A Bayesian fusion approach for high-spatiotemporal-resolution measurement of structural vibration using vision-based and sparse-sensor data

This paper aims to develop a Bayesain approach for high-spatiotemporal-resolution (HSTR) measurement of structural vibration by fusion of multi-sensor data including vision-based and sparse acceleration/displacement sensor data. Vision-based measurement is now an emerging technology in structural tests for the high-spatial-resolution (HSR) and non-contact nature, but its temporal resolution is generally low, leading to mode aliasing when the related Nyquist frequency is less than some active natural frequency of the structure. To improve the temporal resolution of vision-based measurement in a cost-effective manner and avoid mode aliasing, sparse-sensor data of high-temporal-resolution (HTR) is additional introduced and fused within a Bayesian framework. The key lies in the establishment of a joint Gaussian distribution that correlates the multi-sensor data and target modal coordinates. Subsequently, a simplified autocorrelation function (ACF) incorporating multi-sensor data and different time lags is proposed to quickly compute the covariance matrix of this joint distribution. Then, the modal coordinate with high temporal resolution is quickly estimated with mean and variance through Gaussian process regression (GPR), along with which the HSTR responses are obtained by simple modal superposition. Numerical and experimental validations demonstrate the effectiveness and accuracy of the proposed approach to achieve HSTR vibration measurements using vision-based and sparse-sensor data.