**6. Summary**

Mining and mineral processing are relevant for numerous disciplines and have significant impacts on the operation of various sectors of the economy, especially in raw material management within the metal value chain production. An increasing number of mining companies are facing problem concerning decreases in orebody grades and finer mineralization due to the depletion of deposits. At such a time, the idea of zero-waste economy gains importance and popularity. These aspects give rise to the development of mineral processing technology and the more efficient utilization of raw material. Efforts are focusing more on the effective utilization of recent techniques in mechanical processing than on the introduction of brand new feed material treatment technology. This article presented select problems that are especially popular in contemporary mineral processing at the stage of mechanical processing. The increased effectiveness of specific operations can be observed from different scopes, but energy efficiency and useful mineral loss seem to be of major importance. The development of computational techniques and new methods of material analysis will undoubtedly create new opportunities and potential improvements of operation effectiveness.

Not all directions of development have been covered, and the visual analysis and characterization of grained materials are only mentioned. Nevertheless, the results of many investigations and the operational practice of mineral processing plants, show that the stage of the mechanical processing of raw materials preliminarily impacts the potential of effective separation and useful metal recovery.

It is also necessary to highlight major critical aspects and gaps that should be the objects of investigations both in the near future and from a longer-term perspective. There is some consensus that the high energy consumption of comminution processes stands among the most significant issues within the field. However, the problem lies in the more efficient utilization of energy for the breakage and limitation of losses, particularly in fine grinding operations. This is connected to the need for handling the fine mineralized feed material. The scale problem also needs to be solved in electromagnetic grinding, as well as in high-voltage pulse breakage. To some extent, this is also valid for other operations of mechanical processing, such as vibrating mills, SAG and AG grinding, and HPGR. It is also necessary to remember that, when facing the depletion of deposits, (Table 5) it is harder to maintain the overarching aim of mineral processing: achieving a high level of useful mineral recovery.



**Funding:** This research received no external funding.

**Conflicts of Interest:** The author declares no conflict of interest.

## **Abbreviations**


## **References**


**Natalia Duda-Mróz, Sergii Anufriiev \* and Paweł Stefaniak**

KGHM Cuprum Research and Development Centre Ltd., Gen. W. Sikorskiego 2-8, 53-659 Wroclaw, Poland; natalia.duda@kghmcuprum.com (N.D.-M.); pawel.stefaniak@kghmcuprum.com (P.S.)

**\*** Correspondence: sergii.anufriiev@kghmcuprum.com

**Abstract:** The main task of mineral processing plants is to further process the raw material extracted in the mining faces into a concentrate with the highest possible concentration of the final product. In practice, it is a complex process in which several stages can be distinguished. After the ore has been transported to the surface by the skip shaft, one of the first steps is sieving the ore, which is typically performed using vibrating mining screens. In a typical Ore Enrichment Plant, the screening process is carried out by several such machines. This is a typical bottleneck in the technological chain. For this reason, the main challenge for users is to achieve the highest reliability and efficiency of these technical facilities. The solution is to focus on predictive maintenance strategies based on the development of monitoring and advanced diagnostic procedures capable of estimating the time of safe operation. This work was developed as part of an advanced diagnostic system ensuring comprehensive technical conditioning and early fault detection of components such as the engine, transmission, bearings, springs, and screen. This article focuses on vibration data. The problem of damage detection in the presence of periodically impulsive components resulting from falling feed material on the screen and its further screening process has been considered. These disturbances are of a non-Gaussian noise nature, the elimination of which is essential to extract the fault-related signal of interest. One solution may be to properly smooth and filter the raw signal. In this article, a wavelet filtering technique is applied. First, the wavelet filtering procedure is described. In the next step, the performance of a wavelet filter is investigated depending on its parameters. Then, the results of wavelet filtering are compared with such methods as low-pass filtering and smoothing using a moving average. Finally, the impact of wavelet filtering on the calculation of screen trajectories is investigated.

**Keywords:** mineral processing; sieving screen; diagnostics; predictive maintenance; wavelet transformation

#### **1. Introduction**

Currently, in the mining sector, there is a rapid development of technology ensuring operational supervision of processes and technical facilities based on online monitoring. A typical mining enterprise wishing to remain competitive in the mineral resources market must plan the production process, maintenance, and materials management in advance based on real data. If we look at machinery systems as a network of interconnected vessels, the bottlenecks are one of the most critical. In order to avoid downtime and to carry out maintenance works in a controlled manner, it is crucial to develop advanced diagnostic systems [1]. The key is to provide appropriate sensors that significantly exceed the human senses but also to develop advanced procedures for the extraction of fault-oriented features, procedures for inferencing the diagnostic state of individual components, and procedures for estimating the residual lifetime. Currently, predictive maintenance is developed strongly based on the assumptions of the Industrial Internet of Things technologies, in which the sensed objects are connected to the Internet and can communicate with each other and the superior system [2–7].

**Citation:** Duda-Mróz, N.; Anufriiev, S.; Stefaniak, P. Application of Wavelet Filtering to Vibrational Signals from the Mining Screen for Spring Condition Monitoring. *Minerals* **2021**, *11*, 1076. https:// doi.org/10.3390/min11101076

Academic Editors: Daniel Saramak, Marek Pawełczyk and Tomasz Niedoba

Received: 22 July 2021 Accepted: 26 September 2021 Published: 30 September 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

In this article, one of the critical technical objects of the Ore Enrichment Plant—the vibrating screen used for the sieving process—is considered. The main purpose of sieving is to separate the fine fraction (suitable for milling) from the coarse fraction (requiring crushing). The horizontal schema of the vibrating screen is shown in Figure 1. vibrating screen used for the sieving process—is considered. The main purpose of sieving is to separate the fine fraction (suitable for milling) from the coarse fraction (requiring crushing). The horizontal schema of the vibrating screen is shown in Figure 1.

