Joint Estimation of Inputs and States for Multi-Axis Vibration Environment Testing

Monitoring inputs and states of a structural dynamic system is often challenging, as direct measurements are costly or even infeasible. A virtual sensing methodology is presented for jointly estimating the input and state of a structure when subjected to multi-directional base excitations. The approach uses a tuned Kalman Filter combined with a model-order reduction of the system model to ensure a low computational cost whilst allowing accurate estimation from a limited number of acceleration measurements. This enables real-time virtual health monitoring strategies and reduction in instrumentation during data acquisition without additional information such as location and direction of application about the inputs. The proposed methodology is validated numerically and experimentally using a notched aluminum beam excited on a multi-directional shaker table, driven simultaneously in two in-plane directions. The study demonstrates accurate full-field estimation of multiple responses along the beam as well as a joint-input-estimation. The results highlight the relevance of multi-axis vibration environments and the importance of multiple-input-multiple-output testing for dynamic characterization and structural health monitoring applications.