Spectral and Wavelet Analysis in the Assessment of the Impact of Corrosion on the Structural Integrity of Mining Equipment

Abstract

Corrosion is a major problem in the mining industry, significantly affecting the durability and reliability of mining equipment. In order to better evaluate and understand these effects, in the first part of this study, the analysis by the finite element method of the metallic structure of the rotary arm of an ERc 1400-30/7 bucket excavator type, produced in Romania in 1985, is presented. This paper presents an analysis of the impact of corrosion on the structural integrity of mining equipment. The focus of the research is on the use of advanced spectral analysis methods and the implementation of wavelet analysis. These methods allow an increase in the degree of accuracy of the information and results obtained. The study also focused on the impact of corrosion on the natural frequencies and structural changes in mining equipment, which were evaluated based on advanced methods of structural analysis. The obtained results show that corrosion deeply affects the dynamic behaviour of the metallic structure, leading to significant changes in the dominant frequencies. It was found that the measured dominant frequencies show a tendency to increase with the increase of structural degradation, an observation that is consistent with the physical aspects of the phenomenon.

1. Introduction

In the modern economic approach to industrial production carried out under the pressure of market demand and competition, the cost involved in using the means of production amounts substantially to the expenses for the maintenance and repair of equipment and/or technological machinery [1], which often totals to a surprisingly large amount for any mining company [2,3,4]. One of the major disadvantages in terms of productivity and production results is equipment failure, as it negatively influences production times and increases expenses at the organisation level [2]. Although mining technological equipment and machinery are designed so that they can function for long periods of time, they are nevertheless affected by various factors that determine the degradation of various component elements. Keeping mining equipment in good working condition involves the use of methods that can be used to evaluate the state of the component elements of their infrastructure.

The corrosion of metal structures is widely encountered in various industrial fields. To monitor the corrosion phenomenon, there are different methods based on certain principles. These methods are subject to applicability limits [5,6,7]. Non-destructive (ND) techniques are crucial to identifying corrosion early on [8,9], allowing for timely maintenance and the prevention of potential safety hazards. By implementing ND techniques, industries can ensure the longevity and reliability of their materials without compromising performance [9]. In the study of the corrosion of carbon steel pipes, May et al. [10] propose a hybrid machine learning approach to feature extraction and classification for corrosion detection and severity assessment. This approach combines Wavelet Packet Transform (WPT) algorithms integrated with Fast Fourier Transform (FFT) and Linear Support Vector Classifier (L-SVC) algorithms. [10]. The integration of WPT and FFT allows the analyst to capture both time and frequency domain information, enhancing the accuracy of feature extraction. The use of L-SVC provides a robust classification model that can effectively predict the severity of corrosion based on the extracted features [10]. The results obtained by the authors confirmed that the proposed automatic learning approach can be used effectively for corrosion detection and severity assessments in SHM applications. Researchers have highlighted different AE-based corrosion detection [5,6,11,12], prediction, and reliability assessment models for online condition monitoring of carbon steel pipelines [9,13,14,15] and acoustic emission signal forecasting [16,17], also highlighting the importance of acoustic emission (AE) techniques compared to other non-destructive methods [9]. A hybrid method using the Hilbert-Huang transform and the wavelet transform was implemented by Hoshyar et al. [18] for the detection and localisation of structural damage. The numerical results obtained from the experimental models surpass those of the other models in terms of accuracy and prediction rate. Wang et al. [19] applied structural damage detection techniques based on wavelet analyses of spatially distributed structural response measurements. Thus, different local disturbances that cannot be highlighted from the measured total response data could be perceived from the component wavelets.

The corrosion of mining equipment frequently occurs due to the periodic mechanical demands to which their structural elements are exposed and the environmental conditions in which this equipment operates. The corrosion of mining equipment can occur as an effect of various causes, including structural properties, material properties, chemical factors, and environmental factors (Figure 1).

Equipment exposed to corrosive environments is susceptible to degradation and loss of structural integrity, which can lead to severe damage and structural instability. Natural frequencies are essential characteristics of any structure, reflecting its dynamic behaviour in the absence of external disturbances. They are influenced by the geometric properties of the structural elements, the materials from which these elements are made, and the loading conditions. Corrosion, as a chemical phenomenon of material degradation, can significantly impact the structural integrity of mining equipment by affecting its natural frequencies and dynamic behaviour. Following the inspection of mining equipment at the Oltenia lignite quarry, it was found that the structural integrity of some parts had been compromised due to corrosion, leading to changes in the geometric properties and thickness of load-bearing structural elements.

