Bayesian strain modal analysis under ambient vibration and damage identification using distributed fiber Bragg grating sensors

Strain-based damage identification approaches have been proven to be more effective than traditional displacement or acceleration measurements. Both considering the uncertainties and the spatial dependence among the distributed strain measurement, this paper aims to develop a more practical damage identification system using fiber Bragg grating as the distributed sensing system. In practical situations, the measurement of the vibration response of a structure is generally more convenient than that of the excitation source; furthermore, the measurement and modeling error are inevitable. In this paper, strain modal analysis under ambient vibration excitation and the corresponding identification of structural damage are investigated by considering inevitable measurement noise and modeling error from the perspective of Bayesian statistics. Considering the uncertainties, the strain modal parameters and associated uncertainties are identified based on the Bayesian strain spectral method by only measuring the output dynamic strain response without input excitation. The uncertainty information provides the confidence level of the identified results and can help to determine the sources causing the variation of identified parameters. An improved stochastic simulation method based on slice sampling is proposed to solve the high-dimension integral in the Bayesian formula. Considering the spatial dependence during the distributed measurement, the spatial statistical significance test of the damage indexes is used to located damage and to determine the optimal sensor configuration. Finally, a plate structure experiment simulating one part of the mechanical structure is conducted to demonstrate the proposed method.