Full-field strain estimation of subsystems within time-varying and nonlinear systems using modal expansion

Virtual sensing allows for the estimation of stress and/or strain response in unmeasured locations of a system. Often, these virtual sensing techniques assume a linear and time-invariant system with proportional damping. In this article, one virtual sensing technique - the modal expansion - is proven applicable for stress/strain estimation of subsystems within time-varying and nonlinear systems with general viscous damping where the time-varying and nonlinear effects act externally on the subsystems. This technique uses the mode shapes of the subsystem to expand the response by a subspace projection. It is proven that the mode shapes of the underlying undamped and linear system form a basis for the response of the time-varying and nonlinear systems with general viscous damping. Therefore, a truncation of the mode shapes results in modal truncation errors that depend on the span of the applied mode shapes. Thus using an appropriate set of undamped and linear mode shapes of the subsystem, the modal expansion allows for estimation of the stress/strain response for “linear” subsystems within time-varying and nonlinear systems with general viscous damping. This concept is proven both numerically and experimentally.