Advances in Machine Learning Techniques Used in Fatigue Life Prediction of Welded Structures

Abstract

In the shipbuilding, construction, automotive, and aerospace industries, welding is still a crucial manufacturing process because it can be utilized to create massive, intricate structures with exact dimensional specifications. These kinds of structures are essential for urbanization considering they are used in applications such as tanks, ships, and bridges. However, one of the most important types of structural damage in welding continues to be fatigue. Therefore, it is necessary to take this phenomenon into account when designing and to assess it while a structure is in use. Although traditional methodologies including strain life, linear elastic fracture mechanics, and stress-based procedures are useful for diagnosing fatigue failures, these techniques are typically geometry restricted, require a lot of computing time, are not self-improving, and have limited automation capabilities. Meanwhile, following the conception of machine learning, which can swiftly discover failure trends, cut costs, and time while also paving the way for automation, many damage problems have shown promise in receiving exceptional solutions. This study seeks to provide a thorough overview of how algorithms of machine learning are utilized to forecast the life span of structures joined with welding. It will also go through their drawbacks and advantages. Specifically, the perspectives examined are from the views of the material type, application, welding method, input parameters, and output parameters. It is seen that input parameters such as arc voltage, welding speed, stress intensity factor range, crack growth parameters, stress histories, thickness, and nugget size influence output parameters in the manner of residual stress, number of cycles to failure, impact strength, and stress concentration factors, amongst others. Steel (including high strength steel and stainless steel) accounted for the highest frequency of material usage, while bridges were the most desired area of application. Meanwhile, the predominant taxonomy of machine learning was the random/hybrid-based type. Thus, the selection of the most appropriate and reliable algorithm for any requisite matter in this area could ultimately be determined, opening new research and development opportunities for automation, testing, structural integrity, structural health monitoring, and damage-tolerant design of welded structures.

1. Introduction

Around 90% of welded structures and components are said to fail due to fatigue [1]. By altering the chemical make-up and metallurgical structure of the native metal and filler metal present in the weld pool, welding as a manufacturing method specifically affects a structure locally. In addition, the process’s high temperature would probably change the microstructure of the areas near the weld pool. All these elements can be a source of stress concentration and alter the mechanical qualities of the materials, such as hardness, creep, ductility, toughness, or yield stress [2].

Apart from that, when residual stresses or welded joint flaws (planar, non-planar, shape imperfections) are inadvertently introduced into structures, fatigue is triggered. Equally, when the joints are poorly constructed or heavily loaded, the severity of these flaws is increased. Moreover, the weld toe angle, plate thicknesses, and kind of loading are additional factors that affect these constructions’ fatigue lives in addition to the welding method and stresses (design and residual) [3].

Similarly, analysis indicates that faults of different kinds introduced during various stages of engineering design, production, testing, inspection, maintenance, and service are to blame for the premature beginning of fatigue cracks in components or structures [4]. Overall, these cracks can lead to assemblies or components failing due to the cyclic nature of loading that happens during operation, even if these cyclic loads are below the yielding of the base metal and filler metal [5].

Accordingly, actions are needed to effectively examine all the elements that cause fatigue damage during assembly, in service, and post-weld treatment, even though there are post-weld improvement techniques such as peening, machining, and painting that can improve the weld profile, residual stress conditions, and environmental conditions of these elements or structures.

Nevertheless, the approaches for the fatigue examination of welded joints are nominal stress, structural hot-spot stress, effective notch stress, fracture mechanics, and component testing, where the assessment procedure depends on data from fatigue action (e.g., stress type) and fatigue resistance (expressed as S-N curves) [6].

For component testing, non-destructive post-production testing is pertinent for assessing the mechanical characteristics of manufactured components in industry [7]. Likewise, in order to verify structures using the fracture mechanic procedure, which is paramount for fatigue crack growth investigations, fatigue crack propagation limit curves can be determined to show that a flaw will not evolve to a critical size within a designated time or has an extended Fatigue Life (FL) than an adjacent standard weld detail.

Furthermore, these curves are established by the simple and two-stage crack growth relationship which is based on the Paris–Erdogan law, and they aid in engineering critical assessment (ECA) and structural integrity calculations.

Moreover, assessing a flaw in a flawed structure can help determine its fitness for service and calculate its defect tolerance. As a result, estimating the FL in welded joints is crucial for ensuring the reliability, safety, and endurance of various engineering structures and components. Typically, the FL phase is in three periods: initiation, crack growth, and final failure which are accounted for by the stress concentration factor, stress intensity factor, and fracture toughness, respectively [6,8,9].

Generally, the methods used to predict the FL of components or structures are physics based, data driven, or a combination of both as shown in Figure 1.

Until recently, numerous numerical simulation techniques (physics based) have been used to address issues with FL prediction, which utilizes finite element programs to determine stresses and distributions in structures as well as model welds with second-order solid elements and determines the hot spot stress at the weld toe of the investigated details with the quadratic surface stress extrapolation technique recommended by IIW [11]. However, their effectiveness is constrained by their high computing costs, model reliability, lack of self-improvement, and failure to grasp the variation law.

Moreover, the coupling of multiple elements, including materials, size correlation, manufacturing methods, and service conditions, adds uncertainty to the safety of structures in certain applications. This prompted industry and academics to explore techniques that independently continuously improve while cutting costs and time. To highlight the relationship between influencing factors and targets, identify characteristics of the current damage state, and forecast fatigue life, the machine learning approach uses data from experiments and simulations [10].

Any machine learning method can also be expository (akin to finding previously unforeseen patterns), prognostic (akin to interpolations based on cognition), or stipulatory (akin to improvement based on machine learning driven decision making) [12]. Though, the focus of this research is an appraisal of their expository capabilities in the context of fatigue life, since the machine learning process has recently produced desirable results in solving damage problems in structures, which is the motivation for this study.

In exemplification, Braun et al. [13,14,15] was able to predict fatigue failure locations with regards to stress concentration factors in small-scale butt-welded joint specimens through explainable machine learning and deep neural networks. Also, Lu et al. [16] evaluated the fatigue reliability of welded steel bridge decks subjected to stochastic truck loads employing machine learning, whose computational efficiency was demonstrated to be superior to the Monte Carlo simulation. Considering these prospects, it is possible to improve the methodologies for forecasting FL in a larger range of applications.

