Interpretation and generalization of complexity pursuit for the blind separation of modal contributions

Complexity pursuit (CP) has recently been proposed as an elegant and simple solution to blindly (i.e. without measuring the inputs) separate the modal contributions in the vibration responses of a structure. This potentially finds considerable interest in operational modal analysis and related applications. This paper analyses the theoretical ins and outs of the method. It also revises its physical interpretation in the modal analysis context. CP is found to separate components which are the least dispersive (i.e. invariant under linear filtering), a property that well characterizes the modal responses of lightly damped systems. However, it is also found to suffer from the same limitations as other blind source separation methods used in the state-of-the-art, namely the difficulty to separate strongly coupled modes and to identify complex mode shapes. Finally a generalization of CP is proposed which intends to widen its applicability. Interestingly, the generalized CP happens to include the well-known SOBI algorithm as a particular case.