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1

Two-stage instrumental variables identification of polynomial Wiener systems with invertible nonlinearities

Janczak Andrzej, Korbicz Józef

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 3

571--580

EN

A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter estimates are consistent, the number of parameters of the transformed Wiener model is much greater than that of the original one. Moreover, there is no unique relationship between parameters of the inverse nonlinear function and those of the transformed Wiener model. In Stage II, based on the assumption that the linear dynamic model is already known, parameters of the inverse nonlinear function are estimated uniquely using the IV method. In this way, not only is the parameter redundancy removed but also the parameter estimation accuracy is increased. A numerical example is included to demonstrate the practical effectiveness of the proposed approach.

2

Parameter identification and estimation for stage-structured population models

Coll Carmen, Sánchez Elena

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 2

327--336

EN

A stage-structured population model with unknown parameters is considered. Our purpose is to study the identifiability of the model and to develop a parameter estimation procedure. First, we analyze whether the parameter vector can or cannot uniquely be determined with the knowledge of the input-output behavior of the model. Second, we analyze how the information in the experimental data is translated into the parameters of the model. Furthermore, we propose a process to improve the recursive values of the parameters when successive observation data are considered. The structure of the state matrix leads to an analysis of the inverse of a sum of rank-one matrices.

3

Mach-Zehnder non-zero chirp intensity modulator static characteristics parameters estimation based on intensity data

Lach Z.

Elektronika : konstrukcje, technologie, zastosowania

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2012

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Vol. 53, nr 11

12-14

PL

Zaproponowano parametryzację charakterystyki statycznej modulatora amplitudowego Mach-Zehndera typu non-zero chirp za pomocą pięciu parametrów wraz z metodą ich estymacji z próbek mocy optycznej. Praktyczną użyteczność parametryzacji i metody ich estymacji zweryfikowano w eksperymencie laboratoryjnym.

EN

Five parameters that describe a static characteristics of a non-zero chirp Mach-Zehnder intensity modulator and a method for their estimation from intensity samples are proposed. The practical value of the parameters and of the method of their estimation is examined in laboratory experiments.

4

The applications of fixed-point theorem in optimisation problems

Chwastek K.

Archives of Electrical Engineering

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2012

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Vol. 61, nr 2

189-198

EN

The fixed-point theorem is widely used in different engineering applications. The present paper focuses on its applications in optimisation. A Matlab toolbox, chich implements the branch-and-bound optimisation method based on the fixed-point theorem, is used for solving different real-life test problems, including estimation of model parameters for the Jiles-Atherton model.

5

An optimal input design using the sensitivity criterion for parametric identification of pharmacokinetic models

Kalicka R., Pietrenko-Dąbrowska A.

Biocybernetics and Biomedical Engineering

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2005

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Vol. 25, no. 2

3-18

EN

The parametric approach to the identification of the SISO state space compartmental models of pharmacokinetic systems is presented. The model structure is formulated basing on the a priori knowledge. The initial parameter estimates are calculated on the base of the output measurements collected during the intuitive experiment. They are used for designing the optimal input, which ensures the best accuracy of the parameter estimates. The sensitivity criterion is adopted and presented in terms of nonlinear programming problem with constraints. Two classes of optimal inputs are considered: equidose and equienergy inputs. The results obtained with optimal and standard inputs are presented and compared.