phd thesis complete

University of Nottingham School of Chemical, Environmental, and Mining Engineering APPLICATION OF ARTIFICIAL NEURAL NETWORK SYSTEMS TO GRADE ESTIMATION FROM EXPLORATION DATA by Ioannis K. Kapageridis M.Sc. Thesis submitted to the University of Nottingham for the Degree of Doctor of Philosophy October 1999 Abstract i Abstract Artificial Neural Networks (ANN) become increasingly popular within the resources industry. ANN technology provides solutions to problems characterised by shortage or bad quality of input data. It is a purpose of this research work to show that estimation of ore grades within a mineral deposit is one of these problems where ANNs can be applied successfully. Ore grade is one of the main variables that characterise an orebody. Almost every mining project begins with the determination of ore grade distribution in three- dimensional space, a problem often reduced to modelling the spatial variability of ore grade values. At the early stages of a mining project, the distribution of ore grades has to be determined to enable the calculation of ore reserves within the deposit and to aid the planning of mining operations throughout the entire life of a mine. The estimation of ore grades/reserves is a very important and money-consuming stage in a mine project. The profitability of the project is often depending on the results of grade estimation. For the last three decades the mining industry has adopted and applied geostatistics as the main solution to problems of evaluation of mineral deposits. Geostatistics provide powerful tools for modelling most of the aspects of an ore deposit. However, geostatistics and other more conventional methods require a lot of assumptions, knowledge, skills and time to be effectively applied while their results are not always easy to justify. The work that has been undertaken in the AIMS Research Unit at the University of Nottingham aimed at assessing the suitability of ANN systems for the problem of ore grade estimation and the development of a complete ANN based Abstract ii system that will handle real exploration data in order to provide ore grade estimates. GEMNET II is a modular neural network system designed and developed by the Author to receive 3D exploration data from an orebody and perform ore grade estimation on a block model basis. The aims of the system are to provide a valid alternative to conventional grade estimation techniques while reducing considerably the time and knowledge required for development and application. Abstract iii Affirmation The following papers have been published based on the research presented in this thesis: Kapageridis I., Denby B. Ore grade estimation with modular neural network systems – a case study. In: Panagiotou G (ed) Information technology in the minerals industry (MineIT ’97). AA Balkema, Rotterdam, 1998. Kapageridis I., Denby B. Neural network modelling of ore grade spatial variability. In: Proceedings of the International Conference for Artificial Neural Networks (ICANN 98), Vol. 1, pp 209 – 214, Springer-Verlag, Skovde, 1998. Kapageridis I., Denby B., and Hunter G. Integration of a Neural Ore Grade Estimation Tool In a 3D Resource Modeling Package. In: Proceedings of the International Joint Conference on Neural Networks (IJCNN ’99), International Neural Network Society, and The Neural Networks Council of IEEE, Washington D.C., 1999. Kapageridis I., Denby B., Schofield, D., and Hunter G. GEMNET II – A Neural Ore Grade Estimation System. In: 29 th Internation Symposium on the Application of Computers and Operations Research