Single-Point Response-Based Damage Identification for Short- and Medium-Span Bridges Using Wavelet Packet Energy of Modal Components

China possesses a large number of short- and medium-span bridges that are widely distributed throughout its transportation network.Ministry of Transport proposed that health monitoring for such bridges should prioritize lightweight implementation and be promoted through market-oriented approaches.Consequently,there is an urgent demand for low-cost and easily deployable damage identification methods.Traditional structural health monitoring systems require numerous sensors and complex instrumentation,leading to high installation and maintenance costs that limit their large-scale application on short- and medium-span bridges.To address this issue,we introduced a lightweight damage identification method based on the wavelet packet energy of modal components derived from a single sensor on the bridge.The displacement response under moving load was interpreted as two parts:a quasi-static component formed by the superposition of multiple vibration modes and a high-frequency component associated with modal dynamic responses.By removing the high-frequency dynamic components,the remaining quasi-static response essentially represented a superposition of high-resolution modal shapes.Multi-scale low-pass filtering was subsequently applied to extract two quasi-static components dominated by lower-order modes.Wavelet packet decomposition was performed at different scales,and a damage index was constructed from the difference in high-frequency sub-band energy to identify damage locations without requiring baseline data.Numerical simulations and experimental tests on a simply supported beam confirm that the proposed method accurately located damage under both single- and multiple-damage conditions while demonstrating strong robustness against noise.This method provides a feasible solution for the application of lightweight health monitoring of medium and small-span bridges.