This paper proposes a method for analysing and evaluating the impact of corrosion on mining equipment’s infrastructure through spectral and wavelet analysis, which are versatile methods for assessing the natural frequencies of structures. The analysis allowed the observation of how corrosion influences the frequency spectra of mining equipment and the identification of potential signs of structural damage. Our study emphasises the importance of natural frequencies in evaluating the performance and reliability of mining equipment, thereby contributing to the development of effective maintenance and repair strategies to minimise the risk of structural failures and maximise the durability and operational efficiency of equipment in corrosive environments.

2. Atmospheric Corrosion and Impact on Natural Frequencies

Open-pit mining in the Oltenia Carboniferous Basin, Romania, involves the excavation and storage of lignite. Essentially, after excavation and transport to the stockpiles of quarries or power plants, lignite is exposed to air, interacting with oxygen in the air and leading to the formation of carbon dioxide, sulphur dioxide, and water vapour, which affect the surfaces of steel parts in the resistance elements of mining machinery [20,21,22,23,24]. In order to evaluate the degree of damage to the structures by corrosion, as well as the decrease in the thickness of the material of the resistance elements and the influence of this degradation on the load-bearing elements, it is necessary to analyse this phenomenon by means of a method that takes into account the geometric elements of the load-bearing structure of the machine as well as the decrease in mass.

The corrosion of the metal structures of mining equipment in surface pits for the exploitation of lignite is a complex process influenced by several environmental and chemical factors. The main causes of corrosion in this context are: high humidity (water from precipitation or ambient humidity can condense on metal surfaces, forming an environment conducive to corrosion); the presence of oxygen (oxygen in the air contributes to the oxidation of metals, a basic chemical process that contributes to corrosion); sulphides and sulphur compounds (lignite can contain sulphur, and mining can release these compounds into the environment); sulphur and its compounds (for example, sulphur dioxide (SO₂)) can accelerate the corrosion of metals; and abrasive particles (lignite dust and other abrasive particles (quartz from waste material) can mechanically damage the surface of metals, exposing more reactive areas to corrosion). In the presence of moisture and oxygen, iron oxidises to form rust (iron hydroxide). This reaction is one of the main corrosion processes for metallic materials containing iron. Sulphur and its compounds, which are present in lignite, can react with iron and oxygen in water to form iron sulphate, which accelerates the corrosion process and can contribute to the faster degradation of metal structures.

Corrosion, being the chemical process that affects the surface or inner part of metal in resistance materials, can manifest itself in different forms, such as Fe₃O₄ (black magnetite), γ-Fe₃O₄ (brown rust) and γ(FeOOH) (yellow rust). All of these forms of corrosion are observed in the steel structure of the machinery, depending on the nature of the machinery’s interaction with the environment and the general mechanism of corrosion [20,21]. Thus, in general, three forms of corrosion can appear on mining equipment:

• General corrosion (Figure 2) is the most common form of corrosion because it is characterised by a corrosive attack that extends almost uniformly over the entire exposed surface or over a large area [20,22];
• Pitting corrosion (Figure 3) is a localised form of corrosion in which cavities or “holes” are produced in the material of the load-bearing structure when a liquid stagnates, flows slowly, or drips constantly and continuously on the metal surface. The central core of the cavity is considered to be more dangerous than uniform corrosion damage because it is more difficult to detect at depth [11,21,23,24,25]. Pitting corrosion is characterised by localised and deep changes in natural frequencies due to the formation of cavities. These changes are detectable through modifications in the energy distribution in the frequency spectrum;
• Exfoliation corrosion (Figure 4) is an advanced form of intergranular corrosion and is manifested by the lifting of the surface grains of a metal due to the expansion force produced by the corrosion occurring at the grain boundaries just below the surface [20,22,26]. Exfoliation involves intergranular weakening of the metal structure, affecting vibration modes at different frequencies compared to pitting. Wavelet analysis can highlight these differences through higher temporal and frequency resolution.

Natural frequencies are essential characteristics of any structure, and they reflect its dynamic behaviour in the absence of external disturbances. They are influenced by the geometric properties of the structural elements, the material from which these elements are made, and the loading conditions.

Corrosion can significantly affect the structural integrity of mining equipment [21,23,26]. The geometric elements of these machines, exposed to corrosive environments, can undergo significant changes over time due to the effects of corrosion. Thus, it is essential to understand how corrosion influences the natural frequencies and dynamic behaviour of mining machinery. The study of natural frequency analysis and the structural changes caused by corrosion gives us a deep insight into the performance and reliability of mining equipment. By identifying and evaluating these issues, we can develop effective maintenance and repair strategies, minimising the risk of structural failures and maximising the durability and operational efficiency of mining machinery in corrosive environments.

