Analysis of Uncertainty in Conveyor Belt Condition Assessment Using Time-Based Indicators

Abstract

This study analyzes the impact of the type of transported material (overburden, lignite, mixture) on the rate of core damage accumulation in Type St conveyor belts in open-pit mines. The research was conducted using the DiagBelt+ diagnostic system, which enables the assessment of belt core condition without dismantling the belt. Data were collected from over 100 conveyor belt loops, covering segments of varying lengths, ages, and operational histories. Damage density and area were assessed, and differences were analyzed depending on the material type. The results indicate that belt age and damage density vary significantly with material type, while the Resurs indicator (percentage of expected operating time) shows no clear dependence on the material type. A multiple regression analysis was also performed to predict failure density based on operational variables, such as Age, Resurs results, Loop Length, and Segment Length. The regression model explains approximately 46% of the variability in damage density, indicating the need for further research to improve predictive accuracy. The study emphasizes the importance of using non-destructive diagnostic systems to optimize maintenance planning and enhance conveyor belt reliability.

1. Introduction

Belt conveyor systems are an indispensable component of mining infrastructure, particularly in open-pit mines, where they enable continuous and automated transport of large volumes of overburden and coal [1]. Their reliability and operational availability are critical for production continuity; any downtime resulting from conveyor belt failures leads to significant economic losses [1,2].

The belt itself is the central element of these transport systems. Its design—especially the inclusion of steel-cord reinforcement in the core—determines its mechanical strength, resistance to dynamic loading, and durability under harsh operating conditions [3,4]. Numerous studies have shown that belt wear encompasses not only surface degradation, such as cover abrasion, but also internal damage: cracks, bends, crushes, and corrosion of the steel cords [5,6,7].

Internal core defects are particularly hazardous, as they remain hidden from external inspection for extended periods and are often detected only after failure has occurred. Consequently, the development of diagnostic techniques capable of identifying these hidden defects has become a major focus in maintenance engineering. Contemporary non-invasive inspection methods include magnetic systems (e.g., DiagBelt) [3,8], X-ray imaging [9,10], and advanced vision-based systems for detecting surface damage [5,11,12]. Parallel to these methods, machine-learning algorithms are being developed to support belt condition classification and prediction, ranging from classical support vector machines [11] and regression models [13] to advanced deep learning architectures such as generative adversarial networks [12].

In comparison to alternative methods, such as X-ray imaging [9,10] or vision-based surface inspection systems [5,11,12], the DiagBelt+ system provides continuous online scanning of the belt core, detecting internal defects without interrupting conveyor operation. Unlike classical magnetic systems, DiagBelt+ offers higher spatial resolution and automated defect quantification, making it suitable for high-throughput diagnostics in large-scale open-pit mines. From the perspective of fracture mechanics and conveyor system design, studies on belt resistance to dynamic impact (punctures), where lumps of material fall from height and strike the belt at discharge points, are essential [14,15,16]. Parameters such as mass, shape, sharp edges on the falling objects, drop height, and belt handling at loading points, including belt support, influence stress distribution and potential damage. Drop-test experiments and computed tomography have demonstrated that heavy impacts can cause steel-cord fractures and cuts, delamination of rubber covers, and micro-damage, subsequently developing into long-term core defects [15,16].

Equally significant are the properties of the transported material—its hardness, shape, granulation, and content of fine mineral fractions. Studies [2,17,18] have shown that abrasive, aggressive materials—particularly overburden—cause significantly greater cover wear and internal damage than milder loads, such as lignite. Laboratory tests using dry-sand/rubber-wheel apparatus [17] and field analyses [2] have unequivocally demonstrated that higher abrasivity can reduce belt lifespan significantly.

Another vital research area is identifying defect causes and systematizing them using quality-analysis tools such as the Ishikawa (fishbone) diagram [19,20]. This diagram organizes factors affecting belt damage into six main categories: (1) material characteristics; (2) belt construction; (3) operational parameters; (4) condition of discharge points; (5) maintenance and diagnostic quality; and (6) environmental factors. Causal analysis facilitates the identification of “bottlenecks” in operations and planning of corrective and preventive actions. To structure knowledge of potential degradation causes of steel-cord conveyor belts, Figure 1 presents an Ishikawa diagram.

