Estimation of depth from defocus as polynomial system identification

Transfer function estimation of turboalternator from practical operating data by spectral analysis

Recently, neuro-transfer function (neuro-TF) has become a recognized method for electromagnetic (EM) parametric modeling. The existing neuro-TF methods use the vector fitting technique to perform transfer function (TF) parameter extraction, commonly encountering nonsmoothness and discontinuity issues for the extracted TF parameters with respect to geometrical parameters. This letter proposes an advanced autoencoder TF parameter extraction technique for neuro-TF parametric modeling of microwave components. In the proposed technique, the autoencoder is introduced to extract a set of TF parameters as TF parameters from the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$</tex-math> </inline-formula> -parameters with the encoder part and generate a decoder function as the TF in the original neuro-TF model. The TF parameters extracted using the proposed technique behave much smoother than the TF parameters extracted using traditional vector fitting. Meanwhile, the proposed technique avoids the discontinuity problem caused by vector fitting in the standard neuro-TF method. Parametric modeling using the smooth TF parameters can thus have higher accuracy than modeling with nonsmooth TF parameters. The proposed technique is demonstrated by two examples of EM parametric modeling of microwave components.

On Padé-type model order reduction of J-Hermitian linear dynamical systems

In this study, transfer function of an active suspension system of a quarter car model is modeled via parametric system identification methods. It is tried to obtain a method that can provide the best representation of the transfer function of the system by utilizing different transfer function modeling tools. Most of mechanical systems include active suspension system of a quarter car model are modeled as mass spring damping systems. Proposing the best system identification method that represents the transfer function model of a system examined in this study is a crucial task to make a generalization for modeling of these type of systems. Numerical simulation studies are realized in Matlab environment to observe the performances of these methods and present them in a comparative manner. As a result of these simulations it is observed via the comparative results that Output Error (OE) transfer function model is an useful system identification tool for the mentioned purpose.

The state‐space realization of linear systems is of utmost importance in linear systems theory. After the realization problem for the time‐invariant case was solved, particular attention was paid to the case of linear periodic systems. Recently, such systems have regained importance, for instance, in the context of coding theory where periodic convolutional encoders play an important role. The majority of the contributions within this area only concern the realization of transfer functions (or impulse responses), thus excluding the case of input/output linear systems without coprime representations. By the end of the eighties of the last century, Jan C. Willems suggested an approach (nowadays known as the behavioral approach) that considers a wider class of systems and allows to overcome this drawback. According to this approach, the central object in a system is its behavior which consists of all the signals that satisfy the system laws (also called system trajectories). Consequently, the behavior of a system with an input/output representation that is not coprime contains more trajectories than the set of input/output signals defined by the system transfer function. Our work takes this fact into account. In previous research conducted by the authors, some results on the realization of periodic behavioral systems were obtained, which, despite their importance, are conservative with respect to the dimension of the obtained realizations. In this paper, we revisit the behavioral periodic realization problem and give further insight into this question. This allows to derive new results and set up an algorithm to compute low‐dimensional state‐space realizations.

Steady-state, harmonic response and moments of linear systems with periodic jumps

A procedure is developed for obtaining the transfer function of a linear system from the frequency-response data in terms of its poles and zeros. The method is based upon the fact that the transfer function is an analytic function of the complex variable s at all points in the s plane except the isolated points which are the poles of the function. Hence if the function is specified along the jω axis, it is possible to extend the function in the left-half or right-half s plane by means of conformai mapping techniques. The curvilinear squares in the G(s) plane corresponding to a grid of constant σ and constant ω lines in the s plane can be constructed with fair accuracy after a little practice. The particular values of σ and ω, for which the lines pass through the origin of the s plane, can thus be determined by locating the zeros of the transfer function. The poles are similarly obtained by working with the inverse function. Since there are several values of s satisfying G(s) = 0, the mapping from the s plane to the G(s) plane is not entirely a one-to-one mapping, and several regions in the s plane are mapped on to the same region in the G(s) plane. A method is suggested to overcome this difficulty and to obtain, step-by-step, all the zeros and poles of the transfer function corresponding to the given frequency-response locus. The method is illustrated by means of three numerical examples.

