A method for identifying causality in the response of nonlinear dynamical systems
This addresses a critical issue in fields like structural dynamics and neuroscience for researchers needing to distinguish modeling errors from noise in data-driven models, offering a novel solution where none existed before.
The paper tackles the problem of identifying causal input-output relationships in nonlinear dynamical systems when only noisy output measurements are available, presenting a method that calculates a nonlinear coherence metric to measure causality without requiring a high-fidelity model.
Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires experimental measurements of the system input and output, but it can be difficult to determine whether inaccuracies in the model stem from modelling errors or noise. This paper presents a novel method to identify the causal component of the input-output data from measurements of a system in the presence of output noise, as a function of frequency, without needing a high fidelity model. An output prediction, calculated using an available model, is optimally combined with noisy measurements of the output to predict the input to the system. The parameters of the algorithm balance the two output signals and are utilised to calculate a nonlinear coherence metric as a measure of causality. This method is applicable to a broad class of nonlinear dynamical systems. There are currently no solutions to this problem in the absence of a complete benchmark model.