Most studies indicate that belt wear evolves non-linearly, with increasing rates of defect formation and area growth, particularly in later life stages [3,6]. This implies that older belts degrade faster, requiring more frequent inspections and timely repairs or replacements of segments. Predictive models based on canonical correlation analysis [14] and non-linear regression [13] enable forecasting of the critical point, when degradation reaches levels necessitating belt shutdown according to user-defined replacement strategies [21,22].

The aim of this study is to analyze the influence of the transported material type—overburden, lignite, or a mixture—on the rate of core-damage accumulation in Type-St belts. Diagnostic data were obtained from the DiagBelt+ system, which facilitates the assessment of steel-cord condition without dismantling the belt [23]. Over 100 belt-loop scans were used, comprising segments of varying length, age, and operational history. For each segment, the transported material type, belt age, Resurs (percentage of expected operating time), and failure density and area were determined. This approach enables identification of differences in degradation rates depending on material type and supports formulation of technical recommendations for belt selection, discharge-point design, maintenance scheduling, and replacement strategies in open-pit mines [24,25,26,27,28].

2. Materials and Methods

This study was conducted at one of Poland’s largest open-pit lignite mines, equipped with an extensive belt-conveyor system for transporting both lignite and overburden. The conveyors utilize steel-cord-reinforced belts (Type St) designed for heavy mass transport. The DiagBelt+ diagnostic system enables non-invasive, dynamic scanning of belt condition during normal conveyor operation.

Data were collected from over 100 conveyor belt loops comprising various belt segments. A belt segment is defined as a continuous span between joints, supplied in a single spool (at Bełchatów Mine, segments may reach up to ~300 m). For each segment, the following were recorded: Material Type (lignite, overburden, or mix), Belt Age (in months), Resurs (% of expected operating time), Segment Length (m), Loop Length (m), number of core defects, defect density (defects per meter), defect area (m²), and defect area density (m² per meter). Only segments that began their operation on the tested conveyor and had not undergone reconditioning were included: 274 segments (39 carrying lignite, 46 carrying mixed material, 189 carrying overburden). Figure 2 shows the length distribution by Material Type.

Figure 3 depicts the distribution of belt age at the time of inspection per material type.

All the analyzed belts were of the same construction: steel-cord belts with a strength class of 3150 kN/m and cover thicknesses of 14 mm (top) and 7 mm (bottom). Due to their uniform technical specification, these characteristics were not included as model variables.

The DiagBelt+ system, developed at Wrocław University of Technology, uses inductive magnetic methods to magnetize steel cords and register magnetic-field disturbances caused by internal core discontinuities—cord breaks, wire fractures, corrosion, or at belt joints. The system was deployed at Bełchatów Lignite Mine under an NCBR project (PO-IR.01.01.01-00-1194/19-00) and is routinely used for conveyor belt scanning. Prior to its introduction, only visual inspections were conducted, which limited detection to large surface defects. DiagBelt+ enables continuous monitoring of belt core condition during operation, without stopping or dismantling the belt—a significant innovation. Magnetic diagnostics reveal the state of the steel cords hidden beneath the rubber cover. Figure 4 illustrates the installation scheme on the conveyor belt.

