The Proposal of a Method for Rock Classification Using a Vibration Signal Propagated during the Rotary Drilling Process

Abstract

This research aims to classify rock types based on the vibration signal propagated from the experimental rotary drilling process, where the generated vibration signal is a source of information. Its measurement and processing provide important information about the rock disintegration process, the drilled rock, the drilling tool, and the drilling parameters. For the design of a suitable classification method, several attributes of the vibration signal were calculated for two different signal recording lengths. A cluster dendrogram, an ANOVA test, and a boxplot were used to determine attributes and proper signal length. The classification rule was found using a decision tree, a machine-learning tool. This publication gradually describes the process of creating the classification method and the results of the reliability verification of the proposed classification method. The disintegrated rocks were andesite, granite, limestone, and concrete used as artificial rock. This proposed method classified these three rock types and concrete with a reliability of 100% from a vibration signal record lasting 1/4 s.

1. Introduction

The technological properties of rocks affect their behaviour during the disintegration process, as well as during uncoupling and processing. Disintegration is the rock’s ability to resist disconnection work tools and is one of the first rock properties encountered when drilling. The disintegration of rock through drilling depends on the rock type, its properties, and the drilling tool’s method [1,2]. As technology evolves, new types of drilling equipment and various modifications are developed for easier acquisition of Earth’s resources. New, fundamentally progressive technologies mean a substantial increase in the quality of drilling work and the speed of the drilling process. They are differentiated according to the applied technologies in the industry [3,4,5].

The basic division remains according to the method of rock disintegration. Practically all available technologies are used to implement drilling operations, which allows for the necessary tests and measurements during drilling to obtain the required geological or mining information [6,7,8,9].

During the disintegration process of rock separation (drilling), vibrations arise. The resulting vibrations depend on the properties of the disintegrating rock. Thus, identifying the type and properties of rocks is one of the most essential diagnostics that can be performed during the drilling process.

Vibration analysis is the process of monitoring vibration levels and investigating vibration signals. The signal is directly examined based on time, frequency, and/or the time–frequency spectrum obtained by applying the Fourier transform.

Several authors [10,11,12,13,14,15,16,17,18] have studied vibroacoustic signals and rock properties using the Fourier transform to time waveform. Khoshouei et al. [11] found that the spectrum of each rock is distinct from those of other rocks, but within each rock type, the states of the spectra are similar. The dominant frequencies of each rock can be used to determine and predict the properties of the rock. The study above showed that it is possible to install acoustic sensors on drilling machines and to process the propagated acoustic signals to detect the type of rocks. In his work [13], Min Qin illustrated the application of a vibration sensor and a special broadband acoustic sensor method to distinguish specific time–frequency characteristics generated by drilling in different rock types. His research found that vibration and acoustic spectral characteristics are different and can be used to recognise rock types. Using multiple regression analysis, Rajest Kuman et al. [19] tried to estimate the relationships between the noise level produced during rotary drilling and rock properties concerning drilling parameters.

Jiang et al., in their work [20], proposed a new method for the automatic identification and recognition of microseismic and explosive rock fracture signals based on their time–frequency spectrum characteristics.

Wang et al. [21] proposed a model to identify rock hardness during tunnelling based on analysing various signals (vibration signals, acoustic emission signals, cutting current signals, and temperature signals). He based its design on multisensory information fusion and the Dempster–Shafer theory.

