Onboard Optimization-Based Modal Identification for Indirect Bridge Monitoring

Indirect monitoring of railway bridges using onboard measurements from traversing vehicles has emerged as a promising and cost-effective alternative to conventional structural health monitoring. This approach allows the assessment of numerous bridges using only a limited number of roving sensors and leverages continuously available data from in-service trains. Over the years, many methods have been developed, with early approaches relying on simple Fourier transform analyses or frequency domain decomposition of vehicle-acquired data to estimate the bridge’s natural frequencies. As an advancement, later studies adopted subspace identification techniques that additionally separate the vehicle dynamics from those of the bridge and use the residual response between two vehicle passages to suppress the influence of track roughness. These approaches have shown great potential for accurately identifying bridge frequencies, yet their performance remains dependent on signal length and algorithmic parameters, i.e., model order and Hankel matrix dimensions, leading to biased or unstable estimates of the bridge’s dynamic properties. Furthermore, these methods cannot determine damping ratios and often rely on assumed bridge mode shapes, preventing direct estimation of modal characteristics. The present study seeks to enhance the accuracy of such indirect identification approaches through an optimization-based refinement scheme. This scheme minimizes the discrepancy between the measured bridge response and that reconstructed from the identified modal parameters. In doing so, it simultaneously estimates the corresponding damping ratios and mode shapes—quantities that conventional indirect approaches fail to capture. The proposed methodology addresses critical limitations in indirect bridge monitoring by refining frequency estimates, extending modal identification capabilities, and enabling reliable inference of bridge dynamics even when only partial prior information is available.