We start from the equation of the motion of a linear harmonic oscillator, which is [27,28,29]:

$$m\times {\displaystyle \frac{d^{2}x}{d{t}^2}}+c\times {\displaystyle \frac{dx}{d{t}^2}}+kx=F(t),$$

(1)

$$m\times {\displaystyle \frac{d^{2}x}{d{t}^2}}+kx=0,$$

(2)

The general solution of this equation has the form:

$$x(t)=A\sin \left({\omega }_{n}t+\varphi \right),$$

(3)

where A—initial amplitude; ω_n—damped natural frequency; Φ—initial phase; m—oscillator mass; c—damping coefficient; k—elasticity constant; F(t)—external force as a function of time.

By substituting the general solution of (3) into (2), we get the equation:

$$m\left(-{\omega }_n^{2}A\sin \left({\omega }_{n}t+\varphi \right)\right)+k\left(\sin \left({\omega }_{n}t+\varphi \right)\right)=0,$$

(4)

After simplifying and isolating ω we obtain:

$$k=m{\omega }^2\Rightarrow {\omega }_n=\sqrt{{\displaystyle \frac{k}{m}}},$$

(5)

This formula shows that the natural frequency of oscillations is directly proportional to the square root of the stiffness constant and inversely proportional to the square root of the oscillator mass. Thus, greater stiffness or less mass will lead to a higher natural frequency of oscillation. For a simple harmonic oscillator, the frequency f (expressed in hertz) is given by the formula:

$$f={\displaystyle \frac{1}{2\pi }}\sqrt{{\displaystyle \frac{k}{m}}},$$

(6)

This formula expresses the relationship between the oscillation frequency, the stiffness constant, and the mass. The higher the stiffness constant and the lower the mass of the oscillator, the higher the frequency of oscillations will be. For a bar, embedded at one end and free at the other, acted upon by a force, the stiffness constant (k) is related to the material characteristics of the bar, such as the modulus of elasticity (E) and the moment of inertia (I), which is a function of the geometric characteristics of the bar determined according to the following relation:

$$k={\displaystyle \frac{3EI}{L^3}},$$

(7)

For a plate, the stiffness constant depends on the geometry of the plate and the material from which it is made. In general, for a plate under uniform loading, the stiffness constant can be expressed as a function of the modulus of elasticity of the material, the thickness of the plate (t), and the moment of inertia of the cross section of the plate. The formula for the stiffness constant of a plate is given by:

$$k={\displaystyle \frac{E{t}^3}{12\left(1-\nu \right)}},$$

(8)

where ν is the Poisson’s coefficient of the material [30,31].

3. Materials and Methods

3.1. Defining the Values of Material Losses in the Context of the Evaluation of the Corrosion Phenomenon

Corrosion is a complex phenomenon based on the degradation of a material or its properties due to its reaction with the environment. Many factors and variables are involved. The nature of the attack and the rate of corrosion are consequences of the system, which consists of metallic materials, the atmospheric environment, and the operating conditions. Correction factors are introduced in the design stages to guarantee the integrity of the structure during its useful life. However, the difficulty of quantifying the material loss causes unnecessary oversizing. The value of the loss of thickness due to corrosion (D, mm) on a steel surface exposed to weathering in the free atmosphere throughout the designed service life of the machine (Tf = 50 years) is calculated as follows [32,33]:

$$D\left(t\le 20\right)=r_{corr}\times t^b,$$

(9)

$$D\left(t>20\right)=r_{corr}\left[{20}^b+b\left({20}^{b-1}\right)\left(t-20\right)\right]$$

(10)

where t—material thickness, mm and b—time exponent values for forecasting and estimating corrosion attack (Table 2, ISO 9224:2012 [32]).

Based on Relations (8) and (9) and taking into account the corrosion class considered, according to ISO 9224:2012 [32], class C5I, with an annual corrosion rate of r_corr = 80–200 μm/year, a graph was drawn up for the amount of material loss from corrosion (Figure 5). The maximum period of 50 years was chosen according to the standard for mining machinery, DIN 22261/2 [33,34].

