direct simulation of the influence of the pore structure on the diffusion process in porous media in this paper we numerically study the influence of pore structures on diffusion processes in porous media the porous media geometry models are constructed based on two dimensional voronoi diagrams and they feature randomly connected channels with large pores embedded to simulate the heterogeneity of porous media a link type two relaxation time ltrt lattice boltzmann lb method is employed to solve the diffusion equation the tortuosity is characterized as a function of porosity and pore structure from numerical results a correlation for the tortuosity as a function of porosity is derived for voronoi geometries without large pores geometries with large pores at the same total porosity have higher tortuosity which indicates that geometric heterogeneity slows down the diffusion

identification of systems containing linear dynamic and static nonlinear elements identification of nonlinear systems which can be represented by combinations of linear dynamic and static nonlinear elements are considered previous results by the authors based on correlation analysis are combined to provide a unified treatment for this class of systems it is shown that systems composed of cascade feedforward feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only

a blind approach to hammerstein model identification this paper discusses the hammerstein model identification using a blind approach by fast sampling at the output it is shown that identification of the linear part can be achieved based only on the output measurements that makes the hammerstein model identification possible without knowing the structure of the nonlinearity and the internal variables

brief paper convergence of the iterative algorithm for a general hammerstein system identification the convergence of the iterative identification algorithm for a general hammerstein system has been an open problem for a long time in this paper it is shown that the convergence can be achieved by incorporating a regularization procedure on the nonlinearity in addition to a normalization step on the parameters

an instrumental least squares support vector machine for nonlinear system identification least squares support vector machines ls svms originating from statistical learning and reproducing kernel hilbert space rkhs theories represent a promising approach to identify nonlinear systems via nonparametric estimation of the involved nonlinearities in a computationally and stochastically attractive way however application of ls svms and other rkhs variants in the identification context is formulated as a regularized linear regression aiming at the minimization of the 2 loss of the prediction error this formulation corresponds to the assumption of an auto regressive noise structure which is often found to be too restrictive in practical applications in this paper instrumental variable iv based estimation is integrated into the ls svm approach providing under minor conditions consistent identification of nonlinear systems regarding the noise modeling error it is shown how the cost function of the ls svm is modified to achieve an iv based solution although a practically well applicable choice of the instrumental variable is proposed for the derived approach optimal choice of this instrument in terms of the estimates associated variance still remains to be an open problem the effectiveness of the proposed iv based ls svm scheme is also demonstrated by a monte carlo study based simulation example

adaptive digital control of hammerstein nonlinear systems with limited output sampling this paper is motivated by the practical control considerations that nonlinearity is abundant in industrial processes and output sampling rates are often limited due to hardware constraints in particular for a hammerstein nonlinear sampled data system in which the output sampling period is an integer multiple of the input updating period we derive by using a polynomial transformation technique a mathematical model which is suitable for parameter estimation with dual rate measurement data further we present an adaptive control scheme for such a dual rate nonlinear system the parameter estimation based adaptive algorithm can achieve virtually asymptotically optimal control and ensure that the closed loop system is stable and globally convergent the simulation results are included

subspace identification methods for hammerstein systems rank constraint and dimension problem this article studies the subspace identification methods sims for hammerstein systems with major focus on a rank constraint and the related dimension problem we analyse the effects of the rank constraint on the three steps of a unifying framework for sims the rank constraint has no effect on the first two steps but does so on the third step if the rank constraint is ignored as in the existing over parametrised method opm for hammerstein system identification the optimality of the resulting estimate can still be established even so the opm may suffer from the dimension problem resulting in a low numerical efficiency to resolve the dimension problem we propose a new subspace based method named as the least parametrised method lpm for identification of hammerstein systems with non coupling input nonlinearities simulation results are provided to demonstrate the effectiveness of the lpm and show the necessity of considering the rank constraint to improve the numerical efficiency

adaptive multiregression in reproducing kernel hilbert spaces the multiaccess mimo channel case this paper introduces a wide framework for online i e time adaptive supervised multiregression tasks the problem is formulated in a general infinite dimensional reproducing kernel hilbert space rkhs in this context a fairly large number of nonlinear multiregression models fall as special cases including the linear case any convex continuous and not necessarily differentiable function can be used as a loss function in order to quantify the disagreement between the output of the system and the desired response the only requirement is the subgradient of the adopted loss function to be available in an analytic form to this end we demonstrate a way to calculate the subgradients of robust loss functions suitable for the multiregression task as it is by now well documented when dealing with online schemes in rkhs the memory keeps increasing with each iteration step to attack this problem a simple sparsification strategy is utilized which leads to an algorithmic scheme of linear complexity with respect to the number of unknown parameters a convergence analysis of the technique based on arguments of convex analysis is also provided to demonstrate the capacity of the proposed method the multiregressor is applied to the multiaccess multiple input multiple output channel equalization task for a setting with poor resources and nonavailable channel information numerical results verify the potential of the method when its performance is compared with those of the state of the art linear techniques which in contrast use space time coding more antenna elements as well as full channel information

