“…Instead of fitting an empirical model to the Frequency Response Function (FRF) from artificial excitations (e.g., hammer strikes) as the traditional approach does, the SSI technique accounts for dynamic changes caused by the rotations of the spindle without the need for artificial excitations, and extracts the modal parameters from its measured output only, thus satisfying the requirement of online operation. Mathematically, the SSI technique is formulated and solved using a discrete time-state space model of a linear, time-invariant system (e.g., the spindle) without known external inputs according to the following equation: Xk+l =: Axk + Wk lYk Cxk + Vk (2) where xk=x(kAt) is the discrete-time state vector, Yk is the system response vector, A is the state matrix, and C is the output matrix. The two components, Wk and Vk, represent the disturbance noise to the spindle and measurement noise due to sensor inaccuracy, respectively, and are stochastic in nature.…”