Spectral characteristics of asynchronous data in operational modal analysis

Operational modal analysis (OMA) has gained popularity for identifying the modal properties of a structure for its high economy and feasibility. Conventionally, time synchronisation among data channels is required to determine mode shape. OMA can be conducted more flexibly if synchronisation is not required. The power spectral density (PSD) matrix of data and its spectral properties are often used for analysing potential modes. Conventionally known properties assume synchronous data and do not carry over to asynchronous data. This paper investigates the spectral properties of asynchronous OMA data. A stationary process with imperfect coherence is proposed that is conducive to OMA while capturing the key asynchronous characteristics. The theoretical properties of PSD matrix are derived and validated using synthetic and experimental data. Although conventional methods do not allow mode shape to be determined from asynchronous data, the present work reveals the possibility by noting that the data are measured under the same excitation and hence share a common PSD in the modal force. On this basis, a simple method is proposed for determining the mode shape. For perfectly incoherent data channels, it is not possible to determine the relative sense of their mode shape values, which is a fundamental limitation of such data. In implementation, the sense can be determined from intuition or estimated from the residual coherence between channels. Experimental application reveals practical issues in OMA with asynchronous data. This work aspires to provide the pathway for more flexible implementation of OMA, for example, using asynchronous data from multiple smart phones.