Roadheader performance prediction using Machine Learning Methods  

Case Study: San Manuel Mine, Arizona 
 

 

 

by 

Askar Omirzak 

 

 

 

THESIS SUPERVISOR 

Saffet Yagiz 

 

  

 

 

 

 

Thesis submitted to the School of Mining and Geosciences of Nazarbayev University in 
Partial Fulfillment of the Requirements for the Degree of  

Bachelor of Science in Mining Engineering 
 
 
 
 

Nazarbayev University 
May 2025 

  



 

ORIGINALITY STATEMENT 

I, Askar Omirzak, hereby declare that this submission is my own work and to the best of my 

knowledge it contains no materials previously published or written by another person, or 

substantial proportions of material which have been accepted for the award of any other degree 

or diploma at Nazarbayev University or any other educational institution, except where due 

acknowledgement is made in the thesis. 

Any contribution made to the research by others, with whom I have worked at NU or elsewhere 

is explicitly acknowledged in the thesis. 

I also declare that the intellectual content of this thesis is the product of my own work, except 

to the extent that assistance from others in the project's design and conception or in style, 

presentation and linguistic expression is acknowledged. 

 

Signed on 03. 05. 2025 

 
_______________________________________
 



 
 

 i 

ABSTRACT 

This thesis is dedicated to the development and evaluation of predictive models for the 

performance of roadheader machines (ICR) using machine learning algorithms under 

conditions of limited data. The scarcity of available datasets is primarily due to high collection 

costs, issues of commercial confidentiality, and heterogeneous geological conditions, which 

significantly complicates the application of traditional prediction models. To address this 

challenge, the study employs data synthesis techniques that expand the training set by 

generating artificial observations through the addition of Gaussian noise, as well as alternative 

approaches based on Ridge Regression and Random Forest methods. A comparative analysis 

of various models is conducted, including linear methods (Ridge, Lasso, ElasticNet), ensemble 

algorithms (Random Forest, Gradient Boosting, Extra Trees), and nonlinear approaches (SVR, 

MLP). The results demonstrate that ensemble methods achieve the highest prediction accuracy, 

as evidenced by high R² values and low MSE values, even when using synthetically expanded 

datasets. However, while data synthesis improves model performance, it does not fully replace 

real-world observations, necessitating further validation of the developed models under 

practical conditions. The findings hold practical significance for optimizing planning processes 

and economic evaluations in the mining and construction industries, and they point to the 

promising prospects of integrating data synthesis techniques with real-time monitoring systems 

to enhance the robustness and interpretability of predictive models. 

  



 

 ii 

 

ACKNOWLEDGMENT  

 

I want to express my sincerest gratitude to my thesis supervisor, Professor Saffet Yagiz, for 

his invaluable guidance and support through this research. His expertise, encouragement, and 

constant feedback have been instrumental in shaping my work. 

 

Also, I would like to thank my friends for their support and mentorship, especially – Ulan 

Sharipov, a person who giuded me through the world of Machine Learning.  

 

Special thanks to Abylai Salimzhanov, Sultan Turan, Adel Kolesnikov, Alibek Abilgazym, 

Abylai Kubeyev, Yersultan Tursyn, Zhandos Dauletov, Arsen Kenzhebekov, and many others 

who was with me during my time at Pochinki and School 

 

Also, Faculty Development Competitive Research Grant program of Nazarbayev University 

(Grant Number 201223FD8837) for funding this research is acknowledged. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   



 

 iii 

TABLE OF CONTENTS 

ABSTRACT i 
TABLE OF CONTENTS iii 
LIST OF FIGURES iv 
LIST OF TABLES vi 
1. INTRODUCTION 1 

1.1 Background 1 
1.2 Objectives of the Thesis 10 
1.3 Justification of the Research 10 
1.4 Scope of Work 11 

2. LITERATURE REVIEW 12 
2.1. Introduction to the topic and Relevance of the study 12 
2.1.1 Problem statement: "small data" and complex geology 12 
2.1.2 Purpose and objectives of the literature review 13 
2.2 Key Parameters Affecting the Performance of Roadheader Machines 14 
2.3 Machine learning and its implementation in the mining industry 15 
2.4 Analysis of existing studies on ICR prediction for roadheaders 17 
2.5. Critical analysis and identified gaps 22 
2.6. Future research directions 24 
2.7. Literature Review Summary 26 

3. CASE STUDY – SAN MANUEL MINE 27 
4. METHODOLOGY 31 

4.1 Data collection and description 31 
4.2 Data Preprocessing and Feature Generation 31 
4.3 Synthetic Data Generation 32 
4.4 Cross-validation and evaluation metrics 38 

5. DATA ANALYSIS 40 
5.2 Model training and evaluation 45 
5.3 Performance Comparison 64 

6. DISCUSSION 69 
7. CONCLUSIONS AND RECOMMENDATIONS 71 
REFERENCES 72 
APPENDICES 76 
 
  



 

 iv 

LIST OF FIGURES 

Figure 1: Comparison of Roadheader Machine Excavation with Drilling and Blasting in a 

Mining Environment (Krzystof &Piotr, 2019). 

Figure 2: Transverse Roadheader and Axial roadheaders. 

Figure 3: Geologic Map of San Manuel area (Schwartz, 1953) 

Figure 4: RMR table and Machine Performance Graph 

Figure 5: Visualization for Random Forest Regressor Labeling.  

Figure 6: Correlation Heatmaps of the Original Data. (Figure A - Heatmap of the Base 

Features, B - Polynomial Features) 

Figure 7: Histograms of Standardized Original Data Distributions (Histogram A - UCS, B - 

RQD, C - RMR value).  

Figure 8: Base Features Correlation Heatmaps of the Synthetic Data. (Figure A – Ridge,  B - 

Gaussian, C - Random Forest).  

Figure 9: Polynomial Features Correlation Heatmaps of the Synthetic Data. (Figure A – Ridge, 

B - Gaussian, C - Random Forest)  

Figure 10: Synthetic Data Distribution for Ridge Regression Labeling (Figure A - RQD, B - 

RMR, C - UCS). 

Figure 11: Synthetic Data Distribution for Gaussian Noise Labeling (Figure A - RQD, B - 

RMR, C - UCS). 

Figure 12: Synthetic Data Distribution for Random Forest Regression Labeling (Figure A - 

RQD , B - RMR, C - UCS). 

Figure 13: ICR plots for Linear Models trained on Ridge Regression Labeling data (Scatterplot 

A - Ridge regression, B - Lasso, C - ElasticNet). 

Figure 14: ICR plots for Ensemble Models trained on Ridge Regression Labeling data 

(Scatterplot A - Random Forest, B - Gradient Boosting, C - ExtraTrees). 

Figure 15: ICR plots for Non-Linear Models trained on Ridge Regression Labeling data 

(Scatterplot A - MLP, B - SVR). 

Figure 16: ICR plot for Base Model trained on Ridge Regression Labeling data(ZeroR). 

Figure 17: ICR plots for Linear Models trained on Gaussian Noise Labeling method 

(Scatterplot A - Ridge regression, B - Lasso, C - ElasticNet). 

Figure 18: ICR plots for Ensemble Models trained on Gaussian Noise Labeling method 

(Random Forest, Gradient Boosting, ExtraTrees). 



 

 v 

Figure 19: ICR plots for Non-Linear Models trained on Gaussian Noise Labeling data 

(Scatterplot A - MLP, B - SVR). 

Figure 20: ICR plot for Base Model trained on Ridge Regression Labeling data(ZeroR). 

Figure 21: ICR plots for Linear Models trained on Random Forest Regression Labeling data 

(Scatterplot A - Ridge Regression, B - Lasso, C - ElasticNet). 

Figure 22: ICR plots for Ensemble Models trained on Ridge Regression Labeling data 

(Scatterplot A - Random Forest, B - Gradient Boosting, C - ExtraTrees).  

Figure 23: ICR plots for Non-Linear Models trained on Random Forest Regression Labeling 

data (Scatterplot A - MLP, B - SVR). 

Figure 24: ICR plot for Base Model (ZeroR) trained on Random Forest Regression Labeling.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 



 

 vi 

LIST OF TABLES 

Table 1: General Comparison of Axial vs Transverse Roadheaders (Taylor & Francis Group, 

2014) 

Table 2: Atlas Copco – Eickhoff classification 

Table 3: Neil et. al classification 

Table 4: Dataset Utilized for Model Establishing 

Table 5: EDA summary for the Original Dataset 

Table 6: EDA summary for the Polynomial features of the Original Dataset 

Table 7: Example Outputs of Predicted ICR values 

Table 8: Performance Metrics – Ridge Regression Labeling 

Table 9: Performance Metrics – Gaussian Noise Labeling 

Table 10: Performance Metrics – Random Forest Regression Labeling 

Table 11: Ranking table for models trained on Ridge Regression Labeling data. 

Table 12: Ranking table for models trained on Gaussian Noise Labeling data. 

Table 13: Ranking table for models trained on Random Forest Regression Labeling data. 

 
 
 
 
 

 

 

 

 
 



 

 
 

1 

1. INTRODUCTION  

The mining industry is constantly evolving, adopting advanced technologies to improve 

efficiency, safety, and environmental sustainability. One of the key technological advances is 

the use of roadheader machines, versatile excavators equipped with a rotating cutting head that 

were originally developed for coal mining and are now widely used in various mining and 

tunneling projects due to their flexibility and accuracy. 

The implementation of machine learning methods in predicting the performance of roadheaders 

is complicated by the limitation of available datasets, which are often small in size and do not 

fully cover all relevant parameters. Therefore, this study focuses on small dataset methods, 

aiming to develop robust and accurate forecasting models that can operate effectively even with 

a limited amount of data. 

1.1 Background 

Roadheader machines are highly specialized equipment for the precise and efficient crushing 

of rock, soil and other geological formations. Unlike traditional methods that rely on drilling 

and blasting, these machines use mechanical cutting heads equipped with carbide picks that 

continuously crush the material. This technology has revolutionized the fields of underground 

mining, tunneling and civil engineering, offering a more controlled and safer alternative to 

traditional mining methods. 

The origins of roadheader machine technology date back to the mid-20th century Europe 

(Kogelmann & Schenck, 1982), when the need for mechanized excavation methods increased 

due to the limitations and dangers associated with conventional blasting methods. Roadheader 

machines were initially developed primarily for coal mines, where their excavation efficiency 

made them indispensable. Over time, improvements in machine design, the use of new materials 

and the development of automation have expanded the scope of application of roadheader 

machines, and today they are successfully used even in difficult geological conditions, 

including work in hard rocks. 

Modern roadheader machines are equipped with automated control systems and modern 

sensors, which allows optimizing the drilling process and significantly increasing operational 

safety. These improvements ensure stable operation of the equipment, help reduce production 

costs and improve the quality of mining operations. 



 

 
 

2 

Advantages Over Traditional Excavation Methods 

Traditional mining methods such as drilling and blasting present a number of operational 

challenges. Blasting generates significant vibration, noise and dust, which can have a negative 

impact on worker health and the surrounding rock mass. In addition, the unpredictability of 

blasting results in re-fracturing of the rock, which requires additional stabilization of the 

workings and increases the cost of transporting the material. 

In contrast, roadheader machines provide a more controlled and continuous mining process. 

The use of a mechanical cutting head allows the workings to be formed with high accuracy, 

which minimizes excess material removal and reduces the requirements for working 

stabilization. As described by Sandbak (1985) - the ability to cut rock without excessive 

vibration makes roadheaders especially valuable for tunneling projects in urban areas and 

geologically sensitive areas, where it is critical to minimize structural disturbance. Ozdemir 

(1997) highlighted another important advantage of roadheaders - their ability to operate in 

varying geological conditions with minimal downtime. Unlike blasting operations, which 

require scheduled delays for loading and detonation, roadheader machines allow continuous 

drilling, which helps to reduce project deadlines and increase overall productivity. The 

advanced automation technologies implemented in these machines include real-time 

monitoring and adaptive control systems, which allow for prompt adjustment of operating 

parameters depending on rock characteristics and equipment specifications. These innovations 

increase the efficiency of the cutting process and make roadheaders the preferred choice for 

underground operations where high precision and reliability are required. 