in the Minerals Industries (APCOM ’99), Denver, Colorado. Kapageridis I, Denby B., and Hunter G. Ore Grade Estimation and Artificial Neural Networks. Mineral Wealth Journal, Jul. – Sep. 99, No. 112, The Scientific Society of the Mineral Wealth Technologists, Athens. Kapageridis I., Denby B. Ore Grade Estimation Using Artificial Neural Networks. In: 2 nd Regional VULCAN Conference, Maptek/KRJA Systems, Nice, 1999. Abstract iv Acknowledgements I would like to thank Professor Bryan Denby for his guidance and help through the duration of my studies at the University of Nottingham. I would also like to thank him for introducing me to the exciting world of the AIMS Research Unit. Thanks should go to everyone at the AIMS Research Unit, people who have been there and others who still are, and who made it all so much easier. Special thanks to Dr. Damian Schofield for being such a good friend and teacher, and also for sharing his music CD collection with me. A big thank you goes to the State Scholarships Foundation of Greece for making it all possible. Their investment in me was most appreciated. Many thanks to everyone at the Nottingham office of Maptek/KRJA Systems for the help and support over the last year of my studies. In particular, I would like to thank Dr. Graham Hunter, David Muller, and Les Neilson for their help and advice. Finally, I would like to thank all my friends and in particular David Newton, Marina Lisurenko, and Stefanos Gazeas for their support and for some unforgettable times in Nottingham. Contents v Contents ABSTRACT I AFFIRMATION III ACKNOWLEDGEMENTS IV CONTENTS V LIST OF FIGURES VIII LIST OF TABLES XIII 1. INTRODUCTION 1 1.1 THE PROBLEM OF GRADE ESTIMATION 1 1.2 GRADE DATA FROM EXPLORATION PROGRAMS 3 1.3 EXISTING METHODS FOR GRADE ESTIMATION 7 1.3.1 General 7 1.3.2 Geometrical Methods 7 1.3.3 Inverse Distance Method 10 1.3.4 Geostatistics 12 1.3.5 Conclusions 15 1.4 BLOCK MODELLING & GRID MODELLING IN GRADE ESTIMATION 16 1.5 ARTIFICIAL NEURAL NETWORKS FOR GRADE ESTIMATION 18 1.6 RESEARCH OBJECTIVES 19 1.7 THESIS OVERVIEW 20 2. ARTIFICIAL NEURAL NETWORKS THEORY 23 2.1 INTRODUCTION 23 2.1.1 Biological Background 23 2.1.2 Statistical Background 25 2.1.3 History 27 2.2 BASIC STRUCTURE – PRINCIPLES 29 2.2.1 The Artificial Neuron – the Processing Element 29 2.2.2 The Artificial Neural Network 31 2.3 LEARNING ALGORITHMS 33 2.3.1 Overview 33 2.3.2 Error Correction Learning 33 2.3.3 Memory Based Learning 35 2.3.4 Hebbian Learning 35 2.3.5 Competitive Learning 36 2.3.6 Boltzmann Learning 37 2.3.7 Self-Organized Learning 39 2.3.8 Reinforcement Learning 40 2.4 MAJOR TYPES OF ARTIFICIAL NEURAL NETWORKS 40 2.4.1 Feedforward Networks 40 2.4.2 Recurrent Networks 42 2.4.3 Self-Organizing Networks 43 2.4.4 Radial Basis Function Networks and Time Delay Neural Networks 44 2.4.5 Fuzzy Neural Networks 46 2.5 CONCLUSIONS 48 3. RADIAL BASIS FUNCTION NETWORKS 23 3.1 INTRODUCTION 23 3.2 RADIAL BASIS FUNCTION NETWORKS – THEORETICAL FOUNDATIONS 24 3.2.1 Overview 24 3.2.2 Multivariable Interpolation 24 Contents vi 3.2.3 The Hyper-Surface Reconstruction Problem 26 3.2.4 Regularisation 28 3.3 RADIAL BASIS FUNCTION NETWORKS 31 3.3.1 General 31 3.3.2 RBF Structure 31 3.3.3 RBF Initialisation and Learning 32 3.4 FUNCTION APPROXIMATION WITH RBFNS 39 3.4.1 General 39 3.4.2 Universal Approximation 39 3.4.3 Input Dimensionality 40 3.4.4 Comparison of RBFNs and Multi-Layer Perceptrons 41 3.5 SUITABILITY OF RBFNS FOR GRADE ESTIMATION 42 4. MINING APPLICATIONS OF ARTIFICIAL NEURAL NETWORKS 71 4.1 OVERVIEW 71 4.2 ANN SYSTEMS FOR EXPLORATION AND RESOURCE ESTIMATION 