Automated algorithm for impact force identification using cosine similarity searching

A similarity searching technique is adopted to identify the impact force applied on a rectangular carbon fibre-epoxy honeycomb composite panel. The purpose of this study is to simultaneously identify both the location and magnitude of an unknown impact using the measured dynamic response collected by only a single piezoelectric sensor. The algorithm assumes that a set of impact forces are concurrently applied on a set of pre-defined locations. However, the magnitude of all the impact forces except one is considered to be zero. The impact force at all potential locations is then reconstructed through an l(2)-norm-based regularisation via two strategies: even-determined approach and under-determined approach. In an even-determined approach, the reconstruction process is performed independently for each pair of sensor and potential impact location. However, in an under-determined approach, the captured vibration signal is the superposition of the responses of the simultaneous 'assumed' impacts at the potential locations. Using either approach, a reconstructed impact force is obtained for each potential impact location. The reconstructed impact forces at spurious locations are expected to have zero magnitude as no impact has actually occurred at these locations. However, there might be some non-zero reconstructed impact forces at spurious locations. Therefore, it is worth designing an automated algorithm capable of detecting the most probable location. Cosine similarity searching is adopted to measure the intensity of the relationship between the reconstructed forces and an impact-like signal with various scale parameters. The largest value of cosine among all reconstructed forces corresponds to the most probable impact location. The results illustrate successful identification of the impact force location and magnitude for both even-determined and under-determined approaches.