 

Figure 1: Comparison of Roadheader Machine Excavation with Drilling and Blasting in a Mining Environment 

(Krzystof &Piotr, 2019).  



 

 
 

3 

Roadheader Technical Components 

Roadheaders are complex machines that consist of several key components that provide 

efficient excavation, mobility, and material handling. The main systems include the cutting 

head mechanism, hydraulic and electrical systems, and advanced navigation and control 

systems. 

Cutting Head Mechanism 

The cutting head is the primary excavation tool in a roadheader machine, responsible for 

breaking up rock and soil using mechanical force. It consists of a rotating drum equipped with 

multiple tungsten carbide picks strategically positioned to maximize cutting efficiency. The 

cutting process is accomplished through a combination of rotary motion and forward thrust, 

allowing the machine to effectively penetrate rock masses and break up their structure. 

Roadheaders are equipped with two main types of cutting heads: transverse and axial 

(longitudinal). Transverse heads have a horizontally oriented drum, which makes them 

particularly effective in soft rock, where wide, uniform cuts facilitate faster excavation. In 

contrast, longitudinal heads with a vertically rotating drum provide deeper penetration and high 

efficiency in hard rock, concentrating the cutting force on a smaller contact area. The choice of 

cutting head orientation is determined by the geological conditions of the excavation site and 

the requirements of the specific project. 

The efficiency of a cutting head depends on several factors, including tooth geometry, material 

composition, and cutting force distribution. Proper tooth spacing is critical to optimizing rock 

fragmentation and preventing excess energy consumption. Research shows that improper tooth 

spacing can lead to uneven force distribution, accelerated tool wear, and reduced overall 

excavation efficiency. In addition, advances in materials science, such as the use of 

polycrystalline diamond coatings, have improved tool wear resistance and extended tool life. 

Modern developments in automation and real-time monitoring have further improved cutting 

head efficiency. Sensor-based systems are now able to analyze cutting force data in real time, 

allowing automatic adjustments to the cutting parameters to optimize the process. Furthermore, 

the integration of water jet cutting technologies has proven effective in reducing cutting 

resistance, minimizing dust, and reducing the risk of cutting failure. 

 



 

 
 

4 

Hydraulic and Electrical Systems 

The hydraulic and electrical systems of a roadheader machine play a critical role in its 

operational efficiency, providing the necessary power for excavation, maneuverability, and 

control. The hydraulic system is responsible for actuating the cutting head, controlling boom 

movement, and driving the machine’s crawler tracks. High-pressure hydraulic cylinders adjust 

the position of the cutting head, providing precise adjustments that improve excavation 

efficiency. The responsiveness of the hydraulic system directly affects cutting performance, 

especially in hard rock conditions where greater force is required to penetrate the rock mass. 

To optimize energy consumption, modern roadheader machines use variable displacement 

hydraulic pumps that dynamically adjust fluid flow based on cutting conditions. This allows 

hydraulic power to be used as efficiently as possible, reducing energy loss and extending the 

life of the machine. Additional advances in hydraulic drive design have improved machine 

stability, enabling the machine to maintain consistent cutting performance even in challenging 

geological conditions. 

The machine’s electrical system powers key components including the cutter head motor, 

integrated sensors and lighting. Programmable logic controllers (PLC) and advanced sensors 

are integrated into modern machine systems to improve accuracy and automate processes. 

Variable frequency drive systems dynamically change the cutter head speed, enabling the 

machine to adapt to changing rock conditions in real time. Remote monitoring capabilities 

provide continuous feedback on machine performance, facilitating predictive maintenance and 

reducing unplanned downtime. 

Navigation and control systems 

The integration of modern navigation and control systems has significantly improved the 

accuracy and efficiency of roadheader. Previously, traditional machines required skilled 

operators to manually adjust cutting parameters based on visual judgment and experience. 

However, modern machines are equipped with automated guidance systems that use 

geotechnical sensors, GPS, and laser scanning to improve cutting accuracy. 

Geotechnical sensors integrated into the machine continuously measure rock properties such as 

uniaxial compressive strength (UCS) and abrasiveness. These sensors provide real-time data, 

allowing adaptive control systems to dynamically adjust cutting force, speed, and tooth rotation. 



 

 
 

5 

The use of 3D mapping technologies further improves cutting accuracy by allowing operators 

to visualize the process and ensure compliance with tunnel or excavation design requirements. 

Remote control capabilities have also become an important feature of modern machines, 

improving the safety and efficiency of underground mining operations. Wireless 

communication systems allow operators to control the machine from the safety of operating 

rooms, reducing direct exposure to hazardous working conditions. In addition, machine 

learning algorithms are increasingly being used to analyze cutting patterns and optimize cutting 

parameters based on historical performance data. The future of roadheader machine control 

systems is moving towards full autonomy, where AI-based decision making and robotic drives 

have the potential to revolutionize underground mining methods. 

According to Yin (2024), the integration of these advanced automation technologies enables 

modern roadheader machines to operate with higher excavation efficiency, improved safety, 

and enhanced adaptability to diverse mining and tunneling conditions. Continued development 

of automated, sensor-based control and monitoring systems is expected to further enhance the 

accuracy and reliability of these machines in the coming years. 

Classification of Roadheaders 

Roadheaders are complex equipment used for various purposes and working conditions, which 

determines the existence of various types and classifications of this equipment. In the literature, 

several key criteria for classifying roadheaders are distinguished: by the type of cutting head, 

machine power, movement method and area of application. 

Classification by cutting head type 

There are two types of roadheaders according to cutting head type: 

Transverse head roadheaders: characterized by a cutting head located perpendicular to the 

axis of the machine (Figure ). Such roadheaders are most effective when driving large-diameter 

tunnels and provide an accurate contour of the workings, which makes them suitable for the 

construction of transport and utility tunnels. Transverse cutting heads, commonly referred to as 

the ripping method, are devices adapted from continuous mining machines that rotate 

perpendicular to the boom axis. This method is particularly effective in soft rock, where high 

extraction efficiency and greater adaptability to changing geological conditions are achieved. 



 

 
 

6 

Transverse machines generate turning forces at right angles to the gripping force, which makes 

them more stable when cutting rock. The design of these machines allows them to cut rock with 

strengths up to 100 MPa (15,000 psi), with the most powerful models capable of working at 

strengths up to 150 MPa (22,000 psi). However, optimum performance is achieved at rock 

strengths of around 30 MPa (5,000 psi), making them ideal for coal mining, sedimentary work, 

and soft rock tunneling (Hemphill, 2012). 

Axial head roadheaders: have a cutting head located parallel to the longitudinal axis of the 

machine. This type of roadheader is mainly used for narrow workings, as well as inclined and 

vertical passages, due to its high stability and lower vibration level. An axial cutting head, also 

known as an inline drilling head, rotates parallel to the boom axis. This design provides 

maximum forward cutting force, making it particularly effective in hard rock. Due to the lower 

cutting speed, axial machines consume fewer picks, which reduces wear and operating costs. 

They are often equipped with telescopic booms, which provide the necessary force for direct 

penetration into the rock mass. In hard rock conditions, axial machines are stabilized by 

hydraulic jacks or support arms, similar to the outriggers on a crane, which increases cutting 

stability. However, when working in soft rock, support arms may not be effective enough due 

to the low strength of the rock, and in wide tunnels, the fixed length of the booms limits 

maneuverability. 

Table 1: General Comparison of Axial vs Transverse Roadheaders (Taylor & Francis Group, 2014) 

Profile smoothness Favorable Unfavorable 

Muck loading 

efficiency 
Unfavorable Favorable 

Application limits 
For UCS < 60–80 

MPa, non abrasive 

Soft to medium-strength rocks (UCS < 

100–120 MPa), moderately abrasive 

Production rate 
Higher for UCS < 

40–60 MPa 
Higher for UCS > 60–80 MPa 



 

 
 

7 

 

Figure 2: Transverse Roadheader and Axial roadheaders. 

Classification by weight 

There are several approaches to classifying roadheaders by weight: 

According to Tucker's classification (Tucker, 1985): 

Light: weight up to 30 t, able to cut rock with a strength of up to 70 MPa. 

Medium: weight from 34 to 45 t, able to cut rock with a strength of up to 100 MPa. 

Heavy: weight over 45 t, able to cut rock with a strength of up to 120 MPa. 

According to Atlas Copco – Eickhoff classification (Schneider, 1988): 

Table 2: Atlas Copco – Eickhoff classification (1988) 

Class Weight (tons) 

Class 0 less than 20 t 

Class I 20 to 30 t 

Class II 30 to 50 t 

Class III 50 to 75 t 

Class IV over 75 t 

   



 

 
 

8 

According to Neil et al. (1994) classification: 

Table 3: Neil et. Al. (1994) classification 

Class Weight (tons) 

Small less than 20 t 

Medium 20 to 30 t 

Large 30 to 50 t 

Rock cutting mechanics of Roadheaders 

The efficiency of roadheader machines is determined by the rock cutting mechanics, which 

include the interaction between the cutting tools and the rock surface. The ability of the machine 

to effectively crush rock depends on factors such as rock properties, cutting tool geometry, 

applied forces, and control systems. The cutting process is based on mechanical fragmentation, 

where the picks of the cutting head create local stresses in the rock, which leads to its destruction 

by crushing, shearing, or tensile tearing. 

Rock destruction during machine operation occurs primarily through indentation, crack 

propagation, and chip formation. When the tooth of the cutting tool penetrates the rock surface, 

it creates local stress concentrations, leading to the formation of an initial crushing zone directly 

below the tool. As the penetration depth increases, radial and lateral cracks propagate outward, 

which ultimately leads to fragmentation of the material. The main failure mechanisms are: 

- tensile failure, which occurs when tensile stresses exceed the tensile strength of the rock, 

causing crack propagation and fragmentation; 

- shear failure, associated with displacement of material along shear planes, typical of plastic 

or layered rocks; 

- compressive failure, which occurs when the applied forces exceed the compressive strength 

of the rock, which leads to its fragmentation - this mechanism predominates in hard and dense 

rock masses. 



 

 
 

9 

The machine's cutting performance depends on a number of geomechanical and operational 

factors. The uniaxial compressive strength (UCS) of the rock is one of the key parameters: soft 

rocks with a UCS below 50 MPa are easily fragmented, while hard rocks with a UCS above 

100 MPa require greater efforts and specialized tooth configurations. Another important 

indicator is the Cerchar Abrasiveness Index (CAI), which measures the abrasiveness of the rock 

and its effect on tooth wear – highly abrasive rocks such as quartzite cause rapid tool wear, 

which increases maintenance costs and reduces cutting efficiency. 

The choice of pick geometry and material is critical to cutting efficiency. Picks with a wide tip 

angle generate higher cutting forces, making them suitable for hard rocks, while picks with a 

sharp angle are better suited for soft rocks, reducing energy consumption and improving the 

degree of fragmentation. Modern picks are made of tungsten carbide, which has high wear 

resistance and impact resistance, and picks with a polycrystalline diamond coating are 

successfully used for cutting hard rocks, significantly extending tool life and reducing 

downtime (Huff, 1980). 

In addition, performance is affected by operating parameters such as cutting speed, thrust force, 

torque and power consumption. Higher cutting speeds improve fragmentation but increase tooth 

wear, and excessive pushing forces can lead to premature tool failure. Higher torque allows 

deeper cutting, especially in hard rock conditions. Modern machines employ advances in 

automation, real-time monitoring, and adaptive control systems to optimize cutting efficiency. 

