Recursive variational mode decomposition enhanced by orthogonalization algorithm for accurate structural modal identification

Modal identification is critical for structural condition monitoring. Variational mode decomposition (VMD) has been widely applied to identify modal parameters and has achieved excellent performance. It is crucial for VMD to predefine the decomposition parameters, that is, the mode number and balance factor. However, in practical engineering, abnormal impulses and heavy noise render it difficult to preset the mode number and balance factor. Therefore, a novel method, termed orthogonal and recursive VMD (ORVMD), is proposed to overcome the difficulty of setting decomposition parameters in advance. ORVMD consists of two components: recursive VMD (RVMD) and a rough-to-precise decomposition scheme based on an orthogonal algorithm. RVMD is an iterative method of VMD that is used to circumvent the difficulty of predefining the mode number. A rough-to-precise decomposition scheme based on an orthogonal algorithm is proposed to address the difficulty of setting the balance factor. Furthermore, the proposed ORVMD in combination with the Hilbert transform (HT) is employed to estimate the modal parameters of the structures. The raw signals are pre-processed by using the random decrement technique (RDT) to obtain its random decrement signature (RDS) and then the proposed method is applied to the RDS to identify the modal parameters of a simulated system and a real arch bridge. The obtained results show that the proposed method outperforms other existing methods in separating multicomponent signals; thus, it is an efficient method for identifying the natural frequencies and damping ratios of structures.