Predicting the Young's Modulus and Uniaxial Compressive Strength of a typical limestone using the Principal Component Regression and Particle Swarm Optimization

Abstract

In geotechnical engineering, rock mechanics and engineering geology, depending on the project design, uniaxial strength and static Youngchr('39')s modulus of rocks are of vital importance. The direct determination of the aforementioned parameters in the laboratory, however, requires intact and high-quality cores and preparation of their specimens have some limitations. Moreover, performing these tests is time-consuming and costly. Therefore, in this study, it was tried to precisely predict the desirable parameters using physical characteristics and ultrasonic tests. To do so, two methods, i.e. principal components regression and support vector regression, were employed. The parameters used in modelling included density, P- wave velocity, dynamic Poisson’s ratio and porosity. Accordingly, the experimental results conducted on 115 limestone rock samples, including uniaxial compressive and ultrasonic tests, were used and the desired parameters in the modelling were extracted using the laboratory results. By means of correlation coefficient (R2), normalized mean square error (NMSE) and Mean absolute error (MAE), the developed models were validated and their accuracy were evaluated. The obtained results showed that both methods could estimate the target parameters with high accuracy. In support vector regression, Particle Swarm Optimization method was used for determining optimal values of box constraint mode and epsilon mode, and the modelling was conducted using four kernel functions, including linear, quadratic, cubic and Gaussian. Here, the quadratic kernel function yielded the best result for UCS and cubic kernel function yielded the best result for Es. In addition, comparing the results of the principal components regression and the support vector regression indicated that the latter outperformed the former.