Generally, the machine learning process typically begins with data (analytical, experimental, or numerical), then is followed by data exploration and preparation (data cleaning), model application, and lastly, model evaluation for performance as depicted in Figure 2 [17].

Neural networks, time series, text mining, regression, decision trees, cluster analysis, Bayesian methods, random forests, factor analysis, deep learning, anomaly detection, uplift modeling, rule induction, link analysis, genetic and revolutionary algorithms, multivariate adaptive regression splines (MARS), ensemble methods, survival analysis, association rules, and Monte Carlo methods are the most widely used machine learning techniques [18].

2. Materials and Methods

In this research, a thorough assessment of the literature was carried out in November 2023 to assess how well the FL prediction machine learning models performed. The number of publications in the database under consideration was shown to illustrate the rising demand for fatigue prediction studies. The PRISMA declaration as shown in Figure 3 was followed in conducting this systematic literature review [19]. One citation database was used for a literature search: Scopus for studies published between 1 January 2013 and 28 November 2023. The literature search started based on five search terms: “machine learning”, “fatigue”, “weld”, “metals”, and “predict”. This search query extracted articles that applied machine learning models to predict fatigue life.

2.1. Selection Procedure and Data Extraction

To get the final number of papers that were analyzed, which is 108 publications, the initial query from Scopus generated 262 papers by combining the common types of machine learning algorithms with the common metals that are welded incorporating the characteristic of fatigue prediction. Afterwards, it was scaled down by offsetting articles published before 2013 and or conference reviews amounting to 142 papers, before removing the 8 articles which were not published in English as further illustrated in Figure 3. Thus, the query is provided in the next section.

2.2. Information Sources and Search Strategy

(TITLE-ABS-KEY (“machine learning” OR “Artificial Neural Network” OR “Reinforcement learning” OR “Supervised Learning” OR “Semi-supervised learning” OR “Unsupervised learning” OR “Neural Networks” OR “Time Series” OR “Text Mining” OR “Regression” OR “Decision Trees” OR cluster * OR bayes * OR “Random Forests” OR “Factor Analysis” OR “Deep Learning” OR “Anomaly Detection” OR “Uplift Modeling” OR “Rule Induction” OR “Link Analysis” OR “Genetic Algorithms” OR “Revolutionary Algorithms” OR “Genetic and Revolutionary Algorithms” OR “Multivariate Adaptive Regression Splines (MARS)” OR “Ensemble Methods” OR “Survival Analysis” OR “Association Rule” OR “LSTM” OR “Gaussian Process Reduction” OR “Support Vector Regression” OR “Support Vector Machine” OR “Monte Carlo Methods”) AND TITLE-ABS-KEY (fatigue *) AND TITLE-ABS-KEY (weld *) AND TITLE-ABS-KEY (metal * OR steel OR titanium OR copper OR alumi *) AND TITLE-ABS-KEY (predict * OR assess * OR forecast * OR prognosis *)) AND (EXCLUDE (DOCTYPE, “cr”)) AND (LIMIT-TO (PUBYEAR, 2023) OR LIMIT-TO (PUBYEAR, 2022) OR LIMIT-TO (PUBYEAR, 2021) OR LIMIT-TO (PUBYEAR, 2020) OR LIMIT-TO (PUBYEAR, 2019) OR LIMIT-TO (PUBYEAR, 2018) OR LIMIT-TO (PUBYEAR, 2017) OR LIMIT-TO (PUBYEAR, 2016) OR LIMIT-TO (PUBYEAR, 2015) OR LIMIT-TO (PUBYEAR, 2014) OR LIMIT-TO (PUBYEAR, 2013)) AND (EXCLUDE (LANGUAGE, “Chinese”) OR EXCLUDE (LANGUAGE, “Turkish”)).

The intended outcomes were obtained by using the export option to obtain the results in CSV format and mentioning them utilizing the free reference management program Mendeley.

2.3. Distribution of Papers

The statistical distribution of publications (mainly articles) over the years shows a lot of potential and activity in this research area as depicted in Figure 4 and Figure 5.

2.4. Classification and Definitions

Consequently, from the publications analyzed, the machine learning algorithms are divided into six taxonomies:

(a)

Regression (R)-based methods,

(b)

Monte Carlo (MC)-based methods,

(c)

Numerical (N)-based methods,

(d)

Neural network (NN)-based methods,

(e)

Structural health monitoring (SHM)-based methods,

(f)

Random/hybrid (RH)-based methods.

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. Sung 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 (Haibach and Miner) and multiple regression analysis to assess the appropriate fracture probability.

Similarly, Bertini 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 Farreras 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, Kuskov 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. Duraffourg 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.

Wang 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.

Peng et al. [28] conducted an experimental data assessment to enhance stainless steel welded connections’ fatigue design by regressing an S-N curve. Myung 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, Musa 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, Mohamed 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.

Heng 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, Fuentes-Huerta 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 Oh [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.

Peng 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].

Rahmanli 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 Bhatia et al. [38] to examine fatigue behavior and impact the strength of carbon steel Friction Stir-Welded (FSW) joints. Moreover, based on the Bootstrap approach, linear regression analysis and residual analysis, Zhang et al. [39] performed a simulation and authentication of the principal S-N curves of titanium alloy welded frames.

Baisukhan et al. [40] created an experimental model and regression equations to forecast residual stresses in the Gas Tungsten Arc Welding (GTAW) procedure.

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, Park 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, Park 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, Ahmadi [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, Bucas 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, Grous 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 D’angelo 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.

Romano 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 Liu et al. [49]. Therein, the Monte Carlo Method (MCM) was used to calculate the reliability index.

Heng 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, Wu 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 Ekaputra 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, Ekaputra 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, Chang 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. Wang et al. [55] used MCS and the Pipeline Research Council International (PRCI) technique to evaluate the data on the growing rate of fatigue cracks. Furthermore, Wang et al. [56] performed a fatigue assessment of orthotropic steel decks, specifically RD-welded junctions, employing probabilistic fracture mechanics (PFM) and MCS. Meanwhile, an equivalent structural stress (ESS) and Monte Carlo (MC) simulation-based stochastic assessment of FL in steel bridges was conducted by Su et al. [57].

