Automatic separation of temperature effects from Bridge cable force Data based on the VMD-PE-KLD Algorithm, 247-258.

Temperature fluctuation leads to changes in bridge cable force data and may submerge the structural response to the load, thus disturbing the judgement of the bridge-structural state. To accurately separate the influence of temperature on bridge cable force monitoring data, this paper proposes a new method for the automatic separation of data components, which integrates variational mode decomposition (VMD), permutation entropy (PE), and Kullback-Leibler divergence (KLD). First, the VMD was employed to decompose the filtered cable force to obtain several intrinsic mode functions (IMFs). Second, the PEs were calculated, and the IMFs with similar PEs were superimposed. Subsequently, the KLDs were obtained by kernel density estimation to eliminate the illusive components, by which the effects of daily and annual temperature differences on the cable force were derived. Meanwhile, the temperature was also decomposed into daily and annual variation components, and the Pearson correlation coefficient between the temperature and the cable force was used to evaluate the separation effect. Finally, the effectiveness of the proposed method was verified using the monitoring data of a suspension bridge. The results demonstrate that: (a) the proposed method combines the advantages of VMD and PE-KLD and achieves a satisfactory separation effect, and (b) in comparison with the EMD-PE-KLD, the VMD-PE- KLD model results in a superior separation effect. The correlation coefficients of the daily and annual components of cable force and temperature are improved by 25.80% and 3.95%, respectively, and the mean absolute error of the annual temperature difference effect is reduced by 45.51%.