In this article, one of the critical technical objects of the Ore Enrichment Plant—the

Internet of Things technologies, in which the sensed objects are connected to the Internet

*Minerals* **2021**, *11*, 1076 2 of 14

**Figure 1.** The schema of the vibrating screen. **Figure 1.** The schema of the vibrating screen.

This process is the first stage to which the ore is subjected after direct transport to the surface, precisely before crushing and milling. At this stage, most of the metal components (e.g., anchors) are also captured using an electromagnet. The research was conducted in one of the Polish underground copper ore mines of KGHM, where the vibrating screens are located close to a mine shaft. Depending on the mining plant, the mesh size in the screen ranges from 20 to 40 mm. In all mines, the number of these objects is very limited (Polkowice—3, Lubin—3, Rudna—6); therefore, the vibrating screen is one of the typical bottlenecks in the entire processing plant. In practice, there are various types of vibrating screens. We can distinguish, among others, rotating vertical cylindrical screens and vibrating horizontal linear screens. The ore separation process in terms of grain size is based on induced vibrations. These vibrations are generated by one or two rotating shafts This process is the first stage to which the ore is subjected after direct transport to the surface, precisely before crushing and milling. At this stage, most of the metal components (e.g., anchors) are also captured using an electromagnet. The research was conducted in one of the Polish underground copper ore mines of KGHM, where the vibrating screens are located close to a mine shaft. Depending on the mining plant, the mesh size in the screen ranges from 20 to 40 mm. In all mines, the number of these objects is very limited (Polkowice—3, Lubin—3, Rudna—6); therefore, the vibrating screen is one of the typical bottlenecks in the entire processing plant. In practice, there are various types of vibrating screens. We can distinguish, among others, rotating vertical cylindrical screens and vibrating horizontal linear screens. The ore separation process in terms of grain size is based on induced vibrations. These vibrations are generated by one or two rotating shafts of unbalanced masses driven by drive units with belt transmission. A standard multi-deck vibrating screen is made of the main box and side plates which are connected by transverse reinforcing beams, upper and lower sieving decks, a deck under the screen, and multiple springs as supports. The feed is transferred to the plates by the conveyor and a dispenser located above the screen (Figure 2) [8].

of unbalanced masses driven by drive units with belt transmission. A standard multi-deck vibrating screen is made of the main box and side plates which are connected by transverse reinforcing beams, upper and lower sieving decks, a deck under the screen, and multiple springs as supports. The feed is transferred to the plates by the conveyor and a dispenser located above the screen (Figure 2) [8]. The current demands of users of these devices are related to the development of monitoring systems and early response tools to the development of damage to components such as the engine, transmission, bearings, springs, or the screen itself [9]. Analyzing the literature, you can find many monitoring systems available on the market designed for processing machines; some of them are strictly dedicated to vibrating screens. Most of the commercial solutions [10–14] concern rolling bearings diagnostics based on vibration signals. Leading manufacturers also offer the expansion of the system with additional temperature sensors and lubrication oil particle (i.e., wear debris) counters. This device is exceptionally specific from a diagnostic point of view due to non-stationary operating conditions but also due to the presence of random high-impulse disturbances resulting from the grains bumping into the screen structure. If we do not separate the non-informative impulses from the informative pulses, the further diagnostic process will not be reliable. This

issue has been strongly developed as a part of the project financed from EU funds under the acronym OPMO (Operation monitoring of mineral crushing machinery, [15]), which aims to build an advanced diagnostic system for selected mineral processing assets [16]. In this article, we will focus on the problem of diagnosing supporting springs that play a key role in the sieving process. Critical is their stiffness, which determines the effective operation of the entire screen. In the case of steel springs, a linear deformation characteristic up to a certain degree of deformation is observed. As the time of operation progresses, the stiffness of the springs is lost, which affects the amplitude and frequency of vibrations. Over time, they break as a result of high-cycle fatigue (HCF). Due to their complicated geometry and continuous movement during the screen operation, the number of possible diagnostic methods is limited. The optimal source of data can be vibration data, not only for the diagnosis of flexible springs but also for rolling bearings. One approach may be to plot orbits from two orthogonal vibration signals. Given this representation of the spring motion, it is possible to identify anomalous spring behavior with the knowledge of the correct operating parameters. In [8], the authors presented the main assumptions of such an approach. They described the dynamic model of the vibrating screen and paid special attention to the stochastic influence of the feed on the disturbance of the vibration signal, especially impacts from material falling on the upper deck and impacts from the material inside the screen. They also proposed a spring failure simulation procedure. The method was further developed in [17]. In the case of diagnosing the vibrating screen state, the key is to take into account two phenomena: time-varying load (due to the variable amount of feed on decks) as well as impulsive load considered to be impulsive background noise. In this article, we focus on the problem of signal denoising from these non-informative components. So far, this problem has been solved mainly in the field of diagnostics of rolling bearings, where the important issue is the detection of the cyclic impulse signal in the presence of non-cyclic impulse noise [18–21]. *Minerals* **2021**, *11*, 1076 3 of 14

**Figure 2.** The investigated technical object—vibrating screen: (**a**) view of the whole device; (**b**) feed; **Figure 2.** The investigated technical object—vibrating screen: (**a**) view of the whole device; (**b**) feed; (**c**) upper sieving deck.

