A Novel Operational Strain Modal Identification Method Based on Strain Power Spectrum Density Transmissibility (SPSDT)

Compared with conventional displacement modal analysis, the strain modal analysis has remarkable advantages in structural damage detection. Identifying the operational strain modal parameters directly from only dynamic strain time–history response measurements of a structure under operational conditions is a challenging issue. In this paper, the strain power spectrum density transmissibility (SPSDT)-based approach is presented to identify the operational strain modal parameters. The SPSDT is first defined by selecting a strain response measurement point as a reference. It is then theoretically proved that the defined SPSDT converges to the ratio of strain mode amplitudes at the system poles. Based on this unique property, the SPSDT matrix is constructed by selecting different strain response measurement points as the references. Singular value decomposition (SVD) is implemented in the matrix at the system pole. The first left singular vector is used to estimate strain mode shape. A simulated three-span continuous beam, a simply supported beam model tested in the laboratory and a full-size arch bridge tested in field are employed to verify the applicability and effectiveness of the proposed SPSDT-based operational strain modal identification method. The obtained results are compared with those of other available methods. It is found that a good agreement is achieved. It is demonstrated that the proposed SPSDT-based method is capable of identifying the operational strain modal parameters of a structure where only the dynamic strain time–history responses are measured. The proposed SPSDT-based method does not need white noise assumption under a single load condition.