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By P. Babak, E. Insalaco, O. Babak, P. Henriquel

"Detection of outliers is an important primary step in geomodelling. Geological datasets often contain errors due to problems such as measurement device limitations and recording glitches. In this paper, a robust Mahalanobis distance–based approach is successfully applied to particle size distributions of the Joslyn lease, an oil sands development site near Fort McMurray, Alberta, Canada. Automatic outlier detection and geological review were combined. Outliers from the Mahalanobis distance approach were compared with their respective core photographs to determine if laboratory measurements and facies classification were correct. A checking procedure for laboratory technicians is proposed.RÉSUMÉ La détection des valeurs aberrantes constitue une étape primaire importante de la modélisation géologique. Les ensembles de données géologiques contiennent souvent des erreurs en raison de problèmes tels que les limitations des instruments de mesure et des pépins d’enregistrement. Dans le présent article, une méthode robuste basée sur la distance de Mahalanobis a été mise en oeuvre avec succès aux granulométries du bail minier Joslyn, un site de sables bitumineux en développement à proximité de Fort McMurray, Alberta, Canada. La détection automatique des valeurs aberrantes a été combinée à une étude géologique. Les valeurs aberrantes de la méthode de la distance de Manalanobis ont été comparées avec leurs photographies respectives de carottes de forage afin de déterminer si les mesures en laboratoire et la classification des faciès étaient correctes. Une procédure de vérification pour les techniciens de laboratoire est proposée."

Jan 1, 2015

By Oy Leuangthong

Red Dog mine is the world's largest Zn producer. The deposit consists of sulphide ore zones in sedimentary exhalative (sedex) deposits, and is characterized by the presence of multiple metals and multiple ore types. The objective of the case study is to characterize seven different minerals, Zn, Pb, Fe, Ba, sPb, Ag and TOC, within eight different rock types. Geostatistical models were constructed for each variable within the eight rock types, and subsequently assembled to give 40 realizations for six 25ft benches. The stepwise conditional transformation was used to account for the complex multivariate relations. In addition to reproducing the input data, histogram and variogram, the resulting models also respect multivariate relations locally and globally. This paper documents the methodology to construct these models. A thorough validation procedure was implemented. Comparisons with blasthole data show that the conditional simulations and the long-term models agree in expected value. The main advantages of the conditional simulations are (1) the explicit accounting of multivariate relations between the data in model construction, and (2) the ability to quantify variability and uncertainty at any scale. A small exercise comparing the profit from a kriged and a simulated model is also examined. Results show that the simulation approach showed a 3% increase in profit, relative to the conventional estimation approach.

May 1, 2004

By Graeme Lyall, Oy Leuangthong, Clayton V. Deutsch

There are many variables to consider in the evaluation of nickel laterite deposits including the concentrations of nickel, iron, silica, and magnesia. These variables show complex relationships with each other such as mineralogical constraints, non-linear correlation, and heteroscedasticity. The complex multivariate relationship between the variables cannot be reproduced by conventional Gaussian or indicator geostatistical techniques. We introduce the stepwise conditional transformation method as a pre- and post-processing multivariate transform for the stochastic simulation of a nickel laterite deposit. Transformed data are multiGaussian and independent at h = 0; thus, cosimulation can be avoided after verification that variables are independent at all lag distances. Back transformation restores the features of the input multivariate distribution to the simulated realizations. The complex multivariate correlations are reproduced and sensitivity issues are addressed.

