blind separation of positive sources by globally convergent gradient search the instantaneous noise free linear mixing model in independent component analysis is largely a solved problem under the usual assumption of independent nongaussian sources and full column rank mixing matrix however with some prior information on the sources like positivity new analysis and perhaps simplified solution methods may yet become possible in this letter we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded which means that they have a nonzero pdf in the region of zero it can be shown that in this case the solution method is basically very simple an orthogonal rotation of the whitened observation vector into nonnegative outputs will give a positive permutation of the original sources we propose a cost function whose minimum coincides with nonnegativity and derive the gradient algorithm under the whitening constraint under which the separating matrix is orthogonal we further prove that in the stiefel manifold of orthogonal matrices the cost function is a lyapunov function for the matrix gradient flow implying global convergence thus this algorithm is guaranteed to find the nonnegative well grounded independent sources the analysis is complemented by a numerical simulation which illustrates the algorithm

exact ltp representation of the generalized periodic reference fxlms algorithm the analysis of the filtered x least mean square fxlms algorithm can be based either on a stochastic or deterministic approach one of the drawbacks of the stochastic analysis is that it relies on several assumptions which are not justified if the reference signal is time periodic to overcome these limitations several deterministic methods have been suggested however useful results have been reported only for setups with certain filter length secondary path model or reference signal in this paper an exact linear time periodic ltp representation is proposed assuming only that the reference is synchronously sampled the representation is derived for a general fxlms system which also covers the multichannel topology of several parallel filters and its common narrowband modification the representation is found to have a linear time invariant lti form if the filter length is suitably chosen the usability of the method is demonstrated in a numerically computed example by comparing it to an approximate lti model

fuzzy model validation using the local statistical approach the local statistical approach for fault detection and isolation is applied to fuzzy models validation the method detects the inconsistencies between a fuzzy rule base and the modelled system it can also identify which are the faulty parameters of the fuzzy model the fisher information matrix explains the detectability of changes in the parameters of the fuzzy model simulation tests illustrate the method s credibility

frequency domain approach to optimally robust residual generation and evaluation for model based fault diagnosis methods of residual generation and evaluation for model based fault diagnosis in uncertain linear dynamic systems are investigated with the aid of frequency domain approaches and h optimization techniques based on the factorization technique the construction of residual generators in terms of a parametrization concept is proposed with its help the fault detection and isolation problem with perfect model uncertainty decoupling is studied and moreover by its optimal approximation the problem of optimally robust residual generation is treated the optimization problem is solved by h techniques to increase the robustness of residual evaluation a frequency domain residual evaluation index is introduced and optimal input adaptive fault thresholds are derived with respect to the frequency domain evaluation index the results are illustrated in terms of an inverted pendulum example

zero stability properties of the three ordinate variable stepsize variable formula methods consider the systemy f x y y a x a b y r n wheref is continuous and lipschitzian with respect to the second argument very often linear multistep variable stepsize variable formula methods lm vsvfm s are used to computey k y xk on the points of the grid a x 0 x1 x2 xn b the general lm vsvfm is based on formulae of the following type y k sum limits i 1 s k alpha i bar h k sk y k i sum limits i 0 s k h k i beta i bar h k s k f x k i y k i whereh k xk xk 1 bar h k h k h k 1 ldots h k s k s k k k 1 1 n the coefficients i and i depend on the lasts k 1 stepsizes and on the formula used at stepk only the zero stability properties of some special classes of lm vsvfm s as for example those based on adams formulae were investigated in the literature a class of three ordinate lm vsvfm s is defined in this paper some results concerning the zero stability properties of these methods are proved it is shown that some well known results are simple corollaries of the results found for the three ordinate lm vsvfm s it is easily seen that similar results hold for the corresponding one leg vsvfm s finally the use of the theoretical results in the practical implementations is briefly discussed

generating directional residuals with dynamic parity relations abstract it is shown how diagnostic residuals which exhibit directional properties at all times in response to an arbitrary mix of input and output faults can be generated using dynamic parity relations the parity relations are applied directly to the observables of the monitored plant the design relies on the plant s dynamic input output model this residual generator can be made computationally polynomial moving average by including the invariant zero polynomial of the fault system in the specified fault responses the polynomial design yields moving average noise transfers as well white noise transfer and disturbance decoupling are achieved by extending the response specification the parity relation approach is compared with the traditional detection filter design and is shown to be more straightforward and have milder existence conditions if subjected to the same specification the two approaches yield identical residual generators