Machine learning algorithms analyze rock properties on the fly and adjust cutting force, tooth 

angle, and speed to achieve optimal efficiency. Water-jet-assisted cutting technology has been 

developed to reduce cutting resistance and minimize wear, and vibration-assisted cutting with 

ultrasonic vibrations can reduce required cutting forces by up to 30%, improving productivity 

in hard rock conditions (Grosso, 2014). 

 

 

 



 

 
 

10 

1.2 Objectives of the Thesis 

1.2.1 To develop a predictive model for estimating the performance of Roadheaders 

using machine learning methods, taking into account rock properties, machine 

specifications, and operational parameters. 

1.2.2 Conduct a comprehensive analysis of existing performance prediction methods 

and identify the most effective approaches for use in conditions of limited and 

small datasets 

 

1.3 Justification of the Research 

The mining industry is increasingly challenged by the need to improve operational efficiency 

and safety, particularly in the context of limited and heterogeneous datasets. Traditional models 

for predicting the performance of roadheader machines often fail to account for the nonlinear 

and multifactorial interactions present in complex geological conditions. This shortcoming 

results in unreliable productivity forecasts and can lead to significant operational delays and 

increased costs. 

Furthermore, existing research was largely focused on large datasets, leaving a gap in 

methodologies that can effectively handle “small data” scenarios. By integrating advanced 

machine learning techniques with synthetic data generation, this research aims to bridge that 

gap. The innovative approach not only leverages the predictive power of ensemble algorithms 

and neural networks but also enhances the data landscape through carefully generated synthetic 

observations. 

The practical benefits of this study include more accurate productivity forecasts, optimized 

equipment utilization, and a reduction in the economic risks associated with overestimating 

machine performance. Scientifically, this research contributes to the field by combining 

classical mining engineering principles with modern data-driven methods, offering a novel 

perspective that could be applied to a range of similar challenges in the mining and construction 

sector 



 

 
 

11 

1.4 Scope of Work 

The primary objective of this research is to develop and validate a predictive model for 

estimating the performance of roadheader machines under conditions of limited data. To 

achieve this, the study will: 

2. Define the Research Objectives: Focus on the development of machine learning 

models that incorporate synthetic data generation to overcome the constraints imposed 

by small sample sizes. 

 

3. Data Preprocessing and Feature Engineering: Describe the methods used for 

cleaning the dataset, normalizing features, and expanding the feature space with 

polynomial transformations to capture nonlinear relationships. 

 

4. Synthetic Data Generation: Evaluate three distinct methods—Ridge Regression-

based labeling, Gaussian noise-based labeling, and Random Forest-based labeling—to 

augment the dataset, and assess their impact on model performance. 

 

5. Model Development and Validation: Compare the performance of various predictive 

models, including linear models, ensemble methods, and neural networks, using 

standard evaluation metrics such as the coefficient of determination (R²) and mean 

square error (MSE). 

 

6. Analysis and Comparison: Analyze the robustness of each model and synthetic data 

approach, providing insights into the conditions under which the models perform 

optimally. 

 

7. Limitations and Future Work: Discuss the inherent limitations of synthetic data 

generation and the challenges associated with small datasets, as well as propose 

potential directions for further research. 

 

 



 

 
 

12 

2. LITERATURE REVIEW  

2.1. Introduction to the topic and Relevance of the study 

With the development of the mining industry and large-scale construction of underground 

structures (transport tunnels, mine shafts, workings for laying communications), mechanized 

mining technologies are becoming especially important. One of the key types of equipment in 

this area is roadheaders. These machines allow for safer and more efficient work compared to 

the traditional drilling and blasting method. Due to their mobility and the ability to continuously 

extract rock, roadheaders reduce downtime, cut costs and increase productivity. 

However, despite the obvious advantages, the actual cutting rate (Instantaneous Cutting Rate, 

ICR) can vary greatly depending on many factors: geological (strength, fracturing, abrasiveness 

of rocks), technical (type of machine, power, cutting head), as well as organizational and 

technological (shift schedule, availability of qualified personnel, ventilation scheme, etc.). 

Incorrect performance assessment can lead to schedule delays, budget overruns and increased 

risks on the project. Therefore, a reliable ICR forecast is one of the most important elements of 

planning and economic assessment of future work. 

2.1.1 Problem statement: "small data" and complex geology 

San Manuel Mine, due to it’s complex geological structure represents the classical problem 

faced by the researchers trying to develop ML models for mining purposes. Classical 

approaches to performance assessment or forecasting widely use empirical formulas (Bilgin et 

al. 1990, Copur et al. 1998, Thuro & Plinninger 1990, etc.), which take into account key rock 

parameters (UCS, RQD, RMR) and the characteristics of the machine itself. However, the 

versatility and accuracy of such models are often questioned. The main limitation is that each 

formula is obtained for specific conditions (a certain type of rock, class of equipment) and can 

give large errors outside the "native" range of values. 

In recent years, machine learning (ML) and data mining methods have been increasingly used 

to solve engineering problems. For ICR prediction, the most interesting are artificial neural 

networks (ANN), support vector machine (SVM), decision tree, random forest, ensemble 

methods (boosting, bagging). These methods are better at “capturing” nonlinear dependencies 

and, given a sufficient set of examples, are capable of self-training, increasing the accuracy of 

forecasts. 

 



 

 
 

13 

However, the mining industry often faces the problem of “small data”: there are few real 

projects with a full range of measurements, mining and geological conditions are often 

different, and some information may be unavailable due to commercial secrecy and other 

restrictions. As a result, many ML models begin to overtrain and lose accuracy due to 

insufficient sampling. 

Thus, the problem comes down to the need to create methods that can build reliable forecasts 

even with a small amount of input data, and also take into account the heterogeneity of 

geological and operational factors. In this context, methods of synthetic data extension, model 

regularization, and hybrid approaches (combination of empirics and ML) are of particular 

interest. 

2.1.2 Purpose and objectives of the literature review 

The main purpose of the review is to analyze existing approaches to predicting the productivity 

of roadheaders and identify key trends and “blank spots” in research. 

 

To achieve this goal, it is proposed to solve the following tasks: 

 

● Characterize the role and types of roadheader miners, showing their importance for 

modern underground construction and mining. 

● Analyze modern approaches using machine learning, to evaluate their effectiveness 

and typical problems (in particular, small data sets). 

● Formulate the main gaps in research that require more in-depth study or a new 

methodology. 

● Justify the choice of a specific direction (for example, the use of ML algorithms in 

conditions of a limited sample) for further research work. 

 

 

 

 

 

 

 

 

 



 

 
 

14 

Structure of the further presentation 
The literature review is divided into several subsequent sections: 

 

● Section 2 briefly describes the evolution of roadheaders and the key technical parameters 

that affect their performance. 

 

● Section 3 is devoted to the analysis of traditional empirical and statistical methods for 

predicting ICR. 

 

● Section 4 considers the use of machine learning methods, including neural networks, SVR 

and ensemble approaches, as well as the specifics of application in mining. 

 

● Section 5 contains a critical analysis of the state of research, discussing the issues of “small 

data” and variability of geological conditions. 

 

● Section 6 summarizes the review, highlighting the directions that will form the basis for the 

methodological part and future experiments. 

 

2.2 Key Parameters Affecting the Performance of Roadheader Machines 

In the process of mechanized mining, the speed of rock extraction and the efficiency of work 

(Instantaneous Cutting Rate, ICR) depend on a combination of mining and geological, technical 

and organizational factors. In this section, the paper will consider the main parameters that, 

according to a number of studies (Bilgin et al. 1990, Copur et al. 1998, Ebrahimabadi et al. 

2011, Seker & Ocak 2011, etc.), have the most significant impact on the result. 

 

Geological and geomechanical factors 
 

Uniaxial compressive strength (UCS): UCS is considered one of the main parameters for 

assessing the rigidity and difficulty of rock destruction. The higher the UCS value, the more 

difficult the cutting process is and the lower the potential productivity of the machine, all other 

things being equal. Various authors (e.g. Balci et al., 2004) point out that in most empirical 

models UCS can be included as a linear or power function to predict ICR. 



 

 
 

15 

Rock Quality Designation (RQD) and Classification Systems: RQD (Rock Quality 

Designation): reflects the degree of fracturing of the rock mass. With a high RQD, the rock is 

relatively solid, which complicates destruction; with a low RQD, the rock mass is more 

fragmented, and the excavation process can be accelerated. 

 

Rock Mass Rating (RMR) or similar systems: take into account UCS, fracture frequency and 

orientation, joint condition, etc. The higher the class (good rock mass quality), the more difficult 

the mechanical cutting is. Therefore, in some models such as Bilgin et al. (1988), Ebrahimabadi 

et al. (2011), high RMR correlates with lower ICR values. 

 

Analysis of oriented fracturing and soil parameters 

The orientation of cracks (angle α between the working axis and the planes of weakening) can 

significantly change the nature of rock destruction. For example, with a favorable orientation 

of the layers, the cutting process is facilitated. 

 

Abrasivity: the presence of quartz or other hard minerals in the rock leads to accelerated wear 

of the machine cutters, reducing efficiency and increasing tool costs. 

 

Humidity and water saturation: If the massif is saturated with water, deterioration in the 

stability of the roof and side walls is possible. In addition, high water content sometimes reduces 

the strength characteristics of the rock, but, on the other hand, may require additional drainage 

and complicate the organization of work 

Thus, these parameters - UCS, RQD, RMR, fracture characteristics, water saturation, etc. - have 

a complex effect on the instantaneous productivity (ICR). The more accurate the values 

obtained during engineering and geological surveys, the more reliable the forecast for the 

roadheader. 

2.3 Machine learning and its implementation in the mining industry 

In the last decade, machine learning (ML) technologies have been rapidly spreading in the 

mining sector, playing a significant role in the digital transformation processes. One of the key 

reasons for this has been the development of computing power and data collection tools. 

Processing large volumes of information coming from numerous sensors and automated 

monitoring systems has allowed ML analytical algorithms to find hidden nonlinear 



 

 
 

16 

dependencies and form accurate predictive models. For example, Mahdevari et al. (2014) 

studying the relationship between the geomechanical properties of rock and cutting speed, 

showed that neural networks can outperform classical regression methods in complex geology. 

In the mining industry, machine learning is actively used in several main areas. Firstly, to 

predict the productivity of mining equipment (including roadheaders), where ANN models or 

support vector machines (SVM) look for patterns between rock characteristics (UCS, RQD, 

etc.) and the actual rate of advance. Secondly, to analyze the condition of equipment to prevent 

accidents (Predictive Maintenance). Such approaches use data from vibration diagnostics, 

acoustic and thermal sensors, which allows for early detection of failures and prevention of 

downtime. Thirdly, ML technologies are integrated into mining management systems: smart 

algorithms optimize the routes of road trains, distribute excavators and dump trucks, thereby 

increasing the overall efficiency of mining transport complexes. 

Despite all the obvious advantages, such as the ability to identify deep nonlinear dependencies 

and quickly adapt to new data, machine learning methods face the problem of “small data”. In 

the mining sector, large datasets are often unavailable: measurements are taken in unique 

geological conditions, storage formats and levels of detail are different. This entails the risk of 

model overfitting and the impossibility of correct validation of the results. To solve such 

problems, various approaches are proposed in the scientific literature. Seker & Ocak, (2019) 

include regularization algorithms (dropout, L2-regularization), generation of synthetic data 

based on the statistical properties of the original samples, as well as combined approaches 

combining classical mining engineering models with learning algorithms  

Thus, machine learning provides significant advantages in the analysis and forecasting of 

underground and open-pit mining processes. However, to achieve high accuracy and reliability 

of results, it is necessary to take into account both the technical features of the algorithms and 

the specifics of the geological data. In particular, to compensate for the lack of observations, 

ensemble learning (bagging, boosting) or transfer learning mechanisms can be used, when a 

model trained on one data set is further trained on another, similar in characteristics. Such a 

flexible approach provides a more universal solution for variable operating conditions of mining 

equipment (Ebrahimabadi et al., 2011). 