The belt core is magnetized by permanent-magnet bars, and a multi-channel inductive sensor array detects localized field disturbances indicating defects. The sensor head contains over 90 coils spaced 25 mm apart across the belt width. High spatial resolution (25 mm transversely and 2.5 mm longitudinally per 1 m/s belt speed, with 400 Hz sampling) allows detection of small defects—from single-cord cuts and wire fractures to advanced corrosion invisible from the outside. Signals from the coils are collected and processed by a dedicated data-collection unit and DiagBelt software (DiagBelt+ Data Analysis v. 1.0), synchronized to belt displacement (via a tachometer magnet on a pulley of known diameter). This enables localization of defects along the belt loop length and across its width. Detailed system operation is described in [29,30]. The system also automatically recognizes belt-joint signals (displaying distinct magnetic polarity), enabling identification and localization of all joints in the loop, and thus segmentation of belt sections. During a single scanning cycle, DiagBelt+ can scan the entire conveyor loop—several kilometers long and comprising multiple belt segments—without disrupting conveyor operation. For instance, at the lignite mine, a 2.25 m wide, 3–4 km long belt running at ~56 m/s can be fully scanned within minutes. The DiagBelt+ system acquires inductive magnetic signals at a sampling frequency of 400 Hz, resulting in a longitudinal resolution of approximately 2.5 mm per 1 m/s of belt speed. Since the inspected belts operate at a comparable speed of approximately 6 m/s, the effective sampling interval along the belt is 15 mm. The sensor head consists of 90 coils spaced every 25 mm across the belt width, which is either 1.8 m or 2.25 m. This yields 72 or 90 transverse sampling channels, respectively. For every meter of belt length, approximately 67 samples are recorded per channel. Consequently, a single full scan of a 2 km long belt generates approximately 12 million data points, structured as a matrix of 134,000 longitudinal rows (each covering 15 mm) and 90 columns (one per coil), used to map and quantify internal damage signals. The collected data form a 2D map of core defects along the belt length and width. Figure 5 shows an example of such imaging at three different time points.

The software automatically divides the belt into sections (between joints), counts detected defects per section, and computes their total area. Quantitative belt-condition metrics—such as defect density (defects per length) and total defect area per meter—are derived. Results are displayed as color-coded maps and defect profiles, enabling quick identification of high-damage regions. Figure 6 provides an example of a color-coded condition map for a scanned belt loop. Individual belt segments are represented as rectangles, with lengths proportional to the actual segment lengths, and colors indicating the severity of internal damage.

The color scale is progressive—from green (low signal density, good technical condition), through yellow and orange (moderate damage levels), to red and dark brown, which mark significant core deterioration and a potential risk of failure. This visual representation enables rapid identification of belt sections that may require closer monitoring or maintenance intervention.

DiagBelt+ was designed for high-throughput diagnostics of belt-conveyor loops in open-pit mining, where operational continuity is critical. The use of non-destructive diagnostics allows regular, rapid assessment of belt-core condition during operation, significantly reducing the risk of operational failures. Through advanced data analysis algorithms, the system automatically counts defects and provides clear quantitative condition scores. This information enables maintenance teams to effectively plan repairs, reconditioning, or segment replacement at the optimal time, minimizing downtime costs and preventing serious breakdowns [31]. The implementation of DiagBelt+ in mines (e.g., Bełchatów) confirmed its practical utility—diagnostic data supported analysis of defect-growth trends over time and modeling of remaining error-free operational time. Such diagnostics greatly reduce unplanned downtime and streamline belt asset management, enhancing conveyor safety and continuity, and yielding substantial cost savings through extended belt service life compared to conventional visual inspection schedules [32].

In addition to absolute belt age, a time-based indicator known as Resurs (percentage of expected operating time) was used to represent the relative level of belt usage. Resurs is defined as the ratio of the belt segment’s age (in months) to its expected service life, based on manufacturer specifications or operational experience from similar conveyor systems. Expressed as a percentage, it enables normalization of usage across belts of different lengths, installation dates, and operating conditions. While strongly correlated with age, Resurs provides a more contextualized view of expected wear, particularly useful in comparative studies of degradation rates. In the present study, Resurs was one of the independent variables used in statistical and regression analyses to assess its predictive potential for failure density and to compare the degradation behavior of belts transporting different materials. The operational configuration of the conveyor system (including bends, inclinations, and the number of transfer points) is not explicitly included in the model but may affect the degradation rate. However, such effects are partly captured through the Resurs indicator, which reflects cumulative operating time and changing load conditions. It is also worth noting that in open-pit operations, conveyor layouts are periodically modified, e.g., by adding or relocating transfer stations.