(**c**) upper sieving deck. The current demands of users of these devices are related to the development of monitoring systems and early response tools to the development of damage to In this article, a wavelet filtering technique [22–37] was applied to vibrational signals collected in the ore processing plant from a mining screen. The main purpose was to compare the results of wavelet filtering to simple smoothing and filtering techniques, paying special attention to the difference in trajectory calculations. The structure of the

designed for processing machines; some of them are strictly dedicated to vibrating screens. Most of the commercial solutions [10–14] concern rolling bearings diagnostics based on vibration signals. Leading manufacturers also offer the expansion of the system with additional temperature sensors and lubrication oil particle (i.e., wear debris) counters. This device is exceptionally specific from a diagnostic point of view due to nonstationary operating conditions but also due to the presence of random high-impulse disturbances resulting from the grains bumping into the screen structure. If we do not separate the non-informative impulses from the informative pulses, the further diagnostic process will not be reliable. This issue has been strongly developed as a part of the project financed from EU funds under the acronym OPMO (Operation monitoring of mineral crushing machinery, [15]), which aims to build an advanced diagnostic system for selected mineral processing assets [16]. In this article, we will focus on the problem of diagnosing supporting springs that play a key role in the sieving process. Critical is their stiffness, which determines the effective operation of the entire screen. In the case of steel springs, a linear deformation characteristic up to a certain degree of deformation is observed. As the time of operation progresses, the stiffness of the springs is lost, which affects the amplitude and frequency of vibrations. Over time, they break as a result of high-cycle fatigue (HCF). Due to their complicated geometry and continuous movement during the screen operation, the number of possible diagnostic methods is limited. The optimal source of data can be vibration data, not only for the diagnosis of flexible springs but also for rolling bearings. One approach may be to plot orbits from two orthogonal vibration signals. Given this representation of the spring motion, it is possible to identify anomalous spring behavior with the knowledge of the correct operating parameters. In [8], the authors presented the main assumptions of such an approach. They described the dynamic model of the vibrating screen and paid special attention to the stochastic influence of the feed on the disturbance of the vibration signal, especially impacts from material falling on the upper deck and impacts from the material inside the screen. They also proposed a spring failure simulation procedure. The method was further developed in [17]. In the case of diagnosing the vibrating screen state, the key is to take into account two phenomena: time-varying load (due to the variable amount of feed on decks) as well article is as follows: In Section 2, the input data and the methods used for signal processing are described. In Section 3, all the main results are presented. First, the wavelet filtering is compared to moving-average and low-pass filters on raw signals. Then, the trajectory of the screen is calculated for the raw signal, low-pass-filtered signal, and wavelet-filtered signal. In Section 4, the obtained results are discussed, and our conclusions are drawn.

#### **2. Materials and Methods**

## *2.1. Input Data Description*

An overall description of the diagnostic system installed on the investigated mining screen can be found in [18]. The vibrational data from the accelerometers were recorded with a sampling frequency of 16 or 48 kHz. There were 16 accelerometers, one vertical and one horizontal, for each of four bearings and four spring sets. In order to reduce the amount of stored data, a 1 min recording was taken every 15 min. An example of raw data is shown in Figure 3. Based on these data, the trajectory of the screen, which is a key characteristic for screen diagnostics and maintenance, as well as other diagnostic features, can be calculated.

**Figure 3.** Vibrational signal recorded from a single accelerometer installed on the vibrating screen during (**a**) one-minutelong measurement session (**b**) and a close-up look.

On the left plot, one can see the whole signal recorded during a single measurement. Some significant excitation is observed around the fifteenth second of the measurement, which probably corresponds to a large piece of ore falling onto the screen. Such rocks can be detected using computer vision and audio processing technics based on recorded video signals of the incoming ore flow [22]. Based on the results of this detection, such excitation can be filtered out, which is planned in the future but has not been performed in this article due to the unavailability of video data for the studied period. On the right, a closer look at the same signal is shown, on which natural vibrations of the screen are visible.

The first step of data processing was the transformation of electric signals from the accelerometers into SI units (m/s<sup>2</sup> ). The following formulas were used for springs:

$$a = \frac{0.1733 \cdot L}{\text{S} \cdot \text{g}} \tag{1}$$

where *L* is the measured value from the accelerometer, *S* is the sensitivity of the accelerometer (*S* = 100mV/g), and *g* = 9.81 m/s<sup>2</sup> is the standard gravity.

The Fourier transformation of the signal for a spring set is shown in Figure 4. In Plot (a), the whole spectrum is shown. There is one dominating frequency of about 15 Hz, which corresponds to the rotation frequency of the shafts. Besides, some excitations are observed in the frequency range of 150–10,000 Hz, which are visible clearly in Plot (c). Generally, the amplitude of these excitations is much lower than the amplitude of the

*Minerals* **2021**, *11*, 1076 5 of 14

screen's working frequency. For frequencies higher than 10 kHz, almost no excitations are observed, although this range could be important for bearings diagnostics. screen's working frequency. For frequencies higher than 10 kHz, almost no excitations are observed, although this range could be important for bearings diagnostics.

where is the measured value from the accelerometer, is the sensitivity of the

observed, although this range could be important for bearings diagnostics.

accelerometer ( = 100 mV g⁄ ), and = 9.81 m s<sup>ଶ</sup> ⁄ is the standard gravity.

