Octonion structural response vector and potential structural damage identification method

A promising method based on octonion structural response vector is proposed for the identification of structural damages according to the database acquired via long-term structural health monitoring. An octonion structural response vector consists of eight elements: seven for structural responses, including normalized static strains at specific positions and natural frequencies of a structure, and one for null. For a perfect structure the octonion structural response vector is a point in the phase plane, whereas for developing damages in the structure the octonion structural response vector manifests itself as a definite trajectory in the phase plane. Therefore, the development of damages in a structure could be investigated by analyzing the trajectory of octonion structural response vector obtained from the data of a long-term structural health monitoring or scheduled routine structural examinations. To demonstrate the implementation of this octonion structural response vector-based method, a two-dimensional numerical model of a simply-supported beam was built with crack-like damages of given location and depth. The octonion structural response vector of the beam corresponding to each state of damages was calculated to draw the trajectory related to the developing damages in the phase plane. The results show that the trajectories are significantly different for different devolvement of damages, even when the damages are in good symmetry. It indicates that the octonion structural response vector-based method recommended in the article could be effective to identify damages of structures using data of structures from long-term structural health monitoring or routine scheduled examinations.