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 Blacha 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, Hassanifard 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. Song 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 Lepov 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, Luo 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 orthosective analysis method were employed in Yu-Qing et al.’s [64] investigation. The ideal solder joint parameter combination was found, and simulation was used to confirm it.

Chiocca et al.’s [65] investigation focused on the impact of residual stresses on welded joints’ fatigue lives considering torsional and bending loads. Meanwhile, Jiang 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 Shoheib [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 Bézier extraction base extended isogeometric method (Bézier base XIGA), and FEM analysis.

2.4.4. Neural Network Based Methods

Artificial neural networks simulate biological neuronal connections by representing them as weights between nodes. Each input is given a weight before being added together. A linear combination is the term used to describe this activity. Within networks, which can draw inferences from a complicated and seemingly unconnected set of information, self-learning resulting from experience is possible [68]. As a result, a set of neuronal connections that can be used to predict FL forms this group. A group of neuronal connections depicted in Figure 9. In this, Back-Propagation Neural Network (BPNN) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) in conjunction with Ultrasonic Testing (UT) were used by Amiri et al. [69] to forecast the static strength and fatigue response of spot-welded connections.

The Rough Set Theory-Ant Colony Optimization-Back Propagation Neural Network (RST-ACO-BPNN) methodology was used by Yang et al. [70] to investigate a soft computing technique for predicting fatigue behaviors of welded junctions. To obtain forecast values (life cycles), several combinations of structural stress, ratios, thickness, and material type were used. Also, by using a Multilayer Feed Forward Neural Network (MFNN) and fuzzy C-means clustering, Casalino et al. [71] was able to predict and categorize the degrees of flaws in a Ti6Al4V alloy butt joint coalesced zone.

Based on a hybrid intelligent technique, Yang et al. [72] predicted welding components’ fatigue lives. It applied the Particle Swarm Optimization (PSO) algorithm, BP neural network, and rough set theory. Vineeth et al. [73] conducted a numerical analysis on the FL of spot-welded joints via FEA and ANN. Without performing any extra fatigue testing, the developed maximum stress equation can estimate the fatigue design criteria for spot-welded joints with optimal measurements. To forecast residual stresses in resistance spot-welded joints, Afshari et al. [74] also employed FEA along with ANN. The input parameters were the welding time, electrode force, and welding current while the output parameter was the remaining stress.

The viability of super alloy for green and thermal power plants was examined by Hwang et al. [75]. In their investigation into the welding of dissimilar materials. Methods for accelerated life testing and neural networks were employed. Equally, Ahmad et al. [76] applied the accelerated life technique and neural network approach to conduct a probabilistic FL prediction of dissimilar material fusion. Levenberg–Marquardt (LM) and Bayesian regularization (BR) were the two training techniques used to train the ANN.

Oswald et al. [77] established the notch determinants for welded cruciform connection through numerical analysis and metamodeling. The developed techniques offer reliable ways to quickly and accurately derive stress concentration parameters that might also be incorporated into more sophisticated applications as programmed solutions. A computational and experimental survey on steel strands subjected to the coupling effect of cyclic loads and a salt spray environment was conducted by Yu et al. [78]. In this study, the neural network method and multi-dimensional linear regression technique were used to set up a stochastic pitting-corrosion model. Therefore, the component’s fatigue notch factor might then be calculated using the stress concentration factor.

Sensitivity analysis of the ANNs in a set-up to predict C45 steel forging tools durability was carried out by Mrzygód et al. [79]. Feng et al. [80] estimated the non-deterministic FL of welded plate connections under uncertainty in arctic areas by applying a Genetic Algorithm and Neural Network (GA-NN) approach coupled with a metamodel.

Mashayekhi et al. [81] implemented ANN for fatigue fracture identification in welded steel bridge structural components. An ANN-based FL evaluation of FSW AA2024-T351 aluminum alloy was created by Masoudi et al. [82]. In this context, the multi-objective optimization method was used to identify standard welding parameters. A sensitivity analysis was then carried out to ascertain the influence of rotational and traverse speeds on fracture toughness and the rate of fatigue crack propagation.

Time-dependent examination of fatigue in RD-welded connections was conducted by Wang et al. [83] utilizing ANN-based techniques embedding an atmospheric corrosion model, and a hypothetical fatigue vehicle load model. However, by considering the uncertainty of parameters in limit-state functions, Monte Carlo (MC) simulations were used to compute the time-variant fatigue reliability. Xiao et al. [84] developed an ANN-themed prediction of SCF at the intersection of Concrete-Filled Steel Tube (CFST) Y-joints. The system involved using the BPNN model and FEA. In this context, the multi-dimensional scaling relationships between the affecting parameters and the SCF distributions were ascertained.

Gomes et al. [85] detected damages in offshore jacket structure using ANN and FEA. They created an ANN to identify damage using the modal parameters. This ANN was then verified using a test set before being used to forecast the structural damage in an offshore jacket structure. Deng et al. [86] performed a fatigue damage projection in OSDs with Long Short-Term Memory (LSTM). It was discovered that data-driven LSTM may greatly maintain the precision of fatigue damage predictions over time. In contrast, Park et al. [87] conducted a thermal elastic–plastic analysis on butt-welded joints by varying the member thickness, lateral constraint, and bending constraints.

2.4.5. Structural Health Monitoring-Based Methods

Systems for monitoring the structural health of machines and structures are reliant on sensors and structural prototypes. Standards established on categorization and prediction data, including machine-learning algorithms in SHM systems, require the collection of trustworthy data, which is driven by computational breakthroughs in sensing devices and the computational capacity of embedded gadgets [88]. For this reason, it is important to map out a set of techniques that predict FL based on the data acquired therewith as exemplified in Figure 10. In this case study for OSDs, Deng et al. [89] evaluated fatigue reliability using long-term strain monitoring, the Rainflow algorithm, probabilistic models, the fatigue limit state, and an explicit formula, or MCS.

Meanwhile, as an illustration, structural health monitoring along with fatigue analysis of retrofitted web stiffeners on steel highway bridges were performed by Ghahremani et al. [90]. When measures of deflection and strain were contrasted with FEA estimates. It was discovered that the genuine fracture depth and damage assessments based on strains at the key hot area are highly connected. In a similar vein, Thöns and Faber [91] used structural risk analysis and Bayesian pre-posterior decision analysis to evaluate the worth of structural health monitoring. Accordingly, the case studies discussed the impact of the performance-related uncertainty of SHM on the value of SHM.

