Structural Health Monitoring (SHM) systems have been heavily studied worldwide in the past decades. In this field, extensive research has been carried out on vibration-based damage detection (VBDD) techniques in civil structures, especially in bridges. Dynamic responses of a structure manifest a certain degree of sensitivity not only to structural damage but also to any change in operational and environmental conditions, these last factors can mask structural damages. In this sense, the main objective of this paper is to separate structural damage conditions from the changes caused by the environmental effects in a numerical benchmark bridge structure. Temperature is chosen as a global environmental parameter for its significant impact on the waveform, and the Instantaneous Phase Difference (IPD) obtained from an analysis of the Hilbert spectral is studied as the vibration damage feature. Principal Component Analysis (PCA) is applied mainly to the IPD in order to eliminate the environmental influence. Due to the lack of experimental data including the temperature effects, the effectiveness and robustness of the proposed procedure is applied to a numerical benchmark bridge structure generated as part of COST Action TU1402 on quantifying the value of information (VoI) in SHM. The benchmark model consisted of a two-span steel bridge under operational (vehicular traffic) and environmental variability, in which two levels of damage were introduced. The dynamic responses in both healthy and structural damage conditions were obtained from a nonlinear time-history analysis using an open access Python code. As the main concluding remark, the suitability of Hilbert-Huang Transform combined with a PCA-based approach and the instantaneous phase difference to achieve a more robust damage assessment algorithm is verified for the numerical benchmark bridge.