Rock disintegration is one of the basic processes of mineral extraction. The drilling process is economically, energetically, and ecologically very demanding. Therefore, the optimal setting of mode parameters, the optimisation of energy consumption, the prediction of drilling tool wear, drilling efficiency, and the recognition of drilled rocks are all being investigated in this field [1,2,22,23]. Zhongwen Yue et al. [23] investigated the response characteristics of parameters when drilling into a rock mass. A comprehensive analysis of multiple sets of parameters found that the identification of the layered rock interface can be recognised. Their study confirmed that the material’s structure affects some drilling parameters. Therefore, many authors study the relationships between the petrophysical and petrographic properties of rocks [24,25,26]. The authors Suping Peng and Jincai Zhang [27] discussed underground rocks’ physical, geomechanical, and geophysical properties under various combinations of stresses and pressure environments. Their publication provides examples of problems that occur during mining at greater depths, increases in the in situ stress and pore pressure, and temperature changes. These problems include borehole and tunnel instabilities, casing failures, water rushes into active mining areas, rock and coal spills, and mining-induced seismicity.

Several researchers have used complex machine learning and deep learning models to determine classification models [28,29,30,31]. In their study, Xiaolei Yue et al. [32] found a clear response pattern between rock strength and sound pressure levels at constant rotations and thrust rates.

This research aims to classify the rock type based on the vibration signal propagated during rotary drilling in an experimental laboratory. The motivation for this research is to consider the benefits of knowing, with a high reliability, which type of rock is disintegrated during deep drilling. The identification and determination of the type of rock according to the vibration signal will help to predict drilling progress and select appropriate operating parameters when disintegrating rock.

This study consists of several parts. Section 2 describes the properties of disintegrated rocks, the methods of conducting experimental drilling, the methods of vibration signal acquisition, and the procedures for the research task. Section 3 includes determining signal attributes for classification and record length for attribute calculation. Section 4 includes rock classification, the classification rule, and the decision tree graph for the train set, as well as a table evaluating the reliability of the classification, its percentage expression, and an evaluation of the success of the classification for each rock.

2. Methodology

The research methodology presented here consists of the procedure by which the data were obtained and a description of the methods and techniques used to process the obtained data.

2.1. Experimental Drilling and Sensing Methodology

This section describes the properties of the disintegrated rocks, the methods of conducting experimental drilling, and the recording of the vibration signal.

The primary objective of rotary diamond core drilling is to obtain a drill core in the shape of a cylinder, the compactness of which is determined by the rock’s drill ability and physical mechanical properties. The quality of the work is evaluated by the core yield, which is the ratio of the drilled length of the well to the length of the obtained core.

When drilling, the primary parameter is the number of revolutions (speed) and compressive (pressure) force of the diamond drilling tool. For experimental works, the selected revolutions are n = 1000 rpm and the compressive force F = 5000 N. The drilling used a 6-channel drilling tool. The drilled rocks were andesite, granite, limestone, and artificial rock concrete.

The drilled rocks were selected based on their availability from the surrounding quarries. The rock samples selected (

Table 1. The properties of the tested rock [27,33,34].

Rock Name	Rock Sample	Compressive Strength (MPa)	Density (g/cm3)	Grain Size
Andesite—a		Very strong 100–250	2.5–2.8	Very fine-grained
Granite—g		Extremely strong > 250	2.5–2.8	Medium- to coarse-grained
Limestone—l		Very strong 100–250	2.5–2.8	Fine-grained
Concrete—c		Medium strong 25–50	2.2–2.4	Coarse-grained

) are very fine-grained (limestone), fine-grained rock (andesite), and medium- to coarse-grained rock (granite). Concrete was selected as a soft, artificial rock with a coarse-grained material. Andesite and granite are igneous rocks, and limestone is a sedimentary rock.

Selected properties of the tested rocks are below [27,33,34] (Table 1):

• Andesite is an igneous rock that is grey to dark grey with frequent porphyritic growths of minerals. It contains essential minerals such as plagioclase, amphiboles, pyroxenes, biotite, and quartz. Andesite can also contain secondary minerals such as opal from cavities in basalts.
• Granite is a hard igneous rock that can be white, pink, grey, or orange, depending on the mineral composition. It contains essential minerals, mainly feldspar quartz, and secondary minerals in smaller quantities, such as biotite, muscovite, amphibole, and others.
• Limestone is a sedimentary rock that is typically white, grey, or tan. It contains mainly essential minerals such as calcite carbonate, usually in the form of calcite or aragonite. It may also contain magnesium carbonate (dolomite) and minor components such as clay, iron carbonate, feldspar, pyrite, and quartz.
• Concrete is a solid building material consisting of aggregate (gravel and sand) and binder (water and cement). It has the properties of natural stone. The nearest natural rock to concrete is sandy limestone. The typical concrete mix comprises roughly 10% cement, 20% air and water, 30% sand, and 40% gravel.

