Novel integration method of measured acceleration to velocity and displacement based on zero initial condition

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The displacement and velocity of a structure is very important in scientific research and practical engineering in the field of earthquake engineering, structural vibration control and structural health monitoring. Because of the limitation of technical specification and working conditions, most measured signals from experiments is acceleration, and it is necessary to integrate acceleration to get velocity and displacement. However, the absence of initial conditions often makes the integration process affected by significant “drift” errors. To solve this problem, a novel integration method is proposed, in which the zero points of velocity and displacement during steady state vibration are sought for and determined utilizing basic rules of vibration, and are regarded as the initial values of integration. Moreover, the “drift” caused by the error of sampling spacing and stochastic vibration is further removed by detrending the integrated displacement. Responses of a single degree of freedom structure and a multiple degree of freedom structure are simulated under harmonic and earthquake excitation. The maximum relative error between the calculated value and the accurate ones are compared. In the end, the proposed method is applied to five typical seismic motion records. The integrated velocity and displacement are compared with given ones, and it shows that the maximum relative error at extremes is less than 3%, which powerfully demonstrates that the proposed integration method is accurate and practical.