geometry models of porous media based on voronoi tessellations and their porosity permeability relations in this paper we present methods that directly model the random structure of porous media using voronoi tessellations three basic structures were generated and they correspond to porous medium geometries with intersecting fractures granular interconnected tubes tubular and fibers fibrous fluid flow through these models was solved by a massively parallelized lattice boltzmann code we established the porosity permeability relations for these basic geometry models it is found that for granular and tubular geometries the specific surface area is a critical structural parameter that can bring their porosity permeability relations together under a unified kozeny carman equation a connected fracture network superimposed on the basic voronoi structure increases the dimensionless permeability relative to the kozeny carman equation isolated large pores vugs on the other hand decreases the dimensionless permeability relative to the kozeny carman equation the kozeny carman equation however cannot distinguish a heterogeneous structure with an embedded partially penetrating fracture the porosity permeability relation for fibrous geometries in general agrees with those established for simple cubic body centered cubic and face centered cubic models in the dilute limit however the dependence on the solid fraction is weaker in voronoi geometries indicating weaker hydrodynamic interactions among randomly interconnected fibers than those in the idealized models

identification of a class of nonlinear systems under stationary non gaussian excitation this paper provides new solutions to the nonlinear system identification problem when the input to the system is a stationary non gaussian process we propose the use of a model called the hammerstein series which leads to significant reductions in both the computational requirements and the mathematical tractability of the nonlinear system identification problem we show that unlike the volterra series one can obtain closed form expressions for the hammerstein series kernels and the quadratic coherence function in the non gaussian case estimation of the kernels and quadratic coherence function is discussed a comparison with a nonlinear system identification approach that uses the volterra series is provided an automotive engineering application illustrates the usefulness of the proposed method

identification of mimo hammerstein models using least squares support vector machines this paper studies a method for the identification of hammerstein models based on least squares support vector machines ls svms the technique allows for the determination of the memoryless static nonlinearity as well as the estimation of the model parameters of the dynamic arx part this is done by applying the equivalent of bai s overparameterization method for identification of hammerstein systems in an ls svm context the siso as well as the mimo identification cases are elaborated the technique can lead to significant improvements with respect to classical overparameterization methods as illustrated in a number of examples another important advantage is that no stringent assumptions on the nature of the nonlinearity need to be imposed except for a certain degree of smoothness

identification of discrete hammerstein systems using kernel regression estimates in this note a discrete time hammerstein system is identified the weighting function of the dynamical subsystem is recovered by the correlation method the main results concern estimation of the nonlinear memoryless subsystem no conditions concerning functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is presented the algorithm is a nonparametric kernel estimate of regression functions calculated from dependent data it is shown that the algorithm converges to the characteristic as the number of observations tend to infinity for sufficiently smooth characteristics the rate of convergence is o n 2 5 in probability

identification of state dependent parameter models with support vector regression a support vector regression approach is presented for the identification of state dependent parameter arx models whose parameters are described as functions of past inputs and outputs the problem of identifying the state dependent parameters reduces to a standard support vector regression problem with a kernel function which is defined in terms of the kernels used to represent the individual parameters numerical examples show that the support vector method gives accurate parameter estimates for systems which have a state dependent parameter representation

model structure selection by cross validation two criteria for choosing between different model structures are proposed their derivation is within a natural cross validatory assessment context and is fairly assumption free in particular the two criteria can be used for discriminating between non nested model structures and more importantly the true system is not required to belong to the considered set of models should the true system belong to the model set the two proposed criteria will asymptotically reduce to some well known structure selection criteria this is believed to be a desirable feature of our proposals on the other hand it provides a nice cross validation interpretation of some well known model structure selection rules also the cross validation interpretation helps one to choose which criteria to use in a given application the paper also has a second purpose somewhat decoupled from that mentioned above it contains an extensive survey of the literature that is useful in its own right