In an investigation, Ye et al. [92] collated stress signals from a bridge monitored by the Fiber Bragg Grating (FBG) system. Furthermore, the Bayesian criteria, wavelet multi-resolution analysis, Kolmogorov–Smirnov (K-S) goodness-of-fit test, finite mixture distribution, FBG sensors, and genetic algorithm were used in this research. The monitoring data were also used to evaluate the SCF’s stochastic property, which demonstrated that it followed a normal distribution.

Long et al. [93] quantified the ensuing benefits of SHM campaigns. Regression models of gauged stresses, road temperatures, and traffic densities paved the way for pre-posterior decision support to be used to optimize the design of monitoring campaigns for comparable bridges. The overall objective was to demonstrate the cost effectiveness of SHM approaches compared to civil infrastructure management. Rocher et al. [94] created a two-scale non-deterministic time-variant fatigue model for offshore steel wind turbines utilizing records from SHM. Nosov et al. [95] created nanotechnologies for controlling material strength. This nanotechnology arbitrarily records the accrued damages in the material both prior to and after the formation of cracks in the waiting phase for its next leap.

2.4.6. Random/Hybrid Based Methods

These methods are a combination of two or more methods from the predefined groups and or a unique methodology. To illustrate this, an exemplification is depicted in Figure 11. Therewith, a unique hybrid Single-Parameter Decision-Theoretic Rough Set (SPDTRS-CS-ANN) technique, developed by Feng et al. [96], was used to forecast fatigue properties of welded junctions.

Li et al. [97] conducted a probe into the FL prognosis of fused tube connections within signal support systems. This was carried out through the Bayesian updating of the fatigue growth model, specifically, the stochastic coefficients. Conversely, the fracture approach and bi-linear fatigue technique were implemented by Khan et al. [98] to analyze an offshore structure’s safety through a marine riser’s non-linear analysis. With FORM and the MCS approach, the failure probability was calculated. By applying Mixed Dimensional Modeling (MDM), MCS, Rainflow counting, and Palmgren–Miner’s rule, Yan et al. [99] forecasted a cable-stayed OSD’s fatigue life.

Lu et al. [13], by deterministic simulation and probabilistic modeling, assessed the fatigue dependability of bridges under stochastic truck loads, whereas a maintenance decision model for steel bridges was provided by Attema et al. [100] with a case study. Thus, with the Bayesian network alongside a probabilistic model, it was feasible to perform a root cause analysis and identify the factors that control the outcome of the model.

Data-based models for the fatigue dependability of OSDs were developed by Farreras et al. [101] based on data from temperature, strain, and traffic monitoring. The model used a mix of the time-series model, polynomial regression models, and MCS. The outcomes measured the detrimental impact on FL caused by either greater heavy traffic loads or higher future pavement temperatures or both.

Marulo et al. [102] assessed the fatigue strength of thin-walled laser welded joints made of mild and high-strength steel. FEA was used to determine the stress field in the notch ligament for each specimen shape in the database. Moreover, three typical stress approaches: the highest notch stress, the stress averaging approach, and the critical distance were used to quantify fatigue. Moreover, for laser lap welding, Ozkat et al. [103] created a decoupled multi-physics simulation that takes the part-to-part gap into account. The methodology was created using the energy balancing method. The created model can be used to monitor important geometrical features while they are being created, and it is also a crucial tool for creating an adjustment that can be applied to remote laser welding.

Based on the expected growth in traffic flow, with FEA, MCS, and regression, Fu et al. [104] performed a fatigue evaluation of the steel floor of a bridge. The roof weld was among the structural features taken into consideration to be the most likely to crack according to the diaphragm section’s fatigue damage assessment. Wang et al. [105] considered determining the Macro-Crack Initiation Life (MCIL) of an OSD while looking at weld heterogeneity and diverse traffic loading. MCS and the adaptive multi-scale approach (XFEM and FEM) were used. Under coupled dynamic stresses, Zhu et al. [106] made a non-deterministic evaluation of fatigue in coastal thin bridges. Stochastic load models, multi-scale FEA, Rainflow counts, the linear fatigue damage rule, Support Vector Regression (SVR), and the derivation of a limit state function were used to achieve this.

Using the 3D-extended finite element toolkit for Abaqus (XFA3D) and machine learning methods in a digital twin setting, Ren et al. [107] predicted a structure’s FL and discovered that the adoption of a digital twin strategy for the complete life management of aging structures requires the incorporation of as-manufactured attributes and uncertainties. Mi et al. [108], while examining the lifecycle of a welded A-type frame in a mining vehicle, considered the material attribute unpredictabilities along with load and structural geometry through experimental data, FEA, and NSGA-II.

Tchemodanova et al. [109] used the critical plane analysis, the augmented Kalman filters, the Craig–Bampton approach, and sparse measured strain locations to estimate the remaining useful life forecast of an amusement ride (roller coaster) subjected to multiaxial loads that are nonproportional. The effect of corrosion in dissimilar FSW high-strength aluminum alloys was examined by Rodriguez et al. [110]. Consequently, a fatigue model that considers microstructures was created. A collaboration of the entropy-based neighborhood rough set and PSO-SVRM model was created by Zou et al. [111] for the motive of predicting titanium welded junctions’ fatigue lives.

In order to optimize fatigue reliability in welded A-type frames while weighing several sources of uncertainty, Mi et al. [112] developed a solution, in which the following techniques were used: membership function, Latin hypercube sampling, response surface methodology, and genetic algorithm (GA). In another work by Zou et al. [113], they created an intelligent approach for forecasting the life of aluminum welded connections after fatigue. MnS inclusion distributions in high-strength steel were investigated on a multi-scale extent by Sakaguchi et al. [114]. This technique involved a modification of coefficient of variation of the mean near-neighbor distance of inclusions, serial sectioning technique, and principal component analysis. Furthermore, the computation of the fatigue crack initiation as well as the total FL were carried out after distributions of inclusions were applied to the model.