 

 
 

17 

2.4 Analysis of existing studies on ICR prediction for roadheaders 

The first works by Sandbak (1985), attempted to relate the instantaneous cutting rate (ICR) of 

a roadheader and rock parameters (usually UCS, fracturing index) to the installed power. The 

models remained relatively simple and did not reflect the multifactorial nature of the cutting 

process in complex geology. 

Gehring (1989) presented formulas for two types of roadheaders: 

For a transverse roadheader (power ≈250 kW): 

𝐼𝐼𝐼𝐼𝐼𝐼 =  (
719
𝜎𝜎𝑐𝑐0.78) 

(1) 

For an axial roadheader (power ≈230 kW): 

𝐼𝐼𝐼𝐼𝐼𝐼 =  (
1739
𝜎𝜎𝑐𝑐1.13 ) 

(2) 

where σc is the uniaxial compressive strength of the rock (MPa). The higher the σc, the lower 

the ICR value. 

Later, Bilgin et al. (1990) used more detailed empirical relationships. In particular, the study 

proposed the formula: 

𝐼𝐼𝐼𝐼𝐼𝐼 =  0.28 ×  𝑃𝑃 ×  (0.974)𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 

(3) 

where P is the cutting head power (hp). The RMCI index is calculated as follows: 

𝐼𝐼𝑅𝑅𝐼𝐼𝐼𝐼 =  𝜎𝜎𝑐𝑐 × (
𝐼𝐼𝑅𝑅𝑅𝑅
100

)2/3  

(4) 

σc is UCS (MPa), RQD is the core integrity index (%). It was assumed that for a fixed power, 

an increase in RQD often leads to a decrease in ICR, since the rock becomes more integral.  



 

 
 

18 

In the works of Copur et al. (1998), the emphasis shifted to the machine weight and specific 

energy. The authors derived the relationship: 

𝐼𝐼𝐼𝐼𝐼𝐼 = 27.511 × 𝑒𝑒𝑒𝑒𝑒𝑒(0.0023 × 𝐼𝐼𝑃𝑃𝐼𝐼), 

(5) 

where RPI = (P × W) / σc, P is the power (kW), W is the weight of the machine (tons), σc is 

UCS. It was shown that more massive machines (with equal power) better stabilize the cutting 

process in hard rocks. 

In the studies of Thuro & Plinninger (1999) using the example of a 132 kW machine, a trend 

relationship was found: 

𝐼𝐼𝐼𝐼𝐼𝐼 =  75.7 −  14.3 ×  𝑙𝑙𝑙𝑙(𝜎𝜎𝜎𝜎) 

(6) 

where σc (MPa) is the uniaxial compressive strength. The model gave acceptable results in the 

given UCS range (about 30–100 MPa). 

Since the early 2000s, ML technologies have become increasingly used (Yagiz et al., 2009; 

Mahdevari et al., 2014), but empirical methods have also continued to develop. Thus, Balci et 

al. (2004) consider the cutting depth (d): 

For d = 5 mm:  

𝐼𝐼𝐼𝐼𝐼𝐼 =  0.8 ×  𝑃𝑃
0.37

𝜎𝜎𝑐𝑐0.86     

(7) 

For d = 9 mm: 

𝐼𝐼𝐼𝐼𝐼𝐼 =  0.8 ×  𝑃𝑃
0.41

𝜎𝜎𝑐𝑐0.67  

(8) 

where P is the power (kW), σc is the UCS (MPa). The value of 0.8 was determined empirically. 

Also Keles (2005) proposed an expression for the MK2B (milling type) roadheader: 



 

 
 

19 

𝐼𝐼𝐼𝐼𝐼𝐼 =  163.93 ×  𝜎𝜎𝑐𝑐−0.5737 

(9) 

Among more modern variants, Ebrahimabadi et al. (2011) can be noted. The authors applied 

the rock mass brittleness index (RMBI) and took into account the orientation of the layers. One 

of the models looked like this: 

𝐼𝐼𝐼𝐼𝐼𝐼 =  5.56 ×  𝐼𝐼𝑅𝑅𝑅𝑅𝐼𝐼 +  0.60 ×  𝑎𝑎 −  8.17 

(10) 

where a is the bedding angle of the layers, and RMBI is calculated based on UCS, RQD and 

rock brittleness indices. Another formula relates ICR to the specific energy (SE): 

𝐼𝐼𝐼𝐼𝐼𝐼 =  −0.18 ×  𝑆𝑆𝑆𝑆³ +  28.57 ×  𝑆𝑆𝑆𝑆 −  92.82. 

(2.11) 

Earlier, the idea of the SE (specific energy) approach was also developed by Rostami et al. 

(1994), proposing: 

𝐼𝐼𝐼𝐼𝐼𝐼 =  𝑘𝑘 ×  (
𝑃𝑃
𝑆𝑆𝑆𝑆

) 

(12) 

where k is the energy transfer coefficient (0.45–0.55 for roadheader), P is the power (kW), SE 

is the specific energy (kWh/m³). 

Finally, Choudhary et al. (2017) can be mentioned, who reused the cubic dependence on SE, 

similar to Ebrahimabadi et al. (2011). This emphasizes the trend towards a more “energy” view 

of the rock cutting process. 

Thus, the evolution of ICR models goes from the simplest dependencies such as Gehring 

(1989), to taking into account an extended set of rock-mechanical indicators – e.g, Bilgin et al., 

(1990), Copur et al. (1998), and then to complex indices of the massif structure as in work of 

Ebrahimabadi et al. (2011), and specific energy characteristics as in Rostami et al. (1994). 

Today, many authors combine these formulas with machine learning methods, which allows 

them to refine the coefficients and increase the reliability of models when expanding the range 

of conditions. 



 

 
 

20 

Key Works Focusing on Geotechnical parameters 

A significant part of the early ICR prediction formulas was built around UCS (uniaxial 

compressive strength). For example, Gehring (1989), derived an equation for a 250 kW 

roadheader (transverse) in the form: 

𝐼𝐼𝐼𝐼𝐼𝐼 =  
719
𝜎𝜎𝑐𝑐0.78 

(13) 

and for 230 kW (axial): 

𝐼𝐼𝐼𝐼𝐼𝐼 =  
1739
𝜎𝜎𝑐𝑐1.13 

(14) 

where 𝜎𝜎𝑐𝑐 is UCS (MPa). An increase in 𝜎𝜎𝑐𝑐  leads to a decrease in ICR. 

Another common parameter is RQD (Rock Quality Designation). For example, Bilgin et al. 

(1990) included in the formula: 

 

𝐼𝐼𝐼𝐼𝐼𝐼 =  0.28 ×  𝑃𝑃 ×  (0.974)𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 

(15) 

Where P is the cutting head power (hp). The RMCI index is calculated as follows:  

𝐼𝐼𝑅𝑅𝐼𝐼𝐼𝐼 =  𝜎𝜎𝑐𝑐 × (
𝐼𝐼𝑅𝑅𝑅𝑅
100

)2/3  

(16) 

At higher RQD (more solid rock), there is a tendency for productivity to decrease at a fixed 

power P. 

The third basic parameter is RMR (Rock Mass Rating), which summarizes UCS, RQD, 

orientation and state of cracks. An increase in RMR indicates a higher quality rock mass, 

which complicates mechanical cutting and, accordingly, reduces ICR. The problem is the 



 

 
 

21 

ambiguity of RMR calculation methods: different authors can use slightly different scales and 

weighting factors. 

Therefore, UCS, RQD and RMR form a triad, which is most often encountered in predictive 

models. However, there is no single universal equation that can accurately account for all the 

diversity of geology. Many researchers have to combine classical mining and mechanical 

formulas with correction factors or pay attention to the specifics of the equipment, such as the 

mass and design of the cutting head. 

 

Comparison of Machine Learning Approaches 

Since the early 2000s, machine learning (ML) methods have become increasingly popular, 

which are capable of analyzing the relationships between several dozen parameters at once. The 

most frequently mentioned are: 

ANN (artificial neural networks), 

SVR (support vector regression), 

Random Forest, 

Gradient boosting and other ensemble methods. 

Seker & Ocak (2019) compared a range of such algorithms on a dataset that included UCS, 

RQD, machine weight, cutting head power, and actual ICR values. It turned out that ensemble 

methods (Random Forest, Gradient Boosted Trees) gave 5–10% higher accuracy than single 

models (e.g., simple neural network or linear regression). 

Ebrahimabadi et al. (2011) used a hybrid approach, combining empirical formulas with the 

concept of RMBI (Rock Mass Brittleness Index). For example, one of the models: 

𝐼𝐼𝐼𝐼𝐼𝐼 =  5.56 𝐼𝐼𝑅𝑅𝑅𝑅𝐼𝐼 +  0.6𝑎𝑎 −  8.17 
(17) 

where a is the bedding or fracturing angle, and RMBI is calculated using UCS, RQD and 

brittleness indices. Further optimization of the coefficients was carried out using training 

algorithms (ANN, SVR), which allowed to increase the accuracy. 

The main advantage of the ML approach is its flexibility and the ability to “learn” from data 

from different deposits. However, a high-quality result requires careful tuning of 



 

 
 

22 

hyperparameters and a sufficient number of observations, which is not always achievable in 

mining. 

Experience with small data sets 

Data limitations are one of the most pressing issues in building predictive ICR models. 

Performance measurements are usually taken over narrow intervals and are highly dependent 

on the unique local geology. This often leads to overfitting and reduced reliability of forecasts. 

Salsani et al. (2013) and Seker & Ocak (2019) proposed several strategies to improve the 

situation: 

Synthetic sample expansion: introducing “artificial” points around existing values (based on 

KNN). 

Cross-validation (k-fold or Leave-One-Out): allows each observation to be used as a test one in 

turn, increasing the objectivity of the accuracy assessment. 

Regularization: in neural networks, this can be dropout or L2 regularization, and in trees, a 

depth limit or a minimum number of observations per leaf. 

Such techniques help keep the model from overfitting to noisy data and make it more robust to 

the variability of mountain conditions. The final results are usually better than those of classical 

empirical equations, which are designed only for a narrow range of input parameters. 

2.5. Critical analysis and identified gaps 

This part of the research aims to identify the gaps present in the previous works. Here, a brief 

analysis of the works aimed at empirical models, and more recent works on ML implication 

was performed.  

Analysis of the accuracy and limitations of various models 

Some researchers (Bilgin et al., 1990; Copur et al., 1998) emphasized the importance of a 

comprehensive accounting of mining and geological factors (UCS, RQD, RMR), but their 

formulas often show good convergence only in the initial data range. When trying to extend 

such empirical dependencies to other types of rocks or other types of tunneling machines 

(differing in weight, power), the accuracy drops significantly. Limitations in the generalizing 

ability - or, in the language of machine learning, in generalization - arise due to the fact that 

each model is "tied" to a specific set of conditions and features. 



 

 
 

23 

Another obstacle to comparing the results is the variety of initial data processing methods. Some 

authors may include rock abrasiveness in the calculation (CERCHAR, CAI), while others may 

not take this parameter into account at all. A similar problem concerns the method of measuring 

(or calculating) RMR: there are different "branches" of classification (Bieniawski 1973 vs. 

modifications of 1989, 1993, etc.), leading to variations in the massif assessment. As a result, 

direct comparison of models or their combination may be incorrect if the feature spaces are not 

consistent. 

