Structural damage detection based on fundamental Bayesian two-stage model considering the modal parameters uncertainty

In structural health monitoring (SHM), damage detection is a final target to know the real status of the objective structure. Vibration-based damage detection is a commonly used method, since it makes full use of the dynamic characteristics. Improving the efficiency of this kind of methods has attracted increasing attentions. The existing uncertainty of identified modal parameters using measured data may significantly affect the detection accuracy. Furthermore, an optimization algorithm with a better convergence speed can improve the detection accuracy and reduce the computational time. This article presents the work to develop a novel damage detection method based on fundamental Bayesian two-stage model and sparse regularization. In this method, the most probable value of modal parameters and the associated posterior uncertainty are combined to investigate the effect of uncertainty on damage detection. The usage of the sparse regularization in the objective function can decrease the complexity of modeling and avoid the overfitting problem. A machine learning method combining intelligent swarm optimization algorithm with K-means clustering was used to carry out the optimization. Finally, a method combining three existing theory, that is, fundamental Bayesian two-stage model, sparse regularization, and I-Jaya algorithm, was developed. To investigate the efficiency of the proposed method, the traditional objective functions with and without the sparse regularization were also used for the comparison. The proposed method was verified by an ASCE benchmark example, and then it is applied into an experimental structure. The results show that due to the consideration of uncertainty, the objective function based on the fundamental Bayesian model and sparse regularization has a better performance.