# Advances in Machine Learning Techniques Used in Fatigue Life Prediction of Welded Structures
## 2 Materials and Methods
### Classification and Definitions
#### 2.4.1 Regression Based Methods  
These models learn relationships between input and output data from labeled training data to be able to predict trends and outcomes using regression techniques [20]. An example of the application of this method is illustrated in Figure 6. [PERSON] et al. [21] evaluated a high-speed railway in Korea's continuous welded rails to calculate the time when rails will be replaced. Hence, they used linear accumulated fatigue analysis theory ([PERSON] and Miner) and multiple regression analysis to assess the appropriate fracture probability. Similarly, [PERSON] et al. [22] used two local stress approaches, the peak stress method (PSM) along with notch stress approach (NSA), and carried out regression analysis to evaluate welded joints' fatigue lives, while [PERSON] et al. [23; 24] employed linear regression to assess the welded junctions in orthotropic steel decks (OSD) by altering road temperatures and traffic densities, then recording the output strains. In a subsequent study, hourly data using multiple linear regression (least squares approach) were adapted. Using fatigue testing, [PERSON] et al. [25] investigated the nature of fatigue in welded pipes with various strength classes and thereafter developed regression equations that can be used to forecast the remaining life of a specific pipeline section. [PERSON] et al. [26] created a novel set of criteria for fatigue in spot welds and fatigue data editing techniques to calculate the fatigue lifecycle of full body-in-white via optimization with a non-linear multiple regression method. Figure 6: A regression-based method used to calculate the time rails would be replaced [21]. [PERSON] et al. [27] examined the fatigue response of GMAW (Gas Metal Arc Welding) welded connections coupled by longitudinal corrugated plates using fracture mechanics analysis and regression. [PERSON] et al. [28] conducted an experimental data assessment to enhance stainless steel welded connections' fatigue design by regressing an S-N curve. [PERSON] et al. [29] found that the data of FL of a composite plate and the projected values obtained applying the Total Strain Energy Density (TSED) approach agreed well. In a parametric investigation, [PERSON] et al. [30] developed parametric equations for the maximum stress concentration factors (SCF) for concrete filled steel tubular T-connections by simulation with three-dimensional (3D) finite element (FE) models together with multiple non-linear regression analysis under in-plane and out-of-plane bending. Equally, [PERSON] et al. [31] also developed parametric equations to predict the SIF of cracked tubular T/Y-joints through finite element analysis and non-linear regression analysis by varying crack propagation angles. [PERSON] et al. [32] carried out a non-deterministic fatigue analysis of the rib-to-deck (RD) connections employing thickened edge U-ribs. This was carried out using nominal and hot spot stress techniques of fatigue along with regression analysis. On the contrary, [PERSON] et al. [33] harnessed the Maximum Entropy Regression Model (MEM) and the Generalized Maximum Entropy (GME) framework to model and estimate the lives of GMAW fused joints, while [PERSON] [34] employed a baseline regression model to investigate the distribution of fatigue strength along with a stochastic evaluation of stainless steel joined components subjected to mixed mode loading. [PERSON] et al. [35] analyzed the fatigue behavior of austenitic stainless steel Load-Carrying Fillet-Welded (LCFW) cruciform welds through experimental tests coupled with regression to the S-N curve with reference to Eurocode 3 [36]. [PERSON] et al. [37] used linear elastic finite element analysis and non-linear regression analysis to create an SCF database and derive empirical equations for SCFs in multi-planar DKT joints, respectively. Also, regression analysis was used by [PERSON] et al. [38] to examine fatigue behavior and impact the strength of carbon steel Friction Stir-Welded (FSW) joints.