基于零初值的测试加速度积分速度与位移的方法

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

在地震工程、结构振动控制和结构健康监测等研究领域,结构在振动过程中的位移和速度对科学研究和实际工程应用都具有重要意义.由于技术条件及环境因素限制,测试过程中获得的大多为加速度响应信号,需要通过积分获得速度及位移.但是由于初始条件的缺失,导致了测试加速度信号在积分速度和位移过程中产生明显的漂移现象.为解决此问题,本文利用结构的振动规律,在稳态振动阶段寻找速度和位移的零点,并以此作为初值进行积分,最后利用趋势项处理去除零点确定误差产生的漂移.本文数值模拟了单自由度体系和多自由度体系在简谐振动和地震动作用下的结构振动响应,并比较了计算值与准确值的最大相对误差;最后,将该方法应用于5条具有代表性的真实地震动记录,与给出的地面速度和位移进行比较,结果显示在极值处的最大相对误差均小于3%,表明该方法具有较高的计算精度和实际应用价值.

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.