Bayesian synchronisation of multi-channel ambient vibration signals

In vibration tests, multiple sensors are commonly used to measure the vibration response from different locations. Time synchronisation is required when using conventional modal analysis techniques to estimate structural dynamic properties, especially those related to spatial features such as mode shapes. This requires provisions in data acquisition hardware or time-stamping protocols, which cannot be taken for granted. Motivated by practical needs, a Bayesian method is proposed to pre-process potentially asynchronous ambient vibration data so that they can be used in applications mainly but not limited to modal identification as if the data were synchronised. While asynchronisation generally arises not only from shifted start time but also from time-varying drift between sensor clocks, the proposed method leverages the empirical fact that for typical time windows in downstream processing, i.e. operational modal analysis, the overall asynchronous effect can be effectively captured by an equivalent shift of the start time. It also exploits the fact that normal mode components of synchronous data from different structural locations are inherently in (or 180^∘ out of) phase. Efficient yet simple computational algorithms are developed for practical implementation, where the equivalent time shift is estimated by maximising the likelihood of Fast Fourier Transform of data within the selected frequency bands of normal modes. After shift-compensation in the time domain, the resulting ‘algorithmically synchronous’ data can be used for modal identification regardless of the specific modal identification method to be used downstream. The proposed method is verified using synthetic and laboratory data, then applied to full-scale field data.