Theory of inner product vector and its application to multi-location damage detection

Structural damage detection methods using time domain vibration responses have shown appeal in recent years. In previous papers by the authors, the inner product vector (IPV) was proposed as a damage detection algorithm which uses cross correlation functions between vibration responses under white noise excitation or band pass white noise excitation. The proposed algorithm was verified by some simulative and experimental examples featuring a single damage location. However, damage at multiple locations was not considered. Therefore, this paper extends the application of IPV-based structural damage detection to the problem of multiple damage locations. Firstly, the theory of the IPV and its implementation in a damage detection context is reviewed. Then, two strategies for detecting multiple damages utilizing IPV are proposed. Finally, a damage detection experiment of a honeycomb sandwich composite beam is adopted to illustrate the feasibility and effectiveness of the IPV-based damage detection method.