Description of Measurement Locations: Measurements were taken on the bucket wheel arm of the ERc 1400-30/7 excavator on the beams shown in Figure 6, which are deteriorated and affected by corrosion, especially at the end of the arm in the discharge area of material from the bucket wheel, as shown in Figure 6. This is the area most affected by corrosion due to material deposits that are not collected by the bucket wheel’s hopper. In this area, the material accumulates on the lower field of the metal structure for an extended period.

General Guidelines for Measurements: (a) Surface preparation. Before taking measurements, the surface must be cleaned and properly prepared to ensure adequate sensor contact. (b) Equipment calibration. The measurement equipment must be calibrated according to the manufacturer’s specifications to ensure measurement accuracy. (c) Sensor positioning. Sensors must be placed firmly and stably at the specified locations to avoid unwanted movements and ensure precise measurements. (d) Measurement documentation. Each measurement must be recorded, and a minimum of five measurements must be taken for each location, including environmental conditions and equipment settings, to facilitate the reproduction and verification of results.

From the ultrasonic measurements carried out in situ with a SAUTER TD225 type device on five machines that have been in operation for 30–35 years, the following average values were determined in the areas where the material deposits are persistent (clamping areas of the rotating platform). (See Figure 6 and

Table 1. Mean measured values of stiffeners.

Nominal Value, mm	Measured Value, mm	Difference, %	Difference Values, mm
10	6.70	−33	3.30
10	6.80	−32	3.20
10	7.40	−26	2.60
10	6.80	−32	3.20
10	6.40	−36	3.60
	Mean	−31.80	3.18
16	13.90	−13.13	2.10
16	13.60	−15	2.40
16	13.70	−14.38	2.30
16	14.10	−11.88	1.90
16	13.90	−13.13	2.10
	Mean	−13.50	2.16

). Ultrasonic measurements for the stiffeners in Figure 6 were made for two material thicknesses of 16 mm and 10 mm, respectively, in accordance with the manufacturing documentation of the rotating platform machine (Figure 7). The measurement of the thickness of the material made using an ultrasonic transducer was carried out after performing the operation of roughening the material affected by corrosion first with abrasive discs (50–60 grain), and then with lamellar abrasive discs with 80–120 grain, after which the material was cleaned and a coupler was used for the ultrasonic transducer.

On the other hand, according to the TGL 13500/01 standard [35], the laminated products of location categories I and II, for which the decrease in thickness (Δs) upon corrosion is Δs = 0.50 mm, with material thicknesses s > 16 mm, and the category of location III, for which Δs = 0.25 mm with material thicknesses s > 8 mm, corrosion should not be taken into account. From the in situ analysis of two adjacent surfaces, according to Figure 7, with different thicknesses, we determined that the plate with the smallest thickness had the highest material loss through corrosion, as can be seen from Table 1.

3.2. Impact of Corrosion on the Structural Integrity of the Bucket Wheel Arm of the ERc 1400-30/7 Excavator

The bucket wheel arm was chosen as the study sub-assembly for natural frequency modelling and analysis because it is the first sub-assembly that comes into contact with the excavated material, and material deposition on it is continuous (Figure 8). Corrosion losses will be considered for 30 years for an r_corr = 80 μm and an r_corr = 140 μm, according to ISO 12944-2, class C5I (Figure 5), correlated with in situ measurements (Table 1).

3.3. Analysis of Natural Frequencies for the Bucket Wheel Arm

To analyse the influence of corrosion on the natural frequencies on the metal structures of the mining equipment in the lignite quarries [34], we considered the equipment that is most commonly used: a wheel excavator with type ERc 1400-30/7 buckets (Figure 9). We also conducted tests on the bucket wheel arm of the ARS assembly (the excavator itself) (1). The bucket ladder is connected to the machine tower through the joint (9), which allows it to rotate in the vertical plane. At the other end is the battery of pulleys (2’), over which the lifting and lowering cables (2) pass. The cables are type Warrington-Seale 40M-6×36-1760/BG-s/z, with metal cores. According to Figure 8, we have: the support for the bucket wheel mechanism (8); and the clamping support (6) of the bucket wheel reducer (5), which is attached to the shaft. The reducer acts through a bucket wheel shaft (4). Also attached to the top is the wheel guard with cups. From the excavator, through the connecting bridge (10), the connection is made with the deposition truck on the front belt.

