# Advances in Machine Learning Techniques Used in Fatigue Life Prediction of Welded Structures
## 2 Materials and Methods
### Classification and Definitions
#### 2.4.2 Monte Carlo Based Methods  
These are templates that are founded on the understanding of the impact of risk and uncertainty in prediction models [41]. To exemplify, this template was portrayed in Figure 7. By using the probabilistic stress-life method, [PERSON] et al. [42] examined the fatigue dependability of steel welded members. To accomplish this, it incorporated Monte Carlo simulation along with the Haibach's rule, Miner's rule, and the Modified Miner's rule. Also, [PERSON] et al. [43] assessed the fatigue dependability of a joint. In this case, the determinant was larger than that of any other probability distribution and served as the standard for evaluating the fitness level. In addition, [PERSON] [44] created a central brace SCF sample database based on the findings of the FE analyses performed on DKT joints. Whereas to improve tower crane design, [PERSON] et al. [45] took a probabilistic approach to fatigue design to develop a fatigue resistance model. The reliability of the analyzed elements was then evaluated using Monte Carlo simulations (MCS) in terms of the number of years in service of the crane. Based on a power law accelerated Birnbaum-Saunders life model in collaboration with GUM (Guide to expression of Uncertainty under Measurement), MCS, and Paris law, [PERSON] et al. [46] quantified the uncertainties associated with the fatigue reliability of a welded construction. On the contrary, a calibration of partial safety factors for the fatigue blueprint of steel bridges was performed by [PERSON] et al. [47]. In this research,the Maximum Likelihood (ML) and MCS approaches were used to describe the fatigue resistance S-N curves for loadings. [PERSON] et al. [48] employed the use of the Monte Carlo technique to model fatigue fracture propagation, characterize weld material, and predict daily failure probability with the motive of establishing inspection intervals for welded rail connections on a regional network. The influence of temperature loading and traffic flux was examined in relation to the fatigue dependability for OSDs by [PERSON] et al. [49]. Therein, the Monte Carlo Method (MCM) was used to calculate the reliability index. [PERSON] et al. [50] utilized a Dynamic Bayesian Network (DBN) support system comprising a probabilistic model and MCS to evaluate fatigue dependability in OSDs. As a result, this enabled component and system-level forecasting of fatigue reliability. Similarly, for OSDs, [PERSON] et al. [51] used LEFM (linear elastic fracture mechanics) and MCS to assess the fatigue impedance of an RD-welded joint. It concluded that if the first crack is deep or wide, the fatigue resistance is lower. The Monte Carlo method (MCM) was used by [PERSON] et al. [52] to conduct a stochastic study of the fatigue crack growth rate (FCGR) for longitudinal Tungsten Inert Gas (TIG)-joined Al 6013-T4 subjected to varied post-weld heat treatment set-ups. The outcomes show that the upper and lower bounds of the confidence interval were depicted on the FCGR curves. Apart from that, [PERSON] et al. [53] reassessed the validity of the FCGR of heat-treated TIG-welded Al 6013-T4 using two-parameter Weibull, probabilistic distribution method (PDM), mean value method (MVM), and the least square fitting method (LSFM). Furthermore, the probabilistic analysis of the FCGR with the 85% confidence interval was successfully evaluated by the MCM (Monte Carlo method). For junctions made of nuclear stainless steel, [PERSON] et al. [54] performed an uncertainty modeling of fatigue fracture formation and probabilistic life prediction with the Mei Te Si (MTS) fatigue analysis equipment, in conjunction with the application of a fatigue fracture propagation rate model, and MCS. [PERSON] et al. [55] used MCS and the Pipeline Research Council International (PRCI) technique to evaluate the data on the growing  
Figure 7: Monte Carlo-based method used to analyze fatigue reliability [42]. rate of fatigue cracks. Furthermore, [PERSON] et al.