Jan 1, 2002

By S. A. Hosseini, O. Asghari

"The quantification of mineral resources and evaluation of process performance in mining operations at Gole Gohar iron ore deposit requires a precise model of the spatial variability of three variables (Fe, P, and S) which must be determined. According to statistical analysis there are complex multivariate relationships between these variables such as stoichiometric constraints, nonlinearity, and heteroskedasticity. Due to the impact of these complexities in decision-making, they should be reproduced in geostatistical models. First of all, in order to maintain the compositional and stoichiometric constraints, additive log-ratio (alr) transformation has been applied. In the next step cosimulation, using stepwise conditional transformation (SCT) and sequential Gaussian simulation (SGS) has been used to simulate multivariate data. Through statistical and geostatistical validations it is shown that the algorithms were able to reproduce complex relationships between variables, both locally and globally. IntroductionThe key steps in mining projects are the quantification of mineral resources, definition of mining reserves, and production scheduling. They rely on the construction of a block model that is used to represent basically the spatial distribution of ore grades (Montoya et al., 2012). The determination of grades and tonnages affects risk assessment and economic evaluation of mining projects. Evaluation of process performance in mining operations requires geostatistical modelling of many related variables (Barnett and Deutsch, 2012). Iron ore quality is characterized by multiple variables: not only the iron grade but also the contaminants that interfere in the subsequent steel manufacturing processes. Consequently, the spatial variability of multiple variables must be determined. Key variables are frequently correlated, and such correlations must be honoured during estimation and simulation. Data from iron ore deposits constitutes compositional data; furthermore, relationships the between assay data are often heteroskedastic."

Jan 1, 2016

By J Ferreira

To speed up multivariate geostatistical simulation it is common to transform the set of attributes into spatially uncorrelated factors that can be simulated independently. One decorrelation method is the method of minimum/maximum autocorrelation factors (MAF), where a two structure linear model of coregionalisation is assumed. The transformation decorrelates the theoretical model exactly, but the actual data are only approximately decorrelated. The MAF transformation can therefore be seen as a special case of a non-orthogonal approximate diagonaliser of a set of symmetric matrices. A more general approach for approximate joint diagonalisation (AJD) has been developed in the context of blind source separation. For these AJD algorithms no assumptions are made beyond symmetry of the individual matrices and so they can be applied to a family of experimental semivariogram matrices. In their application there are no restrictions on the number of structures in the linear model of coregionalisation (LMC) thus removing one of the conditions placed on the subsequent modelling of the spatial structure of the factors. In this paper the general background for the U-WEDGE AJD method is presented. It is shown that the U-WEDGE method achieves better spatial decorrelation than the MAF method. The factors derived from U-WEDGE are simulated using conditional turning bands simulation and then backtransformed to attribute space.

Sep 26, 2011

By David Verrelli, Melissa Kistner, Leanne Smith, Chris Aldrich, Lidia Auret, Warren Bruckard

In this investigation, different mixtures of realgar and orpiment particles were floated in a laboratory batch flotation cell and multivariate image analysis was used to estimate the arsenic content in the froths. The analysis was based on the froth colour, as well as extraction of three groups of textural features, namely those based on grey level co-occurrence matrices (GLCMs), wavelets and local binary patterns (LBPs). Collectively, these features provided better information on the arsenic content of the froths than any one of the individual groups of features. Partial least squares models could explain approximately 78% of the variance in the arsenic by using all the features combined. The colour content, particularly the green component in the red-green-blue (RGB) features, provided almost as much information as each of the three sets of texture-base features individually.