The drilling experiments were conducted by securing a sample of the chosen rock into a mechanical fixture on the drilling stand. The appropriate drilling mode was then selected, and the ADASH 3900-II measurement system recorded the vibration signal produced during the rock drilling. The vibration acceleration signal was measured for 20 seconds with a sampling frequency of 18 kHz and a sampling period of 0.55 ms, which covers a frequency range from 0 to 9 kHz. These vibration signal characteristics are consistent across all drilled rocks. Since the vibration signal is stationary for management purposes, it can be represented by {x_i}ⁿ_i−1, where n = 16,384 is the number of samples in the signal.

2.2. Solution Process Methodology

The following describes the mathematical and statistical tools used and the procedure for solving the research task.

Since the mathematical and statistical tools used are described in many works of literature, we do not present all formulas and statistical hypotheses in this publication. Instead, we describe the method used, its purpose, and the literature source if it is a primary source.

Statistical testing is evaluated using a p-value with a significance level of 0.05.

The subject of investigation is the vibration signal obtained and recorded in the rotary drilling process for three types of rocks—andesite, granite, limestone, and concrete.

The classification task consists of two steps:

• Selection of appropriate signal attributes for classification and estimation of the proper length of record for attribute calculation;
• Classification rule findings and verification.

In the first step of the classification task, the cluster dendrogram tool was used to determine the signal attributes for classification and the record length for calculating the attributes. The horizontal axis represents objects and clusters, while the vertical axes on the dendrogram show the distance of the clusters, i.e., their dissimilarity. Each split of the two clusters is shown on the diagram by dividing the vertical line into two vertical lines. The position of the split, shown by a short line, indicates the distance (dissimilarity) between the two clusters.

From the original record, objects defined by a vector of vibration signal attributes were created for each type of material. The goal was to find such attributes of the vibration signal and such length of the vibration signal for which there are as many objects of the same material as possible in each cluster, preferably all objects of the same material.

The one-way ANOVA statistical test was used to search for suitable signal attributes for individual vibration signal attributes and lengths of vibration signal [35]. The sorting factor was the material type. The assumptions for the use of ANOVA are: the population of residuals must be close to a normal distribution (the Shapiro–Wilk test was used to verify this condition [36]), and population variances must be equal (i.e., homoscedastic). Bartlett’s test of homoscedasticity was used [37].

The Tukey pairwise test was used for pair comparison of attributes between groups formed by individual materials. The decision criterion was the value of p_adj, which is compared with the level of significance and the p-value [38].

In the second step of the classification task, the decision tree classifier algorithm was used to determine the classification rule [39].

A decision tree for classification tasks works as follows: Each internal node is labelled with an input feature. The leaves from the node marked by the input character are marked with each of the possible values of the destination character, or the leaf leads to a child decision node on the next input character. Each tree leaf is labelled with a class or a probability of distribution within the classes [40]. The AdaBoost process is based on boosting algorithms that first build a model on the training data set and then build a second model to correct the errors present in the first model. This procedure continues until the errors are minimised and the data set is correctly predicted. Boosting algorithms work similarly, combining multiple models (weak learners) to produce a final output (strong learners) [41].

The objects consisting of vectors and attributes of the vibration signal of the material were randomly divided into a train set and test set in the ratio of 80% and 20% of the whole [42]. The train set was used to create a classification rule using a decision tree classifier. In the test set, a classification rule was used, and subsequently, the reliability of the classification was verified—using a classification table in which the numbers of correct/incorrectly classified objects were recorded.