The fatigue reliability of pipeline’ weldments subject to negligible visible faults were evaluated by Duan et al. [115]. According to the Bayesian technique, damage tolerance theory, and FORM, the pipeline weldments’ total dependability is significantly influenced by the direction of the faults. In a review of artificial intelligence implementations for FSW by Eren et al. [116], the author concluded that the ANN was the most popular ML technique. However, hybrid systems employed in conjunction with ANN have higher accuracy. Ullah et al. [117] investigated the impact of localized delta ferrite number and microstructural evolution on the rate of high-cycle fatigue crack initiation. Paris curves and MATLAB image processing programs demonstrated the influence.

A probabilistic multi-scale framework was developed by Jiang et al. [118] to forecast steel bridges’ fatigue lives utilizing a digital twin-driven architecture. Crystal plastic finite element method, the modified Fine and Bhat model, and Bayesian inference (Markov Chain Monte Carlo Sampling) were all used in the probabilistic multi-scale model. Through ANN, response surface modeling technique, hypothetical parametric 3D FEA, FORM, and using the SHM data of wave loads, wind loads, and soil attributes, Shittu et al. [119] conducted analogous research between the S-N and fracture mechanics (FM) method on the reliability prognosis of offshore wind turbine jacket foundations.

Wang et al. [120] used response surface methodology (RSM) and NSGA-II surrogate modeling to carry out the fatigue optimization of structural variables for OSDs. Meanwhile, a probabilistic fatigue crack growth evaluation of OSDs using mixed failure models, GPR, DBN, FEA, and the Probability Fatigue Crack Growth (PFCG) model was created by Heng et al. [121].

He et al. [122] used the LEFM and random forest approach to conduct a machine-learning-centered assessment of the impact of defect/inclusion on the fatigue behavior of steels. Heng et al. [123] performed a machine learning-assisted probabilistic fatigue assessment of RD joints in OSDs using the GPR surrogate model, DBN, and PFCG model in a subsequent study. The modified posterior model exhibits better concordance with the test data when compared to the old PFCG model. Jiang et al. [124] used RSM, GA, and Multi-Attribute Decision Making (MADM) to reinforce fatigue fractures at U-rib to diaphragm joints in OSDs. This improved comprehension of how to strengthen the joints with CFRP and permitted the best use of CFRP material in preserving aging steel structures.

A novel method for assessing the mechanical performance of different welded joints was devised by Carone et al. [125] by fusing the thermographic method, multiple-cut contour technique, and X-ray diffraction. Van Dang et al. [126] showed the relevance of the risk-based maintenance of lock gates by combining failure probabilities with projected costs for various occurrences and DBN. An adaptive neuro-fuzzy-based system was created by Biswas et al. [127] for the forecast of surface roughness in wire arc additive manufacturing.

In a study, Shankhwar et al. [128] used a trilinear interpolation method, an interactive Mixed Reality (MR)-based user interface, a Gradient Boosted Regression Tree (GBRT) model, and FEA to visualize the results of hand metal arc welding. In a cyclically loaded structural steel, the Acoustic Emission (AE) examination of proximate fracture was carried out by Rastegaev et al. [129] using AE data. A combination of criteria based on power spectrum and pattern recognition, as well as energy data and spectral density functions was used.

In an attempt to upgrade the Eurocode and IIW codes for higher strength steels in certain fatigue classes such as butt welds and transverse stiffeners, Karabulut et al. [130] subjected welded cruciform joints to experimental and finite element models. Subsequently, the reliability of the upgrade was upheld using Weibull models found in survival analysis. In research by Peng et al. [131], they developed a particle-filter based Fatigue Crack Growth (FCG) prediction technique for a base metal and butt-welded specimen to deal with the uncertainty in the FCG process. Yu et al. [132] developed a novel technique incorporating both ML and FEA to forecast F-N fatigue curves of high-strength steel RSW joints. The influences of thickness and width of the sheet as well as nugget diameters were measured.

3. Results and Discussion

In recent years, there has been a consistent use of the N, NN, and RH as illustrated in Figure 12. Also, there is a steady significant use of the R/H methods.

In the study where the peak stress and notch stress methodology of evaluating FL were compared. The experimental data included a variation in terms of thickness and stress conditions for a different variety of welded joint configurations to calculate the notch stress intensity factors (NSIF). Although, both techniques yielded a regression line that was shallower than the design reference curve as depicted in Figure 13a,b [22].

While in the work that varied monitoring data and traffic densities, there was generally a good agreement between the monitored-based performance indicator profiles and model simulations, the only drawback was that it was deterministic.

When examining the unique features of fatigue failure for steel pipes with various strength levels, it was discovered that the stress range no longer influences the number of cycles once maximum tensile stress is reduced to 6–8%, However, regression equations that can be used to forecast the remaining life of a specific pipeline section were created [25]. Similarly, the number of required analyses to obtain SIF and FL in pipes would become less by about 20%, if the technique by Shobeib was implemented [67].

In GMAW (Gas Metal Arc Welding) welded connections, it was deduced that longitudinal corrugated plates’ welded joints’ fatigue failure mechanisms are equivalent to those of the corrugated beams’ fatigue failure whose welded features’ fatigue strength can be effectively represented by a suggested simple test specimen [27]. In addition, GME has the benefit of quick calibration, and it is feasible to anticipate welded joint fatigue accurately in GMAW joints [33].

To determine the optimum rail replacement time for continuously joined rails on top of the concrete slab track, as demonstrated by the Korea High-Speed Railway, it is important to compute the fitting fracture probability considering diverse vehicles alongside track circumstances in reality [21]. Also, when MCS was implemented to institute a probabilistic model for estimating the propagation lifespan of the weld toe of aluminothermic rail welds, a semi-probabilistic approach should be considered including the influence of loads at the welds [40]. Subsequently, a non-deterministic probabilistic structural integrity model was created to account for the lifespan of weld toe cracks of the rail joints [48].

