New insights into coherence analysis with a view towards extracting structural natural frequencies under operational conditions

Abstract

Coherence function as a fundamental measure of the degree of relationship between two time series has numerous applications in diversified fields such as financial economics, stochastic simulation and signal processing. In this study, the magnitude-squared coherence function which enables one to identify frequency-domain correlation between two time series is revisited with a view towards extracting natural frequencies directly for dynamic structural systems. This study makes a successful attempt at mathematically proving that coherence function in the modal domain converges to unit while coherence matrix converges to a matrix of ones as the frequency approaches the system poles. On the basis of these results, three new indexes incorporating the information of coherence functions or singular spectrum of coherence matrix are formulated as effective tools for natural frequency detection. A numerical example of a shear building is analyzed to illustrate the accuracy and efficiency of the proposed methods. Furthermore, a case study is performed using data measured from an operational vibration test of the Canton Tower located in China. The real application of this high-rise building demonstrates that all three new indexes proposed in this study for structural natural frequency identification can achieve satisfactory results. Compared to the conventional peak picking approach using power spectral density directly, the proposed methods are able to reduce the risk of identifying false modes. Both the simulated data and field testing data confirm the efficiency and robustness of the proposed coherence-based methods for structural natural frequency identification under operational conditions.