Disadvantages and advantages of research for "small data" 

In mining, there are often situations when the set of empirical ICR measurement points is 

limited to tens of observations, and the measurements themselves may contain noise or errors. 

Under such conditions, even the most advanced machine learning algorithms risk overfitting, 

i.e. fitting the model to random fluctuations instead of stable patterns. In addition, there is often 

no independent test sample: all available data are used in training, and it becomes difficult to 

correctly assess the real accuracy of predictions. 

Insufficient variability of geological conditions also plays a role. If, for example, the entire 

sample is taken from one mine or only one object, the model can "remember" these specific 

parameters. When transferred to another deposit (with different UCS, RQD, fracture 

orientation), the forecast accuracy decreases sharply. 

Despite all the risks, research in the field of "small data" also has a positive side: it stimulates 

the search for adaptive or hybrid approaches, when basic empirical models and modern ML 

methods are combined. This can give a more practical result than universal formulas calculated 

for thousands of observations, because it is difficult or almost impossible to obtain so many 

observations in a real project. 

The need for an integrated approach 

Modern practice shows that one linear (or purely empirical) model is not enough to fully take 

into account all aspects that determine the instantaneous productivity of a roadheader. Many 

authors such as Ebrahimabadi et al., (2011), Seker & Ocak, (2019) emphasize the benefits of 

combining classical geomechanical equations of Bilgin et al. (1990), Copur et al. (1998), 

Rostami et al. (1994) with machine learning methods. An empirical formula or specific indices 

(RMBI, SE) provide the supporting “physical logic”, and the ML model refines the coefficients 

and better adapts to the local features of the massif. 



 

 
 

24 

Additionally, expert opinion (soft computing) can be used when working with incomplete or 

fuzzy data. For example, in conditions of a shortage of UCS, RQD and other key indicators, a 

fuzzy description is allowed. Expert systems based on the knowledge of geology specialists 

allow for high-quality model calibration where classical statistical learning is inapplicable due 

to a lack of numerical data. 

Thus, the main problem identified in most studies is the lack of a single “universal” solution 

capable of producing stable results on any sample. The optimal path of development is a 

combination of several approaches: from traditional mining-mechanical equations to hybrid 

ML algorithms taking into account expert assessments. Such a comprehensive path gives a 

chance not only to improve the accuracy of forecasts, but also to ensure the adaptability of the 

model to new or poorly studied conditions. 

2.6. Future research directions 

Integration with additional technologies 

Current research tends to connect roadheaders with complex sensor systems and real-time data 

analysis systems. Li & Gao (2021) showed that the use of laser scanners and 3D face 

visualization can significantly improve the accuracy of automatic assessment of the working 

geometry and, accordingly, influence the choice of the optimal cutting mode. 

In parallel, the idea of continuous monitoring of machine parameters is being developed: Zhang 

et al. (2022) implemented a set of sensors to record acoustic signals and vibrations of cutters in 

order to record the transition from “normal” operation to potential emergency modes. Such data 

was integrated with machine learning algorithms that quickly update the instantaneous 

productivity forecast (ICR). 

Given a sufficient volume of accumulated observations, a number of authors (Mahdevari et al., 

2014; Ghasemi et al., 2020) talk about the prospects of deep learning. For example, LSTM or 

transformer architectures can use time series recorded during mining. So far, these methods 

remain relatively rare in mining due to the difficulties in generating “big data”, but with the 

advent of expanded datasets, the result can be very promising. 

Strengthening the robustness of ML models 

Many studies such as Chang & Peng (2020) emphasize the need for regularization and 

optimization of models to cope with noisy and heterogeneous mining data. One of the key 



 

 
 

25 

techniques is strict cross-validation (k-fold), which allows for a reliable assessment of the 

generalization ability of the algorithm with a small number of observations. 

An important direction is the introduction of hybrid methods. For example, Seker & Ocak 

(2019) proposed ensembles (bagging, boosting) for working with a small set of training data. 

Other authors (Salsani et al., 2013; Ghasemi et al., 2020) are experimenting with combining 

classical neural networks and evolutionary algorithms (genetic algorithms, particle swarm 

optimization) for selecting hyperparameters. This strategy makes it possible to quickly find 

optimal settings for network depth, activation function, etc., reducing the risk of overfitting. 

Bayesian regression approaches deserve special mention, allowing one to estimate prior 

distributions of UCS, RQD, or other features when the data is too sparse (Li et al., 2022). Such 

models not only predict ICR, but also generate a probability interval, which provides a more 

complete picture of uncertainty. 

Model transferability 

Transferability (or transfer learning) becomes an important factor when a model trained on one 

field must quickly adapt to other geolocations. Zhang et al. (2022) experimentally showed that 

if you have a “base” neural network for a narrow range of UCS, then using an additional 10-15 

points from a new field, you can fine-tune the network and achieve accuracy comparable to 

“pure” training on a large dataset. 

Alternatively, Chang & Peng (2020) point to the idea of forming a “universal” set of features 

(e.g. UCS, RMR, CAI, machine weight, power, cutter head type), standardized by measurement 

methods. This will allow researchers from different regions to “put” data into a common 

database and obtain more universal ML models. In the long term, such a step will accelerate 

the implementation of drilling optimization algorithms already at the design stage, where an 

engineer will be able to pre-calculate the expected ICR without expensive field tests. 

To summarize, further research should cover at least three areas of development: integration 

with real time via sensors, enhancing the robustness of ML models using regularization and 

hybridization, and increasing portability through transfer learning and unification of methods 

for measuring mining and geological parameters. 

 



 

 
 

26 

2.7. Literature Review Summary 

Summary of Key Results 

The analysis of existing works on forecasting the instantaneous productivity (ICR) of 

roadheaders revealed that the development of methods went from simple empirical formulas 

such as Gehring et al. (1989), Bilgin et al. (1990), Copur et al. (1998), taking into account 

mainly UCS and RQD, to more complex models reflecting many factors: crack orientation, 

abrasiveness, design features of the miner itself. At the same time, machine learning methods 

(ANN, SVR, ensemble approaches) are gaining popularity, which are able to better capture 

nonlinear relationships in data and expand the applicability of models. 

At the same time, an important condition for high-quality ICR forecasting remains the presence 

of a representative observation base. However, in mining practice, the problem of small data 

volumes is often encountered, which leads to difficulties in training models and in assessing 

their generalizing ability. To overcome these limitations, synthetic data generation, strict cross-

validation and regularization are used. 

Justification of the Selected Scientific Direction 

Summarizing the results of the review, several critical gaps can be identified. Firstly, most 

empirical formulas (Bilgin et al. 1990, Copur et al. 1998, Thuro & Plinninger 1990) are 

designed for a narrow range of geological conditions or for certain types of machines, which 

means that their accuracy drops sharply when changing a deposit or when working with a new 

type of roadheader. Secondly, even multifactor models (taking into account RMR, RMBI, SE) 

remain vulnerable to noise data and fluctuations in geological properties. 

On the other hand, machine learning shows promise with sufficient variability and quantity of 

data. However, “small data” complicates the use of deep neural networks and requires improved 

techniques to combat overfitting. Therefore, it is logical to move towards an integrated 

approach, in which nonlinear features are added to classical mining and mechanical parameters, 

and regularization and synthetic generation mechanisms are incorporated into the model. 

Transition to methods and experimentation 

Based on the identified gaps in the study, a methodological part will be proposed, where the 

main focus is on methods for processing limited data sets and expanding the feature space. In 

particular: 



 

 
 

27 

It is planned to use procedures for generating artificial observations (data augmentation) to 

increase the model's resistance to noise. 

It is envisaged to introduce second-order polynomial features reflecting potential nonlinear 

interactions (e.g., UCS × RQD, RMR², etc.). 

Various machine learning algorithms (neural networks, SVM, ensembles) will be used to train 

the models, to which a set of regularization measures and strict cross-validation are added. 

Therefore, the next chapter will detail the methodology based on the results of the literature 

review: what data features are taken into account, how the hyperparameters of ML models are 

selected, and why the proposed techniques are especially important for predicting ICR in a 

limited sample. 

3. CASE STUDY – SAN MANUEL MINE, ARIZONA USA 

The San Manuel Mine, located in Arizona's Lower San Pedro River Basin, was a significant 

underground copper mine and a cornerstone of the region's mining industry. Operational from 

the 1950s, the mine utilized various methods, including block caving, open-pit mining, and in-

situ leaching, to adapt to changing technological advancements and resource extraction 

demands. However, due to economic constraints and resource depletion, the mine ceased 

operations in 1999 (BHP Copper Inc., 2002). 

Geologically, the mine is characterized by an ore body hosted in granodiorite porphyry and 

quartz monzonite, intersected by fault systems such as the San Manuel, East, and West Faults. 

These structural features provided pathways for mineralization but also posed operational 

challenges due to zones of weakness and variability in rock strength. The depth of ore deposits, 

which extended from 700 to 3,000 feet below the surface, further complicated mining 

operations (Arizona Geological Society, 1987). 

In response to these challenges, roadheader technology was tested and utilized at the San 

Manuel Mine to enhance drift excavation. Roadheaders, such as the DOSCO SL-120, were 

employed to overcome the limitations of conventional drill-and-blast techniques, particularly 

in fractured and jointed rock environments. The technology demonstrated its ability to achieve 

faster excavation rates, reduced overbreak, and improved stability of drifts. Tests conducted in 

the San Manuel and Kalamazoo ore bodies revealed that roadheaders could be a viable 



 

 
 

28 

alternative, particularly in areas where structural complexities and variable rock properties 

necessitated precision excavation (Sandbak, 1985). 

 

Figure 3. Geologic Map of San Manuel area (Schwartz, 1953). 

 



 

 
 

29 

 

Figure 4. RMR table and Machine Performance Graph 

Table 4: Dataset Utilized for Model Establishing 

# Geology RQD RMR UCS ICR 
 Description (%) (-.) (MPa) (m^3/hr) 

1 Good Rock 72 70 200 8,309 

2 Good Rock 70 68 170 6,492 

3 Good Rock 62 64 150 8,547 

4 Poor Rock 35 34 120 12,115 

5 Poor Rock 50 37 137 15,016 

6 Poor Rock 58 31 116 17,406 

7 Poor Rock 25 24 127 18,789 

8 Poor Rock 38 27 172 18,491 

9 Poor Rock 53 28 162 19,199 

10 Very Poor Rock 5 15 130 20,06 

11 Very Poor Rock 18 18 100 21,099 

12 Very Poor Rock 3 15 75 21,807 

13 Poor Rock 19 27 60 22,167 

14 Poor Rock 28 31 88 18,997 

15 Poor Rock 42 34 103 13,809 

16 Poor Rock 22 25 95 12,317 

17 Poor Rock 39 26 90 14,357 



 

 
 

30 

18 Poor Rock 39 29 92 16,567 

19 Poor Rock 55 30 85 19,45 

20 Poor Rock 18 27 90 16,446 

21 Fair Rock 54 45 115 13,952 

22 Fair Rock 52 44 130 14,665 

23 Fair Rock 63 49 157 12,182 

24 Fair Rock 52 44 130 11,044 

25 Fair Rock 50 48 145 12,596 

26 Poor Rock 7 34 70 12,79 

27 Poor Rock 47 40 115 13,151 

28 Poor Rock 44 38 120 14,193 
 

Roadheader Operational Features 

The San Manuel mine has served as a testbed for roadheader technology. Field studies, 

including those conducted by Sandbak, have demonstrated that roadheaders significantly 

reduce the risk of fracturing and excessive rock failure compared to conventional blasting 

methods. In the Kalamazoo and San Manuel deposits, roadheading achieved development rates 

up to 38% higher, especially in weak, highly fractured, and hydrothermally altered rocks. 

