Sparse l1 optimization‐based identification approach for the distribution of moving heavy vehicle loads on cable‐stayed bridges

Summary A method for identifying the distribution of moving heavy vehicle loads is proposed for cable-stayed bridges based on a sparse l1 optimization technique. This method is inspired by the recently developed compressive sensing (CS) theory, which is a technique for obtaining sparse signal representations for underdetermined linear measurement equations. In this study, sparse l1 optimization is employed to localize the moving heavy vehicle loads of cable-stayed bridges through cable force measurements. First, a simplified equivalent load of vehicles on cable-stayed bridges is presented. Then, the relationship between the cable forces and the moving heavy vehicle loads is established based on the influence lines. With the hypothesis of a sparse distribution of vehicle loads on the bridge deck (which is practical for long-span bridges), moving heavy vehicle loads are identified by minimizing the ‘l2-norm'of the difference between the observed and simulated cable forces caused by the moving vehicles penalized by the ‘l1-norm’ of the moving heavy vehicle load vector. A numerical example of an actual cable-stayed bridge is employed to verify the proposed method. The robustness and accuracy of this identification approach (with measurement noise for multi-vehicle spatial localization) are validated. Copyright © 2015 John Wiley & Sons, Ltd.