Quantification of uncertainty of geometallurgical variables for mine planning optimisation

Interest in geometallurgy has increased significantly over the past 15 years or so because of the benefits it brings to mine planning and operation. Its use and integration into design, planning and operation is becoming increasingly critical especially in the context of declining ore grades and increasing mining and processing costs. This thesis, comprising four papers, offers methodologies and methods to quantify geometallurgical uncertainty and enrich the block model with geometallurgical variables, which contribute to improved optimisation of mining operations. This enhanced block model is termed a geometallurgical block model. Bootstrapped non-linear regression models by projection pursuit were built to predict grindability indices and recovery, and quantify model uncertainty. These models are useful for populating the geometallurgical block model with response attributes. New multi-objective optimisation formulations for block caving mining were formulated and solved by a meta-heuristics solver focussing on maximising the project revenue and, at the same time, minimising several risk measures. A novel clustering method, which is able to use both continuous and categorical attributes and incorporate expert knowledge, was also developed for geometallurgical domaining which characterises the deposit according to its metallurgical response. The concept of geometallurgical dilution was formulated and used for optimising production scheduling in an open-pit case study.Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Civil, Environmental and Mining Engineering, 201

Méthode heuristique d’optimisation stochastique de la planification minière et positionnement des résidus miniers dans la fosse

RÉSUMÉ : La planification minière à long terme est essentielle afin d’estimer la viabilité d’un projet, d’obtenir les investissements nécessaires et d’optimiser les ressources disponibles. La recherche opérationnelle est en mesure de répondre efficacement à ce problème, plusieurs modèles mathématiques de programmation linéaire mixte ont été développés. La principale source d’incertitude, encore très peu considérée conventionnellement, est géologique. Pour la prendre en compte, des simulations conditionnelles, représentations équiprobables du gisement, peuvent être utilisées comme données d’entrée à un modèle stochastique en nombres entiers. Ainsi, l’objectif est de maximiser la valeur présente nette moyenne tout en proposant un ordonnancement de la production robuste à l’incertitude. En ajoutant un nombre conséquent de blocs, plusieurs périodes et destinations ainsi que de nombreuses contraintes opérationnelles, les modèles deviennent trop complexes à résoudre de manière exacte avec un solveur. Des méthodes heuristiques doivent alors être envisagées pour obtenir la meilleure solution possible en un temps réduit. Le travail exposé dans ce mémoire est composé de deux parties correspondant à deux différents articles. La première partie présente la résolution d’un modèle stochastique d’optimisation d’une mine à ciel ouvert à l’aide d’une nouvelle méthode heuristique. Sont tout d’abord proposées deux méthodes d’accélération : une relaxation partielle de la binarité des variables d’extraction en utilisant la structure particulière du modèle et les fortes relations entre variables et une convergence du modèle relaxé vers une solution quasi-binaire. Ensuite, un algorithme de tri topologique stochastique est proposé afin d’obtenir rapidement une solution complètement binaire à partir des résultats issus des stratégies d’accélération précédentes. Les résultats obtenus, testés sur un cas réel, sont concluants par leur rapidité et gap par rapport à la solution optimale. La deuxième partie modélise le stockage des résidus miniers et stériles au sein de la fosse au fur et à mesure de l’exploitation. Cette idée, souhaitée par le partenaire industriel lors de l’étude de faisabilité, permet de s’affranchir d’un espace de stockage limité autour de la fosse, de réduire l’impact environnemental de l’exploitation et de diminuer les coûts de remaniement lors de la réhabilitation finale du site. Cette fois, une méthode heuristique de fenêtre de temps sur un horizon fuyant a été utilisée pour résoudre le modèle. Les résultats sont prometteurs puisque l’impact de la disposition de matériel dans la fosse lors de l’exploitation ne dégrade la solution initiale que de 1.77%.----------ABSTRACT : Long-term mine planning is an essential step in order to estimate the viability of a project, to attract investments and to optimize available resources. Operations research is well suited to assess this kind of problem, several mixed integer programming models have been developed over the last decades. Even if still not conventionally considered, the geology is the main source of uncertainty in such a model. To consider it properly, a set of equiprobable conditional simulations of the deposit are used as input in a stochastic integer programming model. The objective is then to maximize the expected net present value while having a robust production schedule to the geological uncertainty. When many blocks are considered but also several destinations and operational constraints, the problem becomes too complex to solve by a general purpose solver. If an exact method is not conceivable, heuristic methods must be used to obtain the best solution as possible in a limited time. The study presented in the thesis is composed of two parts corresponding to two articles. The first one presents a new heuristic method to solve a stochastic open pit mine production scheduling problem. First, two acceleration strategies are proposed: a partial relaxation of the binarity of the extraction variables using the special structure of the model and the strong inter-correlations of the variables; a convergence of the fully relaxed model toward a quasi-binary solution. Then, a stochastic topological sorting algorithm is proposed to quickly obtain a binary solution from the result of the previous acceleration strategies. Applied on a real case study, the results are interesting for their rapidity and their gap to the optimality. The second part establishes a model to store tailings and waste materials directly inside the pit during the operations. This idea was raised in the feasibility of the industrial partner to overpass a limited space for eternal stockpiles, to reduce the environmental impact and the re-handling costs of the rehabilitation phase. This time, to solve the problem, a sliding window time heuristic method was used and the results are promising: the Cplex objective function is only 1.77% lower while considering the in-pit storage and the heuristic method than the initial model solved with an exact method

