A New Impact Localization Method Based on Spatially Sparse FRFs: Evaluation Using an FE Beam Model

Impact localization refers to the problem of estimating the location of a spatially concentrated impulsive force acting on a mechanical structure, using vibration measurements from a sensor network (in this chapter, accelerometers). Obtaining accurate location estimates is challenging due to three incident wave distortion factors; namely: (1) wave reflections from boundaries, (2) wave dispersion (frequency-dependent wave propagation speeds), and (3) frequency-dependent damping. In this chapter, a new frequency-domain impact localization method is introduced, where the aforementioned distortion factors are eliminated by prior collection of a few frequency response functions (FRFs), corresponding to a sparse number of known impact locations (calibration points (CPs)). This calibration phase is done offline as a prerequisite to localization. Furthermore, the calibration phase includes a spline interpolation step, which adds more FRF impact points via interpolating between the initial CPs, effectively increasing the density of the FRF calibration grid. Upon detection of an impact, recorded sensor signals are used—within an optimal search framework—to estimate the impact’s location. The search for the impact location is done using the interpolated FRFs from the calibration phase. The method is evaluated using a finite element (FE) beam model. Results show promising accuracy and justify further development of the approach.