The Fourier transformation of the signal for a spring set is shown in Figure 4. In Plot (a), the whole spectrum is shown. There is one dominating frequency of about 15 Hz, which corresponds to the rotation frequency of the shafts. Besides, some excitations are observed in the frequency range of 150–10,000 Hz, which are visible clearly in Plot (c). Generally, the amplitude of these excitations is much lower than the amplitude of the

where is the measured value from the accelerometer, is the sensitivity of the

(a), the whole spectrum is shown. There is one dominating frequency of about 15 Hz, which corresponds to the rotation frequency of the shafts. Besides, some excitations are observed in the frequency range of 150–10,000 Hz, which are visible clearly in Plot (c). Generally, the amplitude of these excitations is much lower than the amplitude of the screen's working frequency. For frequencies higher than 10 kHz, almost no excitations are

The Fourier transformation of the signal for a spring set is shown in Figure 4. In Plot

accelerometer ( = 100 mV g⁄ ), and = 9.81 m s<sup>ଶ</sup> ⁄ is the standard gravity.

*Minerals* **2021**, *11*, 1076 5 of 14

**Figure 4.** The frequency spectrum of the acceleration signal: (**a**) low-frequency range; (**b**) high-frequency range. **Figure 4.** The frequency spectrum of the acceleration signal: (**a**) low-frequency range; (**b**) high-frequency range. In this subsection, the procedure of wavelet filtering is described. The wavelet

#### *2.2. Wavelet Denoising Procedure* denoising procedure consists of three main steps (for more detail, read [23–38]):

*2.2. Wavelet Denoising Procedure*  In this subsection, the procedure of wavelet filtering is described. The wavelet In this subsection, the procedure of wavelet filtering is described. The wavelet denoising procedure consists of three main steps (for more detail, read [23–38]): • Multilevel wavelet decomposition. • Finding thresholds for detail coefficients.


• Reconstruction of the signal. Wavelet transform is a tool that cuts up the signal into detail coefficients ( ), approximation coefficients (), and downsamples (Figure 5). The detail coefficients can be defined as high-frequency coefficients ሾሿ = ∑ ሾሿℎሾ2 െ ሿ <sup>ஶ</sup> ୀିஶ , and the approximation coefficients can be defined as low-frequency coefficients ௪ሾሿ = ∑ ሾሿሾ2 െ ሿ <sup>ஶ</sup> ୀିஶ , where is a sampling data point, is the size of the sampling data, ሾሿ is the raw signal, and ሾ2 െ ሿ and ℎሾ2 െ ሿ are low-pass and high-pass filters. The wavelet function is composed of the scaled and translated copies of the scaling Wavelet transform is a tool that cuts up the signal into detail coefficients (*CD*), approximation coefficients (*CA*), and downsamples (Figure 5). The detail coefficients can be defined as high-frequency coefficients *yhigh*[*n*] = ∞ ∑ *i*=−∞ *s*[*i*]*h*[2*n* − *i*], and the approximation coefficients can be defined as low-frequency coefficients *ylow*[*n*] = ∞ ∑ *i*=−∞ *s*[*i*]*g*[2*n* − *i*], where *i* is a sampling data point, *n* is the size of the sampling data, *s*[*i*] is the raw signal, and *g*[2*n* − *i*] and *h*[2*n* − *i*] are low-pass and high-pass filters. The wavelet function is composed of the scaled and translated copies of the scaling function *φ*(*x*) = ∑ *n h*(*n*) √ 2*φ*(2*x* − *n*) and √ approximation coefficients (), and downsamples (Figure 5). The detail coefficients can be defined as high-frequency coefficients ሾሿ = ∑ ሾሿℎሾ2 െ ሿ <sup>ஶ</sup> ୀିஶ , and the approximation coefficients can be defined as low-frequency coefficients ௪ሾሿ = ∑ ሾሿሾ2 െ ሿ <sup>ஶ</sup> ୀିஶ , where is a sampling data point, is the size of the sampling data, ሾሿ is the raw signal, and ሾ2 െ ሿ and ℎሾ2 െ ሿ are low-pass and high-pass filters. The wavelet function is composed of the scaled and translated copies of the scaling function ሺሻ = ∑ ℎሺሻ√2ሺ2 െ ሻ and the mother wavelet function ሺሻ =

function ሺሻ = ∑ ℎሺሻ√2ሺ2 െ ሻ and the mother wavelet function ሺሻ = the mother wavelet function *ψ*(*x*) = ∑ *n g*(*n*) 2*φ*(2*x* − *n*). ∑ ሺሻ√2ሺ2 െ ሻ .

**Figure 5.** A conceptual schema of a multilevel wavelet decomposition procedure. **Figure 5.** A conceptual schema of a multilevel wavelet decomposition procedure. **Figure 5.** A conceptual schema of a multilevel wavelet decomposition procedure.

