Displacement and velocity estimation of the earthquake response signals measured with accelerometers

Abstract

We propose in this paper a method to calculate the antiderivative of signals that have the integral close to null, as the signals measured on structures during earthquakes are. The method implies performing a series of numerical integration considering the initial value being zero. Afterward, the average value for the primitive function is calculated and considered as initial value: this solves the initial value problem with acceptable precision. Because of the minor errors, the second antiderivative that is the displacement in our case will gain a continuously slight increase. We overcome this problem by finding the trendline and extracting it from the signal representing the second antiderivative. In this way, we obtain accurate instantaneous values for the displacement as well. The algorithm, nominated as PySEMO, is implemented in the Python programming language and used to demonstrate the accuracy of the method. At the end of the paper, we make recommendations for the acquisition strategy to guarantee to find precise velocities and displacements. The algorithm can be used for other signals alternating around zero, e.g. those measured on rotating machines, as well.

Integral (antiderivative) learning with APOS perspective: A case study

“…It also takes part in the development of human thinking power. Many studies are related to the use of integrals in technological developments to overcome various problems in the world, as can be seen in the research results of Nedelcu et al (2020), where integrals were used to signal model in earthquake structures; then Albertini (2021), who used integrals in formulating digital wave structures; and Wahba (2022), who studied integrals in fluid mechanics.…”