Abstract
An automatic filtering algorithm is proposed for the accurate estimation of the second derivatives of kinematic signals with impacts. The impacts considered here occur when a moving object hits a rigid surface. The algorithm performs time-frequency filtering in the Wigner representation, to deal efficiently with the non-stationarities caused by such impacts, and adjusts the parameters of its time-frequency filtering function so that the filtering process adapts to the individual characteristics of the signal in hand. Performance analysis and comparative evaluation with experimentally acquired kinematic impact signals demonstrated a higher accuracy, with performance advantages over two widely used conventional automatic methods: linear phase autoregressive model-based derivative assessment (LAMBDA) and generalised cross-validation using quintic splines (GCVQS). For high impacts, the average absolute relative error in estimating the peak acceleration was 5.7% with the proposed method, 17.2% with a Butterworth low-pass filter optimised to yield minimum overall acceleration RMS error (best-case result), 18.3% with the LAMBDA method, and 37.2% with the GCVQS method. For signals with low impacts, the average absolute relative error was 19.4%, 6.9%, 8.3% and 19.1%, respectively, in each case, which indicates that, for signals with a low-frequency content, there is no need for such time-frequency filtering.