a relaxed condition for perfect cancellation of broadband noise in 3d enclosures this paper presents a relaxed condition for perfect cancellation of broadband noise in 3d enclosures on the basis of a truncated modal model it can be shown that the primary and secondary paths belong to a same subspace if a certain condition is satisfied there exists a finite impulse response fir filter transfer function vector for perfect cancellation of the primary paths the analytical result is verified numerically with an active noise control anc system in a 3d rectangular enclosure the proposed anc scheme is shown to fit well into the framework of an existing multichannel least mean squares lms algorithm for adaptive implementation

equivariant adaptive selective transmission in this paper we consider the problem of selective transmission the dual of the blind source separation task in which a set of independent source signals are adaptively premixed prior to a nondispersive physical mixing process so that each source can be independently monitored in the far field following similar procedures for information theoretic blind source separation we derive a stochastic gradient algorithm for iteratively estimating the premixing matrix in the selective transmission problem and through a simple modification we obtain a second algorithm whose performance is equivariant with respect to the channel s mixing characteristics the local stability conditions for the algorithms about any selective transmission solution are shown to be the same as those for similar source separation algorithms practical implementation issues are discussed including the estimation of the combined system matrix and the reordering and scaling of the received signals within the algorithm mean square error based selective transmission algorithms are also derived for performance comparison purposes simulations indicate the useful behavior of the premixing algorithms for selective transmission

on residual generation by observer and parity space approaches a unifying framework for observer design by eigenstructure assignment is described a new technique for structured residual generation based on this framework is proposed one of the main features of this technique is that the equivalence between residual generation by means of observers or parity space devices are made conspicuous more precisely from a computational point of view the equations to solve in both cases are shown to be similar and for implementation both devices are shown to be identical a necessary and sufficient condition for the existence of structured residuals is given finally the sensitivity of structured residuals to nondecoupled failures is studied and a procedure for maximizing this sensitivity is described

on the zero stability of variable stepsize multistep methods the spectral radius approach in this paper we illustrate a novel approach for studying the asymptotic behaviour of the solutions of linear difference equations with variable coefficients in particular we deal with the zero stability of the 3 step bdf method on grids with variable stepsize for the numerical solution of ivps for odes our approach is based on the theory of the spectral radius of a family of matrices and yields almost optimal results which give a slight improvement to the best results already known from the literature the success got on the chosen example suggests that our approach has a good potential for more general and harder stability analyses of numerical methods

damage localization from the null space of changes in the transfer matrix a new theorem connecting changes in transfer matrices to the spatial location of stiffness related damage is presented the theorem states that the span of the null space of the change in the transfer matrix g contains vectors that are laplace transforms of excitations for which the dynamic stress field is identically zero over the portion of the domain where the damage is located an important corollary states that if g proves rank deficient at any s with the exception of the origin in system with rigid body modes it is guaranteed to be rank deficient throughout the plane it is shown that a sufficient condition for rank deficiency in g is that the number of independent measurements be larger than the rank of the change in stiffness resulting from damage implementation of the theorem in the time domain involves evaluation of the null space of g along a discretized bromwich contour numerical inversion of the resulting s functions and evaluation of the dynamic response to the computed signals to identify the regions where the stress field is zero the theorem is most efficiently implemented however in the s domain where numerical laplace inversion is avoided and the number of evaluations of the null of g can reduced to one application of the theorem to locate damage is illustrated in a simple mass spring system and in a fem model of a square plate with free free boundary conditions

development of the filtered u algorithm for active noise control the filtered x algorithm developed by widrow and burgess is an alternate form of the least mean square lms algorithm for use when there are transfer functions in the auxiliary path following the adaptive filter to ensure convergence of the algorithm the input to the error correlators is filtered by a copy of these auxiliary path transfer functions more recently the author has presented a new approach to active noise control in the presence of acoustic feedback that uses an infinite impulse response iir filter structure with an alternate form of the recursive least mean square rlms algorithm this algorithm may be described as a filtered u algorithm since it uses a copy of the auxiliary path transfer functions to filter the generalized input vector u to the error correlators of both the direct and recursive elements of the filter to ensure convergence the relationship of the filtered u to the filtered x algorithm and other earlier concepts is discussed

