All Times EDT
Keywords: : Borehole model, Computer experiment, Gasp model
Despite the rapid growth in computer experiments, some computer models are complex and often too time-consuming to be directly used to mimic real life experiments and predict the output of computer experiments at untried inputs. To overcome this complexity and reduce the computational efforts in applying a computer model, a Gaussian stochastic process (Gasp) model was employed in this paper to emulate a borehole computer model. The efficiency of the Gasp model under exponential and Gaussian correlation functions was examined. A borehole computer experiment developed using orthogonal array (OA)-based Latin hypercube design (LHD) was employed to demonstrate the goodness of the Gasp model. Further performance of the Gasp model at predicting the flow rate of water of a borehole was examined using the two correlation functions. Comparisons were also made on the performances of Gasp model using Relative Average Absolute Error (RAAE) and Relative Maximum Absolute Error (RMAE) respectively. Among the predictors considered for borehole modelling, the Gasp models with exponential and Gaussian correlation functions identified the radius(x1) and the hydraulic conductivity(x8) of borehole as the two most significant factors that influence the rate of flow of water of a borehole (p < 0.001). The estimated RAAE (3.5057e-14) and RMAE (1.7630e-13) provided by the exponential function are relatively smaller than the RAAE (1.9880e-07) and RMAE (3.3040e-07) provided by the Gaussian function. Further results also showed that the Gasp model with exponential function has process variance (0.0192) that is relatively smaller than the one provided by the Gaussian function (0.1018). This study concluded that the Gasp model with exponential function outperforms the one that uses Gaussian function for modelling and predicting the rate of flow of water of borehole at untried inputs. All model developments and analysis were performed in the environment of MATLAB package.