## 7 Conclusions  
The goal of this work was to show how ML models can be used to forecast the fatigue life (N) of plain concrete under uniaxial compression. The fatigue life was forecasted using random forest, neural network, gradient boosting, and AdaBoost models. The models were developed sequentially using three data sets. The first was developed with original data, the second was developed with outliers removed, and the last model was developed with the average value of data with different outputs in the same input. For training and testing of the models, a ratio of training and testing was used as 90:10 in order to secure as much of the training data as possible. From this, we were able to make the following conclusions. 1. Three data files were generated from the original data, which were used in the work of [PERSON] et al. [4]. These files were used to develop the final ML model and were as follows: (a) grouped data with the same input variable value and different output variable log\(N\) value, (b) data excluding outliers selected by three or more outlier detection methods; (c) average data excluding outliers, created by averaging the grouped data after excluding outliers from the grouped data. 2. From the Pearson and Spearman correlation analysis, it was observed that the maximum stress level \(S_{\text{max}}\) had a solid negative relationship with log\(N\), and the loading frequency f had a solid positive relationship with log\(N\). Simultaneously, the height to width ratio (\(h\)/\(w\)) and shape of the tested specimens had weak relationships with log\(N\). 3. Excluding the sustained strength of the concrete variable, originally treated as the seventh input variable in the work of [PERSON] et al. [4], resulted in improving the MSE  
Figure 16: Permutation feature importance of the gradient boosting model. and determination coefficient \(R^{2}\) values. Moreover, the gradient boosting model with the value of the result of minimum error and a high \(R^{2}\) value at 0.753 was an indication of high accuracy in predicting outcomes. 4. Further analysis using the data excluding outliers caused the determination coefficient \(R^{2}\) value to increase to 0.803. Moreover, the average data excluding outliers provided the best correlation with the \(R^{2}\) value at 0.915. 5. Finally, to determine the strength of the relationship between the feature and the target value, a permutation feature importance (PFI) analysis was carried out for the gradient boosting model. The analysis results confirmed that the maximum stress level \(S_{\text{max}}\) and loading frequency \(f\) are critical input variables, followed by compressive strength \(f_{c}\) and the maximum to minimum stress ratio \(R\). Shape and _h/w_ are features that have only a minor influence on the model. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app12199766/s1](https://www.mdpi.com/article/10.3390/app12199766/s1)]([https://www.mdpi.com/article/10.3390/app12199766/s1](https://www.mdpi.com/article/10.3390/app12199766/s1)), The following spreadsheet contains the supplementary data to this article: download spreadsheet (oxKB). * [PERSON] et al. (2009) [PERSON]; [PERSON]; [PERSON]; [PERSON] High frequency fatigue accelerated life test of concrete. _J. Shang. Univ. (Nat. Sci. )_**2009**, _15_, 205-210. * [PERSON] and [PERSON] (2013) [PERSON]; [PERSON] Investigation on the fatigue behavior of recycled aggregate concrete under uniaxial compression. _China Civil Eng. J._**2013**, _46_, 62-69. * [PERSON] and [PERSON] (1996) [PERSON]; [PERSON] Experimental study of the fatigue behavior of high strength concrete. _Cem. Concr. Compos._**1996**, _26_, 1513-1523. [CrossRef]
* [PERSON] and [PERSON] (1979) [PERSON]; [PERSON] [PERSON] A study on compressive fatigue strength of concrete considering survival probability. _Jpn. Soc. Civ. Eng._**1979**, _284_, 127-138. [CrossRef]
* [PERSON] et al. (2004) [PERSON]; [PERSON]; [PERSON] Failure mechanism of concrete under fatigue compressive load. _[PERSON]. Civ.