a time domain feedback analysis of filtered error adaptive gradient algorithms this paper provides a time domain feedback analysis of gradient based adaptive schemes a key emphasis is on the robustness performance of the adaptive filters in the presence of disturbances and modeling uncertainties along the lines of h sup spl infin theory and robust filtering the analysis is carried out in a purely deterministic framework and assumes no prior statistical information or independence conditions it is shown that an intrinsic feedback structure can be associated with the varied adaptive schemes the feedback structure is motivated via energy arguments and is shown to consist of two major blocks a time variant lossless i e energy preserving feedforward path and a time variant feedback path the configuration is further shown to lend itself to analysis via a so called small gain theorem thus leading to stability and robustness conditions that require the contractivity of certain operators choices for the step size parameter in order to guarantee faster rates of convergence are also derived and simulation results are included to demonstrate the theoretical findings in addition the time domain analysis provided in this paper is shown to extend the so called transfer function approach to a general time variant scenario without any approximations

on the stability of adaptation process in active noise control systems the stability analysis of the adaptation process performed by the filtered x least mean square algorithm on weights of active noise controllers has not been fully investigated the main contribution of this paper is conducting a theoretical stability analysis for this process without utilizing commonly used simplifying assumptions regarding the secondary electro acoustic channel the core of this analysis is based on the root locus theory the general rules for constructing the root locus plot of the adaptation process are derived by obtaining root locus parameters including start points end points asymptote lines and breakaway points the conducted analysis leads to the derivation of a general upper bound for the adaptation step size beyond which the mean weight vector of the active noise controller becomes unstable also this analysis yields the optimum step size for which the adaptive active noise controller has its fastest dynamic performance the proposed upper bound and optimum values apply to general secondary electro acoustic channels unlike the commonly used ones which apply to only pure delay channels the results are found to agree very well with those obtained from numerical analyses and computer simulation experiments

non wiener solutions for the lms algorithm a time domain approach a time domain analysis of the lms algorithm is presented for a sinusoidal deterministic reference input for the sinusoidal reference input only the n dimensional time varying linear matrix recursion for the weight vector is solved using a 2 d orthogonal subspace decomposition using this weight vector solution it is shown that there exists a linear time invariant relationship between the desired input and the filter output

the lms algorithm with delayed coefficient adaptation the behavior of the delayed least mean square dlms algorithm is studied it is found that the step size in the coefficient update plays a key role in the convergence and stability of the algorithm an upper bound for the step size is derived that ensures the stability of the dlms the relationship between the step size and the convergence speed and the effect of the delay on the convergence speed are also studied the analytical results are supported by computer simulations

a constrained em algorithm for independent component analysis we introduce a novel way of performing independent component analysis using a constrained version of the expectation maximization em algorithm the source distributions are modeled as d one dimensional mixtures of gaussians the observed data are modeled as linear mixtures of the sources with additive isotropic noise this generative model is fit to the data using constrained em the simpler soft switching approach is introduced which uses only one parameter to decide on the sub or supergaussian nature of the sources we explain how our approach relates to independent factor analysis

properties of fxlms based narrowband active noise control with online secondary path modeling rotating machines such as diesel engines cutting machines fans motors etc generate sinusoidal noise signals that may be effectively reduced by narrowband active noise control anc systems in this paper a typical filtered x lms fxlms based narrowband anc system equipped with an online secondary path modeling subsystem is analyzed in detail first difference equations governing the dynamics of the fxlms algorithm for secondary source synthesis and the lms algorithm for secondary path estimation are derived in terms of convergence in both mean and mean square steady state expressions for mean square error mse as well as the residual noise power are then developed in closed form extensive simulations are performed to demonstrate the validity of the analytical results

study of the acoustic feedback problem of active noise control by using the l1 and l2 vector space optimization approaches this study attempts to explore the acoustic feedback problem that is frequently encountered in feedforward active noise control anc structure from the standpoint of control theories the analysis is carried out on the basis of the youla s parametrization and the l1 norm and l2 norm vector space optimization the anc problem is formulated as a model matching procedure and is solved via linear programming in the dual vector space these methods alleviate the problems caused by the nonminimum phase nmp zeros of the cancellation path the anc algorithms are implemented by using a digital signal processor various types of noises were chosen for validating the developed algorithms the proposed methods are also compared with the well known filtered u least mean square fulms method the experimental results show that the acoustic feedback problem significantly degrades the performance and stability of the anc system regardless which method is used insights into the difficulties due to acoustic feedback a

