## 1 Introduction  
The welded joints of high strength steel are frequently used in bridges and buildings, in light of good mechanical properties and excellent weldability [1]. However, compared with its parental materials, the fatigue strength of welds generally declines due to the existence of possible welding porosity and impurity defects, and tensile residual stress caused by the inconsistent recrystallization process with temperature gradient. In order to ensure sufficient service life at design stage and avoid fatigue failures occurring in welded engineering structures at usage stage, it is necessary to clarify the lifetime estimation model and fatigue damage evolution mechanism [2,3]. The traditional fatigue life evaluation approaches mainly depend on the \(S-N\) curves of welded joints to characterize mathematical relationship between different mechanical responses and lifespans [4]. In the normal stress method, the \(S-N\) curves estimate fatigue life by means of the structural nominal stress range in the presence of possible cyclic loads [5]. Based on the \(S-N\) curves obtained from fatigue tests on actual welded joints, the extrapolated maximum structural stress in consideration of local geometries was utilized to predict life expectancy in the hot-spot stress method [6, 7, 8]. In order to concern detailed geometrical features and stress concentration effects, the maximum notch stress at the weld toe and weld root is treated as lifetime assessment parameter, proposed by the notch stress approach [9,10]. Similarly, the so-called \(E-N\) curves are expressed in terms of plastic and elastic strain energy density (SED) at the weld seam, and relevant number of cycles in the SED method to estimate fatigue life of welded joints [11; 12]. However, the selection of \(S-N\) curves from different fatigue classes could be subjective, since they depend on the geometry of welded joints and loading modes. The corresponding mechanical responses are not easy to precisely determine as well. Another fracture mechanics approach could make the determination of lifetime for cracked welded components based on the Paris law, according to the relationship between the crack growth rate and stress intensity factor range [13]. Nevertheless, it is sensitive to the initial crack size, and thus the known crack is needed. The intrinsic energy dissipation method could rapidly confirm the fatigue limit and evaluate life expectancy, based on the thermal evolution on the surface of welded joints under cyclic loadings obtained from the thermo-graphic measurement [14; 15; 16]. This approach is independent of geometrical characteristics of welded joints, and does not require some given assumptions or prerequisites, compared with the notch stress approach, fracture mechanics method, and so on. This temperature variation is representative of the microstructure's movement and evolution in some way, which could be deemed as the connection between different scales. In the meantime, the intrinsic dissipation method supported by the thermo-graphic technique has great advantages in saving time and specimens. It could rapidly confirm the high-cycle fatigue limit, and construct a fatigue life assessment model via a very limited number of tests without sacrificing the calculation precision, proposed by [PERSON] and [PERSON] et al. [17; 18]. Essentially, the dissipation of energy directly reflects a material's fatigue failure mechanism, caused by the internal friction between the micro-structures. Meanwhile, the direction judgment falls into disuse when the dissipated energy is treated as damage parameter. Currently, a so-called Quantitative Thermo-graphic Methodology (QTM) has been widely used in studying the fatigue behavior of pure metal materials, notched specimens, and welded joints [19; 20]. However, this approach is based on the assumption of a constant temperature increment during the stabilized stage [21; 22], and the temperature is directly considered a fatigue damage parameter.