After signal decomposition into detail and approximation coefficients, it is necessary to threshold detail coefficients. One of the methods is hard thresholding, described by After signal decomposition into detail and approximation coefficients, it is necessary After signal decomposition into detail and approximation coefficients, it is necessary to threshold detail coefficients. One of the methods is hard thresholding, described by

equation *<sup>h</sup>λ*(*x*) = *<sup>x</sup>* × <sup>1</sup>{|*x*|>*λ*} . The signal *x* remains unchanged if its values are lower than –*λ* or greater than threshold *λ*; otherwise, the values are replaced with zeros. Another method is soft thresholding *sλ*(*x*) = sign(*x*) × max(|*x*| − *λ*, 0). Here, values greater in magnitude than the threshold are shrunk towards zero by subtracting the threshold from it. The method that is the combination of both methods explained is semi-soft thresholding, described by the equation below: threshold from it. The method that is the combination of both methods explained is semisoft thresholding, described by the equation below: ఒሺሻ = ⎨ <sup>⎧</sup> , || ଶ, signሺሻ ൈ ଶሺ|| െ ଵሻ ଶ െ ଵ , ଵ || ଶ,

equation ℎఒሺሻ =ൈ1ሼ|௫|வఒሽ. The signal remains unchanged if its values are lower than – or greater than threshold ; otherwise, the values are replaced with zeros. Another method is soft thresholding ఒሺሻ = signሺሻ ൈ maxሺ|| െ , 0ሻ . Here, values greater in magnitude than the threshold are shrunk towards zero by subtracting the

*Minerals* **2021**, *11*, 1076 6 of 14

$$c\_{\lambda}(\mathbf{x}) = \begin{cases} \mathbf{x}, & |\mathbf{x}| > \lambda\_2, \\ \text{sign}(\mathbf{x}) \times \frac{\lambda\_2(|\mathbf{x}| - \lambda\_1)}{\lambda\_2 - \lambda\_1}, & \lambda\_1 \le |\mathbf{x}| \le \lambda\_2, \\ 0, & |\mathbf{x}| < \lambda\_1. \end{cases}$$

Thresholds are calculated for each detail coefficient *d<sup>j</sup>* (i.e., noise). A common threshold choice is, for example, universal threshold *λ* = *σ* p 2 log *n*, where *n* is the length of noise and *σ* is the median of absolute values from noise divided by 0.6745 [39]. Our threshold choice was *λ*<sup>1</sup> = *µ* + 2*σ* <sup>2</sup> and *λ*<sup>2</sup> = *µ* + 3*σ* 2 , where *µ* is the mean and *σ* 2 is the variance of the detail coefficient (Figure 6). threshold choice is, for example, universal threshold =ඥ2 log , where is the length of noise and is the median of absolute values from noise divided by 0.6745 [39]. Our threshold choice was ଵ = 2ଶ and ଶ = 3ଶ, where is the mean and <sup>ଶ</sup> is the variance of the detail coefficient (Figure 6).

**Figure 6.** Semi-soft thresholding.

**Figure 6.** Semi-soft thresholding. Other more widely used thresholding methods are adaptive threshold selection, Other more widely used thresholding methods are adaptive threshold selection, using the principle of Stein's Unbiased Risk Estimate (SURE) [40], and the minimax threshold [40]. (For more about thresholding, read [40–42].)

using the principle of Stein's Unbiased Risk Estimate (SURE) [40], and the minimax threshold [40]. (For more about thresholding, read [40–42].) After thresholding, the signal can be reconstructed by inverse multilevel wavelet transform. The noise is the difference between the raw signal and the denoised signal.

#### After thresholding, the signal can be reconstructed by inverse multilevel wavelet *2.3. Trajectory Calculation Procedure*

transform. The noise is the difference between the raw signal and the denoised signal. *2.3. Trajectory Calculation Procedure*  One of the most important diagnostic characteristics of the mining screen is its trajectory (also referred to as orbit). The trajectory of the mining screen can be determined One of the most important diagnostic characteristics of the mining screen is its trajectory (also referred to as orbit). The trajectory of the mining screen can be determined by double integration of the original acceleration signal in vertical and horizontal directions. The processing steps for the vertical vibrations and the horizontal vibrations are shown in Figure 7. At the start, the input is the acceleration of the horizontal or vertical vibrations. The algorithm must be used separately for both directions. Next, outputs must be merged by time vectors to find trajectory.

by double integration of the original acceleration signal in vertical and horizontal directions. The processing steps for the vertical vibrations and the horizontal vibrations

vibrations. The algorithm must be used separately for both directions. Next, outputs must

be merged by time vectors to find trajectory.

**Figure 7.** Procedure for determining the displacement based on a one-dimensional vibration acceleration signal (horizontal or vertical). **Figure 7.** Procedure for determining the displacement based on a one-dimensional vibration acceleration signal (horizontal or vertical).

The first step was denoising the signal. On the schema, the wavelet denoising is suggested, but some other methods and calculations without filtering at all will be compared later in this article. After wavelet denoising, the signal was integrated with the use of the Euler method, and the velocity was obtained. Then, the velocity values were filtered by a 10-order high-pass Butterworth filter to remove slowly changing trends in data, such as gravity. Significant outliers may appear due to possible breaks in the recorded acceleration signal. This is why Tukey's fences technique [37] was applied to remove outliers. The signal was integrated once more with the use of the Euler method, and the coordinates of the screen were obtained. The trend and outliers in the coordinates The first step was denoising the signal. On the schema, the wavelet denoising is suggested, but some other methods and calculations without filtering at all will be compared later in this article. After wavelet denoising, the signal was integrated with the use of the Euler method, and the velocity was obtained. Then, the velocity values were filtered by a 10-order high-pass Butterworth filter to remove slowly changing trends in data, such as gravity. Significant outliers may appear due to possible breaks in the recorded acceleration signal. This is why Tukey's fences technique [37] was applied to remove outliers. The signal was integrated once more with the use of the Euler method, and the coordinates of the screen were obtained. The trend and outliers in the coordinates were removed in the same way as in velocity signals.

