Black-box system identification for reduced order model construction

For the simulation of multi-physics, multi-scale phenomena, it is often advantageous to build a comprehensive system- or process-model from a collection of sub-models, each of them purposely constructed to describe a certain aspect of the overall problem with high accuracy at low computational cost. Such strategies of divide et impera ("divide and conquer") integrate modeling approaches of different complexity for different phenomena and scales. Reduced order models (ROMs) identified from time series data can play an important part in such a scheme. The present paper reviews a body of work in aero- and thermo-acoustics, where computational fluid dynamics (CFD) simulation is combined with tools from system identification to characterize the dynamic response of a sub-system (an "element") to incoming flow perturbations. The element under consideration is treated as a "black box" with a given structure of inputs and outputs. In general, multiple inputs and multiple outputs are present (MIMO model), in the simplest case only a single input and a single output need be considered (SISO structure). Once the response to a broad-band excitation signal is determined by numerical simulation, a ROM representation of the element dynamics can be deduced with system identification. For that purpose, a wide range of methods is available, selection of the most suitable method for a given problem is a non-trivial matter. Selected results obtained with the CFD/SI approach are reviewed, supplemented by best practice recommendations for successful and accurate identification of ROMs from time series data. Perspectives for the use of this method in other fields of science and engineering are developed.