In comparison to current parametric equations, Mohammed et al.’s proposed equation provides a more accurate forecast of the SIF in cracked tubular T/Y joints. According to the proposed equation’s error analysis, 90% of the results have errors of less than 15%, and 99.7% have errors of less than 30% [30]. The fatigue fracture of austenitic stainless steel LCFW cruciform connections was discovered to be a semi-elliptic crack, one that was distinct from the fracture of LCFW structural steel, which implies higher fatigue and lower SIF [28]. However, it was demonstrated that in accordance with the guidelines of the International Institute of Welding (IIW) and Eurocode 3 (EC3), the fatigue strength of the LCFW cruciform joints made of austenitic stainless steel is higher than that of structural steel [35,36].

The Bootstrap technique tends to be more consistent as it increases the degree of fitting in tests for fatigue in titanium alloy as well as the precision prediction of FL when the sample size is limited. Moreover, it was possible to obtain and verify a rather precise regression for the principal S-N curves of titanium alloy welded frames [39]. Titanium welding can be made to satisfy the stringent requirements of the aerospace and contemporary automotive industries for welding defects because of the ability to forecast the quality of the fused zone provided by a neuro-fuzzy approach. Meanwhile, when predicting the various fatigue behaviors of titanium alloy welded joints, the PSO-BP approach performed better than the traditional BP technique [71,72]. A developed hybrid technique makes it possible to anticipate the fatigue lives more correctly in titanium welded joints, which aids in the structure’s dependability design [111].

The results from the use of a generalized fatigue reliability model based on ESS with other key parameters including arc voltage, arc current, welding speed, and interactions between efficiency and welding speed demonstrates that the suggested approach offers a workable solution to the problem of choosing an appropriate category for the assessment of the probabilistic FL of the welded details in steel bridges. Also, it was ascertained that the obtained failure probability and reliability index are both sensitive to growth of traffic volume [56]. The correctness of an approach to measure fatigue in OSDs is mostly dependent on the quantity of training samples, which unavoidably has an impact on computational efficiency. It was evident that using a learning machine and probabilistic modeling is far more effective than using a typical MCS [99]. Merging a model with a monitoring system while creating a maintenance decision model for a bridge has a considerable impact on the conclusions’ level of uncertainty, even for aspects of the bridge that are not monitored. Meanwhile, the Bayesian technique produces statistical distributions for the formation of fatigue cracks, and equally compute failure probability [95,100].

Contrarily, when evaluating the fatigue dependability of OSDs, the limit state equation is more complex while the variables have distinct probability distributions, whereas the numerical analytical resolutions are consequently challenging [47]. The findings of an OSD’s fatigue reliability assessment show that as service life lengthens, the reliability indices decline dramatically. Likewise, the other three welded elements, apart from an RD detail, are unable to achieve the goal of fatigue reliability during the 100-year service life of the bridge. It is significant to observe that traffic data are necessary for the basic statistical aspects of OSD fatigue measurement. Moreso, a high traffic rate would result in a large sampling number, which would somewhat affect efficiency [99]. The negative impact on FL from rising future pavement temperatures, greater levels of heavy traffic, or both has been quantified by the findings of a data-based model for OSD fatigue reliability. In a case study of the application of the data-based model, it was demonstrated that increased temperature and high traffic levels together had a significant negative impact on fatigue dependability, with a commonly used limit being achieved up to 40 years sooner than under the ‘no change’ baseline scheme. Nevertheless, the LSTM method performs well, as evidenced by validation results from the fatigue damage prognosis of an OSD, where the mean percentage absolute errors of the two types of fatigue susceptible features were less than 10% [86].

Thanks to the method proposed by Bucas et al. [45], relatively extensive statistics on crane utilization may be produced in a short amount of time.

The data showed that no influence of residual stresses on the FL of welded joints was detected in the case of bending loading compared to torsional bending that showed effects as depicted by experimental data and applied damage factors [65]. To forecast the residual stresses in RSW joints using ANN, the results show that the created ANN has a good accuracy in predicting maximum tensile residual stress based on the indicated spot-welding variables. In exemplification, it can dependably predict residual stress in the spot weld of 2 mm thick aluminum 6061-T6 sheets [73,74]. It was discovered that the Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization algorithm can be employed to improve model fitting to experimental data for RSW joints. Hence, the model based on BFGS enables accurate prediction of the F-N fatigue curves of RSW joints without the need for fatigue testing, thereby saving costs and time required for experimentation [132].

Meanwhile, the results of an analysis were used to train a Deep Neural Network (DNN) to be able to forecast the residual stress in the weld toe and center of the joint of butt-welded joints [87]. Moreover, welding residual stress can be precisely forecasted by using the transverse and bending stress components derived from the transverse constraint, bending constraint, and welding residual stress as predictors for learning the DNN model. Also, results from a study showed that the FCG behavior of the butt-welded specimen is more sensitive to the stress ratio than that of the base metal specimen [131].

Conversely, an accelerated lifespan model that was founded on calculations of the mean (µ) and standard deviation (SD) of crack growth can be used for the fatigue design of welded structures [46]. Using neural networks and accelerated life test techniques, the FL and corrosion FL of welds between dissimilar materials were predicted. The projected results and the actual fatigue and corrosion fatigue lives were in good agreement. Particularly, the neural network prediction results outperformed the accelerated life technique in terms of accuracy. Over 90% of the predictions on average were accurate [75]. Similarly, the accelerated life testing method and artificial neural network approach (ANN) were used to evaluate the FL forecast of a dissimilar material weld. When training the ANNs, the Levenberg–Marquardt algorithm performed worse than the Bayesian regularization training approach. Concurrently, the accelerated life testing method was assessed for various distributions, and the most suitable distribution for the fatigue data was the Weibull distribution. Thus, data from FL tests were accelerated with 95% confidence using the Weibull distribution [76]. Meanwhile, it was observed that the FL decreased when the fracture initiation at the corrosion flaws was visible in dissimilar FSW welds. The fatigue life, however, was essentially independent of the exposure time [110].

In the estimation of SCFs for partial or fully penetrated welded cruciform connections with double-filled welds and K- or double-Y-butt welds, the best fatigue behavior was shown by the Concrete-Filled Integral Welded K-joint, which is followed by the Concrete-Filled Rectangular Hollow Section (CFRHS) K-joints, and Rectangular Hollow Section (RHS) K-joints, the latter of which has the worst fatigue behavior. Furthermore, BPNN models can be trustworthy substitutes for complex equations to forecast the distribution of SCFs at CFST Y-joint intersecting lines since their results are near to the FE results [84].

