Sliced Inverse Regression for the Identification of Dynamical Systems

Lyzell, Christian; Enqvist, Martin

doi:10.3182/20120711-3-be-2027.00271

Cited by 3 publications

(3 citation statements)

References 17 publications

(25 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some of these approaches have already been applied in a system identification setting, such as the sliced inverse regression (SIR) [11], the directional regression (DR) [10], and the discretized directional regression (DDR) [28]. More information about using inverse regression for system identification can be found in [14,15]. Another promising, but computationally more expensive, dimension reduction method is the minimum average variance estimation (MAVE) method [13,27], which uses an iterative forward regression approach.…”

Section: Dimension Reductionmentioning

confidence: 99%

See 1 more Smart Citation

Combining the best linear approximation and dimension reduction to identify the linear blocks of parallel Wiener systems

Schoukens

Lyzell

Enqvist

2013

IFAC Proceedings Volumes

Self Cite

View full text Add to dashboard Cite

Section: Dimension Reductionmentioning

confidence: 99%

“…Using a standardized distribution for the applied regressors ϕ, the inverse regression curve E(ϕ|y) lies in the space spanned by the original matrix B. A principal component analysis on the covariance matrix of E(ϕ|y) will yield the estimate of B [10,11,14,15].…”

Section: Inverse Regressionmentioning

confidence: 99%

Combining the best linear approximation and dimension reduction to identify the linear blocks of parallel Wiener systems

Schoukens

Lyzell

Enqvist

2013

IFAC Proceedings Volumes

Self Cite

View full text Add to dashboard Cite

“…The SIR estimator is illustrated for a simple example in Figure 2. The consistency of the SIR estimator is shown in Li [1991] for the case of independent identically distributed regressors and generalized to allow finite dependence in Lyzell and Enqvist [2011]. A MATLAB implementation is freely available via Cook et al [2011].…”

Section: Sliced Inverse Regressionmentioning

confidence: 99%

Inverse Regression for the Wiener Class of Systems

Lyzell

Enqvist

2012

IFAC Proceedings Volumes

Self Cite

View full text Add to dashboard Cite

The concept of inverse regression has turned out to be quite useful for dimension reduction in regression analysis problems. Using methods like sliced inverse regression (SIR) and directional regression (DR), some high-dimensional nonlinear regression problems can be turned into more tractable low-dimensional problems. Here, the usefulness of inverse regression for identification of nonlinear dynamical systems will be discussed. In particular, it will be shown that the inverse regression methods can be used for identification of systems of the Wiener class, that is, systems consisting of a number of parallel linear subsystems followed by a static multiple-input single-output nonlinearity. For a particular class of input signals, including Gaussian signals, the inverse regression approach makes it possible to estimate the linear subsystems without knowing or estimating the nonlinearity.Keywords: System identification; Dimension reduction; Inverse regression. Inverse Regression for the Wiener Class of SystemsChristian Lyzell, Martin Enqvist 2011-11-14 AbstractThe concept of inverse regression has turned out to be quite useful for dimension reduction in regression analysis problems. Using methods like sliced inverse regression (SIR) and directional regression (DR), some high-dimensional nonlinear regression problems can be turned into more tractable low-dimensional problems. Here, the usefulness of inverse regression for identification of nonlinear dynamical systems will be discussed. In particular, it will be shown that the inverse regression methods can be used for identification of systems of the Wiener class, that is, systems consisting of a number of parallel linear subsystems followed by a static multiple-input single-output nonlinearity. For a particular class of input signals, including Gaussian signals, the inverse regression approach makes it possible to estimate the linear subsystems without knowing or estimating the nonlinearity.

show abstract

Identification of block-oriented nonlinear systems starting from linear approximations: A survey

2017

View full text Add to dashboard Cite

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.

show abstract

Sliced Inverse Regression for the Identification of Dynamical Systems

Cited by 3 publications

References 17 publications

Combining the best linear approximation and dimension reduction to identify the linear blocks of parallel Wiener systems

Combining the best linear approximation and dimension reduction to identify the linear blocks of parallel Wiener systems

Inverse Regression for the Wiener Class of Systems

Identification of block-oriented nonlinear systems starting from linear approximations: A survey

Contact Info

Product

Resources

About