PSI - Issue 68

Tea Marohnić et al. / Procedia Structural Integrity 68 (2025) 84 – 90 T. Marohnić and R. Basan / Structural Integrity Procedia 00 (2025) 000–000

85

2

Nomenclature b

fatigue strength exponent fatigue ductility exponent

c

Young’s modulus error criterion goodness of fit

E E f E a

2N f number of load reversals to failure 2N f,exp number of load reversals to failure calculated using experimental fatigue parameters 2N f,est number of load reversals to failure calculated using estimated fatigue parameters R m ultimate tensile strength s width of the scatter band D e /2 total strain amplitude e f ' fatigue ductility coefficient s f ' fatigue strength coefficient LS abbreviation for low strength HS abbreviation for high strength

Existing machine learning-based methods (ML), thus also artificial neural networks (ANNs) based methods, proposed for estimation of strain-life fatigue parameters, are evaluated in different manners, making their comparison difficult. Two aspects of measuring machine learning-based methods performance exist: evaluation of ANNs performance, and evaluation of the fatigue life estimations. The first aspect, which is prevalently dominant, considers evaluation by using different well-known metrics such as mean relative error MRE , coefficient of correlation r , coefficient of determination R 2 , mean absolute percentage error MAPE , root mean square error RMSE and others. The second aspect, that evaluates fatigue life estimations, commonly includes the conventional error criterion E f ( s ), while other criteria proposed by Park and Song (1995), as well as variations in low- and high-strength materials and different fatigue regimes, are usually not addressed. In this study, according to the detailed evaluation methodology based on Park and Song (1995) and proposed by Basan and Marohnić (2024), ANNs developed for estimation of fatigue parameters (Marohnić, 2017) have been evaluated regarding their accuracy and applicability for estimation of low- and high-cycle fatigue lives of low-alloy steels which were further divided into low- and high-strength subgroups. Separate analyses allow for more accurate assessment of ANNs and prevent the averaging of evaluation results. 2. Artificial neural networks for estimation of strain-life parameters of steels Artificial neural networks for estimation of strain-life parameters of steels from monotonic properties that are evaluated in this paper were developed by Marohnić (2017). Furthermore, Marohnić (2017) proposed a methodology whose integral part is detailed statistical analysis – forward selection, which identifies the monotonic properties that contribute the most to estimation of individual strain-life parameter of different groups of steels (unalloyed, low-alloy, high alloy steels) in order to reduce the dimensionality of the data i.e. to set the optimal ratio of material dataset size to number of training datasets. This is due to limitation of quality strain-life data in terms of training the artificial neural networks. For estimation of strain-life parameters of low-alloy steels, four two-layer multilayer perceptrons (MLP) with hyperbolic tangent transfer function in the hidden layer and linear transfer function in the output layer were developed. Forward selection defined the input variables (monotonic properties), while the outputs were parameters of Basquin Coffin-Manson expression: fatigue strength coefficient s f ', fatigue strength exponent b , fatigue ductility coefficient e f ' and fatigue ductility exponent c . The maximum number of neurons in hidden layer H is defined by the amount of training samples available, N train , the number of input variables I and the number of target variables O , and the optimum was determined by combining the growth method (starting from one neuron in the hidden layer) with other tools for improving generalization (for example, early stopping in order to prevent overlearning). For learning (i.e. minimizing