were removed in the same way as in velocity signals. After all the horizontal and vertical coordinates are connected by time vectors, the 2D vector of the position changed in time can be obtained for any period of time. The expected trajectory of the screen is an ellipse. For long-term trajectory analysis, the calculation of some key parameters of the ellipse can be useful. In order to achieve this, an ellipse equation was fitted to the trajectories obtained numerically. The following total After all the horizontal and vertical coordinates are connected by time vectors, the 2D vector of the position changed in time can be obtained for any period of time. The expected trajectory of the screen is an ellipse. For long-term trajectory analysis, the calculation of some key parameters of the ellipse can be useful. In order to achieve this, an ellipse equation was fitted to the trajectories obtained numerically. The following total least squares estimator for 2D ellipses was used:

$$\begin{cases} \begin{aligned} \mathbf{x}\_{l} &= \mathbf{x}\_{c} + a\cos\theta\cos t - b\sin\theta\sin t \\ \mathbf{y}\_{l} &= \mathbf{y}\_{c} + a\sin\theta\cos t + b\cos\theta\sin t \end{aligned} \tag{2} \end{cases} \tag{2}$$

$$d = \sqrt{\left(\mathbf{x} - \mathbf{x}\_t\right)^2 + \left(y - y\_t\right)^2},\tag{3}$$

from the point to the ellipse. By minimizing , the parameters of the elliptical trajectory can be calculated. **3. Results**  where (*x<sup>t</sup>* , *yt*) is the closest point on the ellipse to (*x*, *y*). Thus, *d* is the shortest distance from the point to the ellipse. By minimizing *d*, the parameters of the elliptical trajectory can be calculated.

#### In this section, the main results are shown. The results are presented for a selected **3. Results**

thresholding method.

spring set of a sieving screen. The mother wavelet and level of decomposition were selected based on the Pearson In this section, the main results are shown. The results are presented for a selected spring set of a sieving screen.

correlation coefficient between the raw and denoised signals. The different methods of thresholding have been checked. Satisfactory results have been obtained for the biorthogonal 2.2 wavelet (bior2.2) with the sixth level of decomposition and the semi-soft The mother wavelet and level of decomposition were selected based on the Pearson correlation coefficient between the raw and denoised signals. The different methods of thresholding have been checked. Satisfactory results have been obtained for the

least squares estimator for 2D ellipses was used:

biorthogonal 2.2 wavelet (bior2.2) with the sixth level of decomposition and the semi-soft thresholding method. bearings. (See [26] for an interesting approach for bearings.) The wavelet filter was applied to the vibrational signal from the spring set of the sieving screen. In Figure 8, the signals

First, an example of filtering is shown, then the wavelet filtering is compared to some other method, and finally, the orbit calculation results are compared. In this article, we focus on the signals for springs, although similar analyses could be carried out for

First, an example of filtering is shown, then the wavelet filtering is compared to some other method, and finally, the orbit calculation results are compared. In this article, we focus on the signals for springs, although similar analyses could be carried out for bearings. (See [26] for an interesting approach for bearings.) The wavelet filter was applied to the vibrational signal from the spring set of the sieving screen. In Figure 8, the signals before and after the wavelet denoising, as well as the noise, are presented. before and after the wavelet denoising, as well as the noise, are presented. In the first step of wavelet denoising, the acceleration signal was put into cascaded filters (see Figure 5) with the biorthogonal 2.2 wave. The bior2.2 wave is symmetric, not orthogonal, and biorthogonal. Next, for each detail coefficient, the semi-soft thresholding method was applied (Figure 6).

*Minerals* **2021**, *11*, 1076 8 of 14

**Figure 8.** Wavelet denoising of the vibrational signal recorded on the spring. **Figure 8.** Wavelet denoising of the vibrational signal recorded on the spring.

A key parameter that affects the performance of the wavelet filtering is the level of the filter, i.e., how many steps are performed in the procedure, shown in Figure 5. In In the first step of wavelet denoising, the acceleration signal was put into cascaded filters (see Figure 5) with the biorthogonal 2.2 wave. The bior2.2 wave is symmetric, not orthogonal, and biorthogonal. Next, for each detail coefficient, the semi-soft thresholding method was applied (Figure 6).

Figure 8, a denoise level equal to 6 was chosen. In Figure 9, the denoising results obtained with different levels of wavelet decomposition are compared. As seen for lower values (n = 3), a significant amount of noise is present in the filtered signal. On the other hand, for higher values, either some details of the original signal are lost (n = 9), or the signal is distorted completely (n = 12). We have chosen an intermediate value (n = 6), which gives a smooth enough signal but does not distort it at the same time. A key parameter that affects the performance of the wavelet filtering is the level of the filter, i.e., how many steps are performed in the procedure, shown in Figure 5. In Figure 8, a denoise level equal to 6 was chosen. In Figure 9, the denoising results obtained with different levels of wavelet decomposition are compared. As seen for lower values (n = 3), a significant amount of noise is present in the filtered signal. On the other hand, for higher values, either some details of the original signal are lost (n = 9), or the signal is distorted completely (n = 12). We have chosen an intermediate value (n = 6), which gives a smooth enough signal but does not distort it at the same time.

