Discrete Tangent Stiffness Estimation Method for Pseudo Dynamic Test

In pseudo dynamic (PSD) test, researchers have long recognized the importance and potential benefits of utilizing the tangent stiffness of experimental specimen to correct the restoring force and analyze the energy error. However, improving accuracy and efficiency of the instantaneous stiffness estimation still presents a challenge. Based on the theory of discrete curve parameter recognition and the geometrical analysis approach, this paper proposes a discrete tangent stiffness estimation (DTSE) method to estimate the instantaneous tangent stiffness of a single degree of freedom (SDOF) experimental specimen. For different magnitudes of measurement noise, the proposed method can adaptively select and retain a series of latest valid data and ignore outdated information, of which the advantage is highly improving the accuracy and promptness of instantaneous stiffness estimation. The numerical study shows that the DTSE method has better accuracy and promptness of tangent stiffness estimation when compared with other existing methods. In a PSD test involving a sliding isolator, the DTSE method is utilized to analyze the cumulative energy error, the result of which shows the cumulative energy error is negative and decreases gradually. The analysis of experimental results demonstrates that the undershooting error of actuator added extra energy into the PSD testing system. Thus, the proposed method provides a desirable solution to instantaneous stiffness estimation.