Influence lines identification for uninterrupted operation bridges based on Bayesian theory

Objective The existing bridge influence line identification methods rely on precise axle weight data from single-vehicle. It is difficult to adapt to actual traffic conditions where multi-vehicle passages are common and single-vehicle passages are rare. This study proposes a method for identifying the influence line of uninterrupted operation bridges. Method First, the axle weights and axle spacing information of multiple vehicles were integrated based on the actual multi-vehicle traffic conditions. An axle weight matrix that comprehensively reflected multi-vehicle loads distribution was constructed. Second, a likelihood function, based on statistical relation between measurement data and parameters, was constructed by using the measured bridge displacement response data under traffic loads and combining with the established axle weight matrix. Third, the joint posterior probability density function of influence line was then derived from the likelihood function and prior distribution. Finally, due to the difficulty of directly solving with posterior probability density function, Markov Chain Monte Carlo method was employed to solve posterior probability density function, thereby obtaining the bridge influence line. The proposed method was validated through both numerical simulations and model tests. Result The proposed method can accurately identify the influence line in complex loading conditions with multiple vehicles crossing bridge simultaneously. Moreover, the identification results exhibit good stability and noise resistance at varying levels of random noise interference. Conclusion The proposed method overcomes the strict reliance on single-vehicle load and axle weight information inherent in traditional influence line identification methods. It provides a practical, efficient, and reliable technical solution for identifying bridge influence lines and assessing structural performance in real and continuous natural traffic flow conditions, significantly enhancing the on-site applicability and engineering utility of technology.