72 4.2.1 General 72 4.2.2 Sample Location Based Systems 73 POPULATIONS 79 4.2.3 Sample Neighborhood Based Systems 80 4.2.4 Conclusions 85 4.3 ANN SYSTEMS FOR OTHER MINING APPLICATIONS 86 4.3.1 Overview 86 4.3.2 Geophysics 86 4.3.3 Rock Engineering 89 4.3.4 Mineral Processing 89 4.3.5 Remote Sensing 91 4.3.6 Process Control-Optimisation and Equipment Selection 93 4.4 CONCLUSIONS 94 5. DEVELOPMENT OF A MODULAR NEURAL NETWORK SYSTEM FOR GRADE ESTIMATION 96 5.1 INTRODUCTION 96 5.2 FORMING THE INPUT SPACE FROM 2D SAMPLES 98 5.3 DEVELOPMENT OF THE NEURAL NETWORK TOPOLOGIES 106 5.3.1 Overview 106 5.3.2 The Hidden Layer 107 5.3.3 Final Weights and Output 110 5.4 LEARNING FROM 2D SAMPLES 111 5.4.1 Overview 111 5.4.2 Module 1 – Learning from Octants 112 5.4.3 Module 2 – Learning from Quadrants 115 5.4.4 Module 3 – Learning from Sample 2D Co-ordinates 117 5.5 TRANSITION FROM 2D TO 3D DATA 120 5.5.1 General 120 5.5.2 Input Space: Adding the Third Co-ordinate 121 5.5.3 Input Space: Adding the Sample Volume 122 5.5.4 Search Method: Expanding to Three Dimensions 123 5.6 COMPLETE PROTOTYPE OF THE MNNS 126 5.7 CONCLUSIONS 129 6. CASE STUDIES OF THE PROTOTYPE MODULAR NEURAL NETWORK SYSTEM 131 6.1 OVERVIEW 131 6.2 CASE STUDY 1 – 2D IRON ORE DEPOSIT 133 6.3 CASE STUDY 2 – 2D COPPER DEPOSIT 136 6.4 CASE STUDY 3 – 3D GOLD DEPOSIT 140 6.5 CASE STUDY 4 – 3D CHROMITE DEPOSIT 146 6.6 CONCLUSIONS 149 7. GEMNET II – AN INTEGRATED SYSTEM FOR GRADE ESTIMATION 150 Contents vii 7.1 OVERVIEW 150 7.2 CORE ARCHITECTURE AND OPERATION 152 7.2.1 Exploration Data Processing and Control Module 152 7.2.2 Module Two – Modeling Grade’s Spatial Distribution 159 7.2.3 Module One – Modelling Grade’s Spatial Variability 162 7.2.4 Final Module – Providing a Single Grade Estimate 164 7.3 VALIDATION 167 7.3.1 Training and Validation Errors 167 7.3.2 Reliability Indicator 168 7.3.3 Module Index 170 7.3.4 RBF Centres Visualisation 171 7.4 INTEGRATION 172 7.4.1 Neural Network Simulator 172 7.4.2 Interface with VULCAN – 3D Visualization 176 7.5 CONCLUSIONS 182 8. GEMNET II APPLICATION – CASE STUDIES 185 8.1 OVERVIEW 185 8.2 CASE STUDY 1 – COPPER/GOLD DEPOSIT 1 188 8.3 CASE STUDY 2 – COPPER/GOLD DEPOSIT 2 197 8.4 CASE STUDY 3 – COPPER/GOLD DEPOSIT 3 209 8.5 CASE STUDY 4 – COPPER/GOLD DEPOSIT 4 220 8.6 CONCLUSIONS 226 9. CONCLUSIONS AND FURTHER RESEARCH 185 9.1 CONCLUSIONS 185 9.2 FURTHER RESEARCH 188 APPENDIX A – FILE STRUCTURES 239 A1. SNNS NETWORK DESCRIPTION FILE 239 A2. SNNS NETWORK PATTERN FILE 241 A3. BATCHMAN NETWORK DEVELOPMENT SCRIPT 242 A4. SNNS2C NETWORK C CODE EXTRACT 243 A5. VULCAN COMPOSITES FILE 247 APPENDIX B – CASE STUDY DATA 254 B1. CASE STUDY 1 – 2D IRON ORE DEPOSIT 254 B2. CASE STUDY 2 – 2D COPPER DEPOSIT 254 B3. CASE STUDY 3 – 3D GOLD DEPOSIT 246 B4. CASE STUDY 4 – 3D CHROME DEPOSIT 246 REFERENCES 253 Contents viii List of Figures Chapter 1 Figure 1.1: Drillholes from exploration programme and development, intersecting the orebody (coloured by gold assays – screenshot from VULCAN Envisage). 4 Figure 1.2: Compositing of drillhole samples using interval equal to sample length. 6 Figure 1.3: Polygonal method of ore grade estimation. 8 Figure 1.4: Triangular method of ore grade estimation. 9 Figure 1.5: Search ellipse used during selection of samples for ore grade estimation. 12 Figure 1.6: Frequency histogram (left) and variogram (right) of copper grades (percentages). 15 Figure 1.7: Grid modeling as visualised in an advanced 3D graphics environment. 17 Figure 1.8: Sections through a block model intersecting the orebody. 18 Chapter 2 Figure 2.1: Illustration of a typical neuron [13]. 