The substructure modelling of the bucket wheel arm is carried out using beam and plate finite elements, in accordance with the technical specifications established for this type of mining equipment. Beam elements can be standard, but can also include composite sections or welded sections as shown in Figure 10a. The discretisation of plate-type elements (2’), (6), (8), and (9) will be done with second-order plate elements, especially in the joint area (9), where the structure presents curved elements as illustrated in Figure 10a,b. The transition from beam to plate elements and the connection between the support and the shaft reducer are realised with rigid link-type elements, as shown in Figure 10b, position (5) [33]. An implicit solver was used for both static and dynamic analysis, suitable for both linear and nonlinear problems. The implicit solver provides good accuracy and is an efficient tool for analysing natural frequencies and vibration modes.

To complete the finite element analysis of the bucket wheel arm (bucket ladder), we must also consider the masses associated with the subassemblies, which were not included in the finite element modelling. For example, the bucket wheel guard (3) illustrated in Figure 9 will have mass distributed over its attachment points on the bucket wheel reducer, which is not represented directly in our model. These masses will be considered concentrated or distributed masses on the structure and will be included in the calculation of natural frequencies to obtain a more accurate assessment of the vibration behaviour of the bucket wheel arm under operating conditions.

Inputs in the FE analysis:

1. Geometry of the structure: The complete structural model of the bucket wheel arm, including all major components and structural discontinuities, including the bucket ladder support cables, position 2 in Figure 10, was simulated using truss elements.

2. Materials: The material properties, including the modulus of elasticity, density, and Poisson’s ratio.

3. Boundary conditions: These are the fixing and support conditions of the structure, such as joints and attachment points. In the bucket ladder joint, position 9 in Figure 10b, only rotation around the OY axis is considered, as shown in Figure 10a.

4. Loads: Types of loads applied to the structure, including static loads (LC1–LC14) and dynamic loads (the masses of the structural elements and mechanisms). LC1: Self-weight. LC2: Load from the mass of the reducer. LC3: Maximum output moment of the reducer. LC4: Load from the mass of mechanisms. LC5: Load from the mass of the bucket wheel. LC6: Load from the mass of the loading buckets. LC7: Load from the mass of the cutting buckets. LC8: Load from the mass of material in the buckets. LC9: Loads from RC guards. LC10: Loads from the side bunker guards. LC11: Loads on the impact roller. LC12: Loads from the cutting forces on the conveyor. LC13: Loads from the longitudinal bunker guards. LC14: Loads from the transverse bunker guards. CO2: 1.5LC1 + 1.1LC2 + 1.1LC3 + 1.1LC4 + 1.1LC5 + 1.1LC6 + 1.1LC7 + 1.1LC9 + 1.1LC10 + 1.1LC13 + 1.1×LC14.

The coefficients are according to DIN 22261/2–Excavators, spreaders, and auxiliary equipment in opencast lignite mines—Part 2: Calculation principles.

5. Discretisation: The method of discretising the structure using second-order beam and plate finite elements, with details about the type and size of the finite elements.

Output in FE analysis:

1. Deformations. Distribution of deformations in the structure under different types of loads.

2. Stresses. Stress maps generated in the structure, indicating critical stress points.

3. Vibration modes. Natural frequencies and vibration modes of the structure, showing its dynamic behaviour.

4. Comparative results. Comparison of numerical results with experimental data for model validation.

3.4. Vibrational Analysis of Bucket Wheel Arm under Operating Conditions

Spectral analysis [36,37], and wavelet analysis are two essential methods used to investigate the dynamic behaviour of the structure as a function of corrosion damage, representing deep methods of studying the dynamics of mechanical systems. Wavelet analysis [13,26,29,36,37,38,39] provides a dynamic perspective on the mechanical system, highlighting how the frequency characteristics evolve over time in relation to the degree of damage. This method allows a deeper understanding of the structural dynamics of a system by identifying subtle changes in the frequency spectrum during the damage process. Therefore, wavelet analysis provides valuable information about how corrosion affects the vibration characteristics of the structure and can help to anticipate and manage potential structural integrity problems. For example, it can highlight changes in the dynamic response of the system as a function of time and frequency, thus providing a better understanding of the processes that occur during damage and how they can affect the structural integrity of mining machinery. Spectral analysis is a method used to identify the frequency components of a signal and to evaluate the distribution of the signal’s energy as a function of frequency. This analysis is based on Fourier transforms, which decompose the signal into a sum of sinusoidal components [9,10]. In general, for mechanical systems in which the signals are regular and well defined, the Fourier transform may be preferred for dynamic analysis. For random and non-periodic signals, using the periodogram function provides a robust estimate of the power spectral density and is suitable for analysing signals with time-varying characteristics or complex frequency structures [10,13,14,18,19]. As a method of dynamic analysis, we considered the determination of natural frequencies, because it is known that there is a small difference between natural frequencies and artificial frequencies. Natural frequencies are the frequencies at which a system vibrates naturally or freely, without being influenced by external forces. They are determined by the geometrical, material properties, and boundary conditions of the system. Natural frequencies are characteristic of the structure and mass of the system and are influenced by the way it is constructed or configured. The term natural frequencies of vibration is more common in the contexts of mathematics and theoretical physics and is often used to describe the general concept of frequencies at which a system naturally vibrates. The natural frequencies of vibration are the same as the natural frequencies and are characteristic of that system. To simulate both dynamic and static deterioration over the 30 years of operation for which measurements were taken on the equipment (Figure 6 and Table 1), we will consider the following structural degradation conditions: D [mm]—D30.140 = 4.5 mm for a corrosion rate r.cor = 140 μm, and D30.80 = 3 mm for a corrosion rate r.cor = 80 μm, for the load-bearing elements considered affected by corrosion, as shown in Figure 11. The first ten natural frequencies determined will be compared with the initial state of the structure D0.0 = 0 mm, without any corrosive degradation of the load-bearing structural elements.