 

Detailed geomechanical mapping of test levels (e.g., 2890 and 2375 ft tests) revealed that 

different rock classes, from weak, highly fractured porphyry to massive quartz monzonite, have 

a direct impact on cutting rates (in ft/hour) and cutting tool consumption (bits per foot). The 

results of these tests were used to calibrate the predictive models, confirming that ensemble 

machine learning methods are particularly effective in describing the complex nonlinear 

behavior of rock masses during roadheader operations. 

 

The San Manuel case study demonstrates the practical benefits and challenges of applying 

predictive models to the mining industry. Heterogeneous geological settings, complex 

structural settings, and associated sedimentation require advanced data synthesis techniques 

and robust ensemble models. The analysis suspects that ensemble methods significantly 

outperform simple linear regressions in predicting roadheader performance in such dynamic 

environments. In addition, geomechanical observations provide an important link between 

model output and real mining conditions, which is critical for optimizing mine planning, 

reducing costs, and ensuring mine safety. 

 



 

 
 

31 

4. METHODOLOGY 

This chapter describes the methodological approach used to solve the problem of predicting the 

ICR (roadheader machine performance) using machine learning methods. The stages of data 

collection and description, their pre-processing and feature formation, methods for generating 

synthetic data, as well as the selected models and the strategy for their evaluation are 

considered. 

4.1 Data collection and description 

The research on tunneling and drift excavation at San Manuel, performed by Louis Sandbak in 

1985, contains a complete dataset with the geotechnical parameters for model establishment 

required. This dataset includes measurements of such parameters as rock quality factor (RQD), 

RMR value, and Uniaxial compressive strength (UCS), as well as the target variable – ICR, 

characterizing the equipment productivity in m³/hour. The section describes the data source, the 

conditions for collecting measurements, as well as the main characteristics and statistics of the 

dataset. Such a detailed analysis allows us to understand the original distribution of values and 

identify potential problems, such as the presence of missing values or outliers.  

4.2 Data Preprocessing and Feature Generation 

In this study, data preprocessing and feature generation plays a key role, since the success of 

subsequent modeling depends on the quality of the input data. In the first step, the data is 

carefully extracted from the original dataset: values from the RMR table and Machine 

Performance graphs were extracted and digitalized. It’s important to carefully handle data and 

create a reliable base for further analysis. 

The next important step is data normalization. In the original dataset, features are measured in 

different units (for example, RQD is expressed in percentages, UCS in MPa, and ICR in cubic 

meters per hour), which can lead to machine learning algorithms paying too much attention to 

features of a large scale. To address this issue, standard scaling was applied, transforming all 

features so that their mean is zero and their standard deviation is one. This not only speeds up 

the convergence process of the algorithms, but also ensures that all variables have an equal 

influence on the final result. 

In addition, to enable the models to capture more complex, nonlinear relationships between 

features and the target variable, the original feature space was expanded using a polynomial 



 

 
 

32 

transformation. Specifically, combinations of second-degree features were generated for each 

original variable, revealing hidden patterns not reflected in the original data. Although adding 

polynomial features increases the dimensionality of the dataset, the benefits in terms of the 

improved ability of the model to describe complex dependencies significantly outweigh the 

potential computational costs. Thus, the complex preprocessing includes: removing incomplete 

records to ensure data purity, normalizing features to bring them to a common scale, and 

creating additional polynomial features to reveal nonlinear relationships. This approach forms 

a solid foundation for subsequent stages of analysis, synthetic data generation, and model 

training, contributing to increased accuracy and reliability of predictions. 

4.3 Synthetic Data Generation  

Due to the limited size of the original data set, synthetic data generation methods are used to 

improve the learning ability of models. Three methods are described below, each of which is 

mathematically justified. 

1. The Ridge Regression-based Label Method. 

The idea of this method is to use a linear model with L2 regularization to predict the target 

variable on a bootstrapped sample of features. Mathematically, the Ridge regression problem 

is formulated as the minimization of the loss function: 

|| 𝑋𝑋𝑋𝑋  −  𝑦𝑦||2  +  𝜆𝜆 ||𝑋𝑋||2 

(18) 

where X is the feature matrix, y is the vector of target values, β is the vector of model 

coefficients, and λ is the regularization coefficient. 

After training the model on the original data, synthetic labels are calculated for the bootstrapped 

(randomly selected with repetition) subsample 𝑋𝑋𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏: 

𝑦𝑦𝑠𝑠𝑠𝑠𝑠𝑠𝑏𝑏ℎ𝑒𝑒𝑏𝑏𝑒𝑒𝑐𝑐 == 𝑋𝑋𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 �̂�𝑋. 

(19) 

To simulate natural variability, a small amount of noise is added to the features, for example, 

 



 

 
 

33 

𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑡𝑡′ = 𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑋𝑡𝑡 + 𝜀𝜀, 

(20) 

where 𝜀𝜀 ∼ 𝑁𝑁(0,𝜎𝜎2𝐼𝐼). This approach preserves the linear dependencies present in the data and 

allows for an expanded training sample. 

2. Gaussian Noise Generation Method. 

This method assumes that synthetic labels are generated by adding random noise to the target 

values obtained by resampling. Formally, for a resampled target variable 𝑦𝑦𝑟𝑟𝑒𝑒𝑠𝑠𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑒𝑒 , the 

synthetic label is defined as: 

𝑦𝑦𝑠𝑠𝑠𝑠𝑠𝑠𝑏𝑏ℎ𝑒𝑒𝑏𝑏𝑒𝑒𝑐𝑐 = 𝑦𝑦𝑟𝑟𝑒𝑒𝑠𝑠𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑒𝑒 + 𝜖𝜖, 

(21) 

where the noise ϵ\epsilonϵ is normally distributed, 𝜖𝜖 ∼ 𝑁𝑁(0,𝜎𝜎2). Here, the parameter σ\sigmaσ 

controls the degree of random fluctuations, allowing the synthetic data to mimic the natural 

fluctuations found in real measurements. 

3. Random Forest Regressor -based method. 

Using the Random Forest model, an ensemble of decision trees is trained to predict the target 

variable. Mathematically, Random Forest estimates a function 𝑓𝑓(𝑒𝑒) such that: 

𝑦𝑦 ≈ 𝑓𝑓(𝑋𝑋) =
1
𝑇𝑇
�𝑓𝑓𝑏𝑏(𝑋𝑋)
𝑇𝑇

𝑏𝑏=1

, 

(22) 

where T is the number of trees and 𝑓𝑓𝑏𝑏(𝑋𝑋) is the prediction of the t-th tree. After training, for the 

bootstrapped feature set 𝑋𝑋𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏, the synthetic labels are computed as: 

𝑦𝑦𝑠𝑠𝑠𝑠𝑠𝑠𝑏𝑏ℎ𝑒𝑒𝑏𝑏𝑒𝑒𝑐𝑐 = 𝑓𝑓(𝑋𝑋𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏). 

(23) 

Similarly to the first method, a small noise can be added to the features to increase diversity: 

𝑋𝑋𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏′ = 𝑋𝑋𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 + 𝜖𝜖,  𝜖𝜖 ∼ 𝑁𝑁(0,𝜎𝜎2𝐼𝐼). 



 

 
 

34 

(24) 

This approach allows us to take into account complex nonlinear dependencies present in the 

data and generate synthetic labels that are as close as possible to real ones. 

 
Figure 5: Visualization for Random Forest Regressor Labeling 

In this study, a wide range of machine learning models was considered to address the ICR 

forecasting problem in order to find the optimal balance between accuracy and interpretability. 

Linear methods were analyzed at first (Ridge, Lasso, and ElasticNet), which are well suited for 

situations where simplicity and high generalization ability with a large number of features are 

important. Ridge regression (L2 regularization) helps smooth out possible jumps in coefficients 

and reduce overfitting, while Lasso (L1 regularization) is able to zero out coefficients of 

insignificant features and thus perform partial data filtering. ElasticNet represents a 

compromise, combining the properties of both approaches and often demonstrating more stable 

results, especially in problems with many correlated variables. 

However, given the complexity of the rocks and potential nonlinearities in the data, the analysis 

was suplemented with ensemble methods: Random Forest, Gradient Boosting, and Extra Trees. 

They build multiple decision trees and combine their results, which allows them to model 

complex relationships and deal with noise more effectively. For example, Random Forest 

averages the results of individual trees trained on bootstrapped samples, which reduces the risk 

of overfitting and increases robustness to outliers. Gradient Boosting sequentially corrects the 

errors of previous trees, which helps to better capture subtle patterns in the data, and Extra Trees 

adds additional randomness to the tree construction process, due to which it can work even 



 

 
 

35 

more effectively on heterogeneous datasets. To account for nonlinear relationships, Support 

Vector Regression (SVR) and a neural network in the form of a multilayer perceptron (MLP) 

was included. SVR with an appropriate kernel (e.g., RBF) can handle highly nonlinear 

functions, and a neural network, with the right settings for the architecture and training 

parameters, often outperforms other models in problems where the ability to generalize to 

complex distributions is important. Finally, to assess how much better all these approaches are 

than the trivial option, the DummyRegressor (ZeroR) model, which simply predicts the mean 

value of the target variable, served as the base model.  

The training process for each model consisted of several stages. First, synthetic datasets were 

generated (using three different methods) to expand the training set and make it more diverse. 

Next, cross-validation was performed for each model (usually 5-fold), where hyperparameters 

were selected using Grid Search or alternative optimization algorithms. This helped to refine 

parameters such as regularization coefficients for linear models, the number of trees and depth 

for Random Forest and Gradient Boosting, kernel parameters for SVR, and the number of layers 

and neurons in MLP. After completing the tuning on synthetic data, model trained on the entire 

expanded dataset and tested on the original one (without adding synthetics) to check the real 

generalization ability. This comprehensive approach to model selection and training ensures 

that were considered different classes of algorithms, tested them on a wide range of data, and 

selected those that actually perform best in predicting the performance of roadheader machines. 

Linear models (Ridge, Lasso and ElasticNet) 

For linear methods, it is assumed that the target variable y depends linearly on the set of features 

X. Let X be a matrix of size 𝑙𝑙 × 𝑑𝑑, where nnn is the number of observations, d is the number 

of features, and y is a vector of targets of size n. Observation of a vector of coefficients 𝑋𝑋  ∈

 𝐼𝐼𝑑𝑑 that best approximates the dependence 𝑦𝑦 ≈ 𝑋𝑋𝑋𝑋 is performed. 

Ridge regression (L2 regularization). 

The objective function of Ridge regression is formulated as 

𝑚𝑚𝑚𝑚𝑙𝑙
𝛽𝛽

 ||𝑋𝑋𝑋𝑋 − 𝑦𝑦||2 + 𝜆𝜆||𝑋𝑋||2, 

(25) 



 

 
 

36 

where ∥⋅∥ denotes the Euclidean norm, and 𝜆𝜆 ≥ 0 is the regularization coefficient. The first 

term is responsible for minimizing the forecast error, and the second limits the growth of the 

coefficients, reducing the risk of overfitting. 

Lasso regression (L1 regularization). 

Unlike Ridge, the L1 norm is used here: 

𝑚𝑚𝑚𝑚𝑙𝑙
𝛽𝛽

 ||𝑋𝑋𝑋𝑋 − 𝑦𝑦||2 + 𝛼𝛼||𝑋𝑋||1, 

(26) 

where ||𝑋𝑋||1 = ∑𝑑𝑑
𝑗𝑗=1 𝛼𝛼�𝑋𝑋𝑗𝑗� The parameter α controls the strength of the regularization. Due 

to the L1 norm, some components of β can be set to zero, which gives a feature selection effect. 

ElasticNet (mixed regularization). 

