Interpretable Deep Learning for System Identification Using Nonlinear Output Frequency Response Functions

Deep learning methods contain powerful tools for modelling nonlinear dynamic systems. However, these methods usually lack interpretability, so although they are useful for predicting outputs they tend to be less useful for giving insight into system characteristics. In this paper, we aim to demonstrate a method for interpreting and comparing deep learning models used in nonlinear system identification, using nonlinear output frequency response functions (NOFRFs). NOFRFs describe nonlinear dynamic system behaviour in the frequency domain, which is a classical way of interpreting and understanding system behaviour (via resonances, super and sub-harmonics, and energy transfer). We demonstrate the approach on a real system (a magneto-rheological damper), showing how different types of deep learning model, recurrent networks with gated recurrent units (GRUs) and long short term memory (LSTM), can be interpreted and compared in the frequency domain.