The DiagBelt+ system enables online diagnostics by scanning the entire belt loop during regular operation at full speed. All data are collected in real time and automatically processed to generate condition maps and damage reports accessible immediately after inspection.

The metrological performance of the DiagBelt+ system, including spatial resolution, repeatability, and sensitivity to different fault types, has been validated in prior studies [29,30].

3. Results

The analysis aimed to compare three independent samples of belt segment condition data across different materials—brown coal, brown coal with overburden (mixture), and overburden—using the variables: Age (in months), Resurs (percentage of expected operating time), and Failure Density (failures per meter).

3.1. Descriptive Statistics and Visualizations

Box-and-whisker plots (Figure 7) illustrate the distribution of values for each variable across the material types. The summary statistics are presented in

Table 1. Summary statistics for Age, Resurs, and Failure Density.

Material	Count	Age Avg	Age Median	Age Std Dev	Age CoV	Res. Avg	Res. Median	Res. Std Dev	Res. CoV	Density Avg	Density Median	Density Std Dev	Density CoV
1. Brown coal	39	154.2	168	24.183	0.157	0.938	0.933	0.032	0.034	0.036	0.024	0.036	1.002
2. Brown coal–overburden	50	76.3	78	21.926	0.287	1.079	1.083	0.174	0.161	0.543	0.491	0.308	0.567
3. Overburden	287	66.0	59	27.996	0.424	1.022	1.075	0.287	0.281	0.961	0.711	0.970	1.009
Total	376	76.4	65	37.827	0.494	1.021	1.065	0.261	0.256	0.809	0.513	0.905	1.118
(1−2)/2 [%]		101.93	115.38	10.29	−45.38	−13.10	−13.85	−81.42	−78.62	−93.40	−95.07	−88.34	76.75
(2−1)/2 [%]		16.62	32.20	−21.68	−32.26	5.60	0.77	−39.56	−42.76	−43.53	−31.05	−68.26	−43.80

, which includes means, medians, standard deviations, coefficients of variation, and the percentage differences between the mixture and pure materials. The smallest differences were observed for Resurs, and the largest for Failure Density.

The means and medians for the three samples and three materials presented on the charts (Figure 7) are also included in numerical form in Table 1. There is also information about the standard deviation and coefficient of variation, as well as percentage differences between the brown coal and overburden from the data on their mixture. The smallest differences were for Resurs and the largest for brown coal and overburden.

In Table 1, the summary statistics comprise detailed information about the average, median, standard deviation, and coefficient of variation for three measures of belt condition and materials: 1. brown coal, 2. mixture, and 3. overburden.

Quantile plots (Figure 8) further demonstrate these trends. For Resurs, the distributions are closely aligned across materials, while for Age and Failure Density, the quantile curves are more distinctly separated, indicating stronger material-based differentiation.

3.2. Statistical Significance Testing

The multiple range tests (Figure 9) using Fisher’s LSD method at the 95% confidence level confirmed that:

• Age and Failure Density show statistically significant differences between all the material types.
• For Resurs, the mixture does not differ significantly from either brown coal or overburden, though brown coal and overburden differ significantly from each other.

This suggests that Resurs, as a derived metric from Age and expected lifespan, is less sensitive to material differences.

3.3. Correlation Analysis

The scatterplot matrix (Figure 10) and Pearson correlation table (Figure 11) indicate significant correlations between several variables:

• Loop Length is significantly correlated with section length, Age, and Failure Density.
• Age shows a significant correlation with Resurs and Failure Density.

The correlation between Age and Resurs is expected, as Resurs is calculated using Age and expected operating time (Resurs = Age/expected operating time). However, the correlation between Age and Failure Density is less consistent. Variability can be attributed to differences in conveyor systems: belt segments of the same age may experience different wear rates depending on their location and operational conditions.

Formal analysis of these differences in the form of multiple range tests for Age, Resurs, and Failure Density is presented in the three tables shown in Figure 9.

