Joint estimation of inputs and states for multi-axis vibration environment testing

Monitoring the states of a structural dynamic system is often challenging, as direct measurements are costly or even infeasible. Estimating “hard-to-measure” quantities from a limited set of output-only data is therefore of great interest and useful for the application of Structural Health Monitoring (SHM) systems. This work proposes a virtual sensing methodology for state estimation in structural dynamics based on a tuned Kalman Filter, combined with a model order reduction technique to ensure low computational cost. The approach aims to overcome the limitations of dense embedded physical sensor networks by reconstructing unmeasured responses from limited measurements. The methodology is validated numerically and experimentally on a notched aluminum beam, representative of an overhanging automotive component, subjected to multi-directional base excitations on a 3D shaker to emulate realistic operating conditions.