Utilizing data from small- and large-scale specimen strains, the technique devised for monitoring retrofitted web stiffeners was proven effective. It has been discovered that damage assessments based on strains at the crucial hot point are well connected with the actual fracture depth [90]. It was discovered that the bi-linear techniques produce greater FL measures, which has an impact on the target dependability of the design along with inspection schemes in regard to offshore structures. In the case of such structures, these variations are significant, particularly when the stress range bounds have a greater proportion of low-amplitude cycles [98].

A welded A-type chassis’s FL can be enhanced, and its mass can be reduced. By utilizing the fuzzy fatigue reliability optimization based on evolutionary algorithms, its reliability ranged from 69.47% to 95.12% [108]. Also, it was inferred that a better welding process can help improve the fatigue performance of welded A-type frame in a heavy off-road mining truck [112].

Using a reliable assessment of strain history and critical plane orientation, the FL of a substructure may be forecasted at any site, while estimating the fatigue lifetime at various spots in a bracket and weld also needs more effort. These crucial sites will be used to map the bracket’s and the weld’s hot spots or essential stresses [109]. The results demonstrated that the constructed surrogate response surface model can accurately forecast the local equivalent stress amplitudes by utilizing RSM and NSGA-II to optimize fatigue structural parameters. However, the deck thickness is the most significant factor affecting the fatigue functioning of the U-rib weld alongside the U-rib to diaphragm weld [120].

The use of GPR can cut the cost of solving the PFCG forecast by 1875 times on average [123]. Equally, a way that aids in reducing the quantity of experiments and the expense of carrying out destructive tests with the necessary dependability is the methodology for fatigue evaluation based on UT results which has a very high accuracy when compared to experimental results as depicted in Figure 14 [69].

In a stochastic evaluation of stainless steel joined components subjected to mixed mode loading, the median rank treatment and the three-parameter Weibull approximations provided the closest approach to the measured values. Hence, under various loading situations, the fatigue strengths, limitations, lifetimes, and failure probability became predictable [34]. Also, for the Base Metal (BM) cracks in fatigue cracks, the most-likely (median) FL from the probabilistic analysis is nearly comparable to the FL from deterministic calculations [55].

Through the three-dimensional finite element method, the RSW specimens in tensile-shear were examined to know their fatigue propagation life. On this account, the experimental data and the cross-sectional pictures of the coupons were in excellent agreement with the FE results and anticipated fatigue fracture trajectory [60]. Meanwhile, the analysis’s findings from an ANN set-up to predict C45 forging tool durability is crucial to the operation of the forging system because they help the technologist choose process parameter figures that will prolong the die’s lifetime [79]. Contrarily, it was found that the supplemental ice loading on welded plate joints can reduce the FL by half, compared to that under wave loadings only [80]. Moreover, the use of a comprehensive database of damaged and healthy fatigue damage indices for training ANNs showed that the damage identification method can efficiently detect potential fatigue cracks in welded steel bridge structural components [81]. According to the findings, fatigue dependability indices drastically decline as service life lengthens as illustrated in Figure 15a,b [91].

Utilizing records from SHM, an incremental two-scale model of damage can be updated with new model parameters over time utilizing Bayesian updating of damage variables as well as sensitivity analysis of damage evaluation to material variables [94]. Findings revealed that the susceptible joints to fatigue failure are the butt-welded longitudinal rib joints, the diaphragm of rib-to-diaphragm joints, and the deck plate of RD joints in OSDs. It also became clear that it was impossible to disregard the significant role that the root-to-deck (RTD) and toe-to-deck (TTD) cracking models both play in the fatigue failure of OSDs. More importantly, when mixed failure models were considered, a striking decline in the fatigue dependability of RD joints can be shown. Moreover, the U-rib butt junction and the RD joint are most and least susceptible to fatigue failure, respectively, among the three essential welded joints in a coastal thin bridge [99,106,121]. On another note, experimental findings demonstrated that the Support Vector Machine (SVM) prototype has a greater anti-noise capability and higher forecast in aluminum welded connections after fatigue [113]. For SS 304L, it has been found that ferrite numbers between 15 and 19 offer the best fatigue resistance [117].

A multi-scale model demonstrated the fact that the projected fatigue initiation life together with residual FL closely match the outcomes of the experiments for fatigue in steel bridges [118]. While a case study’s findings illustrated that the initial crack size has a substantial impact on fracture reliability. Thus, it was advised to use the S-N curve technique throughout the design phase and the fracture mechanics strategy when the structure neared its end of design life [119]. Sequel to the evaluation of the impact of defects/inclusion on the fatigue behavior of steels. Findings show that for both materials used, the defect/inclusion predominated the fracture mechanism [122]. Meanwhile, the prediction of S-N curves for welded junctions by the SPDTRS-CS-ANN) coupled with Box-plot and Analytic Hierarchy Process (AHP) approach were found to have low experimental data error as illustrated in Figure 16, since when compared to the experimental data, the fatigue life forecasts under a given stress range fall within an error region of around ±1.2 [96].

Interestingly, welders may swiftly estimate and control welding distortion and residual stress before the actual welding process with the use of this responsive MR-based user interface, and beginners can learn the connection between the welding variables and the stimulated residual stress as well as deformation [128]. Moreover, early detection of crack start and growth in ductile structural steels subjected to cyclic loads was a challenge that was solved using the contemporary AE approach [129]. A comparison of the machine learning attributes for this study can be found in

Table 1. Comparison of attributes of machine learning classification for this research.

