8. Investigation of Using Log-Spectrum Averaging (Cepstral Averaging) for Blind Reconstruction of an Unknown Impact Input Force

Consider the case of a mechanical structure being impacted at an arbitrary location by an unknown loading profile (i.e., force–time curve). Then, estimating the unknown impact loading profile (ILP) based on response vibrations is a challenging problem. If the impact location is also unknown, traditional inverse problem approaches (i.e., deconvolution) cannot reconstruct the ILP. This problem is particularly complex when inferring someone’s footstep loading profile by monitoring floor vibrations. Therefore, this preliminary study attempts to overcome the missing input location issue by producing a blind estimate (without knowledge of excitation location point) of the unknown ILP. Producing a blind ILP estimate is appealing since there is no need to know the location of the input force. Additionally, knowledge of the ILP can potentially uncover important information about the excitation source, such as, for example, identifying individuals from their footfall-induced floor vibration. The blind input reconstruction is done using log-spectrum averaging of the structural response at several locations. Our approach investigation is done via a MATLAB simulation, utilizing a Timoshenko finite element (FE) beam model as the virtual mechanical structure. Simulation results encourage further refinement of the approach.