This repository provides an open-source implementation of the methods described in "Measuring sampling fairness and geochemical consensus for blasthole assays within grade-block mining units" (https://engrxiv.org/preprint/view/2422).
Data analytics, selective mining units, blasthole assays, sampling fairness, geochemical consensus, grade control, reliability, MCD estimator, handling breakdown, split-sequence analysis.
- Scientists and Engineers working in Mining Science and Technology.
- Researchers and readers of Computers & Geosciences, Mathematical Geosciences or Earth Science Informatics.
- People who are thinking of using the MCD estimator to measure robust distances in compositional data, who need a way to overcome estimator breakdown when there is an unknown level of contamination, where the fraction of outliers in a sample may reach as high as 50%.
In the mining industry, current grade control practices lack a standardised framework that can assess the reliability of average grade estimates computed for selective mining units (otherwise known as grade-blocks) within a mining bench. This python code implements two measures that quantify sampling fairness and geochemical consensus. The notion of sampling fairness refers to spatial factors such as sampling density and bias in the spatial distribution of blastholes whereas geochemical consensus considers the agreement between the assay measurements within a grade-block. The voronoi image marked with an asterisk (above) shows a case where there is significant disparity within a block in terms of geochemistry. Geochemical disparity is measured using the MCD robust distance estimator and a masking formula that takes into account the proportion of outliers and magnitude of differences observed above a threshold. However, the MCD estimator can breakdown in practice when the fraction of outliers exceeds (n−k−1)/(2n). For k ≥ 2 variables and a sample size n ≥ 10, this can lead to an underestimation of the true extent and impact of outliers when they exceed 40%. An extension based on split-sequence analysis has been proposed to overcome this limitation. The method is evaluated using anonymised production data from an open-pit iron ore deposit.
The core algorithm is implemented in two modules:
isometric_logratio.pyprovides an implementation of ILR transformation. It maps compositional data from the Aitchison simplex to Euclidean space where differences between two assay samples can be measured by Mahalanobis distance.algorithm_implementation.pycomputes the sampling fairness and geochemical consensus measures. It also implements split-sequence analysis which handles estimator breakdown. The API has the following signature:
run(self, gb_polygon, gb_holes_xy, gb_chemistry, results, randseeds=[8365])
- Required parameters:
gb_polygon(shapely.geometry.Polygon) represents the 2D grade-block boundarygb_holes_xy(numpy.array) denotes blasthole coordinates, shape: (n,2)gb_chemistry(numpy.array) denotes assay measurements, shape: (n,m)results(dict) report the spatial confidence and geochemical consensus scores along with other statistics
- Optional parameter:
randseedlist(int) usually a single random seed [ integer ] is supplied for reproducibility
Other modules:
custom_graphs.pyprovides methods for- drawing block boundaries (polygon regions) and displaying attributes in a colour map.
- producing ternary plots: converting 3D composition vectors to 2D canvas coordinates.
- these features are shown in
evaluate.ipynbandvalidation.ipynb
data/blasthole_assays.csvprovides some test data used inexample.pyx,y,zdescribe the center coordinates of blastholes in an arbitrary framec1,c2,c3describe the normalised concentration of three chemical componentsgradeblock_ididentifies the grade-block associated with these assay samples.
data/gradeblock_geometries.csvdescribes the shape of two grade-blocksgradeblock_idallows a particular grade-block to be linked to blastholesnameis just a more human-friendly identifierboundaryrepresents a shapely polygon string in wkt format.
data/high_breakdown.csvis used to illustrate the estimator breakdown phenomenon. The intermediate steps and output are traced in the example given in Section 4.2 of the paper.data/anonymised_*.csvanddata/synthesized_samples.zipare used inevaluate.ipynbandvalidation.ipynbto replicate experiments and reproduce figures in the paper.
- Python version 3.7.2+
- jupyter ≥ 1.0.0
- matplotlib ≥ 3.3.4
- numpy ≥ 1.19.2
- pandas ≥ 1.3.2
- scipy ≥ 1.6.1
- scikit-learn ≥ 0.24.1
- shapely ≥ 1.7.1
To install requirements (this may not be necessary):
pip install -r requirements.txt
For Anaconda users:
conda env create -n msfgc -f environment.yml
To replicate results for the examples shown in Table 2 and Sec. 4.2 of the paper, run:
python example.py
This work may be cited as:
- Raymond Leung, "Measuring sampling fairness and geochemical consensus for blasthole assays within grade-block mining units," Computers & Geosciences, 2023. DOI: https://doi.org/10.1016/j.cageo.2022.105286. Open-source implementation is available at https://github.com/raymondleung8/sampling-fairness-geochemical-consensus under a GPL-3.0 license.
- The BibTeX entry may be copied from here.
📋 This project is licensed under the terms of the GPL-3.0 license.
MSF-GC. Measuring sampling fairness and geochemical consensus for assays in selective mining units. Copyright (C) 2022 Raymond Leung.
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see https://www.gnu.org/licenses/.
Further information about this program can be obtained from:
- Raymond Leung (raymond.leung@sydney.edu.au)