According to Equation (1) below, the reliability of the classification (R_C) was calculated

$$R_C=\frac{N_{RCO}}{N}$$

(1)

where $N_{RCO}$ is a count of right classified objects; $N$ is a count of objects. The value is given as a percentage (%).

3. Calculation

This section describes the procedure for solving both parts of the classification task. Partial results are presented at each step, and the next step is determined.

• Step 1: Selection for signal attributes for classification and estimate record length to calculate attributes.

There were 16,384 values for each type of rock. In order to obtain information about the nature of the data, time series were created from the data from ranked values, and the following attributes were calculated for them (

Table 2. The properties of the tested rock.

Object	Start Order	Sum_of_abs	Sum_o	Fluctua-tion	Count peaks_10	Count peaks_15	Count peaks_20	Variab	Skew	Kurt
l_1	1	4665.05	180.88	498	125,250	125,249	125,249	136.53	−0.26	3.11
l_2	501	4052.12	−987.00	56	166	77	29	101.65	0. 56	3.17
l_3	1001	4467.58	358.89	63	175	97	41	133.05	−0.10	3.30
g_1	1	4318.03	276.94	499	125,249	125,249	125,249	118.74	0.08	3.01
g_2	501	4809.68	−963.82	50	219	116	34	132.10	0.12	2.37
g_3	1001	4446.05	149.36	56	183	99	34	125.23	0.17	2.81
a_1	1	5946.27	−622.32	499	125,250	125,250	125,250	216.53	0.03	2.64
a_2	501	7080.23	113.09	48	298	206	135	301.41	0.04	2.70
a_3	1001	5583.08	−745.50	48	218	122	67	216.70	−0.42	4.47
c_1	1	3217.27	−953.86	498	125,249	125,249	125,249	63.18	−0.24	3.06
c_2	501	3302.33	68.39	44	109	36	20	74.16	−0.07	3.90
c_3	1001	2982.76	−214.89	42	92	13	0	53.30	−0.03	2.42

):

• Sum_of abs (mm·s⁻²)

$$Su{m}_{o{f}_{abs}}={\sum }_{i=j}^{j+l-1}\left|vibro\_signal\right|$$

(2)

where $j$ is the order of the start point of the time series sequence, $l$ is the length of the time series sequence and the number of points of the time series;

• Sum_o (mm·s⁻²)—the sum of real value (mm·s⁻²)

$$Su{m}_o={\sum }_{i=j}^{j+l-1}vibro\_signal$$

(3)

• Fluctuation—fluctuation through zero is the number of times the sign of the vibration signal changes in the time series;
• Count_peaks_10 is count of the number of points of the time series in which the absolute value of the vibration signal is higher than 10 mm·s⁻²;
• Count_peaks_15 is count of the number of points of the time series in which the absolute value of the vibration signal is higher than 15 mm·s⁻²;
• Count_peaks_20 is count of the number of points of the time series in which the absolute value of the vibration signal is higher than 20 mm·s⁻²;
• Variab is var of time series (mm·s⁻²)²;
• Skew is the skewness of time series, a coefficient, so it has no units;
• • Kurt is a kurtosis time series, a coefficient with no units.

Step 2: Evaluation of the attributes’ suitability

This section describes how the signal sequence’s attributes and length were selected for classification.

Sequences of 500 values were created from the vibration signal recording for each rock. Thus, 32 objects from each rock were created.

Table 2 shows the attributes of the first three objects for each rock. The start order value is the sequence number of the first point of the vibration signal of the rock for which the attributes of the object’s vibration signal have been calculated. Each row of Table 2 is a vector of an object. The object label consists of the first letter of the material name and the object’s serial number.