Looking at the static analysis part, we considered the case of the action of the combination of loads (CO1) in which they are included together with the masses of the subassemblies and the maximum actuation moment of the bucket wheel for a case in which the overload coupling can put the machine out of use. Overload coefficients are given by DIN 22261/2 [33] for each type of load. After calculating (using the finite element method) the three considered situations (Figure 12), we determined the first ten natural frequencies for the bucket wheel arm, as well as the static displacements, which are presented in

Table 2. Dynamic and static values for the three corrosion cases.

Eigenvalue, λ (1/s2)	Angular Frequency, ϖ (rad/s)	Natural Frequency, f (Hz)	Natural Period, T (s)	Displacements (Dynamic) (mm)	Displacements (Static) (mm)
D = 0 mm
75.566	8.693	1.384	0.723	117.9	72.2
D = 3 mm
74.801	8.649	1.376	0.726	118.8	72.3
D = 4.5 mm
74.337	8.622	1.372	0.729	119.4	72.4

. The dynamic deformed shapes for the first natural frequency and the static displacements of a point located on the cup wheel shaft are also graphically illustrated in Figure 13.

From Figure 12, the following can be concluded:

• Case 1 (corrosion degradation D = 0 mm)

• Static: load case CO1. The panel shows the deformations of the structural elements, with a maximum value of approximately 72 mm (red colour) and decreasing to a minimum of approximately 6 mm.
• Dynamic: Vibration mode, I—1.384 Hz.

2.

Case 2 (corrosion degradation D = 3 mm)

• Static: load case CO1. The panel shows the deformations of the structural elements, with a maximum value of approximately 72.3 mm (red colour) and decreasing to a minimum of approximately 6 mm.
• Dynamic: Vibration mode, I—1.376 Hz.

3.

Case 3 (corrosion degradation D = 4.5 mm)

• Static: load case CO1. The panel shows the deformations of the structural elements, with a maximum value of approximately 72.4 mm (red colour) and decreasing to a minimum of approximately 6 mm.
• Dynamic: Vibration mode, I—1.372 Hz.

From the point of view of the graphical representation, in the case of vibration mode I, we have the following values for the first ten natural frequencies: fn_D0 = 1384 Hz, fn_D3 = 1376 Hz, and fn_D4.5 = 1372 Hz. It can be seen from the 2D graph (Figure 13) that the deformed shapes of the graphs for corrosion damage D.3 mm and D.4.5 mm, respectively, preserve the deformed shapes of the initial natural frequencies D.0, the differences being very small in value.

3.5. Wavelet Analysis and Spectral Analysis of Bucket Wheel Arm Dynamics

In this section, we will analyse the application of these methods to assessing the impact of corrosion on the structural integrity of the bucket wheel arm in the context of mining machinery. When performing structural analysis of a system, it is often necessary to identify and evaluate how its frequencies respond to various influences and operating conditions.

The analysis of the first vibration mode, mode I, is considered sufficient to obtain a relevant understanding of the dynamic behaviour of a structure. For heavy mining equipment, such as the type ERc-1400-30/7 bucket wheel excavator, the frequency spectrum of interest is 1–4 Hz. For this type of equipment, which is used in Romania, and based on the finite element analysis, we will extract the first five natural frequencies, presented in

Table 3. The first five natural frequencies of the bucket wheel arm, excavator type ERc-1400-30/7.