stability of multistep methods on variable grids this paper is concerned with the stability of multistep methods for ordinary initial value problems on grids with variable mesh sizes a necessary and sufficient condition for stability is given from which generalizations of recent results by gear et al and by zlatev can be obtained as special cases as an application the stability of the variable bdf formulas is treated

the effect of transfer function estimation errors on the filtered x lms algorithm the filtered x lms algorithm which is commonly implemented in active noise and vibration control systems requires an estimate of the cancellation path transfer function to maintain algorithm stability this correspondence considers the effect of errors in this estimate on the stability of the algorithm implemented in the time domain concluding that while a maximum phase error of spl plusmn 90 spl deg is a bound for stability there is no simple relationship between error and stability within this region

a generalized contrast function and stability analysis for overdetermined blind separation of instantaneous mixtures in this letter the problem of blind separation of n independent sources from their m linear instantaneous mixtures is considered first a generalized contrast function is defined as a valuable extension of the existing classical and nonsymmetrical contrast functions it is applicable to the overdetermined blind separation m n with an unknown number of sources because not only independent components but also redundant ones are allowed in the outputs of a separation system second a natural gradient learning algorithm developed primarily for the complete case m n is shown to work as well with an n m or m m separating matrix for each optimizes a certain mutual information contrast function finally we present stability analysis for a newly proposed generalized orthogonal natural gradient algorithm which can perform the overdetermined blind separation when n is unknown obtaining an expectable result that its local stability conditions are slightly stricter than those of the conventional natural gradient algorithm using an invertible mixing matrix m n

high level primitives for recursive maximum likelihood estimation this paper proposes a high level language constituted of a small number of primitives and macros for describing recursive maximum likelihood ml estimation algorithms this language is applicable to estimation problems involving linear gaussian models or processes taking values in a finite set the use of high level primitives allows the development of highly modular ml estimation algorithms based on simple numerical building blocks the primitives which correspond to the combination of different measurements the extraction of sufficient statistics and the conversion of the status of a variable from unknown to observed or vice versa are first defined for linear gaussian relations specifying mixed deterministic stochastic information about the system variables these primitives are used to define other macros and are illustrated by deriving new filtering and smoothing algorithms for linear descriptor systems the primitives are then extended to finite state processes and used to implement the viterbi ml state sequence estimator for a hidden markov model

statistical dynamics of on line independent component analysis the learning dynamics of on line independent component analysis is analysed in the limit of large data dimension we study a simple hebbian learning algorithm that can be used to separate out a small number of non gaussian components from a high dimensional data set the de mixing matrix parameters are confined to a stiefel manifold of tall orthogonal matrices and we introduce a natural gradient variant of the algorithm which is appropriate to learning on this manifold for large input dimension the parameter trajectory of both algorithms passes through a sequence of unstable fixed points each described by a diffusion process in a polynomial potential choosing the learning rate too large increases the escape time from each of these fixed points effectively trapping the learning in a sub optimal state in order to avoid these trapping states a very low learning rate must be chosen during the learning transient resulting in learning time scales of o n2 or o n3 iterations where n is the data dimension escape from each sub optimal state results in a sequence of symmetry breaking events as the algorithm learns each source in turn this is in marked contrast to the learning dynamics displayed by related on line learning algorithms for multilayer neural networks and principal component analysis although the natural gradient variant of the algorithm has nice asymptotic convergence properties it has an equivalent transient dynamics to the standard hebbian algorithm

efficient goal oriented global error estimators for bdf methods using discrete adjoints in this paper we develop new goal oriented global error estimators for variable multistep backward differentiation formulae bdf methods these estimators use for the first time in the context of multistep methods discrete adjoints computed by adjoint differentiation of the nominal integration scheme the derivation is based on the recently developed petrov galerkin finite element formulation of bdf methods and their discrete adjoint schemes and makes use of the dual weighted residual methodology defect integrals or local truncation errors are used as local error quantities we prove the asymptotic correctness and optimal convergence of the novel estimators for the one step bdf method for multistep bdf methods using a selfstarting procedure we show that the estimator with defect integrals converges but suboptimal and that its effectivity index converges to an offset value on the other hand the estimator with local truncation errors is again asymptotically correct and of optimal order we confirm these results numerically with a real world example from chemical engineering we give promising numerical results for the estimation accuracy in variable bdf type methods with changing orders and stepsizes finally we give a first use of the novel estimators for goal oriented global error control of a challenging stiff test problem

