Decoupling in Black Box Nonlinear System Identification: A Game Changer

A major choice in nonlinear system identification is the selection of a white (grey) or a (pit) black modeling approach (Schoukens and Ljung, 2019). Black box identification is a very flexible and generic approach that comes with the price of an (extremely) large number of model parameters and a lack of physical insight. For that reason the white box approach is often preferred whenever the higher modeling effort can be afforded. Recently, numerical
methods were developed that allow to decompose multivariate polynomials q = f(p) in a decoupled form q = Wg(V T p), with W, V linear transformations, and g a univariate function (g i (x) = g i (x i ), i = 1, . . . , r, with x = V T p). In this article we will show that these new tools remove/reduce the major disadvantages of black box modeling significantly so that at the end of the modeling process a sparse nonlinear model is obtained with less model parameters and a
better (physical) interpretability. This can be a game changer that combines the advantages of black and white box modeling without inheriting the intrinsic disadvantages of both approaches.