Approximating Damped Vibrations of Large Space Structures

It is possible to use data recorded by onboard acceleration sensors to verify mathematical models of large modular space structures in terms of simulating dynamic processes. The paper investigates an approach to approximating damped oscillations caused by dynamic impacts during operation. Initially, we approximate the response of the structure by summing damped harmonics derived from analysing the frequency spectrum of the dynamic process; then we use the Levenberg --- Marquardt algorithm in the parameter space of the harmonic set to find the best match between the real dynamic process and its approximation. We propose a modification of the approach considered which involves employing single harmonics to perform successive approximations of the function of time to be fitted. We show that it is possible to apply the approach proposed to identifying the frequency and dissipative parameters of the structure under consideration. The paper presents the results of testing the approach proposed via artificially generated noisy acceleration functions of time with known parameters, which were reconstructed with a sufficient degree of accuracy. A real-world example provided comprises the results of analysing the ISS accelerometer readings recorded against the background of damped vibrations in its structure that were caused by burns of its attitude control engines