Walsh Transform and Empirical Mode Decomposition Applied to Reconstruction of Velocity and Displacement from Seismic Acceleration Measurement

This paper focuses on reconstruction of dynamic velocity and displacement from seismic acceleration signal. For conventional time-domain approaches or frequency-domain approaches, due to initial values and non-negligible noise in the acceleration signal, drift and deviation in velocity and displacement are inevitable. To deal with this deficiency, this paper develops a Walsh transform and Empirical Mode Decomposition (EMD)-based integral algorithm, or WATEBI in short. In the WATEBI algorithm, the Walsh transform is employed to realize vibration signal reconstruction. Next, the EMD method is used to eliminate the residual in the reconstructed signal. Finally, the trend term in velocity and displacement is removed by linear least-squares fit. This algorithm can be straightforwardly implemented by an ordinary computer. Reconstructed displacements and velocities from vibration of a simulated single-degree-of-freedom system and two-site measured ground motions in earthquakes validated the robustness and adaptiveness of this algorithm. It can be also applied to many other areas, like mechanical engineering and ocean engineering.