Disturbance Source Identication for Flow Control:Problem Formulation for Innitesimal Disturbances

摘要

We introduce a method for identifying sources of disturbances in amixture measured by sensors in shear ows. To recover all disturbancesources from the recorded signals, we consider blind source separation(BSS) techniques in a case where the sources and the mixing processare unknown and only the recordings of the mixtures are available. Weadapt and use the independent component analysis (ICA) method forpreforming BSS. In the theoretical framework we dene the term `source'in shear ows, and derive a model describing the mixtures measured byN_x sensors due to N_s various disturbances generated in shear boundarylayer. We obtain a criterion for successful separation of 3D disturbancesin on N_s×N_x source-sensor system by the ICA-BSS method. The cri-terion dictates the proper placement of sensors in the ow. We study,numerically and analytically, various sensor-actuator arrangements. Inour numerical simulations we consider shear ows with two disturbance-generators and two sensors. Linear stability theory (LST) for planePoiseuille ow (PPF) and Blasius ow with parallel ow assumption areemployed to describe the downstream propagation of small disturbances.Results from application of the ICA-BSS method on simulated measure-ments in shear ow are validated against our theoretical analysis.