the convergence of the stochastic gradient identification algorithm of multi input multi output arx like systems i e multivariable arx like systems by using the stochastic martingale theory this arx like model contains a characteristic polynomial and differs from the conventional multivariable arx system the results indicate that the parameter estimation errors converge to zero under the persistent excitation conditions the simulation results validate the proposed convergence theorem

fuzzy goal programming approach for structural optimization a fuzzy nonlinear goal programming approach is presented for solving multiobjective optimization problems involving vague and imprecise information several computational models including simple additive weighted additive and preemptive priority models are given for the numerical solution of the problem the methodolo gies are illustrated with the help of two structural optimization problems involving multiple goals the solution of the first example is obtained using a graphical procedure whereas the second example is solved using nonlinear programming techniques linear membership functions are used in the numerical work for simplicity the methodologies presented in this work aid in the preliminary design of structural systems involving imprecise and vague information about the goals and or constraints inear goal programming has been extensively used in solving decision making problems involving linear equa tions and multiple conflicting goals the goals can be rank ordered depending on their importance to the decision maker goal programming attempts to achieve as man 7 of these goals as possible by minimizing deviational variables from the goal levels depending on their relative weights linear goal pro gramming algorithms were developed by charnes et al 1 ig nizio 2 and zanakis and gupta 3 the extension of goal pro gramming to nonlinear optimization problems has also been considered by several authors 3 4 a fuzzy programming ap proach for linear programming problems with several objec tives was suggested by zimmerman 5 subsequently several authors proposed different fuzzy goal programming ap proaches for solving linear goal programming problems in volving imprecise statements and information 6 10 narasimhan6 suggested a method for solving fuzzy linear goal programming problems under the assumption of linear membership functions his method involves solving a set of 2k linear programming problems each containing 3k constraints where k denotes the number of goals in the original problem hannan7 indicated a procedure for formulating a fuzzy goal programming problem as an equivalent single linear program ming problem with 2k goal related constraints the problems associated with the definition of fuzzy priorities were dis cussed in ref 7 a brief review of the history and the state of the art in fuzzy multicriteria programming as of 1982 was presented by ignizio 8 the distinction between fuzzy goal pro gramming and fuzzy multicriteria formulations was given in ref 9 models are presented by hannan7 for the use of fuzzy goal programming with preemptive priorities with archime dian weights and with the maximization of the membership function corresponding to the minimum goal a methodology based on the use of a nested hierarchy of priorities for each goal was presented by rubin and narasimhan 10 the impor tance of multiple objectives in the design of practical engineer

linear programming with multiple fuzzy goals abstract this paper describes the use of fuzzy set theory in goal programming gp problems in particular it is demonstrated how fuzzy or imprecise aspirations of the decision maker dm can be quantified through the use of piecewise linear and continuous functions models are then presented for the use of fuzzy goal programming with preemptive priorities with archimedean weights and with the maximization of the membership function corresponding to the minimum goal examples are also provided

bias of some commonly used time series estimates summary we study the bias of yule walker and least squares estimates for univariate and multivariate autoregressive processes we obtain explicit formulae for the large sample bias of yule walker estimates in the scalar first and second order cases and for least squares estimates in the general case both simulations and theory indicate that yulewalker estimates are inferior to least squares estimates for strongly autocorrelated processes yule walker estimates can be severely biased even for comparatively largesample sizes

the asymptotic cramer rao bound for gaussian arma processes with periodically missing data corresp an asymptotic formula is derived for the cramer rao lower bound on unbiased estimates of the parameters of gaussian autoregressive moving average arma processes in the case where the measurements are not contiguous but follow a periodic pattern of misses the formula is then used to illustrate the behavior of the bound for some specific examples

diversity combining for ds ss systems with time varying correlated fading branches diversity combining of multiple time varying and correlated fading branches is investigated for direct sequence spread spectrum systems the correlated branches are modeled and estimated jointly as a vector autoregressive var process the joint estimation is shown to provide performance gain over separate estimation of the fading branches the parameter matrices of the var model are estimated via the method of expectation maximization em with two algorithms the first algorithm using results from kalman smoothing provides a closed form solution to the maximization problem in the iterative em procedure however the iterative em kalman algorithm operates repeatedly on a batch of training data and results in large storage requirements and long processing delays to overcome these disadvantages a new algorithm with only forward time recursions is proposed that approximates the iterative em solution and efficiently adapts to slowly changing doppler spreads as a result the new algorithm significantly reduces memory and training sequence requirements through computer simulations a near ideal bit error rate performance is found for both algorithms and the efficacy of the new adaptive algorithm for channels with changing doppler spreads is demonstrated