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Parallel Wiener-Hammerstein Identification: A case study

Boekbijdrage - Boekhoofdstuk Conferentiebijdrage

System identification is the art of building realistic models for dynamical systems based on observed measurements. These models can be used to understand how a system works, or to predict its future behavior. The last few decades have shown a shift from linear to nonlinear system identification, where the models can better explain the nonlinear effect of the world surrounding us. One possible approach to build nonlinear models is using two kinds of blocks: one kind consists of the linear dynamic part and the other part of the nonlinear static part. These so-called block-oriented models can be used for mechanical and electronical engineering applications, as robotic arms, plane wings and electronical circuits. In this field of nonlinear system identification, multivariate polynomials are essential. Representing such a polynomial as a vector of univariate polynomials can offer useful insight, a significant reduction of the number of parameters, as well as more intuitive understanding of the function and the processes it describes. This will increase the physical insights in the problem and the research of this so-called decoupled representation of the multivariate polynomial is central in our work. The question of decoupling nonlinear functions has been studied in the noiseless case, where an exact decomposition of a given coupled function was assumed to exist. To find this decoupled representation, a tensor-based approach has been developed. A multidimensional array (tensor), containing the first-order information of the coupled function, is decomposed using a technique called the Canonical Polyadic Decomposition. Loosely speaking, this generalizes the matrix singular value decomposition to higher-order tensors. However, decomposing an exact nonlinear vector function lies far away from the real world, where all measured data are inherently noisy. In our work, we have studied how noise and model errors affect the decoupling of nonlinear functions. By considering a weight matrix and incorporating it during the Canonical Polyadic Decomposition, the exact decomposition has been generalized to a weighted and approximate decomposition. The results are promising: considering a weight matrix works at least as good as the earlier exact method. Furthermore, whenever the weightless method does not provide an adequate decomposition, the weighted method reduces the model errors significantly.
Boek:  2016 Leuven Conference on Noise and Vibration Engineering
Pagina's: 2647- 2656
Jaar van publicatie:2016
  • Scopus Id: 85018176443
  • WoS Id: 000392486305013