Jan 1, 2014

By H. Karakul

Determination of P-wave velocity (Vp), which is closely related to intact rock, is a nondestructive, easy and less complicated procedure. Due to these advantages, there is an increasing trend to predict the geomechanical properties of rocks from Vp. In addition to mineral content, cementing material and porosity, degree of saturation (Sr) are also other factors influencing geomechanical properties of the intact rock. However, up to the present, in the studies on the prediction of geomechanical properties of rocks from Vp, the effect of Sr has not been investigated. By considering this issue, in this study, it was aimed to correlate strength properties (uniaxial compressive and tensile strengths) and Young’s modulus with Vp of various rock types under different degrees of saturation. In addition, geomechanical properties of rocks were estimated from theoretical P- and S-wave (Vs) velocities, which were calculated based on their mineralogical compositions. For this purpose, fourteen different rock types were collected from several parts of Turkey and a comprehensive laboratory testing program was conducted. In the statistical analyzes, a series of different prediction relationships were developed by using independent variables such as Vp, Sr and effective clay content (ECC). Simple regression analysis results indicated that although prediction of the geomechanical properties of rocks from Vp at different degrees of saturation was possible, the equations developed would yield some under- or over-predictions. On the other hand, the multivariate equations developed have very high prediction performances and are very useful tools to estimate the geomechanical properties from the measured Vp at any Sr value. In addition to mineralogy, the variation in geomechanical properties with increasing Sr is also associated with the combined effect of porosity and clay content, which is first described in this study by the term Effective Clay Content (ECC). It is also noted that strength properties of rocks at any Sr may also be estimated using the empirical relations based on the theoretical Vp and shear-wave velocity (Vs) values, which are calculated from their mineralogical compositions.

Jan 1, 2015

By Bergh. L. C.

On line monitoring and diagnosis systems of process operating performance are becoming an important part of industrial programs, leading to improve process operation and therefore product quality over time. In processes, such as the contact section of a sulphuric acid plant, a large number of input variables, highly correlated, are presented. These characteristics usually pose more difficulties in modelling the process for monitoring and diagnosis purposes. Multivariate statistical projection methods, such as Main Component Analysis, have been proposed to effectively deal with these situations. The application of these ideas to a section of a 2350 MTD sulphuric acid plant, located at the Caletones Smelter, including dry tower, gas blowers, catalytic reactor and S03 absorber processes, is discussed here. A PCA model with eight main components is used for monitoring and diagnosis of more than seventy operating variables. Hottelling's T2 and Q residuals test were used for detecting measurement problems in relevant variables, and for identifying which set of variables were responsible for driving the process outside its normal operating region. Furthermore, considerable information for the correction of the tested operating problems was given by the use of these techniques.

Jan 1, 2007

By Osvaldo Bascur, Laurent Garrigues, Nouna Kettaneh, Svante Wold

The chemical, oil, semiconductor, mining, and paper and pulp industries, as well as most other modern industries, are rapidly expanding the range of measurements used to characterize raw materials, process steps, intermediates, and final products. In addition, process variables such as temperature, pressure, and flow become more and more numerous, providing extra information on the state of the process. However, no matter how many sensors are added, the underlying sources of variations that drive the process behavior remain constant. On the other hand, the measuring frequency of these data has increased from once a day or once an hour to once, ten, or even hundred times a minute. This gives masses of data that are swelling in both directions (more variables and more observations). These data need to be properly stored, managed, and analyzed to provide diagnostics about the state of the process as well as an understanding of the relationships between different parts of the process and the product properties. Projection methods such as PCA (principal components analysis) and PLS (projection to latent structures) compress process data to informative summaries of the original variables. These can be shown on line, providing an efficient, graphically oriented suite of diagnostics regarding the "health" and performance of the process. The power of these methods is illustrated by two examples of industrial data in the mining industry.

Jan 1, 2000

By C. Montoya

This paper shows, through a case study, the impact of multivariate grade modelling upon mine design and mine planning. A deposit explored by drill holes is considered, in which the grades of five elements (copper, silver, molybdenum, arsenic, and antimony) are of interest. Forty alternative models of the deposit are constructed by fitting the joint correlation structure of the grade variables and using conditional cosimulation. In addition, a reference model, obtained by averaging the alternative models, is also considered. The study shows that the resulting mine design (final pit characteristics and production schedules) is sensitive to the grade model under consideration, and that the design based on the reference model may not be optimal when compared to the alternative models based on cosimulation. However, when assuming a given long-term plan and extraction sequence, the grades and net present value (NPV) calculated on the reference model are unbiased with respect to those calculated on the alternative models with the same extraction sequence. The latter allow assessing the possible dispersion of the actual grades and NPV around their expected values, and are useful for the planner in order to determine the probability of meeting given production targets and of exceeding or falling short of given threshold grades. Additionally, unlike cosimulation, the separate simulation of each grade variable leads to unrealistic resource models and to biased results in mine design and mine planning. This approach should therefore be avoided, unless the grade variables are spatially uncorrelated.

