Optimal actuator and sensor placement for modal and stability monitoring

The purpose of the paper is to introduce a mechanism for excitation and monitoring of those dynamical modes characterizing the occurrence and the type of bifurcation in nonlinear dynamical systems. The main approach here is based on a definition of participation factors to conveniently address the participation of mode in a state, specified as the output, when the excitation signal is injected into another element of the vector field representing the dynamic of system. AWGN is used as the excitation signal and an algorithm based on the input-output cross correlation functions is used as a method for generation of the precursors corresponding to the complex modes of interest. Numerical simulations on a nonlinear model undergoing Hopf bifurcation prove the effectiveness of the idea.