Optimal sensor placement for detection of non-linear structural behavior

Most Structural Health Monitoring (SHM) techniques are based on the variation of modal properties of structures. Modal analysis is established under the assumption that the structure behaviour is linear. However, the presence of non-linearities (local or global, smooth or strong) can affect the dynamic properties of the structure. Most of techniques to detect non-linear behaviour in structural dynamics are based on frequency domain data. Fewer techniques only deal with the use of time responses. The main aim of the present research is to improve the detection of non-linear behaviour by the use of efficient sensor placement methodologies. In addition, a minimal number of sensors and information is considered. Optimal sensor placement algorithms have been extensively employed in modal analysis which have been re-oriented to the case of non-linear behaviour. In particular, the Principal Component Analysis (PCA) technique is applied to the time series of a cantilever beam with an attached non-linear spring at its free end. Two cases are considered, where the beam is excited by harmonic force and by a constant amplitude random force. Several amplitude levels are considered where non-linear behaviour is expected. Numerical results for different number of sensors and configurations are presented.