Jan 1, 2012

By C. Montoya

This paper shows, through a case study, the impact of multivariate grade modelling upon mine design and mine planning. A deposit explored by drill holes is considered, in which the grades of five elements (copper, silver, molybdenum, arsenic, and antimony) are of interest. Forty alternative models of the deposit are constructed by fitting the joint correlation structure of the grade variables and using conditional cosimulation. In addition, a reference model, obtained by averaging the alternative models, is also considered. The study shows that the resulting mine design (final pit characteristics and production schedules) is sensitive to the grade model under consideration, and that the design based on the reference model may not be optimal when compared to the alternative models based on cosimulation. However, when assuming a given long-term plan and extraction sequence, the grades and net present value (NPV) calculated on the reference model are unbiased with respect to those calculated on the alternative models with the same extraction sequence. The latter allow assessing the possible dispersion of the actual grades and NPV around their expected values, and are useful for the planner in order to determine the probability of meeting given production targets and of exceeding or falling short of given threshold grades. Additionally, unlike cosimulation, the separate simulation of each grade variable leads to unrealistic resource models and to biased results in mine design and mine planning. This approach should therefore be avoided, unless the grade variables are spatially uncorrelated.

Jan 1, 2012

By Dr. Kyle Perry, Ryan Sibley

Rock blasting is an inherently difficult field to quantify independent & dependent variables and the specifics of how the energy interacts with the material for a number of reasons. Independent variables such as geology are innumerable and stochastic, thus, on a laboratory and full-scale basis these variables are assumed to be homogenous across the desired rock boundary. Dependent variables are difficult to quantify in the laboratory based on the specific aspect of the fracture mechanisms that caused the fracturing. The same variables are difficult to quantify in the field because of the shear amount of material being blasted. The energy interactions with the material are difficult to quantify due to the rate of the reaction and the lack of quantification of independent variables. The second main issue with laboratory scaled rock blasting is the nature of the small form-factor explosives required for use in a scaled setting. These explosives that are utilized, traditionally PETN detonating cord, have a greater ratio of potential energy converted to shock energy rather than gas energy when compared to traditional field explosives, such as emulsion or ANFO. Research over the past decades has indicated that gas pressure has the greatest contribution to rock blasting performance, such as fragmentation and material throw. The factor of varying ratios of energy production has not been discussed in any of the reviewed publications. Publications discuss dimensionless scaling, dynamic similitude, and length-based scaling, however, none of these scaling methods discuss the ratio of energy production. The main focus will be correlation of energy production ratio of shock versus gas to dependent variables. This paper analyzes previous publications within rock blasting and related field as they pertain to scaling procedures and will highlight the similarities and differences in the various publications and detail the observed omitted variables that possibly lead to skewed data.

Jan 21, 2025

By Barbara C. Williams

U.S. Bureau of Mines researchers conducted field studies at an abandoned copper-gold mine tailings impoundment. Pore water quality was analyzed in the vadose and saturated zones. Three statistical procedures were employed to summarize the variability within and between the two zones. The results indicated that linear combinations of those variables reflecting sulfide oxidation and aluminum-silicate weathering best summarized the variability in each zone, and that the zones were most different on the basis of sulfide oxidation variables. The geochemical computer code WATEQ4F was used to assess the solubility status (saturation index) of minerals. Saturation indices of sulfide oxidation and aluminum-silicate weathering minerals were different in the two zones. It was demonstrated that the statistical analyses produced similar and complementary results to the geochemical code.

