Reducing black-box nonlinear state-space models: A real-life case study

Abstract

A known challenge when building nonlinear models from data is to limit the size of the model in terms of the number of parameters. Especially for complex nonlinear systems, which require a substantial number of state variables, the classical formulation of the nonlinear part (e.g. through a basis expansion) tends to lead to a rapid increase in the model size. In this work, we propose two strategies to counter this effect:1) The introduction of a novel nonlinear-state selection algorithm. The method relies on the non-parametric nonlinear distortion analysis of the Best Linear Approximation framework to identify the state variables which are the most impacted by nonlinearities. Pre-selecting only the most appropriate states when constructing the nonlinear terms results in a considerable reduction of the model size.2) The use of so-called ‘decoupled’ functions directly in the model estimation procedure. While it is known that function decoupling can reduce the model size in a secondary step, we show how a decoupled formulation can be imposed to advantage from the start. The results of this approach are benchmarked with the state-of-the-art a posteriori decoupling technique.Our strategies are demonstrated on real-life data of a multiple-input, multiple-output (MIMO) ground vibration test of an F-16 aircraft, a prime complex and nonlinear dynamic system.