identifying mimo hammerstein systems in the context of subspace model identification methods in this paper we outline the extension of the moesp family of subspace model identification schemes to the hammerstein type of nonlinear system two types of identification problem are considered the first type assumes the polynomial structure of the static nonlinearity to be given and the task is to identify both the linear system dynamics and the unknown proportional constants in the para metrization of the static nonlinearity the second type addresses the identification of both the linear dynamic part and the static nonlinearity where only limited a priori information regarding the structure of the nonlinearity is available the improved robustness properties of the algorithms developed for this second type of hammerstein identification problem over existing correlation based schemes is illustrated by a numerical example

an optimal two stage identification algorithm for hammerstein wiener nonlinear systems abstract an optimal two stage identification algorithm is presented for hammerstein wiener systems where two static nonlinear elements surround a linear block the proposed algorithm consists of two steps the first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases moreover the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise

nonlinear black box models in system identification mathematical foundations we discuss several aspects of the mathematical foundations of the nonlinear black box identification problem we shall see that the quality of the identification procedure is always a result of a certain trade off between the expressive power of the model we try to identify the larger the number of parameters used to describe the model the more flexible is the approximation and the stochastic error which is proportional to the number of parameters a consequence of this trade off is the simple fact that a good approximation technique can be the basis of a good identification algorithm from this point of view we consider different approximation methods and pay special attention to spatially adaptive approximants we introduce wavelet and neuron approximations and show that they are spatially adaptive then we apply the acquired approximation experience to estimation problems finally we consider some implications of these theoretical developments for the practically implemented versions of the spatially adaptive algorithms

nonparametric identification of wiener systems by orthogonal series a wiener system i e a system comprising a linear dynamic and a nonlinear memoryless subsystems connected in a cascade is identified both the input signal and disturbance are random white and gaussian the unknown nonlinear characteristic is strictly monotonous and differentiable and therefore the problem of its recovering from input output observations of the whole system is nonparametric it is shown that the inverse of the characteristic is a regression function and a class of orthogonal series nonparametric estimates recovering the regression is proposed and analyzed the estimates apply the trigonometric legendre and hermite orthogonal functions pointwise consistency of all the algorithms is shown under some additional smoothness restrictions the rates of their convergence are examined and compared an algorithm to identify the impulse response of the linear subsystem is proposed

finite model order accuracy in hammerstein model estimation hammerstein models is one of the most commonly used model classes used for identifying nonlinear systems a static input nonlinearity followed by a linear dynamical part is an adequate way to model many real life systems this paper investigates the asymptotic in terms of sample size variance of hammerstein model estimates the work extends earlier results by ninness and gibson 2002 in the following ways not only frequency function estimation but estimation of general quantities is considered the expressions are not restricted to be valid asymptotically in the model order in addition the results cover model structures having noise models and allow for data generated under feedback the increase in variance due to the estimation of the input nonlinearity is characterized in particular under open loop operation white additive noise and the assumption of a separable process it is shown that the variance increase is exactly a term that was observed in ninness and gibson 2002 to result in good agreement with simulations this term vanishes in the formal asymptotic in model order analysis in ninness and gibson 2002

recursive identification of multi input multi output errors in variables hammerstein systems the note considers the identification of multi input multi output errors in variables hammerstein systems in which both the input and output can be observed but with additive noises being arma processes with unknown coefficients with the help of stochastic approximation combined with the deconvolution kernel function the recursive algorithms are proposed for estimating coefficients of the linear subsystem and for the values of the nonlinear function under some reasonable conditions all the estimates are proved to converge to the true values with probability one these results include identification of the errors in variables linear systems as a special case a simulation example is given justifying the theoretical analysis

design of truncated maximum length ternary signals where their squared versions have uniform even harmonics the design of pseudo random maximum length prml ternary signals with properties suitable for identification of generalized quadratic hammerstein models is considered for such an application it is desirable for the signal to have odd harmonics uniform and even harmonics suppressed with its squared version having odd harmonics suppressed and even harmonics uniform to date the only class of signal known to possess such harmonic properties comprises of prml ternary signals based on galois field gf 3 and its extension fields in this note theoretical conditions for a prml signal to possess these properties are derived and imposed on the design of signals based on higher odd fields to generate truncated prml signals that fulfil the required specifications

subspace identification of hammerstein systems using least squares support vector machines this paper presents a method for the identification of multiple input multiple output mimo hammerstein systems for the goal of prediction the method extends the numerical algorithms for subspace state space system identification n4sid mainly by rewriting the oblique projection in the n4sid algorithm as a set of componentwise least squares support vector machines ls svms regression problems the linear model and static nonlinearities follow from a low rank approximation of a matrix obtained from this regression problem

