A joint determination of horizontal and vertical movement of water through porous medium is addressed in this study through fast multi-output relevance vector regression (FMRVR). To do this, an experimental data set conducted in a sand box with 300 × 300 × 150 mm dimensions made of Plexiglas is used. A random mixture of sand having size of 0.5-1 mm is used to simulate the porous medium. Within the experiments, 2, 3, 7, and 12 cm walls are used together with different injection locations as 130.7, 91.3, and 51.8 mm measured from the cutoff wall at the upstream. Then, the Cartesian coordinated of the tracer, time interval, length of the wall in each setup, and two dummy variables for determination of the initial point are considered as independent variables for joint estimation of horizontal and vertical velocity of water movement in the porous medium. Alternatively, the multi-linear regression, random forest, and the support vector regression approaches are used to alternate the results obtained by the FMRVR method. It was concluded that the FMRVR outperforms the other models, while the uncertainty in estimation of horizontal penetration is larger than the vertical one.
Keywords: cutoff wall; dummy variable; fast multi-output relevance vector regression; porous medium; tracer.