Noise issues of modal identification using eigensystem realization algorithm
Date of Original Version
The eigensystem realization algorithm (ERA) is one of the most popular methods in civil engineering applications for estimating the modal parameters, including complex-valued modal frequencies and modal vectors, of dynamic systems. In dealing with noisy measurement data, the ERA partitions the realized model into principal (signal) and perturbational (noise) portions so that the noise portion can be disregarded. During the separation of signal and noise, a critical issue is the determination for the dimensions of the block Hankel matrix which is built from noisy measurement data. We show that the signal and noise matrices can be better separated when the number of blockrows and number of block-columns of the corresponding block Hankel matrix are chosen to be close to each other. We introduce the concept of using the Frobenius norm (L 2-norm) of the signal and noise matrices to quantify the signal to noise ratio in the global sense (involving multiple signals). We also propose a verification procedure to justify that the estimated modal parameters are noise insensitive and thus indeed associated with the true system. The procedure involves artificially injecting random noise into the measured signals (which are noisy signals) to create noisy-noisy signals, then comparing the identification results obtained respectively from the measured and noisynoisy signals. Using experimental data collected from a test plate, we demonstrate that if signal and noise portions have been properly separated while using the measured data, then the artificial noise would almost completely accumulate to the noise portion. Therefore, the modal estimation based on the signal portion only would remain the same by using either the measured or the noisy-noisy signals.
Li, P., S.-L. J. Hu, and H. J. Li. "Noise issues of modal identification using eigensystem realization algorithm." Procedia Engineering 14, (2011): 1681-1689. doi:10.1016/j.proeng.2011.07.211.