## 1 Introduction
In addition, the split tensile strength [45; 57; 60] and modulus of elasticity [61] of concrete were predicted by using ML techniques. Among the ML methods, artificial neural network (ANN) models are widely used [36; 37; 38; 42; 43; 45; 46; 47; 48; 49; 50; 52; 54; 55; 58; 59; 60; 62]. In addition to ANN, the prediction of mechanical strength properties and mix proportions of concrete using other regression models has recently gained popularity, including the use of support vector regression [39; 47; 52], decision tree [40; 57; 61; 62], random forest [36; 44; 47; 56], AdaBoost [40; 41; 52; 57; 59; 61], gradient boost [40; 53], and ensemble algorithm [51; 61]. In 2019, an ANN-based concrete fatigue strength model was proposed by [PERSON] and [PERSON] [63]. They used 203 data points gathered from the literature. Predicted values analyzed from the ANN model were compared to the existing code expressions. Their ANN model includes the compressive strength of concrete, maximum stress level, and minimum stress level. In 2021, a strength degradation model of concrete under fatigue loading was proposed by [PERSON] et al. [4] using several ML algorithms, such as the random forest, support vector machine, and artificial neural network models. About 1000 experimental data were collected from various independent experiments [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33]. Seven independent variables were chosen in their study, including the compressive strength of concrete, sustained strength of concrete, height to width ratio and shape of the test specimens, maximum stress level, minimum to maximum stress ratio, and loading frequency. The analysis results revealed that the random forest model produces the highest value of the correlation coefficient at 0.85. Due to the nature of the fatigue strength test, outliers can remarkably occur in this test compared to other material strength properties tests. In statistics, an outlier is a data point that differs significantly from other observations [64; 65]. An outlier may be due to variability in the measurement or it may indicate experimental error; the latter is sometimes excluded from the data set. There are various methods of outlier detection, such as [PERSON]'s test [64], [PERSON]'s criterion [66], [PERSON]'s criterion [67], [PERSON]'s Q-test [68], the generalized extreme studentized deviation test [69], [PERSON] and Tau test [70], and the IQR-test [71; 72]. In this study, 1300 samples of experimental data [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33] of concrete fatigue tests originally carried out by [PERSON] et al. [4] were treated using 4 kinds of machine learning models(artificial neural network, random forest, and the gradient boosting and AdaBoost method). Unlike previous studies, this research adopts six independent values, excluding only the sustained strength of the concrete variable used from the work of [PERSON] et al. [4]. For our approach, three data files were generated to compare the actual number of fatigue repetition values (log\(N\)) against the predicted values (log\(N\)). The first data file uses the entire original dataset, which was treated by [PERSON] et al. [4]. However, unlike [PERSON] et al. [4], our research adds the second data file with the grouping data and the third data file that excludes outliers. In this work, [PERSON]'s criterion, [PERSON]'s criterion, the Thompson-Tau criterion and the IQR method were adopted to remove outliers. Finally, a permutation feature importance (PFI) analysis was carried out to determine which input variables are the most critical or minor in the fatigue life model. Our novel approach allows better fatigue life prediction than [PERSON] et al. [4]'s approach.