Vibration Mode	D = 0 mm, Column I, f (Hz)	D = 3 mm, Column II, f (Hz)	D = 4.5 mm, Column III, f (Hz)
1	1.384	1.376	1.372
2	3.611	3.621	3.626
3	4.489	4.509	4.517
4	4.612	4.612	4.612
5	4.982	4.982	4.982
6	5.381	5.378	5.376
7	5.684	5.634	5.600
8	6.857	6.773	6.685
9	7.141	7.131	7.124
10	8.336	8.025	7.479

. We will use these natural frequencies to create the file that will provide us with information about the dynamic behaviour of the bucket wheel arm. To highlight and interpret their evolution, we will use spectral power graphs and wavelet scalograms. In addition, we will denote each data set by column I, column II, and column III to facilitate the interpretation and analysis of the results obtained.

The physical interpretation of dynamic deformation involves analysing the way in which the bucket wheel arm reacts to its state of damage. For example, changes in natural frequencies and modes of vibration may indicate a weakening of the structure due to corrosion or other degradation processes. This can be seen in spectral analysis, where changes in the signal energy distribution as a function of frequency can be associated with changes in the dynamic behaviour of the bucket wheel arm. In wavelet analysis, we can identify subtle changes in the frequency spectrum during the deterioration process. Plotting and analysing spectral power graphs and wavelet analysis scalograms using the frequencies in Table 3 can be done in software such as: Octave 5.2.0 [40], Python 3.8.5 [41] with NumPy 1.19.2 [42], SciPy 1.5.2 [43] and Matplotlib 1.3.2 [44], or MatLab R2023a [45].

4. Results

4.1. Power Spectral Graph

The power spectral plot represents the distribution of signal energy as a function of frequency and provides insight into the frequency components of the signal. Figure 14 shows the spectral power graphs and the spectral power of the dominant frequencies for the three cases.

In the spectral analysis of a corrosion signal, the unit of measurement N/Hz for spectral power provides information about the frequency distribution of energy or force in our study system. The physical interpretation of spectral power expressed in the unit [N/Hz] implies the amount of force or energy distributed per unit frequency. More precisely, for each frequency range, expressed in hertz, the spectral power in the unit N/Hz gives us a measure of the intensity of force or energy present in that specific frequency range. In the context of corrosion, this interpretation has significant implications for how the phenomenon affects the structure or system being monitored. Higher spectral power at certain frequencies may indicate a more intense response of the system to corrosion at those specific frequencies, suggesting a potential vulnerability of the respective material or components to this destructive phenomenon.

4.2. Wavelet Analysis Scalogram

The scalogram is a visual representation of the wavelet analysis, which highlights how the frequency characteristics evolve over time or in relation to the degree of structural damage. This method allows us to identify subtle changes in the frequency spectrum during the damage process and gain a deeper understanding of the structural dynamics as well as the frequency decay time. Figure 15 shows the scalogram of the wavelet analysis for the three cases, and the red circle shows the positioning of the dominant frequencies in time, established in the spectral power graph.

4.3. Correlation of Spectral and Wavelet Analysis Results

By correlating the results obtained from spectral analysis and wavelet analysis, we can gain a more comprehensive understanding of how corrosion influences the structural integrity and performance of the bucket wheel arm in the mining environment. The cumulative wavelet and spectral analyses are presented numerically in

Table 4. Cumulative values wavelet, spectral, and FEM analysis.

Degradation Case	Spectral Power	Dominant Frequency, fdom (Hz)	Wavelet Analysis	FEA Measured Frequency fmeas, (Hz)
D = 0 mm	0.3	0–10 s → constant	constant	1.384
D = 3 mm	1.0	0 ↗ 1.35 s ↘ → 10 s	↘	1.376
D = 4.5 mm	1.2	0 → 4.3 s ↗↗ 7.74 s ↘ → 10 s	↗	1.372

where: → express constant intensity; ↗—increases the spectral intensity; ↘—decreases the spectral intensity.

. This correlation allows us to assess the combined effects of corrosion on the natural frequencies and dynamic behaviour of the structure.

Thus, according to the accumulated values in Table 4, the physical analysis of the mechanical system for the bucket wheel arm can be detailed as follows.

If D = 0 mm, without corrosion:

• The metal structure is in an original state, without any corrosion damage.
• The dominant frequency (f_dom) measured is 0.3 Hz, indicating a specific dynamic behaviour for the initial structure.
• In comparison, the frequency measured by finite element analysis (f_meas) is significantly higher at 1.384 Hz, suggesting greater stiffness or initial mass than originally estimated.