a suboptimal quadratic change detection scheme we address the problem of detecting changes in multivariate gaussian random signals with an unknown mean after the change the window limited generalized likelihood ratio glr scheme is a well known approach to solve this problem however this algorithm involves at least log spl gamma spl rho likelihood ratio computations at each stage where spl gamma spl gamma spl rarr spl infin is the mean time before a false alarm and spl rho is the kullback leibler information we establish a new suboptimal recursive approach which is based on a collection of l parallel recursive spl chi sup 2 tests instead of the window limited glr scheme this new approach involves only a fixed number l of likelihood ratio computations at each stage for any combinations of spl gamma and spl rho by choosing an acceptable value of nonoptimality the designer can easily find a tradeoff between the complexity of the quadratic change detection algorithm and its efficiency

aladins an algebraic splitting time adaptive solver for the incompressible navier stokes equations we address a time adaptive solver specifically devised for the incompressible navier stokes ins equations one of the challenging issues in this context is the identification of a reliable a posteriori error estimator typical strategies are based on the combination of the solutions computed either with two different time steps or two schemes with different accuracy in this paper we move from the pressure correction algebraic factorizations formerly proposed by saleri veneziani 2005 these schemes feature an intrinsic hierarchical nature such that an accurate solution for the pressure is obtained by computing intermediate low order guesses the difference between the two estimates provide a natural a posteriori estimator after introducing the incremental formulation of the pressure correction schemes we address the properties of this approach including extensive implementation details numerical results presented refer to 2d and 3d unstructured problems with a particular emphasis on cardiovascular problems which are expected to largely benefit from time adaptive solvers in memory of f saleri 1965 2007

waveform preserving blind estimation of multiple independent sources the problem of blind estimation of source signals is to estimate the source signals without knowing the characteristics of the transmission channel it is shown that the minimum variance unbiased estimates can be obtained if and only if the transmission channel can be identified blindly it is shown that the channel can be blindly identified if and only if there is not more than one gaussian source this condition suggests that waveform preserving blind estimation can be achieved over a wide range of signal processing applications including those cases in which the source signals have identical nongaussian distributions the constructive proof of the necessary and sufficient condition serves as a foundation for the development of waveform preserving blind signal estimation algorithms examples are presented to demonstrate the applications of the theoretical results

a generalized change detection problem the purpose of this paper is to give a new statistical approach to the change diagnosis detection isolation problem the change detection problem has received extensive research attention however the change isolation problem has for the most part been ignored we consider a stochastic dynamical system with abrupt changes and investigate the multiple hypotheses extension of lorden s 1971 results we introduce a joint criterion of optimality for the detection isolation problem and then design a change detection isolation algorithm we also investigate the statistical properties of this algorithm we prove a lower bound for the criterion in a class of sequential change detection isolation algorithms it is shown that the proposed algorithm is asymptotically optimal in this class the theoretical results are applied to the case of additive changes in linear stochastic models

optimally robust redundancy relations for failure detection in uncertain systems all failure detection methods are based either explicitly or implicitly on the use of redundancy i e on possibly dynamic relations among the measured variables the robustness of the failure detection process consequently depends to a great degree on the reliability of the redundancy relations which in turn is affected by the inevitable presence of model uncertainties in this paper the problem of determining redundancy relations that are optimally robust is addressed in a sense that includes several major issues of importance in practical failure detection and that provides a significant amount of intuition concerning the geometry of robust failure detection a procedure is given involving the construction of a single matrix and its singular value decomposition for the determination of a complete sequence of redundancy relations ordered in terms of their level of robustness this procedure also provides the basis for comparing levels of robustness in redundancy provided by different sets of sensors