25 Figure 2.2: Propagation of an action potential through a neuron’s axon [13]. 26 Figure 2.3: The five major models of computation as they were presented six decades ago [18]. 29 Figure 2.4: Structure of the processing element [32]. 30 Figure 2.5: Effect of bias on the input to the activation function (induced local field) [32]. 31 Figure 2.6: Common activation functions: (a) unipolar threshold, (b) bipolar threshold, (c) unipolar sigmoid, and (d) bipolar sigmoid [33]. 32 Figure 2.7: Basic structure of a layered ANN [32]. 33 Figure 2.8: Structure of the feedforward artificial neural network. There can be more than one middle or hidden layers [33]. 42 Figure 2.9: a) Recurrent network without self-feedback connections, b) recurrent network with self-feedback connections [32]. 44 Figure 2.10: Structure of a two-dimensional Self-Organising Map [32]. 45 Figure 2.11: Basic structure of the Radial Basis Function Network [33]. 46 Figure 2.12: The concept of Time Delay Neural Networks for speech recognition [40]. 47 Figure 2.13: An approach to FNN implementation [44]. 49 Contents ix Chapter 3 Figure 3.1: Regularisation network [32]. 58 Figure 3.2: Structure of generalised RBF network [32]. 61 Figure 3.3: Illustration of input space dissection performed by the RBF and MLP networks [69]. 70 Chapter 4 Figure 4.1: ANN for ore grade/reserve estimation by Wu and Zhou [73]. 77 Figure 4.2: General structure of the AMAN neural system. 80 Figure 4.3: Back-propagation network used in the NNRK hybrid system. 82 Figure 4.4: Drillhole data used for testing the performance of the NNRK system. 83 Figure 4.5: 2D approach of learning from neighbour samples arranged on a regular grid. 85 Figure 4.6: Modular network approach implemented in the GEMNet system [84]. 86 Figure 4.7: Scatter diagram of GEMNet estimates on a copper deposit [84]. 87 Figure 4.8: Contour maps of GEMNet reliability indicator and grade estimates of a copper deposit [84]. 88 Figure 4.9: Back-propagation network used for lateral log inversion [86]. Connections between layers are not shown. 91 Figure 4.10: Estimated grades and assays (red and blue) vs. actual (black) (89). 92 Chapter 5 Figure 5.1: Illustration of quadrant and octant search method (special case where only one sample is allowed per sector). Respective grid nodes are also shown. 104 Figure 5.2: Estimation results from neural network architecture developed for use with gridded data. The use of irregular data has an obvious effect in the performance of the system. 105 Figure 5.3: Neural network architectures receiving inputs from a quadrant search (left) and from an octant search (right). 106 Figure 5.4: Improvement in estimation by the introduction of the neighbour sample distance in the input vector. 108 Figure 5.5: Modular neural network architecture developed for ore grade estimation from 2D samples [113]. 110 Figure 5.6: Partitioning of the original dataset into three parts each one targeted at a different module of the MNNS. 115 Figure 5.7: RBF network used as part of module 1 in MNNS. Training patterns from an octant search were used to train the network. 117 Figure 5.8: Posting of the basis function centres from the RBF network of Fig. 5.7 in the normalised input space (X-Grade, Y-Distance). 118 Figure 5.9: Graph showing the learned relationship between the network’s inputs (grade and [...]