| 1. |
- Juditsky, A., et al.
(författare)
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Nonlinear black-box models in system identification: Mathematical foundations
- 1995
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Ingår i: Automatica. - Linköping : Elsevier BV. - 0005-1098 .- 1873-2836. ; 31:12, s. 1725-1750
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Tidskriftsartikel (refereegranskat)abstract
- 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. Copyright © 1995 Elsevier Science Ltd All rights reserved.
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| 2. |
- Ljung, Lennart, 1946-, et al.
(författare)
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An Integrated System Identification Toolbox for Linear and Nonlinear Models
- 2006
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Ingår i: Proceedings of the 14th IFAC Symposium on System Identification. - 9783902661029 ; , s. 931-936
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Konferensbidrag (refereegranskat)abstract
- The paper describes additions to the MATLAB system identification toolbox, that handle also the estimation of nonlinear models. Both structured grey-box models and general, flexible black-box models are covered. The idea is that the look and feel of the syntax, and the graphical user interface should be as close as possible to the linear case.
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| 3. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
An Integrated System Identification Toolbox for Linear and Nonlinear Models
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The paper describes additions to the MATLAB system identification toolbox, that handle also the estimation of nonlinear models. Both structured grey-box models and general, flexible black-box models are covered. The idea is that the look and feel of the syntax, and the graphical user interface should be as close as possible to the linear case.
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| 4. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
Estimation of Grey Box and Black Box Models for Non-Linear Circuit Data
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Identification of non-linear systems is a challenge, due to the richness of both model structures and estimation approaches. As a case study, in this paper we test a number of methods on a data set collected from an electrical circuit at the Free University of Brussels. These methods are based on black box and grey box model structures or on a mixture of them, which are all implemented in a forthcoming Matlab toolbox. The results of this case study illustrate the importance of the use of custom (user defined) regressors in a black box model. Based on physical knowledge or on insights gained through experience, such custom regressors allow to build efficient models with a relatively simple model structure.
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| 5. |
- Ljung, Lennart, 1946-, et al.
(författare)
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Identification of Wiener System with Monotonous Nonlinearity
- 2006
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Ingår i: Proceedings of the 14th IFAC Symposium on System Identification. - 9783902661029 ; , s. 166-171
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Konferensbidrag (refereegranskat)abstract
- A Wiener system is composed of a linear dynamic subsystem followedby a static nonlinearity. It is well known in the literature that the identifcationof the linear subsystem of a Wiener system can be separated from that of theoutput nonlinearity, if the input signal is a Gaussian noise. In order to deal withthe non Gaussian input case, two new algorithms are proposed in this paper fordirect identifcation of the linear subsystem, regardless of any parametrization ofthe output nonlinearity. The essential assumption required in this paper is thestrict monotonousness of the output nonlinearity.
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| 6. |
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| 7. |
- Ljung, Lennart, 1946-, et al.
(författare)
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Optimality Analysis of the Two-Stage Algorithm Hammerstein System Identification
- 2009
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Ingår i: Proceedings of the 15th IFAC Symposium on System Identification. - Linköping : Linköping University Electronic Press. - 9783902661470 ; , s. 320-325
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Konferensbidrag (refereegranskat)abstract
- 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 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.
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| 8. |
- Sjöberg, Jonas, et al.
(författare)
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Nonlinear black-box modeling in system identification: A unified overview
- 1995
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Ingår i: Automatica. - Linköping : Elsevier BV. - 0005-1098 .- 1873-2836. ; 31:12, s. 1691-1724
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Tidskriftsartikel (refereegranskat)abstract
- 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. Copyright © 1995 Elsevier Science Ltd All rights reserved.
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| 9. |
- Wang, Jiandong, et al.
(författare)
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Revisiting Hammerstein System Identification through the Two-Stage Algorithm for Bilinear Parameter Estimation
- 2010
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 10. |
- Wang, Jiandong, et al.
(författare)
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Revisiting Hammerstein System Identification through the Two-Stage Algorithm for Bilinear Parameter Estimation
- 2009
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 45:11, s. 2627-2633
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
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