Support vector machines and gradient boosting for graphical estimation of a slate deposit

Abstract

Critical for an efficient and effective exploitation of a slate mine is to obtain information on its technical quality, in other words, on the exploitability potential of the deposit. We applied support vector machines (SVM) and LS-Boosting to the assessment of the technical quality of a new unexploited area of a mine, and compared the results to those obtained for kriging and neural networks. Firstly we analyzed the relationship between kriging and semi-parametric SVM in a regularization framework and explored the different alternatives for training these networks. Subsequently, in an attempt to combine both radial and projection structures, we formulated a boosting technique for radial basis function (RBF) networks defined over projections in the input space (RBFPP). The application of these techniques to our test drilling data demonstrated a similar level of performance for all the estimators examined, with the main difference occurring in the shape of the respective deposit reconstructions. Therefore, in choosing between the different techniques, an essential aspect will be their ability to reproduce the morphological characteristics of the true process. In this paper we also evaluate the benefits of using the estimated covariogram as the kernel of the SVMs and compare the sparsity of the different solutions. The results obtained show that the selection of a standard kernel that ignores the variability structure of the problem produces poorer results than when the estimated covariogram is used as the kernel.

Evaluación de la fisibilidad y durabilidad de pizarras de techar mediante microscopía óptica y SEM

“…La calidad de la pizarra viene determinada por diversos parámetros, tanto mecánicos como estéticos, considerados tanto a escala de macizo rocoso como a escala de placa comercial. La valoración de estos parámetros y su tratamiento estadístico en base a métodos estadísticos multivariantes (18) y redes bayesianas (20) ha permitido en los últi-mos años, por una parte, la evaluación de la calidad de la pizarra de techar y, por otra, el desarrollo de modelizaciones de yacimientos en base a técnicas geoestadísticas y sistemas de lógica difusa (15)(16)(17)19 …”

“…Slate quality is determined by various parameters, as much mechanical as aesthetic, considered equally at a rock mass and a slab scale. The valuation of these parameters and their statistical usage with reference to multivariate statistical techniques (18) and Bayesian networks (20) over recent years has permitted both the evaluation of roofing slate and the modeling of mineable deposits, with the application of geostatistical techniques and fuzzy logic expert systems (15)(16)(17)19). However, these techniques suffer the inconvenience that many of the quality parameters are evaluated by means of E C14 = E C5 = E C16 = E C9 = 5 mm > E C25 = E C12 = 4 mm > E C3 = E C4 = E C6 = E C10 = 3,5 mm muchos de los parámetros de calidad son valorados en base a observaciones macroscópicas, realizadas por un experto en pizarra a partir de testigos de sondeo o en los bancos de la explotación.…”

“…Diversas líneas de investigación que vienen desarrollándose con objeto de minimizar el impacto ambiental de estas explotaciones, en base a la aplicación de diversas metodologías para la recuperación de escombreras (10)(11)(12), el reciclado de escombros (13) y la inhibición de la oxidación de los sulfuros de hierro (14), hasta ahora no han obtenido resultados suficientemente satisfactorios. Quizá por ello es aún más importante el desarrollo de estrategias que minimicen la producción de estériles, como la implantación de minería de interior o la adecuada evaluación y planificación de las explotaciones (15)(16)(17). Un factor que interviene de forma relevante en la planificación y modelización de las explotaciones es la correcta estimación de la calidad de la pizarra (18,19), tanto a escala de macizo rocoso como a escala de placa comercial (20).…”

“…Various investigations that have been carried out with the object of minimizing the environmental impact of these mining operations, based on the application of various methods for the recuperation of waste tailings (10)(11)(12), the recycling of waste (13) and the inhibition of iron sulphide oxidation, have not yet obtained satisfactory results (14). This makes it even more important to develop strategies that minimize waste production, such as the implementation of underground mining or adequate evaluation and planning of mining operations (15)(16)(17). An important and relevant factor in the planning and modelling of mining operations is the correct estimation of the quality of the slate (18,19), both at the rock mass and slab scale (20).…”

Regularized kriging as a generalization of simple, universal, and bayesian kriging

“…In fact, both problems apply a similar strategy, i.e., they admit a certain level of bias with a view to reducing the variance and improving, if at all possible, the generalization ability of the corresponding estimator. However, there are important differences given that the two problems are governed by different hypotheses (the mean and the dependency structure are different in each problem) (Matı´as et al 2004b). …”