In Table 2, for the first object from each rock, the Fluctuation and Count_peaks attributes have higher values than other objects of the same material. This fact results from the procedure for recording a vibration signal immediately after starting drilling. The drilling tool has touched the surface, and the initial vibrations that have been recorded have high attribute values and do not match the values of the attribute from the recording at the time when the drilling tool was already in a working position inside the material. Such objects cannot be included in the analysis. Objects for which the Start_order is larger than 500 will be included in the analysis, corresponding to a rise time of 1/36 of a second.

For ten randomly selected objects from each material and attribute vector (Sum_of_abs, Sum_o, Fluctuation, Count peaks_10, Count peaks_15, Count peaks_20, Variab, Skew, Kurt), a dendrogram was created (Figure 1) to verify that the Euclidean distance from the objects is less for objects of the same material than for objects of different materials from each other.

In the dendrogram (Figure 1), we can see that the classification into clusters is as follows:

One cluster on the second level, C1, contains concrete objects (c), two limestone objects (l), and one granite object (g). The first level cluster on the right C3 is compact and contains all andesite objects (a), two limestone objects (l), and two granite objects (g). The second-level cluster in the centre of dendrogram C2 contains limestone objects (l) and granite objects (g).

The sorting efficiency by dendrogram is 48%. If we attempted to classify rocks using such vibration signal attributes for sequences with a length of 500 values, 19 objects out of 40 would be correctly classified.

For the selected vibration signal attributes, we used the ANOVA test (one-factor ANOVA, where the factor is the type of material) and required related tests (Shapiro–Wilk test, Bartlett’s test) to verify which attributes are applicable to distinguish between rocks. We also identified which attributes, if they are a part of objects, cause only noise and impair the possibility of distinguishing between materials (

Table 3. Results of ANOVA and pairwise comparisons for objects created from a sequence of length 500 values.

Attribute	p-Value			Tukey Pairwise p_adj
	ANOVA	Shapiro–Wilk Test	Bartlett’s Test	c-a	l-a	g-a	l-c	g-c	g-l
Sum_of_abs	<2 × 10−16	0.216	0.028	0.000	0.000	0.000	0.000	0.000	0.027
Sum_o	0.002	3.452 × 10−6	0.830	0.999	0.999	0.999	0.999	0.999	0.999
Fluctuation	<2 × 10−16	0.366	0.008	0.000	0.000	0.000	0.000	0.000	0.323
Count Peaks_10	<2 × 10−16	0.683	0.160	0.000	0.000	0.000	0.000	0.000	0.015
Count Peaks_15	<2 × 10−16	0.202	0.009	0.000	0.000	0.000	0.000	0.000	0.029
Count Peaks_20	<2 × 10−16	0.002	3.41 × 10−6	0.000	0.000	0.000	0.000	0.000	0.475
Variab	<2 × 10−16	0.001	9.904 × 10−7	0.000	0.000	0.000	0.000	0.000	0.038
Skew	0.189	-	-	-	-	-	-	-	-
Kurt	0.663	-	-	-	-	-	-	-	-

).

To be suitable for distinguishing between materials, an attribute should have the following properties:

• Rejected null hypothesis for ANOVA;
• Conditions fulfilled distribution normality for residues—Shapiro–Wilk test;
• Fulfilled conditions for homoscedasticity, the not rejected null hypothesis for Bartlett’s test;
• All Tukey pairwise p_adj values are less than 0.05.

Only Count Peaks_10 meets all the criteria (Table 3).

The box chart (Figure 2) shows that the attribute values overlap for individual materials—material cannot be classified using this attribute alone.

Evaluation of findings: The vibration signal attributes used for the specified vibration signal length do not meet the classification purpose. In addition to the differences in the values of the attributes for a vibration signal time series of 1500 values, there are also differences in the variability of some of the attributes.

For this reason, we created new objects from vibration signal attributes with a length of 1500, corresponding to a recording length of 1/12 of a second.