Jan 1, 1992

By J. F. MacGregor, M. Hou, D. Hodouin

"RésuméDe nouvelles méthodes efficaces sont maintenant devenues nécessaires pour traiter les quantités massives de données en temps-réel que collectent les ordinateurs industriels modemes. Les méthodes statistiques multi variables comme l'analyse en composantes principales et la projection sur des structures latentes sont des méthodes analytiques bien adaptées aux données industrielles bruitées et mal conditionnées. L'efficacité de ces méthodes est illustrée sur des données historiques collectées dans une usine de broyage et de flottation. Trois cent cinquante observations de quarante quatre variables de procède ont été utilisées pour démontrer les aptitudes de ces méthodes pour l'analyse préliminaire de données, la classification des régimes opératoires, le contrôle de qualité et la modélisation empirique des precedes.AbstractBecause of the availability of powerful industrial computers which collect huge amounts of real-time data in mineral processing plants, there is a need for efficient methods to extract relevant information from them. Multivariate statistical techniques, such as principal components analysis (PCA) and projection to latent structures (PLS), are well suited to analyze these large sets of noisy and ill-conditioned data. The power of PCA and PLS is illustrated on historical data from a grinding and flotation plant. Three hundred and fifty observations of forty-four process variables are used to show the capacity of these techniques for preliminary data analysis, classification of operating regimes, process monitoring, and process empirical modelling."

Jan 1, 1993

By Knut Conradsen

In the study 208 heavy mineral concentrates (pan samples) from Jameson Land, East Greenland, are considered. Each concentrate has been analysed (by spectroscopy) for the content of (approx.) 25 elements. Furthermore the exact sampling position and the geological characteristics of the environment have been registered. In the study is shown how different multivariate methods combined with geological knowledge of the area can be used in the interpretation and classification of the data. Special emphasis is put on the problem of finding reliable expressions for the background level of the element concentrations in the area. This is done by means of severel discrimination procedures. The other main subject is a demonstration of the applicability of isoscore maps - originating from factor analyses - in the evaluation of the co-variability of the data, and thus give another way of classifying the individual samples according to the content of different elements.

Jan 1, 1977

By Augusto Andres Torres Toledo, João Felipe Coimbra Leite Costa, Luciano Nunes Capponi, Diego Machado Marques

Short-term mine planning to open pit requires defining diglines to orientate the excavation geometry. In deposits with multiple chemical variables, it is necessary to have more rigorous control over the feeding of the processing plant. This study analyzes the impact of incorporating multiple chemical variables, the risks generated by geological uncertainty, and the number and starting point locations of shovels in the sequential design of diglines. The objective is to maintain and preserve the low-grade variability, required tonnage, and continuity in sequentially selecting blocks. To achieve this, the probability distribution function of each chemical variable is used while attempting to maintain the ore grades as constant as possible. As it is difficult to maintain multiple elements with low variability simultaneously, the relevance of each chemical variable in the economic benefit is identified. Weights are assigned to signal the importance of each element based on its significance in the recovery process. Several diglines, consisting of sequential blocks, were generated on the same seed point to meet the weekly ore demand. Optimizing the stationarity of multiple chemical variables, accessing and reducing the geological uncertainty performed through geostatistical simulation of grades and transfers functions, considering the number and location of shovels, while meeting the operational restrictions of the selected blocks. The optimized digline with the multiple grades as stationary as possible is retained. The process is illustrated in a phosphate mine. The results show that the proposed method is viable and allows for a quick solution.

Jun 25, 2023

By C. Leal

Modern production has as goal to reach high and uniform quality in their products. To success with this, it is essential to have a good knowledge of the different variables involved in the process. Investigation or analysis of a process or system has as references the measurements of the variables. These measurements are presented normally in form of data. These data are measured in intervals over time. The aim with measurement of the data in a process is to obtain information about the state of it in order to have it under control. Other goal is to know how the results are affected by the process variables to improve upon product quality, redunding manufacturing cost, better pollution control etc.

