Improved Variational Mode Decomposition Method Based on Particle Swarm Optimization for Separating Temperature Effects in Bridge Structures

Bridge deflection monitoring data, essential for safety management, results from the coupling of multiple load effects, making their separation challenging. This study refines safety analysis by isolating temperature effects within deflection signals. We enhance variational mode decomposition (VMD) by optimizing parameters (penalty factor α , mode number K ) through particle swarm optimization (PSO) guided by minimum envelope entropy. To address the low-frequency similarity between annual temperature effects and long-term deflection, a Butterworth low-pass filter is applied. The method is validated using deflection data from a large-span continuous rigid-frame bridge in Hubei, buttressed by a MIDAS/Civil finite element model simulating temperature effects. Results confirm the combined PSO-VMD and low-pass filtering effectively separates temperature effects from monitoring data, enabling the identification of temperature-induced structural potential risks and providing significant practical value for refined bridge safety management.