ElasticNet combines the properties of Ridge and Lasso by minimizing 

𝑚𝑚𝑚𝑚𝑙𝑙
𝛽𝛽

 ||𝑋𝑋𝑋𝑋 − 𝑦𝑦||2 + 𝛼𝛼(𝜌𝜌||𝑋𝑋||1 + (1 − 𝜌𝜌)||𝑋𝑋||2), 

(27) 

where α and ρ control the degree of contribution of L1 and L2 to the regularization. This helps 

to cope with cases where there is both feature sparseness and cross-correlation. 

Ensemble methods (Random Forest, Gradient Boosting, Extra Trees) 

Ensemble models build several base algorithms (usually decision trees) and combine their 

predictions. 

Random Forest. 

Let us have T trees, each of which is denoted as 𝑓𝑓𝑏𝑏(𝑒𝑒). In regression, the final prediction is 

obtained by averaging: 

𝑦𝑦�(𝑒𝑒) =
1
𝑇𝑇
�𝑓𝑓𝑏𝑏(𝑒𝑒)
𝑇𝑇

𝑏𝑏=1

. 

(28) 



 

 
 

37 

Each tree is trained on a bootstrap sample of the original data, and a random subsample of 

features is used to select features for splitting at each node. This approach reduces the 

correlation of trees and improves generalization ability. 

Gradient Boosting. 

The idea of gradient boosting is that at each step a new tree is built that approximates the 

antigradient of the loss function. Let 𝐹𝐹𝑟𝑟(𝑒𝑒) be the model after the mmm-th step, then at step 

m+1 a tree ℎ𝑟𝑟+1(𝑒𝑒) is built, which approximates the residuals or errors of the previous model. 

The final model takes the form: 

𝐹𝐹𝑟𝑟+1(𝑒𝑒) = 𝐹𝐹𝑟𝑟(𝑒𝑒) + 𝜈𝜈 ⋅ ℎ𝑟𝑟+1(𝑒𝑒), 

(29) 

where 𝜈𝜈 is the learning rate. This iterative scheme allows us to gradually “refine” the 

predictions, reducing the error. 

Extra Trees. 

The Extra Trees (Extremely Randomized Trees) model is similar to Random Forest in many 

ways, but it selects partition thresholds even more randomly. Formally, when constructing a 

tree, a subset of features and random thresholds are randomly selected for each node, rather 

than a detailed enumeration. This additional "loosening" of the tree structure can improve the 

robustness to overfitting on heterogeneous datasets. 

Nonlinear methods and neural networks (SVR, MLP) 

Support Vector Regression (SVR). 

The SVR model searches for a function 𝑓𝑓(𝑒𝑒) = ⟨𝑤𝑤, 𝑒𝑒⟩ + 𝑋𝑋 that fits into the ε -neighborhood of 

the target value and has the minimum norm of the vector w. The problem is formulated as 

follows: 

𝑚𝑚𝑚𝑚𝑙𝑙
𝑤𝑤 𝛽𝛽

 1
2

||𝑤𝑤||2 under constraints {𝑦𝑦𝑒𝑒 − ⟨𝑤𝑤, 𝑒𝑒𝑒𝑒⟩ − 𝑋𝑋 ≤ 𝜖𝜖, ⟨𝑤𝑤, 𝑒𝑒𝑒𝑒⟩ + 𝑋𝑋 − 𝑦𝑦𝑒𝑒 ≤ 𝜖𝜖 }, 

(30) 



 

 
 

38 

where ε defines the error tolerance. When using kernels (e.g., RBF), the regression goes into a 

nonlinear feature space, which helps to capture complex dependencies. 

Multilayer Perceptron (MLP). 

An MLP neural network consists of several layers: an input layer, one or more hidden layers, 

and an output layer. Let there be HHH neurons in the hidden layer, then the output of each 

neuron is calculated as 

𝑧𝑧𝑗𝑗 = 𝜎𝜎 ��𝑤𝑤𝑗𝑗𝑒𝑒
(1)𝑒𝑒𝑒𝑒 + 𝑋𝑋𝑗𝑗

(1)
𝑠𝑠

𝑒𝑒+1

�, 

(31) 

where σ(⋅) is the activation function (e.g. ReLU or sigmoid), 𝑤𝑤𝑗𝑗𝑒𝑒
(1) and 𝑋𝑋𝑗𝑗

(1) are the weights and 

biases for the first layer. The output layer undergoes a similar transformation, and the final 

output of the network gives an estimate of the target variable. The network is trained by 

minimizing the loss function (e.g. MSE) using backpropagation, where the weights are adjusted 

using gradient methods. 

Baseline Model (DummyRegressor, ZeroR) 

The baseline model simply predicts the mean (or median) of the target variable, ignoring the 

feature values. Let 𝑦𝑦 = 1
𝑠𝑠
∑ 𝑦𝑦𝑒𝑒𝑠𝑠
𝑒𝑒=1 . Then for any x, the model predicts 𝑦𝑦�(𝑒𝑒) = 𝑦𝑦. This is the 

simplest approach, which serves as a lower bound on the quality: all other models should 

perform better than the trivial averaging. 

4.4 Cross-validation and evaluation metrics 

For an objective assessment of the quality of the constructed models, our study uses 5-fold 

cross-validation. This method allows dividing the synthetic sample into five equal parts, 

sequentially training the model on four parts and testing it on the remaining one. This approach 

helps to obtain a reliable estimate of the generalization ability of the model, minimizing the 

impact of random data partitioning and preventing overfitting. Cross-validation ensures the 

stability of the results and makes it possible to optimize the hyperparameters of each model, 

which is especially important when working with a small amount of initial data supplemented 

synthetically. 



 

 
 

39 

As metrics for assessing the effectiveness of the models, three main indicators are used - the 

determination coefficient (R²), the mean square error (MSE) and variance accounted for (VAF). 

The determination coefficient R² and VAF are inter-related, and show what proportion of the 

variance of the target variable is explained by the model. An R² value close to 1 indicates that 

the model is able to adequately describe the data, while low values indicate insufficient 

explanatory power of the model. The mean squared error (MSE) measures the average squared 

difference between predicted and actual values. The smaller the MSE, the more accurate the 

model. Using these metrics allows for a comprehensive assessment of both the relative ability 

of the model to explain data variability and the absolute accuracy of its forecasts. The metrics 

are calculated in two modes: during cross-validation on synthetic data, which allows for 

selecting optimal hyperparameters and assessing the stability of the model, and when testing 

the trained model on the original data set. This approach ensures that the achievements obtained 

on synthetic data are actually reflected in the quality of forecasts on the real sample. As a result, 

comparing R² and MSE for different models and methods of generating synthetic data allows 

for choosing the most optimal algorithm for ICR forecasting, ensuring a high level of accuracy 

and reliability of forecasts. 

 

 

 

 

 

 

 

 

 

 



 

 
 

40 

5. DATA ANALYSIS 

Data Analysis 

At this stage of the study, a detailed analysis of the original data set containing the geotechincal 

and roadheader performance parameters from San Manuel mine was carried out. The dataset 

that was obtained contains 28 datapoints, including the RMR, RQD, UCS, and ICR values. 

Initial data is given in the RMR table and Machine performance graph in the figure 3.  

Data preprocessing and expansion of the feature space 

First of all, features were normalized to bring them to a single scale, which is critical for correct 

model training. After that, second-degree polynomial features were generated. This allowed us 

to identify hidden nonlinear relationships between the original characteristics and the target 

variable (ICR). Expansion of the feature space made it possible to detect additional 

dependencies that were not obvious when analyzing the original data. 

Descriptive statistics 

To assess the quality and distribution of data after the preprocessing stages, a descriptive 

statistics table was compiled. It presents the following indicators for each feature (both original 

and generated): 

Count — number of observations (in this case, 28 records). 

Mean — average value of the feature. 

Std — standard deviation, reflecting the spread of values around the mean. 

Min, 25%, 50%, 75%, Max — minimum value, first quartile, median, third quartile and 

maximum value, allowing to estimate the distribution and range of values. 

Examples of statistics interpretation 

For example, for the original RQD feature, the mean value is close to zero, and the standard 

deviation is approximately one. This indicates the correctness of the data scaling. In the case of 

polynomial features, such as RQD² or RQD × RMR, the values of the mean and standard 

deviations also confirm the precision of the scaling. 

 



 

 
 

41 

Table 5: EDA summary for the Original Dataset 

 count mean std min 25% 50% 75% max 

RQD 28.0 40.0 19.459 3.0 24.25 43.0 53.25 72.0 

RMR 28.0 35.786 14.312 15.0 27.0 32.5 44.0 70.0 
UCS 28.0 119.429 34.009 60.0 91.5 118.0 139.0 200.0 

ICR 28.0 15.215 4.151 6.492 12.526 14.511 18.841 22.167 

Table 6: EDA summary for the Polynomial features of the Original Dataset 

Feature count mean std min 25% 50% 75% max 

RQD 28 0 1,00 -1,936 -0,824 0,157 0,693 1,675 

RMR 28 0 1,00 -1,479 -0,625 -0,234 0,584 2,434 

UCS 28 0 1,00 -1,779 -0,836 -0,043 0,586 2,413 

RQD² 28 1 1,096 0,003 0,239 0,576 1,326 3,749 
RQD 

RMR 28 0,798 1,204 -0,377 0,036 0,367 0,825 4,077 
RQD 

UCS 28 0,674 1,116 -0,809 -0,049 0,237 1,024 4,04 

RMR² 28 1 1,571 0,007 0,116 0,391 0,787 5,926 

RMR 

UCS 28 0,636 1,348 -0,984 0,001 0,254 0,683 5,873 

UCS² 28 1 1,286 0 0,1 0,63 1,355 5,821 

Second-degree polynomial features were created to capture complex nonlinear relationships 

between original features. Generating new features, such as squared original features and their 

interactions, produced data with diverse values and large scatter. For example, squared features, 

such as RQD^2, RMR^2, UCS^2 have a mean value 1 with a high standard deviation, indicating 

significant variations in the data. These features can be useful for models as they provide 

additional features that can help in better prediction. 

Interactions between features, such as RQD RMR, RMR UCS, have both positive and negative 

values, reflecting complex relationships between geological characteristics. These interactions 

can help models uncover hidden dependencies and improve predictive ability, especially for 

nonlinear models such as ensemble methods. 



 

 
 

42 

The high scatter and large ranges of polynomial features highlight their importance for machine 

learning models, where such features can improve prediction accuracy. These polynomial 

features enable models to capture more complex relationships, which is especially useful for 

predicting drilling machine performance, where the interaction of different characteristics is 

critical. 



 

 
 

43 

 

Figure 6: Correlation Heatmaps of the Original Data. (Figure A - Heatmap of the Base Features, B - Polynomial 
Features) 
 



 

 
 

44 

 
Figure 7: Histograms of Standardized Original Data Distributions (Histogram A - UCS, B - RQD, C - RMR 

value). 

  



 

 
 

45 

5.2 Model training and evaluation 

This section provides a comparative analysis of the performance of models trained on a 

synthetically expanded sample, followed by an evaluation of their performance on the original 

data. A detailed description of the training process is presented in the methodological section, 

so here the emphasis is on comparing the results and interpreting the obtained metrics. 

Based on synthetically generated data using three different methods (Ridge Regression 

Labeling, Gaussian Noise Labeling and Random Forest Regression Labeling), 5-fold cross-

validation was performed for each model. The main evaluation metrics are the determination 

coefficient (R²) and the mean square error (MSE). These indicators allow us to evaluate the 

extent to which models trained on synthetic data are able to generalize information when 

moving to the original data set. 