This chart (Figure 11) shows Pearson product–moment correlations between each pair of variables. These correlation coefficients range between −1 and +1 and measure the strength of the linear relationship between the variables. Also shown in parentheses is the number of pairs of data values used to compute each coefficient (274). The third number in each location of the table is a p-value that tests the statistical significance of the estimated correlations. p-values below 0.05 indicate statistically significant non-zero correlations at the 95.0% confidence level (in red). The following pairs of variables have p-values below 0.05: Loop Length and Section Length, Loop Length and Age, Loop Length and Density, Section Length and Age, Age and Resurs, Age and Density.

The influence of the conveyor length (belt loop) on the belt operating time is confirmed in the literature [31], as is the section length and operating time [22]. Age and Resurs for the same conveyor are linearly related, but when we analyze data from many conveyors, the correlation drops significantly (Figure 11). The correlation between Age and Failure Density should be obvious, but the downside may be surprising; as with the increase in belt Age, we expect the Damage Density to grow. However, it should be remembered that we are analyzing sections of belts installed on conveyors. Some may already be heavily worn, others may have been recently installed. Even sections of the same age, but operating on different conveyors, may differ in densities. Shorter ones will have a higher Damage Density and lower Density on longer ones. Therefore, the next step will be to try to relate these measures to each other, taking into account other factors.

3.4. Multiple Regression Analysis

To predict Damage Density using available operational metrics, a multiple regression model was constructed with the following variables: Age, Resurs, Loop Length, and Section Length.

Initial Model:

D = 0.00387⋅A + 0.57366⋅R − 0.000215⋅LL + 0.00229⋅SL

(1)

where:

• D—Damage Density [1/m]
• A—Age [months]
• R—Resurs [%]
• LL—Loop Length [m]
• SL—Section Length [m]
• R² = 46.74%, Adjusted R² = 46.31%
• Standard Error = 0.890, MAE = 0.563
• Durbin–Watson Statistic = 0.557 (indicating possible autocorrelation)

While the model showed a moderate fit, the variable Age had a p-value of 0.0575, indicating it was not statistically significant at the 95% confidence level. Therefore, it was removed in the final model.

Final Model:

D = 0.62643⋅R − 0.000138⋅LL + 0.00241⋅SL

(2)

• R² = 46.22%, Adjusted R² = 45.93%
• Standard Error = 0.894, MAE = 0.588
• All the remaining variables are statistically significant (p < 0.05)

For the final model, the Durbin–Watson statistic was calculated and yielded a value of 0.570, indicating strong positive autocorrelation in the residuals. This is likely due to the structure of the dataset, which was sorted by conveyor loop and belt segment. As a result, neighboring rows in the dataset often correspond to segments affected by similar operational conditions.

The predictor variable Age was excluded from the model due to its strong correlation with Loop Length (PPMC = 0.79), which reduced the risk of multicollinearity.

A residual plot (Figure 12) illustrates Studentized residuals plotted against the Resurs value. A group of seven outliers (residuals ≥ 3) is visible, corresponding to segments with Resurs > 0.8, located on a loop of 1881 m, operating in an overburden transport system. These segments showed very high Damage Density values (up to 4–5), indicating severe wear beyond the limits for refurbishment.

Component effect plots (Figure 13) and predicted vs. actual plots (Figure 14) further validate the model’s performance. Though the R² values indicate moderate explanatory power, the model can be a useful tool for forecasting belt Damage Density using existing database parameters, which are retained (Age in months) and calculated (Resurs) for all belt segments in the mine in the Tasma program.

The results are plotted on two charts: the Component Effects Plot (Figure 13) and Plot of Belt Section Density with predicted values (Figure 14). We see significant deviations in actual values from the predicted values. This is a consequence of the fact that the obtained model explains only 46% of the variability.

4. Conclusions

This study analyzed the condition of conveyor belt segments across different material types using statistical and regression analyses. The key conclusions include:

• Material Type Impact:

  ○

  Age and Damage Density vary significantly with material type, while Resurs shows limited sensitivity.