Next, the results of the wavelet filtering are compared with some other techniques of signal processing. In Figure 10, the wavelet denoising is compared with a moving-average filter (AVG), which is one of the obvious choices for smoothing data. The window size of the moving average was equal to 150 observations, which correspond to 0.003125 s. In general, wavelet filtering improves the signal-to-noise ratio of the original signal. It usually fits within the range of the original signal and, at the same time, provides a rather smooth line without small excitations. Slower changes in the signal are caught, while the faster excitations are filtered out. Although the output of the moving-average filter is also very smooth, it does not fit the original signal as well as the wavelet signal. In the case of larger excitations observed in the original signal, some major deviations between the original

signal and the moving-average signal are observed. Those deviations seem to be small, but during further processing steps (for example, orbit calculations), such small errors can accumulate and lead to distorted results and inappropriate screen diagnostics. *Minerals* **2021**, *11*, 1076 9 of 14

**Figure 9.** Comparison of different levels of signal denoising using a multilevel wavelet transformation. Blue line shows the original signal; red line shows the filtered signal. **Figure 9.** Comparison of different levels of signal denoising using a multilevel wavelet transformation. Blue line shows the original signal; red line shows the filtered signal. *Minerals* **2021**, *11*, 1076 10 of 14

**Figure 10.** Comparison of wavelet filtering to signal smoothing using the moving average filter for vertical and horizontal orientations of accelerometers. **Figure 10.** Comparison of wavelet filtering to signal smoothing using the moving average filter for vertical and horizontal orientations of accelerometers.

**Figure 11.** Comparison of wavelet filtering to low-pass filtering for vertical and horizontal orientations of accelerometers.

Finally, the results obtained by filtering the original signal using different techniques were used to calculate the trajectory of the sieving screen. The trajectory was calculated

signal contains very slow excitation, corresponding to the movement of the whole screen with a frequency of 15 Hz. An obvious way to isolate these vibrations is to apply a lowpass filter. The results of the comparison are shown in Figure 11. The wavelet denoising is compared to a two-order low-pass Butterworth filter with a cutoff frequency equal to 18 Hz. The filter must be applied twice: once forward and once backward. The combined filter has a zero phase and a filter order twice that of the original. First of all, the results obtained by applying the low-pass filter are very smooth because, basically, it is a single harmonic excitation. On the other hand, the amplitude of the signal after low-pass filtering is lower, which can result in appropriate screen diagnostics. The wavelet results can be

improved by smoothing or adaptive changing of the level or types of the wave.

orientations of accelerometers.

Next, we compared the results of wavelet filtering with a low-pass filter. The original signal contains very slow excitation, corresponding to the movement of the whole screen with a frequency of 15 Hz. An obvious way to isolate these vibrations is to apply a low-pass filter. The results of the comparison are shown in Figure 11. The wavelet denoising is compared to a two-order low-pass Butterworth filter with a cutoff frequency equal to 18 Hz. The filter must be applied twice: once forward and once backward. The combined filter has a zero phase and a filter order twice that of the original. First of all, the results obtained by applying the low-pass filter are very smooth because, basically, it is a single harmonic excitation. On the other hand, the amplitude of the signal after low-pass filtering is lower, which can result in appropriate screen diagnostics. The wavelet results can be improved by smoothing or adaptive changing of the level or types of the wave. with a frequency of 15 Hz. An obvious way to isolate these vibrations is to apply a lowpass filter. The results of the comparison are shown in Figure 11. The wavelet denoising is compared to a two-order low-pass Butterworth filter with a cutoff frequency equal to 18 Hz. The filter must be applied twice: once forward and once backward. The combined filter has a zero phase and a filter order twice that of the original. First of all, the results obtained by applying the low-pass filter are very smooth because, basically, it is a single harmonic excitation. On the other hand, the amplitude of the signal after low-pass filtering is lower, which can result in appropriate screen diagnostics. The wavelet results can be improved by smoothing or adaptive changing of the level or types of the wave.

Next, we compared the results of wavelet filtering with a low-pass filter. The original signal contains very slow excitation, corresponding to the movement of the whole screen

*Minerals* **2021**, *11*, 1076 10 of 14

**Figure 10.** Comparison of wavelet filtering to signal smoothing using the moving average filter for vertical and horizontal

**Figure 11.** Comparison of wavelet filtering to low-pass filtering for vertical and horizontal orientations of accelerometers. **Figure 11.** Comparison of wavelet filtering to low-pass filtering for vertical and horizontal orientations of accelerometers.

Finally, the results obtained by filtering the original signal using different techniques were used to calculate the trajectory of the sieving screen. The trajectory was calculated Finally, the results obtained by filtering the original signal using different techniques were used to calculate the trajectory of the sieving screen. The trajectory was calculated using the procedure described before in Figure 6 using the raw signal, the signal processed by low-pass filtering, and the signal processed by wavelet filtering. The results are shown in Figure 12. The trajectory calculated on the raw signal is shown in blue, the one calculated after low-pass filtering in orange, and the one filtered by wavelets in red. Although the results are similar, some major differences may be observed. The main issue with the trajectory calculated based on the raw signal is the fact that it is diverging fast. The difference between the two rotations is significant, and it increases further with time. It is even more visible on a magnified plot. This can be explained by the accumulation of errors during the integration of the original signal. Both filtering techniques deal with this issue well: the divergence is much lower for both the low-pass and wavelet filters. Lower divergence of the trajectory will allow the use of longer parts of the signal for trajectory calculation, which will allow for the calculation of the parameters of a trajectory in a more reliable way.

