predicting the young's modulus and uniaxial compressive strength of a typical limestone using the principal component regression and particle swarm optimization

The rock uniaxial compressive strength (ucs) and modulus of elasticity (es) are two key design parameters in geotechnical engineering and rock mechanics. this study tries to accurately 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 coefficient of determination (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 ucs modeling, the values of r2, nmse, and mae obtained from the pcr method for the training set were 0.78, 22.45, and 0.363, respectively. also, the values of r2, mse, and mae obtained for the testing set were 0.76, 22.51, and 0.357, respectively. in es modeling, the values of r2, mse, and mae obtained from the pcr method for the training set were 0.71, 34.23, and 0.421, respectively. also, the values of r2, nmse, and mae obtained for the testing set were 0.7, 34.23, and 0.43, respectively. 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. the values of r2, nmse, and mae were 0.83, 16.98, and 0.329, respectively, for the training dataset using the quadratic function in modeling ucs with the svr method. also, the values of mse, r2, and mae obtained for the testing set were 0.76, 22.15, and 0.296, respectively. in es modeling, the values of r2, mse, and mae were 0.73, 29.11, and 0.45 for the training set, respectively. also, the values obtained for r2, mse, and mae were 0.7, 25.67, and 0.272, for the testing set, respectively. in addition, comparing the results of the principal components regression and the support vector regression indicated that the latter outperformed the former.

predicting the young's modulus and uniaxial compressive strength of a typical limestone using the principal component regression and particle swarm optimization

the rock uniaxial compressive strength (ucs) and modulus of elasticity (es) are two key design parameters in geotechnical engineering and rock mechanics. this study tries to accurately 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 coefficient of determination (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 ucs modeling, the values of r2, nmse, and mae obtained from the pcr method for the training set were 0.78, 22.45, and 0.363, respectively. also, the values of r2, mse, and mae obtained for the testing set were 0.76, 22.51, and 0.357, respectively. in es modeling, the values of r2, mse, and mae obtained from the pcr method for the training set were 0.71, 34.23, and 0.421, respectively. also, the values of r2, nmse, and mae obtained for the testing set were 0.7, 34.23, and 0.43, respectively. 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. the values of r2, nmse, and mae were 0.83, 16.98, and 0.329, respectively, for the training dataset using the quadratic function in modeling ucs with the svr method. also, the values of mse, r2, and mae obtained for the testing set were 0.76, 22.15, and 0.296, respectively. in es modeling, the values of r2, mse, and mae were 0.73, 29.11, and 0.45 for the training set, respectively. also, the values obtained for r2, mse, and mae were 0.7, 25.67, and 0.272, for the testing set, respectively. in addition, comparing the results of the principal components regression and the support vector regression indicated that the latter outperformed the former.