If D = 3 mm, there is a moderate level of corrosion.

• Moderate damage of 3 mm leads to an increase in f_dom to 1.0 Hz.
• f_meas continues to be higher than f_dom with a value of 1.376 Hz.
• This increase in f_dom indicates a significant change in the dynamic behaviour of the structure, probably due to loss of material or stiffness caused by corrosion.

If D = 4.5 mm, there is a high level of corrosion.

• With damage greater than 4.5 mm, f_dom increases significantly to 1.2 Hz.
• f_meas continues to decrease, indicating a further loss of stiffness or mass of the structure.
• This significant change in f_dom indicates a pronounced change in the dynamic behaviour of the structure and can be associated with a significant reduction in its performance and safety.

The results suggest that corrosion profoundly affects the dynamic behaviour of a metallic structure, leading to significant changes in its dominant frequencies. These changes can be used to monitor the health of the structure and assess the need for corrective or preventive interventions to prevent damage and maintain the performance and safety of the structure.

5. Conclusions

1. There is a trend of increasing dominant frequencies with structural degradation (D). Our primary observation shows that the measured dominant frequencies (f_dom) tend to increase with the growth of structural degradation (D). This phenomenon can be explained by reductions in structural rigidity due to corrosion. In accordance with the fundamental principles of structural dynamics, a decrease in structural rigidity and mass caused by corrosion leads to an increase in the natural frequency. This behaviour is consistent with the mathematical relationship described by the natural frequency formula, in which the natural frequency is proportional to the square root of the stiffness and inversely proportional to the square root of the mass. In the context of corrosion, the decrease in the mass and rigidity of the structure contributes to the observed increase in the natural frequency.

2. The stability of measured frequencies under normal conditions (f_meas): The frequencies measured under normal conditions (f_meas) have relatively constant values, suggesting that in the absence of degradation, a structure operates in a consistent and predictable manner. This indicates that the initial structure, unaffected by corrosion, maintains the dynamic properties established during its design and construction.

3. Impact of structural degradation on dynamic behaviour: The physical interpretation of these findings reveals that structural degradation significantly influences the dynamic behaviour of the construction. The increase in dominant frequency is an indicator of the loss of rigidity and changes in structural properties. These changes can negatively affect the performance and safety of the structure, highlighting the need for periodic monitoring and preventive maintenance to prevent critical failures.

4. Role of spectral and wavelet analysis in evaluating structural behaviour: Spectral analysis and wavelet analysis play a crucial role in evaluating structural behaviour and identifying the dominant frequencies associated with different conditions of degradation or loading. Spectral analysis provides information about the power spectrum of the signal and its dominant frequencies, offering an overview of the signal’s energy distribution as a function of frequency. On the other hand, wavelet analysis provides a temporal and frequency perspective of the signal, allowing the identification of significant characteristics and variations over time and frequency.

5. Including spectral and wavelet analysis results for structural health monitoring: Our results emphasise the importance of periodic monitoring and evaluations of the structure’s condition to identify and address potential issues before they become critical. Integrating the results obtained from spectral analysis and wavelet analysis allows for a more comprehensive understanding of how corrosion influences structural integrity and performance. This integrated approach facilitates the development of effective maintenance and repair strategies, thereby ensuring the long-term integrity and durability of metal structures.

6. Implications for the mining industry: Our study provides valuable insights for the mining industry, underscoring the need for rigorous monitoring and maintenance programs for equipment exposed to corrosion. By effectively using spectral and wavelet analysis methods, mining equipment operators can detect early structural degradation and take preventive measures to minimise operational risks and maximise equipment lifespan.

7. Static and dynamic analyses and their limitations: Although static and dynamic analyses for natural frequencies were conducted, changes regarding the influence of the degradation of the thickness of structural resistance elements through corrosion were clearly highlighted only through spectral analysis and wavelet analysis. This aspect underscores the importance of using advanced analysis methods to detect subtle changes in the dynamic behaviour of structures.

8. Influence of steel cables and material deposits: In mining equipment with bucket wheels, the raising and lowering of the arm are performed through steel cables (position 2, Figure 9), which attenuate vibrations in the supporting structure of the equipment. This makes it more challenging to detect corrosion through static analysis or natural frequency analysis, as the steel cables act as an elastic damper. Additionally, material deposits from the excavation process contribute to this difficulty, emphasising the necessity of using advanced methods such as spectral and wavelet analysis for accurate evaluation.