Characterisation of complex system Dynamics from data: A probing excitation method

For complex dynamic systems, due to their intrinsic nonlinearity, time-varying and multivariate interdependence, they usually contain multiple inputs and multiple outputs, and the complex interactions and dynamics within the time and space of the system are also complex for the study of complex system physical properties. Therefore, in order to study complex dynamic systems, obtain their physical properties, and describe and predict the system behavior, this paper adopts a novel data-driven approach with the probing excitation method. The probing excitation method proposed in this paper distinguishes itself from traditional machine learning methods. Complex dynamic systems are usually black-box systems or partially black-box systems, while traditional methods for black-box systems construct black-box models that lack physical interpretability. The method in this paper enables the detection of physical properties of complex dynamical systems by selecting inputs and outputs and constructing models that reflect the physical properties. The probing excitation method involves selecting one input and one output of a complex dynamic system to build a model with interpretability that reflects the physical properties or some of the physical properties of this system. Repeat this process to develop multiple models and integrate them for comprehensive analysis. In this way, we can capture the system's physical characteristics, enhancing interpretability and enabling the prediction and control of system behavior.