The classification into clusters has been improved for the new sequence length of 1500 values, as shown in Figure 3. We can conclude that the Euclidean distance between individual concrete objects (c) in Cluster C1 is smaller than between objects of concrete and other materials. The Euclidean distance between objects of granite (g) and limestone (l) is as small as between individual objects of limestone (l) and individual objects of granite (g) (Cluster C3).

To further improve the classification, we retained only attributes relevant to objects for sorting. The aim is to demonstrate their statistically significant influence on the classification of the object to the correct material and to exclude those attributes that cause noise when calculating Euclidean distance. For selecting appropriate criteria, the same criteria were established for objects created from sequences of length 500 values.

Table 4. Results of ANOVA and pairwise comparisons for objects created from a sequence of length 1500 values.

Attribute	p-Value			Tukey Pairwise p_adj
	ANOVA	Shapiro–Wilk Test	Bartlett’s Test	c-a	l-a	g-a	l-c	g-c	g-l
Sum_of_abs	<2 × 10−16	0.199	0.405	0.000	0.000	0.000	0.000	0.000	0.007
Sum_o	0.871	-	-	-	-	-	-	-	-
Fluctuation	4.2 × 10−15	0.408	0.800	0.000	0.000	0.000	0.000	0.000	0.72
Count Peaks_10	<2 × 10−16	0.360	0.279	0.000	0.000	0.000	0.000	0.000	0.014
Count Peaks_15	<2 × 10−16	0.534	0.427	0.000	0.000	0.000	0.000	0.000	0.021
Count Peaks_20	<2 × 10−16	0.839	0.072	0.000	0.000	0.000	0.000	0.000	0.246
Variab	<2 × 10−16	0.386	0.054	0.000	0.000	0.000	0.000	0.000	0.007
Skew	0.375	-	-	-	-	-	-	-	-
Kurt	0.503	-	-	-	-	-	-	-	-

presents calculated criteria values for objects created from sequences of 1500 values.

Where the criterion that the null hypothesis was not rejected for the ANOVA test was not met, the other criteria were not calculated.

The established criteria have met the following attributes: Sum_of_abs, Count Peaks_10, Count Peaks_15, Variab. In addition to these attributes, the Fluctuation attribute has been retained in the object vector.

The following graphs (Figure 4 and Figure 5) display a box plot for objects and sequences of 1500 values for each selected attribute.

It is clear from the graphs that distinguishing between concrete and andesite materials is easy.

However, this is insufficient for the correct distinction between granite and limestone. On the other hand, it is possible that using all of the selected attributes will make it possible to classify the objects of individual rocks correctly.

A cluster dendrogram (Figure 6) was created from objects of individual materials for five attributes. It has unambiguously Euclidean distances separated into clusters of objects of concrete (c) in Cluster C1 and andesite (a) in Cluster C2. The group of limestone objects (l) is also classified into a single cluster, C3. The right cluster of the third level—C4—looks the worst, with objects of granite (g) and limestone (l).

Evaluation of findings: The vibration signal attributes used for a specified sequence length are unsuitable for classification.

The following procedure is chosen based on looking at the dendrogram (Figure 6) and examining the classification of objects into clusters. It becomes clear that Cluster C3, grouping limestone objects (l), contains at least one of three consecutive objects. That is, from the objects l_2, l_3, l_4, it contains objects l_2 and l_4; of the objects l_3, l_4, l_5, it contains object l_4; of the objects l_4, l_5, l_6, it contains l_4 and l_6; of the objects l_5, l_6 l_7, it contains objects l_6 and l_7; of the objects l_6, l_7, l_8, it contains l_6 and l_7; of the objects l_7, l_8, l_9, it contains l_7 and l_9; of the objects l_8, l_9, l_10, it contains l_9.

Based on this finding, we create each object of material from three consecutive sequences of vibration signals with a length of 1500 values: for each attribute, the object’s attribute value will be the minimum of these three values. The total length of the sequence required to create each object will be 4500 values, this is 1/4 s. The objects created in this way will be used to determine the classification algorithm.

