In this study, a combination of Kriging surrogate method with U-learning function and K-means clustering were used to predict the concrete fracture energy (as an output parameter) based on previous experimental data sets including compressive strength, maximum aggregate size and the water to cement ratio (as the input parameters). Therefore a collection of 246 data series obtained from previous studies was collected. The strength, accuracy, and efficiency of the proposed models were examined by selecting 10%, 30%, and 50% of the data for learning, and the results were compared with the previous equations. The results show that combining the Kriging method with the U-learning function in the work of fracture method (WFM) will increase the predictive power of fracture energy compared to basic Kriging and K-means clustering methods, and the previous relationships. However, the size effect method (SEM), the models created using K-means and 50% of the data has led to better forecasting results than other models. The value of the correlation coefficient (R²) of the proposed Kriging combination models and previous existing relationships are in the range of 0.59–0.95 and 0.14–0.69, respectively. The results show that the combination of the Kriging method, the U-learning function, and K-means clustering will reduce the time and cost of the experiments, as well as increasing the accuracy of concrete fracture energy prediction results using a small number of previous experimental data.

在这项研究中，结合了U-learning函数和K-means聚类的Kriging替代方法，基于抗压强度，最大骨料尺寸和水的先前实验数据集，预测了混凝土的断裂能（作为输出参数）。水泥比（作为输入参数）。因此，收集了从以前的研究中获得的246个数据系列。通过选择10％，30％和50％的学习数据来检查所提出模型的强度，准确性和效率，并将结果与​​以前的方程式进行比较。结果表明，与基本的Kriging和K-means聚类方法相比，将Kriging方法与U-learning函数结合使用在断裂方法（WFM）中将提高断裂能量的预测能力，和以前的关系。但是，尺寸效应方法（SEM），使用K均值创建的模型以及50％的数据已比其他模型带来了更好的预测结果。相关系数的值（R²）提出的Kriging组合模型和先前存在的关系分别在0.59-0.95和0.14-0.69的范围内。结果表明，将Kriging方法，U学习功能和K-means聚类相结合将减少实验的时间和成本，并提高使用少量先前方法的混凝土断裂能预测结果的准确性实验数据。