Jan 1, 1994

By Samir Kumar Pal, Rajasekar Rathanasamy, Gobinath Velu Kaliyannan, Moganapriya Chinnasamy, Sathish Kumar Palaniappan

The research examines the performance of uncoated and coated tungsten carbide-cobalt rock cutting bits. It aims to optimize process variables (cutting speed, depth, coating material) considering multiple output responses (cutting forces, specific energy, wear rate, material removed, angle of reaction forces). The study uses a hybrid optimization technique combining Taguchi design, grey relational analysis, and fuzzy logic. The optimal parameter combination was found to be cutting speed: 200 mm/s, cutting depth: 6 mm, and titanium aluminum silicon nitride coating.

Apr 24, 2022

By Pia-Maria Haselberger, Marc Schiemann, Christian Frühling, Nicolas Richter, Hendrik Wehner, Andreas Kaschube

"The paper provides the principle considerations for a novel vehicle class within the scope of the project Large Modifiable Underwater Mothership (MUM). The main idea for these ships is to create a highly modular building block system for the global layout. This building block system allows for a mission-dependent module assembly. For the purpose of deep sea mining for example, the range of tasks reaches from multipurpose transportation and exploration missions to supporting tasks in up to 5000 m depth, e.g. energy supply. Topics covered in this paper are related to potential missions for these vehicles, the modular layout and the structural layout of a separate block module. The paper closes with a conceptual design example for this class.Index Terms—MUM, UUV, underwater mother ship, autonomous underwater vehicle, modular, deep sea, conceptual designI. INTRODUCTIONAs one of the leading economic nations, Germany is in need of energy and raw materials. In the 21st century, marine resources are a prominent and promising alternative to land based resources. However, there are challenges that need to be considered. Rough and often poorly plannable weather conditions prevail distant to the marginal seas. Ice coverage makes offshore services inefficient and costly in Polar Regions. The average ocean depth of 3500m and the associated environment conditions cause difficulties in fulfilling tasks in the deep sea. The project Large Modifiable Underwater Mothership (MUM) [1] will enable more efficient solutions in order to accomplish undersea duties and services in harsh conditions.This joint project comprises workshares from Atlas Elektronik, EvoLogics, thyssenkrupp Marine Systems, the University of Rostock and the Technische Universität Berlin. The principle idea of the project is the conception of a novel vehicle class. With highly modular autonomous underwater vehicles, this class will be capable of undertaking a variety of different tasks. Classically engineered vehicle structures will be split into single basis modules which can be flexibly assembled with specialized mission modules to form potent systems for individual assignments. The group of basis modules consists of units for navigation, vehicle control, propulsion and energy generation via fuel cell technology. The potential reusability of system relevant modules leads to a significant cost reduction and to shortened development periods compared with conventional vehicle concepts. The integration of newly designed additional mission modules is possible with little effort and a separate commercialization of single modules is feasible."

Jan 1, 2017

By Frank Lucca

This paper includes research and investigation into blast design and blast optimization for vibration control in municipal and tight blasting situations, where specifications were extremely stringent. The paper is written for the field blaster to understand and develop blast plans based on field conditions. The paper includes blast design considerations, utilizing seismograph arrays to check and predict vibration results, and problems encountered in vibration monitoring in extremely tight situations (0-20 feet). Blast vibration frequency, acceleration, peak particle velocities, and relative displacement are discussed with effects in the near and far fields and blast designs utilized to stay under limits. The paper also discusses using the latest in technology for blast design to control vibration. Equipment includes 2D and 3D laser profiling systems, digital video, fragmentation analysis, seismograph arrays, and borehole tracking devices. Other topics are discussed such as public relations, working with regulatory personnel, unions, and other project consultants, and the problems associated with municipal blasting situations, such as, flyrock and proximity of other personnel and equipment on the project.

Jan 1, 2004