Further calculations are unnecessary because it is apparent from the previous consideration that all objects of the same material will be included in the same cluster.

4. Results and Discussion

The classification of each rock was carried out separately in the following way: each rock object was assigned a class attribute. If the object was created from the vibration signal of the classified material, the class value was one; if it was created from the vibrational of other materials, the value of the class attribute was zero.

For classification purposes, objects were created from the vibration signal of rock so that 4 × 100 random start order values from the interval of minimum 501 and maximum 11,884 were generated by a generator of worthy numbers. Random orders were randomly assigned to rocks. In total, 100 objects were created for each material, totalling 400 objects.

The classification was then implemented by a tool from the field of machine learning: a decision tree. In the next section, for each rock, we indicate (

Table 5. The classification for the rocks andesite and concrete.

Classification Rock	Andesite			Concrete
A. Decision rule	Sum_of_abs ≥ 15,277			Sum_of_abs < 10,522
B. Decision tree The proportion of objects from the selected rock in the test set and their classification.
C. Table evaluating the reliability of the classification		real			real
	Classified	0	1	Classified	0	1
	0	74	0	0	75	0
	1	0	25	1	0	24
D. Reliability of classification	99/99 = 100%			99/99 = 100%
E. The success of classification	Excellent			Excellent

and

Table 6. The classification for the rocks granite and limestone.

Classification Rock	Granite			Limestone
A. Decision rule	(Count Peaks_10 ≥ 527) ∩ (Sum_of_abs ≤ 15,277) ∩ (Fluctuation ≤ 132)			(Count Peaks_10 ≥ 527) ∩ (Sum_of_abs ≤ 15,277) ∩ (Fluctuation ≤ 132)
B. Decision tree The proportion of objects from the selected rock in the test set and their classification.
C. Table evaluating the reliability of the classification		real			real
	Classified	0	1	Classified	0	1
	0	72	0	0	76	0
	1	0	27	1	5	18
D. Reliability of classification	99/99 = 100%			94/99 = 95%
E. The success of classification	Excellent			Not good

):

A.

Classification rule;

B.

Decision tree for train set;

C.

Table evaluating the reliability of the classification;

D.

A percentage expression of the reliability of classification;

E.

Verbal evaluation of the success of classification.

To improve the classification rule, we used the AdaBoost method. Based on the modified rule, the number and location of incorrectly classified objects changed, but the reliability increased by only 1% to 96%. Such can be seen in

Table 7. The new classification of limestone via the AdaBoost method.

Table evaluating the reliability of the classification		real
	Classified	0	1
	0	76	0
	1	5	18
Reliability of classification	95/99 = 96%
The success of classification	Not good

.

To achieve excellent classification, we propose the following procedure: In the case of the classification of four types of rocks, for the correct classification of the rock limestone, it is best to gradually exclude the three materials using their sorting criterion while maintaining a reliability of 100% for the classification.

5. Conclusions

This research aims to classify the type of three rocks and concrete based on the recorded vibration signal obtained by rotary drilling in an experimental laboratory, which has been achieved. This research follows the authors’ efforts [43] to classify the rock based on a vibration signal from 2014—when a cumulative periodogram was used as a classification method. The reliability of that classification method was poor, about 40%.

We propose a novel method for rock classification based on the analysis of the vibration signal generated during drilling. This method can classify rocks quickly, taking only about one quarter of a second for recording and a few milliseconds for evaluation. It does not require complex equipment or sensors, as it uses an existing drill, a microphone, and a computing device.

