Structural damage detection of the bridge under moving loads with the quasi-static displacement influence line from one sensor

Abstract

As the bridges continue to age, it is imperative to identify structurally deficient bridges at an early stage to prevent unexpected maintenance needs. A quasi-static method is developed to identify structural damage based on the influence line (IL) from one sensor and an empirical Bayesian threshold estimator. Initially, the empirical Bayesian threshold estimator is utilized to preprocess the measured bridge displacement response to eliminate vehicle-induced dynamic effects. Subsequently, a regularization technique using Elastic Net and displacement response is used for IL estimation, and the Elastic Net that integrates with both L1 and L2 norms is adopted to establish the objective function of IL estimation to deal with the ill-posedness of the inverse problem for specific vehicle configurations. Finally, according to the mechanical relationship between the moving load and the displacement IL, an IL area-based difference index is established to identify the presence of the damage rapidly, raising a flag that leads to a more in-depth investigation to gather information related to structural integrity. The feasibility of the proposed method is verified with the numerical model and laboratory tests. This study introduces innovative contributions in the following three aspects: (1) Elastic Net that integrates with both L1 and L2 norms is adopted to establish the objective function for IL estimation, (2) A single sensor provides a cost-effective and less computationally expensive solution than multi-sensor methods, (3) Compared to other wavelet-based methods, the comparative studies demonstrate that empirical Bayesian threshold estimator can identify damage more clearly.