One of the first decisions to be made when building a mineral resource model is the definition of geological/geostatistical domains. Cluster analysis is a set of techniques in machine learning that can be especially suited for this matter. In order to compare different approaches, two clustering algorithms were investigated in this study: k-means and the dual-space clustering algorithm. Choosing the most appropriate method and the number of clusters can be challenging and some metrics are needed to support these decisions, including the validation of the spatial distribution of the clusters, which is not always appropriately discussed in the literature. We introduce the use of correlograms of the indicators for that matter. Although clustering techniques can be robust for an application in resource modelling, expert knowledge is still necessary when applying cluster analysis to resource modeling, since final decisions should not be based solely on statistical indexes, but also on experience. In this paper, the proposed methodology was tested in a threedimensional dataset related to a phosphate/titanium deposit.
Machine learning is a broad field of study that can be applied in many areas of science. In mining, it has already been used in many cases, for example, in the mineral sorting process, in resource modeling, and for the prediction of metallurgical variables. In this paper, we use for defining estimation domains, which is one of the first and most important steps to be taken in the entire modeling process. In unsupervised learning, cluster analysis can provide some interesting solutions for dealing with the stationarity in defining domains. However, choosing the most appropriate technique and validating the results can be challenging when performing cluster analysis because there are no predefined labels for reference. Several methods must be used simultaneously to make the conclusions more reliable. When applying cluster analysis to the modeling of mineral resources, geological information is crucial and must also be used to validate the results. Mining is a dynamic activity, and new information is constantly added to the database. Repeating the whole clustering process each time new samples are collected would be impractical, so we propose using supervised learning algorithms for the automatic classification of new samples. As an illustration, a dataset from a phosphate and titanium deposit is used to demonstrate the proposed workflow. Automating methods and procedures can significantly increase the reproducibility of the modeling process, an essential condition in evaluating mineral resources, especially for auditing purposes. However, although very effective in the decision-making process, the methods herein presented are not yet fully automated, requiring prior knowledge and good judgment.
Determining geological domains to be modeled is one of the first steps in the mineral resource evaluation process. Prior knowledge regarding the geology of the deposit is fundamental but, in most cases, not enough for a reasonable definition of these domains. A careful statistical analysis of the available data (e.g. geochemical samples) is also of great importance. In order to avoid mixing different populations of data, samples with similar characteristics should be grouped together. In the context of supervised machine learning, cluster analysis can be especially suited for this matter and there are many different algorithms available in the literature. In this paper, two clustering techniques were investigated: the first is the k-means algorithm, one of the most widely used methods in machine learning, based on the iterative analysis of the statistical distribution, while the other one is based on spatial autocorrelation statistics, which takes into consideration the geographic distribution of samples. The choice of the most appropriate technique, as well as the number of domains can be challenging when performing cluster analysis, and the evaluation of an expert is still necessary, as the results are subjective.
Geometallurgical models are commonly built by combining explanatory variables to obtain the response that requires prediction. This study presented a phosphate plant with three concentration steps: magnetic separation, desliming and flotation, where the yields and recoveries corresponding to each process unit were predicted. These output variables depended on the ore composition and the collector concentration utilized. This paper proposed a solution based on feature engineering to select the best set of explanatory variables and a subset of them able to keep the model as simple as possible but with enough precision and accuracy. After choosing the input variables, two neural network models were developed to simultaneously forecast the seven geometallurgical variables under study: the first, using the best set of variables; and the second, using the reduced set of inputs. The forecasts obtained in both scenarios were compared, and the results showed that the mean squared error and the root mean squared error increase in all output variables evaluated in the test set was smaller than 2.6% when the reduced set was used. The trade-off between simplicity and the quality of the model needs to be addressed when choosing the final neural network to be used in a 3D-block model.
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