The solution includes two tasks. For classification purposes, it was first necessary to select the length of the vibration signal and such attributes of the vibration signal that have statistically significantly different statistics for the used materials. Several attributes of the vibration signal were calculated for a time series of 500-length and 1500-length vibration signal data. A cluster dendrogram, an ANOVA test, and a boxplot were used to determine the signal’s useful attributes and correct length. A time series of 4500 data measured in ¼ s was proposed as a suitable length of the vibration signal. Vibration signal attributes were calculated for three time series of 1500 data lengths. The attribute used for classification was determined as the minimum of the three calculated. Suggested attributes of the vibration signal used in the object vector are Sum_of_abs, Count Peaks_10, Count Peaks_15, Variab, and Fluctuation.

The second task consisted of determining and verifying the classification rule. The data were randomly divided into a train set and a test set with a proportion of 80% and 20%. Classification rules were established from train set data using a decision tree machine-learning tool.

The decision rules are: concrete: Sum_of_abs < 10,522; andesite: Sum_of_abs ≥ 15,277; granite: (Count Peaks_10 ≥ 527) ∩ (Sum_of_abs ≤ 15,277) ∩ (Fluctuation ≤ 132); limonite is the rock that remains after sorting.

The measured vibration signal is assumed to be stochastic and stationary. This allows its essential properties and differences during the rock drilling to be characterised with sufficient accuracy even with a sample size of n = 4500. The different nature of vibration signals from drilled rocks and concrete is the basis for successful recognition. By this method, the reliability of the classification of three rocks, andesite, granite, limestone, and concrete, is 100%, which is promising. However, it is necessary to mention that the drilling was conducted under laboratory conditions, and all rock and concrete objects were created from a vibration signal for 20 s.

Given the limited number of samples, possible relationships between differences in the sample values of vibration signal attributes and differences in their petrophysical parameters and petrographic properties will be discussed.

Andesite and concrete were easily distinguishable from the other three materials using one vibration signal attribute, Sum_of_abs, which represents the sum of all absolute values of the vibration signal amplitudes. For andesite, the classification algorithm defines a lower limit, while for concrete, it defines an upper limit. Concrete differs from all other materials in terms of properties such as compressive strength (lowest of all materials) and grain size (highest of all materials).

Andesite differs from granite and limonite in terms of grain size. The grain size for the andesite sample used is very fine-grained, while for granite it is medium- to coarse-grained and for limonite it is fine-grained. Another difference from limonite is its origin. While andesite is an igneous rock, limonite is a sedimentary rock. Andesite and concrete significantly differ from other materials regarding vibration signal attributes such as Sum_of_abs, Sum_o, Fluctuation, Count Peaks_10, Count Peaks_15, Count Peaks_20, and Variab. In addition to the Fluctuation attribute, this difference is visible in Figure 4.

Creating a set of vibration signal attributes that could correctly classify objects created from the attributes of granite and limestone signals was very difficult.

Table 4 shows a significant difference between the averages in the Sum_of_abs, Count Peaks_10, Count Peaks_15, and Variab attributes. However, after creating objects using Sum_of_abs, Count Peaks_10, Count Peaks_15, Variab, and Fluctuation attributes, a sorting algorithm was created that correctly classified all granite objects. The sorting procedure is as follows and must be followed: (1) (Count Peaks_10 ≥ 527); (2) (Sum_of_abs ≤ 15,277); and (3) (Fluctuation ≤ 132).

From the perspective of petrophysical parameters and petrographic properties, the difference between them is in their origin. Granite is an igneous rock and limestone is a sedimentary rock. There is little or no difference in compressive strength. However, there is a difference in grain size. Granite is medium- to coarse-grained while limestone is fine-grained. The mineralogical composition of these rocks is not the same.

However, the research needs to be supplemented with more rock samples with varying properties, such as travertine, talc, and basalt. In order to use the classification based on the vibration signal in practice, it is necessary to move from laboratory conditions to the field. Adjusting the achieved results by following a similar procedure can yield a method applicable for classification in the field. Further research could analyse the relationships between vibration signal attributes, petrophysical parameters, and petrographic properties of the samples in more detail.