Examination of Modal Expansion and Kalman Filtering Techniques for Vibration Estimation

State estimation is a well-established discipline within the field of modern control theory. In the context of vibration analysis, where application areas include damage prognosis and structural control with full state feedback, the topic has, however, emerged during the last couple of decades under the term virtual sensing. Here, the scope is to estimate physical quantities at both measured and unmeasured locations based on vibration signals captured in a limited set of sensors. This paper examines and compares three virtual sensing techniques, namely, modal expansion, direct Kalman filtering and a modified Kalman filter where the true value of the input is replaced by an optimal estimate. The performance of the three schemes is examined in an experimental setup with a cantilevered beam, which is subjected to different input types and installed with a limited set of accelerometers. Based on the experimental findings, some observations and particular recommendations on the use of the different schemes are provided.