“…It occurs because of the installation errors, low rail joints, cumulative track loading and general degradation. 22–24 The geometrical track irregularities consist of vertical and lateral alignment profile, cross-level and gauge irregularities, as shown in Figure 4 and rail track irregularity spectra are expressed as defined in equations (19) to (23). where SVtrue(Ωtrue), Sltrue(Ωtrue), Satrue(Ωtrue) and Sctrue(Ωtrue), are the Power Spectral Density (PSD) functions of the vertical profile, lateral profile, alignment, and gauge irregularities respectively [in m 2 /(rad/m)], and Sgtrue(Ωtrue) is the PSD function of cross-level input [in 1/(rad/m)]; A v , A l, A a , and A g are the roughness coefficients [m 2 /(rad/m)]; Ωc,Ωr and Ωs are cutoff frequencies (rad/m); b is one half of right and left rail center distance.…”