Reconstruction of multiple impact forces by wavelet relevance vector machine approach

In this work, reconstruction of forces generated by multiple impacts occurring on linear elastic structures has been achieved through wavelet relevance vector machine approach to inverse problem solution. The posterior density of probabilities function integrating both the likelihood and prior random information was considered for the particular case of a system being affected by an additive random measurement noise. Compressed sensing technique was used to provide an adequate sparse representation of the inverse problem through using projection on a wavelet basis. Bayesian hierarchical modeling according to the relevance vector machine approximation was then applied in order to estimate the forces generated by impact events. The obtained results were remarkably good as the reconstructed forces were found to be very close to the original forces at the system input. The method was found also to provide a way for localization of impact forces.