Enhancing Vibration-Based Tension Measurement in External Prestressing Tendons Using a Monte Carlo Markov Chain Algorithm

Measuring the tension in external prestressing tendons is crucial for assessing the remaining durability of prestressed bridges. A common method for this measurement is to use the eigenfrequencies of the tendon, modelled as a vibrating cable. However, this method can be quite time-consuming, primarily due to the need to position multiple sensors along the tendon to ensure that no eigenfrequencies are missed due to the impossibility to detect a mode with a sensor positioned on a modal node. In this paper, we propose a more efficient approach by employing a meta-heuristic algorithm to identify the missing modes without the need for multiple sensors. Our approach utilizes a two-stage Monte Carlo Markov Chain Algorithm. In the first stage, the algorithm explores the parameter space related to tension and flexural rigidity. The second stage employs simulated annealing to determine the most likely mode order using the aforementioned parameters as a seed. The algorithm output a couple of parameters—tension and flexural rigidity—that best fit the observed data. These results are then compared with the traditional method, which relies on multiple sensors, to demonstrate the effectiveness of our approach in both numerical and experimental situation.