multiple relaxation time lattice boltzmann model for the convection and anisotropic diffusion equation a lattice boltzmann model with a multiple relaxation time mrt collision operator for the convection diffusion equation is presented the model uses seven discrete velocities in three dimensions d3q7 model the off diagonal components of the relaxation time matrix which originate from the rotation of the principal axes enable us to take into account full anisotropy of diffusion an asymptotic analysis of the model equation with boundary rules for the dirichlet and neumann type specified flux conditions is carried out to show that the model is first and second order accurate in time and space respectively the results of the analysis are verified by several numerical examples it is also shown numerically that the error of the mrt model is less sensitive to the variation of the relaxation time coefficients than that of the classical bgk model in addition an alternative treatment for the neumann type boundary condition that improves the accuracy on a curved boundary is presented along with a numerical example of a spherical boundary

hammerstein system identification through best linear approximation inversion and regularisation abstracthammerstein systems are composed by the cascading of a static nonlinearity and a linear system in this paper a methodology for identifying such systems using a combination of least squares support vector machines ls svm and best linear approximation bla techniques is proposed to do this a novel method for estimating the intermediate variable is presented allowing a clear separation of the identification steps first an approximation to the linear block is obtained through the bla of the system then an approximation to the intermediate variable is obtained using the inversion of the estimated linear block and the known output afterwards a nonlinear model is calculated through ls svm using the estimated intermediate variable and the known input to do this the regularisation capabilities of ls svm play a crucial role finally a parametric re estimation of the linear block is made the method was tested in three examples two of them with hard nonlinearities and was compared with four

input output parametric models for non linear systems part ii stochastic non linear systems recursive input output models for non linear multivariate discrete time systems are derived and sufficient conditions for their existence are defined the paper is divided into two parts the first part introduces and defines concepts such as nerode realization multistructural forms and results from differential geometry which are then used to derive a recursive input output model for multivariable deterministic non linear systems the second part introduces several examples compares the derived model with other representations and extends the results to create prediction error or innovation input output models for non linear stochastic systems these latter models are the generalization of the multivariable arm ax models for linear systems and are referred to as narmax or non linear autoregressive moving average models with exogenous inputs

dynamic reconstruction of chaotic systems from inter spike intervals using least squares support vector machines this work presents a methodology for dynamic reconstruction of chaotic systems from inter spike interval isi time series obtained via integrate and fire if models in this methodology least squares support vector machines lssvms have been employed for approximating the dynamic behaviors of the systems under investigation higher generalization capability and avoidance of local minima constitute the main reasons behind the choice of lssvms as the approximation tool simulation results have shown that established lssvm models possess great potential for the reconstruction of chaotic dynamics in other words they are able to estimate some dynamic invariants of the underlying chaotic systems as well as they can accurately predict short term evolution within the horizon of predictability moreover lssvm models maintain their reconstruction performance even in the case of the existence of noisy data

recursive identification of hammerstein systems convergence rate and asymptotic normality in this work recursive identification algorithms are developed for hammerstein systems under the conditions considerably weaker than those in the existing literature for example orders of linear subsystems may be unknown and no specific conditions are imposed on their moving average part the recursive algorithms for estimating both linear and nonlinear parts are based on stochastic approximation and kernel functions almost sure convergence and strong convergence rates are derived for all estimates in addition the asymptotic normality of the estimates for the nonlinear part is also established the nonlinearity considered in the paper is more general than those discussed in the previous papers a numerical example verifies the theoretical analysis with simulation results

on the series expansion approach to the identification of hammerstein systems a polynomial identification algorithm for recovering a nonlinearity in the hammerstein system is proposed the estimate employs the legendre orthogonal system with adaptively selected number of terms the global consistency along with rates of convergence are established no assumptions concerning continuity of the nonlinearity or its functional form are made a data driven method using the cross validation technique for selecting the number of terms in the estimate is presented

neural network approach for identification of hammerstein systems in this paper four different on line gradient based learning algorithms for training neural network hammerstein models are presented in a unified framework these algorithms namely the backpropagation for series parallel models the backpropagation sensitivity method and truncated backpropagation through time algorithm bptt for parallel models are derived analysed and compared for the truncated bptt it is shown that determination of the number of unfolding time steps necessary to calculate the gradient with an assumed degree of accuracy can be made on the basis of impulse response functions of sensitivity models the algorithms are shown to differ in their computational complexity gradient approximation accuracy and convergence rates numerical examples are also included to compare the performance of the algorithms