penalty function based joint diagonalization approach for convolutive blind separation of nonstationary sources a new approach for convolutive blind source separation bss by explicitly exploiting the second order nonstationarity of signals and operating in the frequency domain is proposed the algorithm accommodates a penalty function within the cross power spectrum based cost function and thereby converts the separation problem into a joint diagonalization problem with unconstrained optimization this leads to a new member of the family of joint diagonalization criteria and a modification of the search direction of the gradient based descent algorithm using this approach not only can the degenerate solution induced by a null unmixing matrix and the effect of large errors within the elements of covariance matrices at low frequency bins be automatically removed but in addition a unifying view to joint diagonalization with unitary or nonunitary constraint is provided numerical experiments are presented to verify the performance of the new method which show that a suitable penalty function may lead the algorithm to a faster convergence and a better performance for the separation of convolved speech signals in particular in terms of shape preservation and amplitude ambiguity reduction as compared with the conventional second order based algorithms for convolutive mixtures that exploit signal nonstationarity

highly continuous interpolants for one step ode solvers and their application to runge kutta methods we suggest a general method for the construction of highly continuous interpolants for one step methods applied to the numerical solution of initial value problems of odes of arbitrary order for the construction of these interpolants one uses along with the numerical data of the discrete solution of a problem provided by a typical one step method at endstep points high order derivative approximations of this solution this approach has two main advantages it allows an easy way of construction of high order runge kutta and nystrom interpolants with reduced cost in additional function evaluations that also preserve the one step nature of the underlying discrete ode solver moreover for problems which are known to possess a solution of high smoothness the approximating interpolant resembles this characteristic a property that on occasion might be desirable an analysis of the stability behavior of such interpolatory processes is carried out in the general case a new numerical technique concerning the accurate determination of the stability behavior of numerical schemes involving higher order derivatives and or approximations of the solution from previous grid points over nonequidistant meshes is presented this technique actually turns out to be of a wider interest as it allows us to infer in certain cases more accurate results concerning the stability of for example the bdf formulas over variable stepsize grids moreover it may be used as a framework for analyzing more complex and supposedly more promising types of methods as they are the general linear methods for first and second order differential equations many particular variants of the new method for first order differential equations that have good prospects of finding a practical implementation are fully analyzed with respect to their stability characteristics a detailed application concerning the construction of c 2 and c 3 continuous extensions for some fifth and sixth order runge kutta pairs supplemented by a detailed study of the local truncation error characteristics of a class of interpolants of this type is also provided various numerical examples show in these cases several advantages of the newly proposed technique with respect to function evaluation cost and global error behavior in comparison with others currently in use

adaptive modal identification of structures with equivariant adaptive separation via independence approach abstract an efficient output only blind source separation bss method was recently introduced for the modal identification of structures bss procedures recover a set of independent sources from their unknown linear mixtures when only mixtures are observed batch data is required for the separation in traditional blind source separation methods these algorithms are however unfavorable as some sets of data are observed one after another in this paper an adaptive blind source separation technique equivariant adaptive separation via independence easi is introduced to overcome the mentioned disadvantage within the structures the easi algorithm is beneficial as it can provide solutions to real time problems while also update the un mixing matrix for each step easi not only avoids increases in size of the relevant matrices and vectors but also decreases the analysis time a synthetic example and a benchmark structure have been used in this paper to better investigate the efficiency of the proposed method the simulation results demonstrate the effectiveness of the easi algorithm in on line identification of modal parameters of structures

optimal sensor location for detecting changes in dynamical behavior we address the problem of optimal sensor location for monitoring the eigenstructure of a multivariable dynamical system the criterions which are optimized are the power of new tests designed for detecting and diagnosing changes in the eigencharacteristics of a system 3 12 the key points are the choice of the parameterization for computing the criterion and the comparison of designs with a different number of sensors the discussion of the numerical results for sensor location includes the analysis of the effect of the geometry of the unknown excitation

blind separation of mixture of independent sources through a quasi maximum likelihood approach we propose two methods for separating mixture of independent sources without any precise knowledge of their probability distribution they are obtained by considering a maximum likelihood ml solution corresponding to some given distributions of the sources and relaxing this assumption afterward the first method is specially adapted to temporally independent non gaussian sources and is based on the use of nonlinear separating functions the second method is specially adapted to correlated sources with distinct spectra and is based on the use of linear separating filters a theoretical analysis of the performance of the methods has been made a simple procedure for optimally choosing the separating functions is proposed further in the second method a simple implementation based on the simultaneous diagonalization of two symmetric matrices is provided finally some numerical and simulation results are given illustrating the performance of the method and the good agreement between the experiments and the theory

