Blind modal identification of non-classically damped structures under non-stationary excitations

In the present paper, we extend a previously developed blind modal identification method to systems with non-classical damping, which have complex-valued mode shapes. Unlike conventional output-only identification methods, blind modal identification method can provide modal property estimates when the input excitations are unknown and non-stationary (e.g., for systems equipped with added dampers or soil–structure problems). In earlier work, we have developed a technique that can be used for non-classically damped systems, but it is only applicable to stationary (i.e., ambient) excitations. Herein, we present an extension to non-classically damped systems under non-stationary (e.g., seismic) excitations. The proposed method yields mode shapes, natural frequencies and damping ratios, sequentially. A critical ingredient in this new method is a combination of generalized eigen-decomposition and rough–fuzzy c-means clustering techniques, which are employed to identify the complex-valued mode shapes. The accuracy of the proposed method is verified through a simulated but realistic example.