The real life example 1
Identification of physical object code and dataThis is an application for identification of the physical object. There are several sources with publicly available datasets. http://www.nonlinearbenchmark.org/ is one of them. This dataset is Wiener-Hammerstein System (2009).
The site has very detailed explanation of the object and how experimental data were collected. The recommended reference to data sources is also provided:
J. Schoukens, J. Suykens, L. Ljung. Wiener-Hammerstein Benchmark. 15th IFAC Symposium on System Identification (SYSID 2009), July 6-8, 2009, St. Malo, France.
The object is static nonlinearity sandwiched between two linear blocks. The length of sample is 188000 input/output pairs. It is recommended to use first half for training the model and second half for validation. Three models are tested in the provided code: linear, single Urysohn and Kolmogorov-Arnold representation. For unseen data (validation record) the linear model shows 3.5% average error, single Urysohn 1.5% and Kolmogorov-Arnold slightly less - between 1% and 1.5%. We can conclude that for this data single Urysohn is a good model already. The last model Kolmogorov-Arnold is provided as reusable code, so people can test it for other data, when single Urysohn is not accurate enough.
