Modeling Parallel Wiener-Hammerstein Systems Using Tensor Decomposition of Volterra Kernels

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10169)


Providing flexibility and user-interpretability in nonlinear system identification can be achieved by means of block-oriented methods. One of such block-oriented system structures is the parallel Wiener-Hammerstein system, which is a sum of Wiener-Hammerstein branches, consisting of static nonlinearities sandwiched between linear dynamical blocks. Parallel Wiener-Hammerstein models have more descriptive power than their single-branch counterparts, but their identification is a non-trivial task that requires tailored system identification methods. In this work, we will tackle the identification problem by performing a tensor decomposition of the Volterra kernels obtained from the nonlinear system. We illustrate how the parallel Wiener-Hammerstein block-structure gives rise to a joint tensor decomposition of the Volterra kernels with block-circulant structured factors. The combination of Volterra kernels and tensor methods is a fruitful way to tackle the parallel Wiener-Hammerstein system identification task. In simulation experiments, we were able to reconstruct very accurately the underlying blocks under noisy conditions.


Tensor decomposition System identification Volterra model Parallel Wiener-Hammerstein system Block-oriented system identification Canonical polyadic decomposition Structured data fusion 



This work was supported in part by the Fund for Scientific Research (FWO-Vlaanderen), by the Flemish Government (Methusalem), the Belgian Government through the Inter-university Poles of Attraction (IAP VII) Program, by the ERC Advanced Grant SNLSID under contract 320378 and by FWO projects G.0280.15N and G.0901.17N. The authors want to thank Otto Debals and Nico Vervliet for help with the use of Tensorlab/SDF and the suggestion to extract the vector \(\mathbf {q}\) into an additional tensor mode.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department VUB-ELECVrije Universiteit Brussel (VUB)BrusselsBelgium
  2. 2.Department of Electrical and Computer EngineeringUniversity of CalgaryCalgaryCanada

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