Development of fuzzy-GMDH model optimized by GSA to predict rock tensile strength based on experimental datasets

The tensile strength (TS) of the rock is one the most key parameters in designing process of foundations and tunnels structures. However, direct techniques for TS determination (laboratory investigations) are not efficient with respect to cost and time. This investigation attempts to develop an innovative hybrid intelligent model, i.e. fuzzy-group method of data handling (GMDH) optimized by the gravitational search algorithm (GSA), fuzzy-GMDH-GSA, for prediction of the rock TS. To establish a database, the rock samples collected from a tunnel site were evaluated in the laboratory and a database (with the Schmidt hammer test, dry density test, and point load test as inputs and Brazilian tensile strength, BTS, as output) was prepared for modelling. Then, a fuzzy-GMDH-GSA model was developed to predict BTS of the rock considering the most influential of this predictive model. In addition, a fuzzy model as well as a GMDH model were constructed to predict BTS for comparison purposes. The performances of the proposed predictive models were evaluated by comparing the values of several statistical metrics such as correlation coefficient (R). R values of 0.90, 0.86, and 0.86 were obtained for testing datasets of fuzzy-GMDH-GSA, GMDH, and fuzzy models, respectively, which show that the fuzzy-GMDH-GSA predictive model is able to deliver greater prediction performance compared to other constructed models. The results confirmed the effective role of the GSA, as a powerful optimization algorithm in efficiency of hybrid fuzzy-GMDH-GSA model. Moreover, results of sensitivity analysis showed that the point load index is the most effective input on output of this study.