novel fxlms convergence condition with deterministic reference a novel analysis of fxlms convergence when the reference signal is deterministic is presented in this paper the simple case of a sinusoidal reference is considered first to be later extended to any combination of multiple sinusoids in both cases we derive an upper bound for the algorithm step size which ensures convergence in the derivation of this result there is no need of any of the usual approximations such as independence between reference and weights or slow convergence which are not suitable for deterministic references instead we consider the common cases where the adaptive system shows linear time invariant behavior the upper bound obtained for the step size is in good agreement with empirical measurements

a linear non gaussian acyclic model for causal discovery in recent years several methods have been proposed for the discovery of causal structure from non experimental data such methods make various assumptions on the data generating process to facilitate its identification from purely observational data continuing this line of research we show how to discover the complete causal structure of continuous valued data under the assumptions that a the data generating process is linear b there are no unobserved confounders and c disturbance variables have non gaussian distributions of non zero variances the solution relies on the use of the statistical method known as independent component analysis and does not require any pre specified time ordering of the variables we provide a complete matlab package for performing this lingam analysis short for linear non gaussian acyclic model and demonstrate the effectiveness of the method using artificially generated data and real world data

a novel approach to feedforward higher harmonic control a novel adaptive filter structure is proposed for the control of systems characterized by higher harmonic response the control approach has been designated the higher harmonic least mean squares hlms algorithm to differentiate it from the standard multifrequency filtered x version of the least mean squares approach in the hlms algorithm a single frequency reference at that of the fundamental is all that is required to implement the controller the remaining harmonics are generated internally based upon simple trigonometric relationships the filtered x lms algorithm is implemented in parallel for each frequency to be controlled minimizing or totally eliminating the contribution of the time varying terms during the convergence process and increasing the rate of convergence for the higher harmonic control application results from the simulation demonstrate that the hlms approach is far superior to the standard multifrequency filtered x lms algorithm in adaptive feedforward higher harmonic control

equivariant adaptive source separation source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed this paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence easi the easi algorithms are based on the idea of serial updating this specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures most importantly the performance of an easi algorithm does not depend on the mixing matrix in particular convergence rates stability conditions and interference rejection levels depend only on the normalized distributions of the source signals closed form expressions of these quantities are given via an asymptotic performance analysis the theme of equivariance is stressed throughout the paper the source separation problem has an underlying multiplicative structure the parameter space forms a matrix multiplicative group we explore the favorable consequences of this fact on implementation performance and optimization of easi algorithms

fault detection and isolation in nonlinear dynamic systems a combined input output and local approach the problem of fault detection and isolation fdi is addressed for nonlinear dynamic systems modeled by polynomial differential algebraic equations ritt s algorithm is used to obtain an input output representation of the monitored system by eliminating unknown variables a local approach to change detection is then applied to the input output representation for fdi residual generation and evaluation simulation results on a microbial growth process are provided which illustrate the relevance of the proposed fdi method

a new structural framework for parity equation based failure detection and isolation abstract the paper describes a new framework for developing parity equations that prevent incorrect isolation decisions under marginal size failures in a decision process that tests each residual independently test thresholds that take the noise conditions into account are set high to reduce the occurrence of false alarms while maintaining the algorithm s ability to detect and isolate larger failures the method is applicable to additive failures on the measured input and output variables and to additive plant disturbances a transformation algorithm provides a multitude of models that satisfy the isolability requirements a search procedure utilizing this model redundancy integrates model robustness considerations into the design

on the zero stability of the variable order variable stepsize bdf formulas this paper contains bounds for the mesh size ratiosh j 1 h j of nonequidistant grids such that any combination of the widely used backward differentiation formulas with ordersl 1 l m m 3 4 5 performs zerostable

on board component fault detection and isolation using the statistical local approach we describe both the key principles and real application examples of a unified theory which allows us to perform the on board incipient fault detection and isolation tasks involved in monitoring for condition based maintenance this theory is known under the name of local approach and it is especially suited to component faults it aims at transforming complex detection problems concerning a parameterized stochastic process into the universal problem of monitoring the mean of a gaussian vector based on a small deviation assumption the key tools are the first order taylor expansion and the asymptotic gaussianity of a convenient parameter estimating function ml ls iv and subspace identification methods are addressed in this perspective in the case of dynamic processes given in state space form the approach may also call for observer based state estimation or state elimination experiments concerning both simulated and real data for linear and nonlinear dynamical processes are reported how the key principles and features of the local approach compare with those of other approaches is discussed

