# Advances in Machine Learning Techniques Used in Fatigue Life Prediction of Welded Structures
## 2 Materials and Methods
### Classification and Definitions
#### 2.4.3 Numerical Approach-Based Methods  
Typically, the nominal stresses and S-N curves presented in the design standards are adopted to ascertain the fatigue strength of structural features. However, more sophisticated techniques are needed to calculate the joint's fatigue strength when conditions differ from those of the experimental specimens. Linear elastic fracture mechanics (LEFM) is one such approach. The factors regulating crack initiation and growth parameters affect the outcomes of an LEFM technique [58]. Thus, this method focuses on the application of machine learning algorithms on fatigue results generated strictly by computational methods such as finite element analysis to predict fatigue life.  
A sample implementation was followed in Figure 8, in which weakest link analysis (based on FEM) was adapted by [PERSON] et al. [59] to address the fatigue design of steel welded joints. With the introduction of an S-N curve for efficient material, and simulation of the volume effect, it was established that such a method regulates, respectively, the fatigue response and geometry of the welded junctions.  
Using the fracture mechanics approach, [PERSON] et al. [60] examined fatigue cracks propagation in spot-welded junctions. In this, SIFs and J-integral were computed by the three-dimensional finite element method. [PERSON] et al. [61] found that by utilizing FEM and a genetic algorithm to calculate the expectations of fatigue strengths in HS40R and EZNCEN spot-welded junctions, it was possible to assess the robustness and stability of the steel sheet.  
Brittle fracture analysis was carried out for steel structures that were operated to the absolute limit by the structural modeling approach (FE and stochastic modeling) by [PERSON] et al. [62]. It was concluded that to prevent the major amendment of the mechanical characteristics of welded constructions, a good non-destructive testing technique would be the microhardness control of the weld and HAZ.  
By using FE and multi-parameter analysis, [PERSON] et al. [63] projected weld root NSIF for RD-welded joints under deck loading configurations. Concurrently, valuable equations were proposed to calculate the averaged strain energy density and stress distributions of single-weld RD-welded joint coupons. Ball Grid Array (BGA) chip torsion tests using finite meta-analysis and orthoselective analysis method were employed in [PERSON] et al.'s [64]  
Figure 8: Numerical-based method used to model fatigue response in welded joints [59].  
investigation. The ideal solder joint parameter combination was found, and simulation was used to confirm it.  
[PERSON] et al.'s [65] investigation focused on the impact of residual stresses on welded joints' fatigue lives considering torsional and bending loads. Meanwhile, [PERSON] et al. [66] numerically and experimentally analyzed the parameters of stress concentration in Concrete-Filled Welded Integral K-joints in steel trusses.  
In a study by [PERSON] [67] to analyze the effects of cyclic internal pressure on pipelines. A new correlation model was implemented which showed an acceptable accuracy in the prediction of SIF and FCGR in the pipes. This model was validated by comparing their results with that of the Bezier extraction base extended isogeometric method (Bezier base XIGA), and FEM analysis.