*This contribution is about the importance of the use of mathematical and statistical tools in the technological and other processes required for the acquisition and processing of earth resources.*

**Introduction**

The digital age, together with rapidly evolving technologies, pointed out the demand for new tools that could help in the analysis and modeling of technological and other processes in the acquisition and processing of earth resources. The language of statistical mathematics assists in designing and interpreting such models.

This is because the optimization of processes can only be achieved by appropriate analysis of systems behavior, by critical assessment of the current state, by planning and developing reproducible techniques and procedures for design and processing, and by evaluating experimental measurements of these technological processes.

Demands for improving efficiency of processes result in the monitoring of various parameters, including, product parameters, parameters of processing conditions and parameters of production and transport processes. Measurements in processes define their properties, confirm compliance with necessary conditions, identify the causes of non-compliance, and analyse the influencing factors. The necessary condition to verify the validity of the data achieved as the objects’ or processes’ parameters, is to perform statistical measurements and evaluations of such results. In turn, this is achieved by transforming problems into mathematical-statistical ones.

**New Ways of Experimenting **

The possibilities to measure or perform experiments on real objects or devices are often limited or even impossible in the conditions in which real technological objects are industrially situated. The big advantage of the coalescence of modern computer-supporting data processing and the tools of mathematics in general (including mathematical statistics and statistical tools of experimental design and machine learning) is the potential to use the models of technological processes instead of provide the experiments on real objects in order to acquire the needed data.

When creating such models the goal is to get to know the ongoing technological processes in them. Via a series of measurements at physical models of technological processes and objects (e.g. heat treatment of metal surfaces, decoupling of rocks by drilling, underground coal gasification) important data is obtained. The tools of graph theory – a part of discrete mathematics – provide new opportunities to increase the information content of measured data. For the data measurement, the possibilities to increase the information content can be tested by machine learning techniques, optimization methods, methods used in quality management and decision theory in addition to tools from graph theory and mathematical statistics. Statistical tools, together with tools of decision theory, facilitate the objectively critical analysis of experiments’ results, the conclusions of which can be re-used to improve the operational efficiency and reliability of technological processes. This approach allows the creation of reproducible techniques and procedures of processing and evaluation of experimental measurements in processes or their models. In this way complex procedures of measurement, processing and evaluation of measurement results can be determined.

Many robust systems for acquiring and processing of earth resources have been used in practice for a long time. This is expected in the future, as well. Therefore, it makes sense to measure the behavior of these systems in order to model them.

There are models of several systems available at the Faculty of Mining, Ecology, Process Control and Geotechnologies of the Technical University of Košice – for example a static model of a belt conveyor, which is used for modeling and analysis of force ratios in a real device during the transport of materials; a laboratory furnace in which processes of heat treatment of metals are modeled; a drilling device, which is a model for the process of rock disconnection by drilling and a model of an underground coal gasification appliance. These models already produce an array of data during several experiments provided there, but measurements based on the new approach described above will be implemented soon, too.

The key component in the new approach to the studied phenomenon is the optimal composition of research teams working within the area. Division of labor by task naturally leads to the formation of several local research teams. Authors of this contribution belong to one of these research units, too.

Some of the data acquired via experimenting on models have already been processed by researchers, while another data will be worked up soon. Tools of mathematics and mathematical statistics always play a key role in this. For example, these tools have been used for the verification of the effect of emitted tension force of a conveyor belt on the size of contact forces induced by the closed conveyor belt on the guide-idlers in the hexagonal idler housing of pipe conveyor – see [1]. Besides the usual methods of descriptive statistics used for the presentation of the data, the nonparametric methods of mathematical statistics have been used here, as well. Furthermore, linear regression models have been used for prediction of the pipe conveyor belt contact forces on the idler rolls in the hexagonal idler housing in [2]. Mathematical models have been used here for the indirect measurement of the contact forces described above. Another example of the application of mathematical tools in indirect measuring can be found in [3]. Here, the real time indirect measurement system of the inner temperatures in the steel roll is evaluated. This system is based on the direct measurement of the atmosphere in the furnace space between the protective bell and the roll. The input to the mathematical model is the measured temperature of the atmosphere. Methods of mathematical statistics have also been used in order to verify whether the physical model of the bell furnace in the research of steel coils annealing processes is suitable in terms of the annealing regimes repeatability – see [4]. We have also used graph theory tools in the research on identification of the factors causing damage to conveyor belts during the transportation of coal – see [5]. We aim to use this approach together with statistical tools of multicriterial data analysis for processing the data from systems inspections in the future.

