## 1 Introduction  
The welded A-type frame of steering system is considered as one main bearing component for mining dump trucks. Its fatigue performance is seriously concerned when the truck runs on poor road surface with hundreds of tons of goods. This frame is welded with different thickness of plates; however, fatigue cracks often start from weld toe located at stress concentration areas [1]. There are several methods to predict fatigue life of a welded structure. These could be categorized into nominal stress [2; 3], structural stress [4], local notch [5], and fracture mechanics approaches [6]. The fracture mechanics method firstly assumes that the crack or crack-like flaw exists in the weld metal,and the stress intensity factor or J-integral is considered as the fatigue damage parameter, related with lifetime or crack growth rate [7]. The local notch approach is defined by using local stress, local strain, or local energy at the notch tip to estimate fatigue strength. The advantage of this method is that the effect of notch characteristics and cyclic material properties could both be included [8; 9]. The structural stress method focuses on a linearly distributed stress along the thickness without considering the stress concentration. Superposing the mechanical responses caused by forces and moments, the linear elastic finite element analysis is often implemented to calculate structural stress and strain, which is coupled into the mathematical model to assess fatigue life [10]. The nominal stress amplitude in the critical cross-section is treated as a fatigue damage parameter without consideration of the stress concentration at the weld toe and dissimilar material properties. This method is based on the S-N curve and preferred in many engineering areas because of its simplicity, such as in vehicles, vessels, and bridges [11]. According to those rules, [PERSON] et al. [12] estimate lifetime of drive axle housing for a mining truck by measuring strains at hot spots, which were transformed to stress spectrum. Then, the stress amplitude and stress mean with their cycles were counted using the Rain-flow method, and [PERSON]'s stress-life equation was utilized to obtain the service lives. [PERSON] et al. [13; 14] conducted a fatigue life assessment of the frame by combining multi-body dynamics analysis with finite element analysis to acquire the stress and strain spectrum. The service life was calculated as Palmgren-Miner's linear damage accumulation rule and normal S-N curve. In order to exactly present fatigue life distribution for a welded mining truck's frame at critical areas, even the total strain energy density was used as a fatigue damage parameter to predict lifetime, based on fitting the relationship between fatigue life and elastic and plastic strain energy density [15]. Moreover, the local strain energy density averaged over the control volume surrounding the crack tip in the weakest point of the roller was supposed to characterize the fatigue strength of welded joints [16; 17]. When the actual fatigue life or predicted lifetime of engineering structures is less than the required one, the fatigue optimization design is indispensable. In order to simultaneously enhance the performance and robustness of the fatigue life for a truck cab, [PERSON] et al. [18] present a dual Kriging surrogate modeling method to overcome the limitation of classical dual response surface method. The reliability-based design optimization is proposed by the [PERSON] et al. [19; 20] and aims to find the most balanced design through a compromise between cost and safety when uncertainties affect the system. Moreover, [PERSON] et al. [21] constructed a lightweight optimization model with static strength and weld fatigue constraints for the welded frame of a three-axle bogie, which is solved by an adaptive sequential approximation optimization method based on Kriging models. Most of optimization procedures mentioned above predominately focus on the single optimization objective, such as minimizing structural weight or maximizing lifetime.