| 1. |
- Johansson, Jimmy, et al.
(författare)
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Interactive Analysis of Time-Varying Systems Using Volume Graphics
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We show how 3-dimensional volume graphics can be used as a tool in system identification. Time-dependent dynamics often leave a significant residual with linear, time-invariant models. The structure of this residual is decisive for the subsequent modelling, and by using advanced visualization techniques, the modeller may gain a deeper insight into this structure than that which can be obtained from standard correlation analysis. We present a development platform that merges a rich variety of estimation programs with state of the art visualization techniques.
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| 2. |
- Johansson, Jimmy, et al.
(författare)
-
Interactive Analysis of Time-Varying Systems Using Volume Graphics
- 2004
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Ingår i: Proceedings of the 43rd IEEE Conference on Decision and Control. - 0780386825 ; , s. 5083-5087
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Konferensbidrag (refereegranskat)abstract
- We show how 3-dimensional volume graphics can be used as a tool in system identification. Time-dependent dynamics often leave a significant residual with linear, time-invariant models. The structure of this residual is decisive for the subsequent modelling, and by using advanced visualization techniques, the modeller may gain a deeper insight into this structure than that which can be obtained from standard correlation analysis. We present a development platform that merges a rich variety of estimation programs with state of the art visualization techniques.
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| 3. |
- Johansson, Jimmy, et al.
(författare)
-
Interactive Visualization as a Tool for Analysing Time-Varying and Non-Linear Systems
- 2005
-
Ingår i: Proceedings of the 16th IFAC World Congress. - 9783902661753 ; , s. 95-95
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Konferensbidrag (refereegranskat)abstract
- This paper shows how 3-dimensional interactive visualization can be used as a tool in system identification. Non-linear or time-dependent dynamics often leave a significant residual with linear, time-invariant models. The structure of this residual is decisive for the subsequent modelling, and by using advanced visualization techniques, the modeller may gain a deeper insight into this structure than can be obtained by standard correlation analysis.
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| 4. |
- Lindgren, David, et al.
(författare)
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Clustered Regression Analysis
- 2002
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Ingår i: Proceedings of the 41st IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 0780375165 ; , s. 1838-1844 vol.2
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Konferensbidrag (refereegranskat)abstract
- Cluster structure in (multicollinear) data can be utilized by pattern recognition methods in order to find adequate subspaces for nonlinear regression. When regressing a particular severely nonlinear function, it is demonstrated that this approach is superior to polynomial PLS. It is also demonstrated that for nonlinear functions, the choice of regressing explained variables onto the explaining variables, or vice-versa, is not arbitrary. Numerical experiments indicate that the classical statistical model is more powerful than the inverse regression approach.
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| 5. |
- Lindgren, David, et al.
(författare)
-
Nonlinear Dynamics Identified by Multi-Index Models
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- For a class of nonlinear systems, the residual of a well fitted model has low intrinsic dimensionality. For these systems, a particular low-dimensional linear projection of the regressor will facilitate both visualization of the nonlinearities and subsequent nonlinear modeling. The least squares fit of polynomial and piecewise affine functions are used as criterion by which numerical programs search for the linear projection that gives the best low-dimensional description of the residual. For a simulated water tank and for real life data sampled from an electronic circuit, the regressor can be projected down to 2 dimensions and still yield a model simulation fit of about 99%. The electronic circuit data can be described by a model structure with far less parameters than conventional, nonlinear black-box models.
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| 6. |
- Lindgren, David, et al.
(författare)
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Nonlinear Dynamics Isolated by Delaunay Triangulation Criteria
- 2004
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Ingår i: Proceedings of the 43rd IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 0780386825 ; , s. 3862-3867 Vol.4
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Inspired by an idea by Q. Zhang, we show that Delaunay triangulation of data points sampled from a system with an additive nonlinearity gives a criterion by which a linear projection can be found that isolates the nonlinear dependence, leaving out the linear one. This isolation means the nonlinear modeling can be confined to a regressor space of lower dimensionality, which in turn means over-parameterization can be avoided. Monte Carlo simulations indicate that a particular criterion built on triangle asymmetries has a minimum that coincides with the sampled system nonlinear part. The criterion is however complex to compute and non-convex, which makes it difficult to optimize globally.
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| 7. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
Nonlinear Dynamics Identified by Multi-Index Models
- 2005
-
Ingår i: Proceedings of the 16th IFAC World Congress. - 9783902661753 ; , s. 32-32
-
Konferensbidrag (refereegranskat)abstract
- For a class of nonlinear systems, the residual of a well fitted model has low intrinsic dimensionality. For these systems, a particular low-dimensional linear projection of the regressor will facilitate both visualization of the nonlinearities and subsequent nonlinear modeling. The least squares fit of polynomial and piecewise affine functions are used as criterion by which numerical programs search for the linear projection that gives the best low-dimensional description of the residual. For a simulated water tank and for real life data sampled from an electronic circuit, the regressor can be projected down to 2 dimensions and still yield a model simulation fit of about 99%. The electronic circuit data can be described by a model structure with far less parameters than conventional, nonlinear black-box models.
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