Experiments on models are more effective than on real objects, especially from an economical point of view. The results obtained on models can be equally used in proposals for entities implementing these processes in practice, aiming to improve reliability and efficiency of processes. Of course, in this case experiments on models have to be complemented by subsequent research on the impact of the technological processes e.g. on the environment. There is a lot of mathematics used in such research. For example, we have used a number of mathematical calculations (see Figure 1) in the analysis of spatial properties of the landscape structure – see e.g. [6], [7]. Such monitoring of landscape changes is important not only for those who work in agriculture and mapping, but also in forestry, regional planning, acquisition and processing of earth resources and ecology – see e.g. [8].

**Funding of Research**

Although the experimentation on models is much cheaper than on real systems, there are still some costs connected with such research. These can be compensated either via research grants of scientific grant agencies, university grants or sponsored directly by entities from the industry.

This research on application of modern methods in the analysis and modeling of technological and other processes used in the acquisition and processing of earth resources in order to optimize them, has been supported by the internal grant system of the Ministry of Education, Science, Research and Sport of the Slovak Republic and Slovak Academy of Sciences – the grant VEGA 1/0264/21.

### Erika Fecková Škrabuľáková

Lecturer

Faculty of Mining, Ecology, Process Control and Geotechnologies

Technical University of Košice,
KOŠICE,
SLOVAKIA

### Monika Ivanová

Lecturer

Faculty of Humanities and Natural Sciences

University of Prešov,
PREŠOV,
SLOVAKIA

[1] V. MOLNÁR et al.: Statistical approach for evaluation of pipe conveyor’s belt contact forces on guide idlers. *Measurement 46* (2013), 3127-3135.

[2] V. MOLNÁR et al.: Mathematical models for indirect measurement of contact forces in hexagonal idler housing of pipe conveyor. *Measurement 47* (2014), 794-803.

[3] B. STEHLÍKOVÁ, P. HOROVČÁK, M. DURDÁN. Statistical evaluation of differences of the inner temperatures in the steel roll measured directly and indirectly. In: *SGEM 2012: 12th International Multidisciplinary Scientific GeoConference: conference proceedings*. 2012, 223-230.

[4] B. STEHLÍKOVÁ, M. DURDÁN. Statistical verification of the repeatability regimes at model of the bell furnace. In: *2016 17th International Carpathian Control Conference (ICCC)*. IEEE, 2016, 697-701.

[5] E. ŠKRABUĽÁKOVÁ et al.: Identification of Factors Causing Damage to Conveyor Belts during the Transportation of Coal*. Applied Mechanics and Materials 683* (2014), Trans Tech Publications, Switzerland, 130 -134.

[6] M. IVANOVÁ. Zmeny krajinnej pokrývky zázemia Zemplínskej šíravy v rokoch 1956-2009, Geografické práce 15/2013, pp. 233.

[7] M. IVANOVÁ et al.: The analysis of some properties of landscape through hierarchical cluster analysis. In: SGEM 2018: *International Multidisciplinary Scientific GeoConference: conference proceedings*. 2018, 877 – 884.

[8] E. MICHAELI, M. BOLTIŽIAR, M. IVANOVÁ. Geoecological structure of the dump of technological waste (Fe-concentrate) at Sereď. *Acta Facultatis Studiorum Humanitatis et Naturae Universitatis Prešoviensis, Folia Geographica 49 *(2009), 180-197.