On closed-loop system identification using polyspectral analysis given noisy input–output time-domain data

This chapter considers the approximation of the transfer function of a linear system in terms of a causal filter bank. Assume that \(f\left( {{\rm{e}}^{{\rm{i}}\theta } } \right)\) with \(\theta \in [-\pi,\pi)\) is the transfer function of an arbitrary discrete-time linear system \({\cal L}\), and let \(\Phi = \left\{ {\varphi _k } \right\}_{k = 1}^\infty \) be a set of transfer functions of an orthonormal filterbank. It is assumed that f as well as all \(\varphi_{k}\) are elements of a certain Banach algebra \({\cal B}\) which characterizes the system theoretical properties of \({\cal L}\) and of the filterbank \(\Phi \). Moreover, since f as well as \(\{\varphi_{k}\}^{\infty}_{k=1}\) should represent causal systems, these transfer functions have to belong to the causal subspace \({\cal B}_ + \,{\rm{of}}\,{\cal B}\). Then, it is desirable to obtain an approximation of f in this filterbank of the form

System identification is concerned with finding a good model from, in general, noisy data, i.e. with data driven modeling. Often the task of identification is so complex that it cannot be performed in a naive way with the naked eye. In addition many identification problems share common features. For these reasons methods and theories have been developed which make system identification a subject of its own. This is the case despite the fact that problems of system identification are treated in different and partly rather separated communities, such as in system and control theory, signal processing, statistics and econometrics; the latter is explained by the fact that system identification is a central issue in many branches of science and has a wide range of areas of applications from control of chemical processes to the analysis of earth quake data or forecasting of sales for firms. Accordingly, we will use the term system identification for data driven modeling in general, i.e. not necessarily relating to system and control theory

A newly developed theory for predicting the response of a linear system to an electromagnetic pulse, based only on the measured continuous-wave magnitude, is applied to the problem of possible electromagnetic interferences at a sensitive part of a torpedo. The measured magnitude representing the system's transfer function is deduced first from the measured response at this sensitive point to a known cw source, supplied by the Naval Surface Warfare Center. We derive an analytic expression for the magnitude square of the transfer function to approximate the measured data and obtain a system transfer function in terms of the complex fi"equency, from which we predict the system's cw phase characteristics and its multiple solutions due to a given impulse source.

Experimental determination of the matrix-to-fracture transfer functions for oil recovery by water imbibition

A novel Hankel theory is developed for non-causal multidimensional linear shift invariant systems. It is shown that the rank of a generalized Hankel operator is related in a fundamental way to the rationality of a multidimensional system's transfer function. This theorem may be viewed as a generalization of Kronecker's ID theorem. These results suggest a new algorithm for multidimensional system identification from impulse response measurements.

Connections between conservative linear systems, Lax–Phillips scattering, and operator model theory are well known. A common thread in all the theories is a contractive, analytic, operator-valued function on the unit disc T(z) having a representation of the form T(z) = D + z C (I − zA)−1 B, known as the transfer or frequency-response function in the system-theory community, the scattering function in the mathematical physics community, and the characteristic operator function in the operator theory community. Here we consider analogues of this circle of ideas in the more general setting of multidimensional systems/multi-evolution scattering systems/multivariable function-theoretic operator theory. Three particular extensions are discussed; from the point of view of system theory, these involve (1) a multidimensional linear system with transfer function a contractive analytic operator function on the unit polydisc in complex Euclidean space, (2) a non-commutative multidimensional linear system with evolution along a free semigroup and with transfer function equal to a formal power series in non-commuting indeterminants, and (3) an overdetermined multidimensional linear system with transfer function identified as a bundle mapping between two Hermitian vector bundles over an algebraic curve embedded in complex projective space. This survey updates an earlier survey by the first author appearing in 2000.

A method is presented for predicting the total response, in both frequency and time, of an unknown linear system when only the measured continuous wave (cw) magnitude is available. The approach is based on approximating the square of the measured magnitude by a rational function, from which various system transfer functions in terms of complex frequency are deduced. These transfer functions may or may not be at minimum phase. The corresponding impulse response is then obtained by taking the inverse Laplace transform of the transfer function. The impulse response of the minimum-phase case rises faster initially to its first maximum than the nonminimum-phase counterparts. This result confirms that, for the same cw magnitude response, the accumulative energy contained in the impulse response is the greatest when the transfer function is at minimum phase. Physical meaning of the energy content is also discussed.