Combining Kriging meta models with U-function and K-Means clustering for prediction of fracture energy of concrete

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.