limitations of feedback properties imposed by open loop right half plane poles an integral constraint on the closed loop transfer function of unstable open loop systems is used to quantify a tradeoff between feedback properties of the closed loop system this results in a lower bound on the peak of the complementary sensitivity function for unstable plants the lower bound illustrates the nature of the tradeoff that is imposed and provides insight into the difficulties imposed on the control of unstable systems it can be used to quantitatively evaluate tradeoffs between the frequency of the open loop unstable pole the peak of the complementary sensitivity functions and the bandwidth of the closed loop system such a relationship has long been recognized and is embodied in the classical design rule of thumb which states that the closed loop bandwidth must be at least twice as large as the frequency of the unstable pole results which give insight into this rule and a theoretical basis for it are provided

identification of block oriented nonlinear systems starting from linear approximations a survey abstract block oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use many different identification approaches were developed over the years to estimate the parameters of a wide range of block oriented nonlinear models one class of these approaches uses linear approximations to initialize the identification algorithm the best linear approximation framework and the approximation framework or equivalent frameworks allow the user to extract important information about the system guide the user in selecting good candidate model structures and orders and prove to be a good starting point for nonlinear system identification algorithms this paper gives an overview of the different block oriented nonlinear models that can be identified using linear approximations and of the identification algorithms that have been developed in the past a non exhaustive overview of the most important other block oriented nonlinear system identification approaches is also provided throughout this paper

identification of a class of nonlinear autoregressive models with exogenous inputs based on kernel machines in this paper we propose a new approach to identify a new class of nonlinear autoregressive models with exogenous inputs narx based on kernel machine and space projection kmsp the well known hammerstein wiener model which includes blocks of nonlinear static functions in series with a linear dynamic block is a subset of the narx models considered in the kmsp based approach kernel machine is used to represent the functions and space projection to separate the represented functions we also discuss two possible ambiguities and give conditions to avoid such ambiguities the asymptotic behavior of the proposed approach is analyzed the performance of the proposed method is verified by simulation studies

structure identification of nonlinear dynamic systems a survey on input output approaches abstract in the past several methods have been elaborated for the identification of nonlinear dynamic systems most of the methods assume that the structure of the system is given a priori therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation however in nonlinear system theory several methods are known to determine the structure of a system in this paper structure identification of block oriented especially cascade models of semi linear dynamic models with signal dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered different structure selection methods are summarized based on step and impulse tests frequency response measurements correlation analysis repeated reproducible tests and normal operating data

brief paper revisiting hammerstein system identification through the two stage algorithm for bilinear parameter estimation the two stage algorithm tsa has been extensively used and adapted for the identification of hammerstein systems it is essentially based on a particular formulation of hammerstein systems in the form of bilinearly parameterized linear regressions this paper has been motivated by a somewhat contradictory fact though the optimality of the tsa has been established by bai in 1998 only in the case of some special weighting matrices the unweighted tsa is usually used in practice it is shown in this paper that the unweighted tsa indeed gives the optimal solution of the weighted nonlinear least squares problem formulated with a particular weighting matrix this provides a theoretical justification of the unweighted tsa and also leads to a generalization of the obtained result to the case of colored noise with noise whitening numerical examples of identification of hammerstein systems are presented to validate the theoretical analysis

nonlinear black box modeling in system identification a unified overview a nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics there has been considerable recent interest in this area with structures based on neural networks radial basis networks wavelet networks and hinging hyperplanes as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules this paper describes all these approaches in a common framework from a user s perspective it focuses on what are the common features in the different approaches the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques it is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space these mappings are discussed separately the latter mapping is usually formed as a basis function expansion the basis functions are typically formed from one simple scalar function which is modified in terms of scale and location the expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach basic techniques for estimating the parameters in the structures are criterion minimization as well as two step procedures where first the relevant basis functions are determined using data and then a linear least squares step to determine the coordinates of the function approximation a particular problem is to deal with the large number of potentially necessary parameters this is handled by making the number of used parameters considerably less than the number of offered parameters by regularization shrinking pruning or regressor selection

identification scheme for hammerstein output error models with bounded noise this technical note presents a method for the identification of hammerstein output error hoe models corrupted by bounded noise the method is based on an iterative scheme using two optimal bounding ellipsoid obe type algorithms the proposed approach allows the joint estimation of the linear part and of the nonlinear part with a low computational burden a numerical example is given so as to show the efficiency of the method