 

 
 

46 

 

Figure 8: Base Features Correlation Heatmaps of the Synthetic Data. (Figure A - Ridge , B - Gaussian, C - 
Random Forest) 
 



 

 
 

47 

 

Figure 9: Polynomial Features Correlation Heatmaps of the Synthetic Data. (Figure A - Ridge , B - Gaussian, C 
- Random Forest) 
 



 

 
 

48 

Following the correlation heatmaps for base and polynomial features, the histograms for the 

synthetic data distribution were plotted:  

 

Figure 10: Synthetic Data Distribution for Ridge Regression Labeling (Figure A - RQD , B - RMR, C - UCS). 
 



 

 
 

49 

 

Figure 11: Synthetic Data Distribution for Gaussian Noise Labeling (Figure A - RQD , B - RMR, C - UCS). 
 



 

 
 

50 

 
Figure 12: Synthetic Data Distribution for Random Forest Regression Labeling (Figure A - RQD , B - RMR, C - 

UCS). 



 

 
 

51 

 

Following the synthetic data generation, the models were trained on the augmented data. After 

the training was performed, models were evaluated on the original dataset which serves the 

purpose of the test set.  

The scatterplots were plotted with the purpose of representing the output: 

 



 

 
 

52 

 

Figure 13: ICR plots for Linear Models trained on Ridge Regression Labeling data (Scatterplot A - Ridge 
regression, B - Lasso, C - ElasticNet). 
 



 

 
 

53 

 

Figure 14: ICR plots for Ensemble Models trained on Ridge Regression Labeling data (Scatterplot A - Random 
Forest, B - Gradient Boosting, C - ExtraTrees). 
 



 

 
 

54 

 

Figure 15: ICR plots for Non-Linear Models trained on Ridge Regression Labeling data ( Scatterplot A - MLP, 
B - SVR). 
 



 

 
 

55 

 

Figure 16: ICR plot for Base Model trained on Ridge Regression Labeling data(ZeroR). 
 

The same plots are made for models trained on Gaussian Noise Labeling method.  

 



 

 
 

56 

 

Figure 17: ICR plots for Linear Models trained on Gaussian Noise Labeling method (Scatterplot A - Ridge 
regression, B - Lasso, C - ElasticNet). 
 



 

 
 

57 

 

Figure 18: ICR plots for Ensemble Models trained on Gaussian Noise Labeling method (Random Forest, 
Gradient Boosting, ExtraTrees). 
 



 

 
 

58 

 

Figure 19: ICR plots for Non-Linear Models trained on Gaussian Noise Labeling data ( Scatterplot A - MLP, B 
- SVR). 
 



 

 
 

59 

 

Figure 20: ICR plot for Base Model trained on Ridge Regression Labeling data(ZeroR). 
 

Scatterplots of ICR values obtained on the models trained on Random Forest Regression 

Labeling. 

 



 

 
 

60 

 

Figure 21: ICR plots for Linear Models trained on Random Forest Regression Labeling data (Scatterplot A - 
Ridge Regression, B - Lasso, C - ElasticNet). 
 



 

 
 

61 

 

Figure 22: ICR plots for Ensemble Models trained on Ridge Regression Labeling data (Scatterplot A - Random 
Forest, B - Gradient Boosting, C - ExtraTrees).  
 



 

 
 

62 

 

Figure 23: ICR plots for Non-Linear Models trained on Random Forest Regression Labeling data (Scatterplot A 
- MLP, B - SVR). 
 



 

 
 

63 

 

Figure 24: ICR plot for Base Model (ZeroR) trained on Random Forest Regression Labeling.  
 
The results show that ensemble methods (e.g. Random Forest, Gradient Boosting, Extra Trees) 

demonstrate the best performance, providing high prediction accuracy and resistance to 

overfitting. At the same time, linear models (Ridge, Lasso, ElasticNet) are inferior in 

forecasting quality, which indicates the difficulty of identifying nonlinear relationships in the 

original data. 

Table 7: Example Outputs of Predicted ICR values 

Model ICR actual Ridge Regression Gaussian Noise R.Forest Regression 
Ridge 8,309 8,662 8,120 8,737 

Lasso 8,309 8,684 8,216 8,783 

ElasticNet 8,309 9,077 9,093 9,539 

RandomForest 8,309 8,451 8,209 8,339 

XGboost 8,309 8,475 8,400 8,438 

ExtraTrees 8,309 8,451 8,257 8,390 

MLP 8,309 8,359 8,447 8,263 
SVR 8,309 8,322 8,421 8,345 
ZeroR 8,309 14,935 14,910 14,736 

 



 

 
 

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By examining the table, results confirm the effectiveness of using a synthetically expanded 

sample for training models. The tables containing the results for all predicted ICR values are 

attached in Appendices 1-9.  

Comparative analysis demonstrated that the optimal balance between prediction accuracy and 

model stability is achieved when using ensemble algorithms. These findings serve as an 

important basis for further practical application of the developed ICR forecasting technique. 

5.3 Performance Comparison  

This section provides a detailed comparison of the models' performance based on the key 

metrics - the coefficient of determination (R²) and the mean square error (MSE). The 

experimental results are obtained for three synthetic data generation methods, which allows us 

to evaluate how the selected models cope with ICR forecasting under different approaches to 

sample expansion. 

 

Table 8: Performance Metrics – Ridge Regression Labeling 
Model CV R² Mean 

(Synthetic) 
CV R² Std 
(Synthetic) 

CV MSE Mean 
(Synthetic) 

Test R² 
(Original) 

Test MSE 
(Original) 

Test VAF 
(Original) 

Ridge 0.9352 0.0092 0.8340 0.7825 3.6142 0.7827 
Lasso 0.9347 0.0096 0.8401 0.7783 3.6826 0.7786 
ElasticNet 0.7484 0.0248 3.2639 0.5776 7.0171 0.5787 
Random 
Forest 

0.9392 0.0102 0.7833 0.7663 3.8832 0.7663 

Gradient 
Boosting 

0.9749 0.0042 0.3227 0.8156 3.0629 0.8157 

Extra 
Trees 

0.8649 0.0195 1.7434 0.7122 4.7816 0.7128 

MLP 0.9676 0.0082 0.4179 0.8084 3.1831 0.8091 
SVR 0.9771 0.0054 0.2934 0.8153 3.0689 0.8154 
ZeroR -0.0058 0.0028 13.0774 -0.0047 16.6920 0.0000 
 
 
 
 
 
 
 
 
 
 



 

 
 

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Table 9: Performance Metrics – Gaussian Noise Labeling 
Model R² Mean 

(Train) 
R² Std  
(Train) 

MSE Mean 
(Train) 

Test R² 
(Test) 

Test MSE 
(Test) 

Test VAF 
(Test) 

Ridge 0.8182 0.0152 2.9544 0.8200 2.9899 0.8204 
Lasso 0.8170 0.0155 2.9743 0.8184 3.0166 0.8188 
ElasticNet 0.5831 0.0383 6.7863 0.5747 7.0662 0.5774 
Random 
Forest 

0.9505 0.0085 0.8039 0.9565 0.7222 0.9566 

Gradient 
Boosting 

0.9831 0.0039 0.2746 0.9841 0.2634 0.9841 

Extra 
Trees 

0.8358 0.0268 2.6580 0.8396 2.6644 0.8406 

MLP 0.9676 0.0056 0.5248 0.9568 0.7177 0.9569 
SVR 0.8915 0.0159 1.7601 0.8913 1.8056 0.8915 
ZeroR -0.0103 0.0076 16.4882 -0.0080 16.7470 0.0000 

 

Table 10: Performance Metrics – Random Forest Regression Labeling 
Model R² Mean 

(Train) 
R² Std 
(Train) 

 MSE Mean 
(Train) 

Test R² 
(Test) 

Test MSE 
(Test) 

Test VAF 
(Test) 

Ridge 0.8261 0.0103 2.0391 0.7674 3.8640 0.7698 
Lasso 0.8255 0.0111 2.0454 0.7633 3.9329 0.7657 
ElasticNet 0.6355 0.0321 4.2635 0.5264 7.8689 0.5329 
Random 
Forest 

0.8743 0.0177 1.4620 0.8081 3.1885 0.8105 

Gradient 
Boosting 

0.9386 0.0126 0.7118 0.8900 1.8272 0.8922 

Extra 
Trees 

0.7877 0.0290 2.4714 0.6999 4.9853 0.7052 

MLP 0.9330 0.0207 0.7737 0.8984 1.6885 0.9033 
SVR 0.9245 0.0105 0.8816 0.8572 2.3724 0.8592 
ZeroR -0.0103 0.0061 11.8555 -0.0138 16.8432 0.0000 
 

In this work, three different synthetic generation methods were used to evaluate the quality of 

the forecasting models: Ridge Regression Labeling, Gaussian Noise Labeling, and Random 

Forest Regression Labeling. Each of these strategies generated synthetic training data, which 

was cross-validated (with R² and MSE estimates), and then the ability of the models to 

generalize to the original dataset was assessed. In addition to the main metrics such as R² and 

MSE, the Test VAF (Variance Accounted For) metric was also calculated, which allows us to 



 

 
 

66 

judge how well the model explains the variance of the target variable, which actually correlates 

with the R² value. 

When using the Ridge Regression Labeling method, linear models such as Ridge and Lasso 

showed high results: the cross-validation R² was about 0.935, and the test R² was about 0.782. 

Test VAF was comparable to the test R², indicating robustness of the explained variance. 

ElasticNet performed slightly worse, with a test R² of around 0.578, indicating weaker 

generalization ability in this configuration. Among the nonlinear models and ensemble 

methods, Gradient Boosting performed outstandingly with a test R² of around 0.816, while SVR 

and MLP also showed comparable values (around 0.815 and 0.808, respectively). Interestingly, 

Random Forest and Extra Trees performed more modestly in this method, while the mean-

predicting ZeroR model did not produce any significant results. 

 

There synthetic data generated for gaussian noise labeling demonstrates the best quality so far, 

as reflected in the cross-validation R² values for the models (CV and Test values are almost 

similar). Due to this, the models achieve high performance on the test set: the test R² for Ridge 

and Lasso reaches around 0.820, and ensemble models such as Random Forest, Gradient 

Boosting, and even MLP demonstrate test R² of around 0.956–0.984. Since the Test VAF is 

almost identical to the Test R², it can be concluded that the data quality allows the models to 

generalize well on the original dataset. 

 

The Random Forest Regression Labeling method shows intermediate results. The cross-

validation metrics for the Ridge and Lasso models are around 0.826, but their test R² values are 

slightly lower (around 0.767 and 0.763, respectively). ElasticNet still demonstrates poor 

generalization ability with a test R² of around 0.526. Among the ensemble methods, Gradient 

Boosting shows good results (test R² is about 0.890), and MLP and SVR models also 

demonstrate satisfactory performance. It is worth noting that for this synthetic generation 

method, Extra Trees turned out to be less robust, which is reflected in a decrease in test scores 

to 0.6999. 

 

Now, the ranking of the models’ performance is conducted. The ranking was done for all three 

methods of data synthesis, however the attention will be focused on Gaussian noise labeling 

since generally the models show higher performance for this method.  

 

 



 

 
 

67 

The ranking is done based on the following criteria:  

 

R² value - The Higher the better; 

MSE - The Lower the better; 

VAF - The Higher the better. 

Now, the ranks for each model are computed: 

Table 11: Ranking table for models trained on Ridge Regression Labeling data. 

Model Rank 
Gradient Boosting 1 
SVR 2 
MLP 3 
Ridge 4 
Lasso 5 
Random Forest 6 
Extra Trees 7 
ElasticNet 8 

 

Strong inter-linked correlation between the performance metrics is seen during the comparison. 

Since the metrics have are mathematically inter-related to each other, they tend to change in 

unity with each other. This may seem like usage of these metrics may not display the 

independence in the computation sources, however, all of these metrics are strong standards for 

assessment of ML models. The same ranking is performed for Gaussian Regression Labeling, 

where the model