... ANNs and specifically the chosen type of ANNs can provide, as this thesis will try to prove, a valid methodology for grade estimation 1.6 Research Objectives Disregarding of the existing methodologies for grade estimation is definitely not one of the aims of this thesis The GEMNet II system described was developed to provide a flexible but complete alternative method, which takes into consideration the... Introduction • To compare the performance of the system with existing grade estimation techniques on the basis of estimation properties, usability and time requirements 1.7 Thesis Overview Given below is a description of the chapters included in this thesis: • Chapter 2 - Artificial Neural Networks Theory Gives a brief discussion on the theory behind ANNs, the main ANN architectures and their main application... to the difficult point of not being able to fit new data coming from the mine to their model There are too many examples of successful application of geostatistics and other existing methods for one to completely disregard them Specifically in the case of geostatistics, this success cannot be credited to luck because as will be discussed later, it is a very painful and time consuming process that leaves... samples in the database and the compositing procedure is reduced to a reconstruction of the database into a single file containing all the information This type of compositing will be used throughout this thesis in order to provide the input data files for the various case studies 5 Introduction Figure 1.2: Compositing of drillhole samples using interval equal to sample length A typical composites file... areas are easy to calculate from the co-ordinates of the three points This method can be applied to the same cases as the polygonal method The last of the three geometrical methods to be mentioned in this thesis, the method of sections, is the most manual one and requires a lot of time and patience The areas of influence of the drillhole samples expand half way to adjacent sections and to adjacent drillholes... the distance between its nodes in both directions, and its dimension in these directions, i.e the number of nodes This structure dramatically reduces the amount of information necessary to represent a complete model of the deposit and has the additional advantage of allowing easy manipulation of the various parameters included by performing simple calculations between the grids Grid modeling is best... gold deposit study 147 Figure 6.10: Scatter diagram of actual vs estimated gold grades 148 Figure 6.11: Gold grade distributions – actual and estimated 149 Figure 6.12: Gold grades distribution of the complete dataset 150 Figure 6.13: Drillholes from a 3D chromite deposit 151 Figure 6.14: Scatter diagram of actual vs estimated chromite grades 153 Figure 6.15: Chromite grade distributions – actual and... minority of the scientists and engineers who are asked to provide with grade estimates based on which large amounts of investment money will be spent In most of the cases people misuse geostatistics or completely avoid them even though they could benefit from their use Many geologists build their own picture of the orebody in their minds using their experience and even their instincts They ‘develop’ . ESTIMATION FROM EXPLORATION DATA by Ioannis K. Kapageridis M.Sc. Thesis submitted to the University of Nottingham for the Degree of Doctor of Philosophy October. the suitability of ANN systems for the problem of ore grade estimation and the development of a complete ANN based Abstract ii system that will handle real exploration data in order to provide. iii Affirmation The following papers have been published based on the research presented in this thesis: Kapageridis I., Denby B. Ore grade estimation with modular neural network systems –