Advances in Computational Intelligence Applications in the Mining Industry

This book captures advancements in the applications of computational intelligence (artificial intelligence, machine learning, etc.) to problems in the mineral and mining industries. The papers present the state of the art in four broad categories: mine operations, mine planning, mine safety, and advances in the sciences, primarily in image processing applications. Authors in the book include both researchers and industry practitioners

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Mine evaluation optimisation

The definition of a mineral resource during exploration is a fundamental part of lease evaluation, which establishes the fair market value of the entire asset being explored in the open market. Since exact prediction of grades between sampled points is not currently possible by conventional methods, an exact agreement between predicted and actual grades will nearly always contain some error. These errors affect the evaluation of resources so impacting on characterisation of risks, financial projections and decisions about whether it is necessary to carry on with the further phases or not. The knowledge about minerals below the surface, even when it is based upon extensive geophysical analysis and drilling, is often too fragmentary to indicate with assurance where to drill, how deep to drill and what can be expected. Thus, the exploration team knows only the density of the rock and the grade along the core. The purpose of this study is to improve the process of resource evaluation in the exploration stage by increasing prediction accuracy and making an alternative assessment about the spatial characteristics of gold mineralisation. There is significant industrial interest in finding alternatives which may speed up the drilling phase, identify anomalies, worthwhile targets and help in establishing fair market value. Recent developments in nonconvex optimisation and high-dimensional statistics have led to the idea that some engineering problems such as predicting gold variability at the exploration stage can be solved with the application of clusterwise linear and penalised maximum likelihood regression techniques. This thesis attempts to solve the distribution of the mineralisation in the underlying geology using clusterwise linear regression and convex Least Absolute Shrinkage and Selection Operator (LASSO) techniques. The two presented optimisation techniques compute predictive solutions within a domain using physical data provided directly from drillholes. The decision-support techniques attempt a useful compromise between the traditional and recently introduced methods in optimisation and regression analysis that are developed to improve exploration targeting and to predict the gold occurrences at previously unsampled locations.Doctor of Philosoph

On the Combination of Game-Theoretic Learning and Multi Model Adaptive Filters

This paper casts coordination of a team of robots within the framework of game theoretic learning algorithms. In particular a novel variant of fictitious play is proposed, by considering multi-model adaptive filters as a method to estimate other players’ strategies. The proposed algorithm can be used as a coordination mechanism between players when they should take decisions under uncertainty. Each player chooses an action after taking into account the actions of the other players and also the uncertainty. Uncertainty can occur either in terms of noisy observations or various types of other players. In addition, in contrast to other game-theoretic and heuristic algorithms for distributed optimisation, it is not necessary to find the optimal parameters a priori. Various parameter values can be used initially as inputs to different models. Therefore, the resulting decisions will be aggregate results of all the parameter values. Simulations are used to test the performance of the proposed methodology against other game-theoretic learning algorithms.</p

Technology and Management for Sustainable Buildings and Infrastructures

A total of 30 articles have been published in this special issue, and it consists of 27 research papers, 2 technical notes, and 1 review paper. A total of 104 authors from 9 countries including Korea, Spain, Taiwan, USA, Finland, China, Slovenia, the Netherlands, and Germany participated in writing and submitting very excellent papers that were finally published after the review process had been conducted according to very strict standards. Among the published papers, 13 papers directly addressed words such as sustainable, life cycle assessment (LCA) and CO2, and 17 papers indirectly dealt with energy and CO2 reduction effects. Among the published papers, there are 6 papers dealing with construction technology, but a majority, 24 papers deal with management techniques. The authors of the published papers used various analysis techniques to obtain the suggested solutions for each topic. Listed by key techniques, various techniques such as Analytic Hierarchy Process (AHP), the Taguchi method, machine learning including Artificial Neural Networks (ANNs), Life Cycle Assessment (LCA), regression analysis, Strength–Weakness–Opportunity–Threat (SWOT), system dynamics, simulation and modeling, Building Information Model (BIM) with schedule, and graph and data analysis after experiments and observations are identified