Taxonomy	Material	Input	Output	Welding Process	Application
Regression	Steel [21,22,23,24,25,28,29,30,38,45], metal composite [29], stainless steel [34,35], titanium [39].	Loading conditions [21], pavement temperatures and traffic levels [23], hourly averaged road temperatures and the number of trucks [24], number of cycles to failure of specimen N, maximum tensile stress σmax, stress range [25], sheet metal thickness, spot weld diameter [26], stress intensity factor (ΔK), critical crack size (ac) and initial crack size (ai) [27], vehicle and track parameters [28], crack propagation angles [29].	Rail bending stress [21], NSIFs [22], strain [23], stress-related performance indicator [24], residual life, impact strength [25], SIF [31], impact energy [38].	Thermite welding [21], fillet welding [22], spot welding [26], GMAW [33], FSW [38].	Rail, motorcycle [21,22], bridges [23,24,32,35], pipelines [25], automotive [26], infrastructure [28,30], offshore [37].
Monte Carlo	Stainless steel [40], steel [42,48,50,51,56,57], aluminum [52,53], titanium [70].	Efficiency, arc voltage, arc current, and welding speed [40], scale parameters [47], Kmax (maximum load) [48], vehicle and temperature loadings [49].	Residual stress [40], partial safety factor (γM) [47], propagation lifetime [48], fatigue stress spectrum [49].	GTAW [47], TIG [51].	Infrastructure [42], bridges [50,51,52,57,63,66], aircraft [53], nuclear power plants [54].
Numerical	Steel [63,65], stainless steel [67].	Tensile-shear strength, indentation depth and nugget size of the specimens [61], cyclic internal pressure [67].	The optimum welding condition of spot-welding joints [61], SIF, FCPR [67].	Spot welding [60,61], soldering [64], GMAW [65]	Automotive [58], electronics [64], pipelines [67]
Neural network	Steel [69,73,77,79,81,83,84,85,87], aluminum [74,82], dissimilar metals [75,76].	Tensile, axial fatigue, and ultrasonic test results [69], ratios, thickness, material type, structural stress [70], joint type, thickness, load ratio, welding process, structural stress [72], sheet thickness, spot diameter and loading conditions [73], welding time, welding current and electrode force [74], materials, corrosion rate, tensile strength, and fatigue load [75], notch radii [77], tool temperature at selected points, number of forgings, type of the applied protective layer, pressure, and path of friction [79], thickness, yield strength, lateral and bending constraints [87].	Prediction values (life cycles) [70], cycles to failure [73], residual stress [74,87], corrosion FL [75], SCF [77].	Spot welding [69,73,74], TIG [72,75], FSW [82], FCAW [87].	Automotive [69,73], thermal power plant [75], bridges [78,81,83,84], tooling [79], artic environment [80], oil and gas [85]
Structural health monitoring	Steel [23,90,91]	Strain and temperature signals [92], measured strains, pavement temperatures and traffic intensities [93].	SCF [92].		Bridges [90,92,93], energy [94].
Random/hybrid	Steel [96,97,102,106,108,109,112,114,115,118,120,121,123,126,129,130,131,132], aluminum [107,110], titanium [108], stainless steel [114,119], CFRP + steel [121], dissimilar [123].	Traffic-flow parameters (growth factors of traffic volume and vehicle weight) [16], crack length data and strain data [97], crack growth parameters [98], stress histories and cycles [99], fatigue crack growth parameters [100], pavement temperatures and heavy traffic intensities [101], keyhole shape and melt pool [103], vehicle loads (axle loads) [104], SIF [105], correlated wind and wave load [106], Joint type, plate thickness [111,132], spindle torque, shoulder design, welding speed, rotational speed, the plunge depth, base material, pin design/profile, tool type [116], wind loads, wave loads and soil properties [119], overlap ratio, welding speed, wire feed speed, and [127], energy data and spectral density functions [129], SCF [130], stress ratio [131], plate widths, nugget diameter [132].	Fatigue stress range [16], remaining FL [97], limit state function [98], fatigue damage index [99], number of cycles to failure [100], stress range distributions [101], stress amplitudes [104], MCIL [105], stress time histories at critical structural details [106] yield strength, welding quality, tensile strength, elongation, hardness, wear rate, residual stress, fatigue strength [129], AE signal [121], FL [130], FCG [131], F-N fatigue curves [132].	Laser welding [102,103], FSW [110,116], MMAW [128], Arc welding [129], GMAW [130], RSW [132].	Traffic signal support structure [97], marine structure [98], bridge [99,100,101,106,118,120,121,123,130], roller coaster [109], automotive [107,111,119,132], nuclear power plants [115], offshore wind turbine (OWT) jacket support structure, water transport [119], aerospace [127], manufacturing [128], pressure vessels, tanks, and pipelines [129].

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4. Conclusions

This study investigated the classes of ML algorithms for the FL forecast of welded articles from the standpoint of the material type, application, welding technique, input, and output parameters. From the trends, it could be observed that the neural network-based methods, numerical approach-based methods and the random/hybrid methods are the ones still mostly deployed to solve FL prediction problems, while various functional parametric equations have been developed over the years. Also, from the results, the latest algorithms have been able to improve the accuracy of the predictions in terms of MAPE, MAE, RMSE, and other evaluation metrics. Furthermore, with the continuous development of these techniques, the need to conduct complex and time-exhaustive experiments along with finite element simulations would be eliminated or reduced as predictions can now be accelerated. In addition, the most susceptible structural features and areas of maximum SCFs can now be deduced effectively. Moreover, it is evident that it is of utmost importance to be able to select the requisite machine learning algorithm and gather enough training data for a fatigue prediction case, while the capability to sort input and output parameters plays a vital role in the credibility of the algorithm. Meanwhile, the authentication and validation of the advanced algorithms cannot be complete without comparing the ML results with experimental and computational results taking into consideration in-service scenarios. Nonetheless, the random/hybrid taxonomy seems to the best candidate to predict FL in most cases as it combines the strengths of the individual algorithms. Illustratively, the data-driven LSTM would be a good fit for applications that require the long-term monitoring and updating of the parameters as shown in its accuracy for the fatigue damage prognosis of OSDs which would eventually benefit the inspection, administration, and decision making for the maintenance of bridges. Meanwhile, for a proper multi-scale fatigue investigation, inclusion distribution and uncertainties should be depicted in the prediction model. Finally, most of the applications have been on bridges, especially OSDs, with steel as the main material. There should be more research on how to apply machine learning algorithms to FL prediction in other sectors such as transport, energy, aerospace, and automotive sectors with focus on other materials and alloys including composites, magnesium, aluminum, and dissimilar combinations. Future research should also adopt a probabilistic or dual (probabilistic and deterministic) approach to FL prediction as well as the application of a digital twin framework to study the lifecycle of components and structures with respect to sources of uncertainties, axiality of fatigue loading, and fatigue evolution. In addition, incorporation of computer vision techniques could aid in efficient fatigue crack image analysis.