  ○

  The mixture of brown coal and overburden behaves similarly to both parent materials in terms of Resurs, suggesting it can be treated flexibly in modeling.

• Predictive Modeling:

  ○

  A multiple linear regression model was developed to estimate Damage Density based on measurable variables: Resurs, Loop Length, and Section Length.

• The final model (Model 2) explains approximately 46% of the variability in damage density and includes only statistically significant predictors. The variable Age was excluded due to its strong correlation with Loop Length (PPMC = 0.79), which helped reduce multicollinearity. Model Limitations and Residual Analysis:

  ○

  The Durbin–Watson statistic for Model 2 was 0.570, indicating positive autocorrelation in residuals. This effect is likely caused by the data structure, in which observations were grouped by conveyor loop and belt segment.

  ○

  A group of seven outliers with Studentized residuals ≥ 3 was identified. These segments exhibited very high wear (Resurs > 0.8) and were located in long loops (1880 m) used in overburden transport. Although these observations affect model fit, they represent real and critical wear conditions.

• Operational Implications:

  ○

  Predictive tools based on Resurs and geometry parameters could assist in maintenance planning and reliability assessment.

  ○

  However, due to moderate predictive power, further enhancement through non-linear modeling or inclusion of categorical variables (e.g., conveyor type or operational intensity) could be beneficial.

• Future Work:

  ○

  Investigate advanced regression methods (e.g., ridge, LASSO, or non-linear models).

  ○

  Incorporate categorical or operational variables for improved accuracy.

  ○

  Validate models using independent datasets or real-time monitoring systems.

Main Conclusions

The study demonstrates that predicting the condition of conveyor belt segments based solely on operational data—such as Resurs, Age, Loop Length, and Section Length—explains only approximately 46% of the variability in Damage Density. This leaves 54% of the variability unexplained, attributed to factors not captured in standard operational databases (such as material fatigue, micro-damages, or local stress concentrations).

The past (before the implementation of the DiagBelt diagnostic system), which relied primarily on visual inspection and calculations based on Resurs, was limited in accuracy and could result in up to 56% uncertainty when assessing the real condition of belt segments. While Resurs is a useful indicator, it cannot fully account for the complex and heterogeneous wear patterns occurring across different conveyor systems.

Therefore, the most effective and reliable approach is the application of a non-invasive diagnostic tool, such as belt scanning technology. These systems can directly measure belt condition and detect early signs of wear or damage that are invisible to the eye or not reflected in calculated indicators like Resurs. In fact, the residual structure of the regression model revealed clear clusters of segments with excessive wear that would not have been detected using Age or Resurs alone. Such diagnostic tools offer a substantial improvement in precision, reduce the risk of unexpected failures, and support more informed maintenance decisions.

In conclusion, while data-driven modeling provides some predictive value, direct condition monitoring through non-invasive diagnostics is essential for achieving accurate, real-time assessment of conveyor belt health and ensuring operational reliability.

The moderate value of R² of the regression model reflects the imperfection of indirect measures of belt condition, such as age and Resurs, in relation to the direct measurement of the number of failures using the magnetic method. Further work is planned on the influence of various factors on the intensity of damage increase in various conveyor operating conditions.

Recent studies have shown that weak multi-harmonic fault features—often buried in noise—can be amplified using stochastic resonance-based methods. For instance, Zhang et al. [33] introduced a stochastic resonance array framework that creates noise-boosted filter banks, improving the detectability of incipient faults in rotating machinery. Although the DiagBelt+ system currently employs deterministic magnetic sensing and signal averaging, incorporating such non-linear noise-assisted enhancement techniques may offer additional sensitivity for detecting early-stage wire breakage or localized corrosion effects that generate low-amplitude responses. The current analysis was based on linear regression models due to their interpretability and ease of implementation in operational settings. However, non-linear machine learning methods such as random forests, gradient boosting, and deep neural networks are currently being tested on the same dataset. These approaches are expected to better capture complex interactions between usage indicators and damage metrics and will be presented in future studies.