a 0 stability of variable stepsize bdf methods abstract in this paper the a0 stability of interpolatory variable coefficient and fixed leading coefficient bdf formulas is considered a comparison of the stability properties of the three methods based on their spectral radius is presented in addition we study the effect of some strategies of stepsize variation employed in usual codes on the stability of these methods

fault detection and isolation observers a design of reduced order observers is proposed for linear time invariant systems with unknown inputs including unknown measurement disturbances based on the unknown input observer design a systematic treatment of designing fault detection and isolation fdi observers is provided the core of the fdi observer design is to find an observable subsystem where the faults of interest show up and the rest of the faults disappear the fdi observer design procedure has a clear physical meaning robust fdi observers for uncertain systems can also be obtained using the fdi observer design provided the uncertainties of the system can be formulated as unknown inputs it is shown that the parity equations of another important fdi method can be generated in an elegant way using a dead beat fdi observer scheme directly in the time domain examples are included to show some concepts and to illustrate the fdi observer design method

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

information criteria for residual generation and fault detection and isolation using an information point of view we discuss deterministic versus stochastic tools for residual generation and evaluation for fault detection and isolation fdi in linear time invariant lti state space systems in both types of approaches to off line fdi residual generation can be viewed as the design of a linear transformation of a gaussian vector the finite window input adjusted observations several statistical isolation methods are revisited using both a linear transform formulation and the information content of the corresponding residuals we formally state several multiple fault cases with or without causality assumptions and discuss an optimality criterion for the most general one new information criteria are proposed for investigating the residual optimization problem

lattice form adaptive infinite impulse response filtering algorithm for active noise control in some situations of active noise control infinite impulse response iir filters are more suitable than finite impulse response fir filters owing to the poles in the transfer function a number of algorithms have been derived for applying iir filters in active noise control however most of them use the direct form iir filter structure which faces the difficulties of checking stability and relatively slow convergence speed for noise composed of narrow band components with large power disparity to overcome these difficulties along with using the direct form iir filters a new adaptive algorithm is proposed in this paper which uses and updates the lattice form adaptive iir filter in an active noise control system full mathematical derivations of the proposed algorithm are presented and the comparison between the proposed algorithm and the commonly used filtered u lms and filtered v lms algorithms shows the superiority of the proposed algorithm

stochastic trapping in a solvable model of on line independent component analysis previous analytical studies of on line independent component analysis ica learning rules have focused on asymptotic stability and efficiency in practice the transient stages of learning are often more significant in determining the success of an algorithm this is demonstrated here with an analysis of a hebbian ica algorithm which can find a small number of nongaussian components given data composed of a linear mixture of independent source signals an idealized data model is considered in which the sources comprise a number of nongaussian and gaussian sources and a solution to the dynamics is obtained in the limit where the number of gaussian sources is infinite previous stability results are confirmed by expanding around optimal fixed points where a closed form solution to the learning dynamics is obtained however stochastic effects are shown to stabilize otherwise unstable suboptimal fixed points conditions required to destabilize one such fixed point are obtained for the case of a single nongaussian component indicating that the initial learning rate required to escape successfully is very low o n 2 where n is the data dimension resulting in very slow learning typically requiring o n3 iterations simulations confirm that this picture holds for a finite system

distributed adaptive algorithms for large dimensional mimo systems an algorithm for multi input multi output mimo adaptive filtering is introduced that distributes the adaptive computation over a set of linearly connected computational modules each module has an input and an output and transmits data to and receives data from its nearest neighbor a gradient based algorithm for adapting the parameters in each module to minimize the global mean squared error is derived using principles of back propagation the performance surface is explored to understand the characteristics of the adaptive algorithm the minimum mean squared error is a many to one function of the parameters therefore upper bounds on each parameter are used to prevent excessive parameter drift and ensure stability with fixed step sizes guidelines for choosing the lms algorithm step sizes and initial conditions are developed several examples illustrate the performance of the algorithm