**Figure 12.** Orbits calculated using different kinds of data filtering techniques: no filtering (blue line), low-pass filtering (orange line), and wavelet filtering (red line). **Figure 12.** Orbits calculated using different kinds of data filtering techniques: no filtering (blue line), low-pass filtering (orange line), and wavelet filtering (red line).

using the procedure described before in Figure 6 using the raw signal, the signal processed by low-pass filtering, and the signal processed by wavelet filtering. The results are shown in Figure 12. The trajectory calculated on the raw signal is shown in blue, the one calculated after low-pass filtering in orange, and the one filtered by wavelets in red. Although the results are similar, some major differences may be observed. The main issue with the trajectory calculated based on the raw signal is the fact that it is diverging fast. The difference between the two rotations is significant, and it increases further with time. It is even more visible on a magnified plot. This can be explained by the accumulation of errors during the integration of the original signal. Both filtering techniques deal with this issue well: the divergence is much lower for both the low-pass and wavelet filters. Lower divergence of the trajectory will allow the use of longer parts of the signal for trajectory calculation, which will allow for the calculation of the parameters of a trajectory in a more

When it comes to a comparison between the results of the low-pass filter and the wavelet filter, the main difference is the magnitude of the trajectory. The length of the trajectory in the case of low-pass filtering is significantly lower than in the case of wavelet filtering. This fact can lead to inappropriate diagnostics of the screen. Many methods for predictive maintenance rely on setting the alarm threshold for such parameters as the length of the trajectory. In the case of calculations using the low-pass filter, the measured When it comes to a comparison between the results of the low-pass filter and the wavelet filter, the main difference is the magnitude of the trajectory. The length of the trajectory in the case of low-pass filtering is significantly lower than in the case of wavelet filtering. This fact can lead to inappropriate diagnostics of the screen. Many methods for predictive maintenance rely on setting the alarm threshold for such parameters as the length of the trajectory. In the case of calculations using the low-pass filter, the measured parameters of the orbit may be lowered, which can potentially lead to unexpected failures due to the fact that the maximum safe magnitude was exceeded.

#### parameters of the orbit may be lowered, which can potentially lead to unexpected failures **4. Discussion and Conclusions**

reliable way.

due to the fact that the maximum safe magnitude was exceeded. **4. Discussion and Conclusions**  In this paper, a novel procedure for technical condition monitoring of a vibrating screen in the presence of impulsive noise has been presented. The methods found in the literature are mainly dedicated to noise reduction for the purpose of detecting local damage to rolling bearings. In this paper, we have focused on springs. One of the popular In this paper, a novel procedure for technical condition monitoring of a vibrating screen in the presence of impulsive noise has been presented. The methods found in the literature are mainly dedicated to noise reduction for the purpose of detecting local damage to rolling bearings. In this paper, we have focused on springs. One of the popular methods of assessing the technical condition of springs is to analyze the trajectory of their movement. In order to estimate orbits, it is necessary to have access to two orthogonal vibration signals. Unfortunately, the presence of impulsive background noise due to large pieces of ore falling down distorts these estimates. One solution may be to properly smooth and filter the raw signal.

methods of assessing the technical condition of springs is to analyze the trajectory of their movement. In order to estimate orbits, it is necessary to have access to two orthogonal vibration signals. Unfortunately, the presence of impulsive background noise due to large pieces of ore falling down distorts these estimates. One solution may be to properly smooth and filter the raw signal. In this article, a wavelet filtering technique is applied for this purpose. The filtering procedure, as well as the procedures for orbit calculation and parametrization, were described. Then, these procedures were applied to vibrational data collected in an ore processing plant from a machine operating in industrial conditions. The results of wavelet filtering are compared with other methods, such as moving-average filtering and low-pass filtering. Next, the trajectory was calculated using different preprocessing techniques, and the results were compared.

Wavelet filtering has shown some improvement compared to both moving-average and low-pass filtering. When compared with the moving-average filter, the wavelet filtering better represents the original signal. The moving average was very sensitive to outliers in the original signal, while the wavelet-filtered signal was, in most cases, within the original signal. Compared to the low-pass filter, the wavelet filter better conserves the magnitude of the original signal.

When it comes to trajectory calculation, preprocessing using wavelet filtering also gave some advantages. Compared to the calculation based on unfiltered data, better convergence of the trajectory was obtained. It will allow for the use of more data for parametrization of the trajectory (fitting and calculation of an ellipse equation to numerically calculated trajectory), which will give more reliable results. On the other hand, compared to lowpass filtering, the magnitude of the orbit calculated using wavelet filtering is closer to the original one, which may allow one to avoid exceeding the working parameters of the screen.

Of course, wavelet filtering has some downsides. First of all, an appropriate decomposition scaling function and the level of the filter need to be chosen properly, which can be time-consuming. However, after optimization of these parameters, wavelet filtering gives good results compared to some other smoothing and filtering techniques. In the future, it is planned to compare the results with some more sophisticated filtering techniques.

**Author Contributions:** Conceptualization, N.D.-M., S.A. and P.S.; Data curation, N.D.-M. and S.A.; Formal analysis, P.S.; Investigation, S.A. and P.S.; Methodology, N.D.-M., S.A. and P.S.; Project administration, S.A. and P.S.; Software, N.D.-M. and S.A.; Supervision, S.A. and P.S.; Validation, S.A. and P.S.; Visualization, N.D.-M., S.A. and P.S.; Writing—original draft, N.D.-M., S.A. and P.S.; Writing—review and editing, S.A. and P.S. All authors will be informed about each step of manuscript processing, including submission, revision, revision reminder, etc., via emails from our system or the assigned Assistant Editor. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by EIT RawMaterials GmbH under Framework Partnership Agreement No. 18253 (OPMO—Operation monitoring of mineral crushing machinery).

**Data Availability Statement:** Restrictions apply to the availability of these data. Data was obtained from KGHM Polska Mied´z S.A. and are available from the authors with the permission of KGHM Polska Mied´z S.A.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.
