ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

20th Conference of the International Linear Algebra Society (ILAS)

20th ILAS Conference

In minisymposium: Tensors for Signals and Systems

Thu 16:00–16:30, Room AV 00.17
Parameter reduction and interpretability in system identification using tensor decompositions
Koen Tiels (Vrije Universiteit Brussel)
Joint work with Maarten Schoukens (Vrije Universiteit Brussel)

System identification is the field of systematically building mathematical models from measured data. The mathematical models range from white-box to black-box models. White-box models only use first principles or physical laws, whereas black-box models use no physical knowledge of the system, but only the measured data. Black-box models are typically flexible mathematical expressions that can well approximate a large variety of system behaviors, but often use a large number of parameters in return.

In this talk, some black-box models will be considered. It will be shown how the canonical polyadic tensor decomposition and variants thereof are used to reduce the number of parameters and increase the interpretability of the considered black-box models.

In particular, the talk will cover Volterra models [1,2], parallel Wiener [3] and parallel Wiener-Hammerstein models [4] including an illustration on a measurement example.

  1. G. Favier and T. Bouilloc, Parametric complexity reduction of Volterra models using tensor decompositions, In 17th European Signal Processing Conference (EUSIPCO), Glasgow, Scotland, Aug. 2009, pp. 2288–2292.
  2. R. D. Nowak and B. D. Van Veen, Tensor product basis approximations for Volterra filters, IEEE Trans. Signal Process., 44 (1996), pp. 36–50.
  3. M. Schoukens and Y. Rolain, Cross-term elimination in parallel Wiener systems using a linear input transformation, IEEE Trans. Instrum. Meas., 61 (2012), pp. 845–847.
  4. M. Schoukens, K. Tiels, M. Ishteva, and J. Schoukens, Identification of parallel Wiener-Hammerstein systems with a decoupled static nonlinearity, In 19th World Congress of the International Federation of Automatic Control, Cape Town, South Africa, Aug. 2014, pp. 505–510.