Real-Time Analysis of Industrial Data Using the Unsupervised Hierarchical Density-Based Spatial Clustering of Applications with Noise Method in Monitoring the Welding Process in a Robotic Cell

Abstract

The application of modern machine learning methods in industrial settings is a relatively new challenge and remains in the early stages of development. Current computational power enables the processing of vast numbers of production parameters in real time. This article presents a practical analysis of the welding process in a robotic cell using the unsupervised HDBSCAN machine learning algorithm, highlighting its advantages over the classical k-means algorithm. This paper also addresses the problem of predicting and monitoring undesirable situations and proposes the use of the real-time graphical representation of noisy data as a particularly effective solution for managing such issues.

1. Introduction

The increasing popularity of artificial intelligence (AI) methods, especially those in machine learning (ML), has found applications in numerous branches of science and technology [1,2,3,4,5,6,7,8,9]. The rapid development of these methods is closely linked to advances in computational power, particularly for big data (BD) processing [10], which has practical applications across various industrial sectors [11]. Examples include food processing technology [12], quality and safety improvement [13], decision support [14], and risk management [15]. Additionally, BD analysis facilitates supply chain continuity [16], material data mining [17], and the prediction of production anomalies [18,19,20,21,22].

A key challenge in BD and AI applications is data visualization, particularly from the perspective of human operators, whether as end-users of software applications or individuals supervising production processes [23,24,25,26,27,28,29,30,31,32,33,34,35,36]. Virtual-reality solutions are of particular interest, as they integrate real-time production data with spatial information about physical objects [37,38,39]. Selecting the appropriate type of production parameter information for workers is essential [40], depending on production activities, such as automated assembly [41], manual assembly [42], or process monitoring and control [43,44]. Though we cannot delve into all related challenges here, issues like the use of virtual reality goggles [45,46,47] and human–machine interfaces (HMIs) [48,49,50] for optimal visualization remain pivotal to industrial progress.

This paper focuses on utilizing the Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) algorithm in real technological scenarios, aiming to provide operators with informative graphical data to support decision making—a key objective of this study.

Furthermore, it must be noted that ML methods in real-world robotic applications are not yet widely implemented. While robotization is substantial in many industries, its geographic distribution is uneven [51,52]. Historically, industry standards have relied on programmable logic controllers (PLCs) for automation [53,54], leaving industrial sensor technology relatively underdeveloped. As a result, while major industry players generate large volumes of data, their practical use often remains underexplored. Key areas of current BD and ML applications include geoscience [55], urban transport monitoring [56], and database numerical analysis [57,58]. In machine industry contexts, k-means algorithms have been applied to process optimization and anomaly detection in the automotive sector [59,60], while HDBSCAN has seen applications in hydropower plant monitoring [61] and fault detection [62,63,64,65]. A comprehensive review of Industry 4.0, emphasizing BD utilization, is available in [66].

We believe that the primary challenge is not the type or quantity of sensors but overcoming barriers to data usage and visualization. Consequently, a secondary objective of this work is to demonstrate the implementation of the HDBSCAN algorithm [67] for predicting undesirable events, including production breakdowns.

The selection of HDBSCAN as the preferred method is based on extensive efforts comparing it against other clustering methods, including standard k-means [68], MiniBatch k-means [69], Mean-Shift clustering [70], Hierarchical Clustering [71], Balanced Iterative Reducing and Clustering using Hierarchies (BIRCHs) [72], and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) [73]. All numerical analyses were conducted using the Scikit-learn Python package ver. 1.4.2 [74], with visualizations generated using the matplotlib library [75].

This paper is structured as follows: the first section describes the technological context and data origins, with time-domain data presentations. Next, the k-means and DBSCAN algorithms are detailed as precursors to illustrating the practical advantages of HDBSCAN. These algorithms were tested for their ability to discern two situations: a stable system and one displaying instabilities during welding. Furthermore, visual information was evaluated from the practical perspective of operators overseeing production. This paper concludes with a summary of the findings.

2. Industrial Data Collection and Methods of Analysis

2.1. Collecting Data

The presented analysis is based on data obtained during a real welding process in a robotic cell using a Fronius^® welding system (TPS500i) manufactured by Fronius GmbH (Wels, Austria) [76]. Data were recorded over a period of 78 min, during which the robot cyclically repeated several welding steps that varied in the length and shape of the welding path. These data were stored at a constant interval of 4.2 s, while the typical amount of data recorded in a single experiment was approximately 1200 points. The experiment was repeated for several welded samples, yielding the same nature of results each time. During operation, the following parameters were recorded: electric current intensity (A), electric power (W), electric voltage of the welding power supply (V), welding time (s), wire feed speed (WFS) (m/min), and system energy consumption (kJ). The welding method used was MIG/MAG (gas metal arc welding) [77]. Heat exchangers for domestic applications, made of ordinary carbon steel, were used as samples for the experiments (Figure 1). The typical length of the weld paths ranged from about 60 mm to 80 mm. There were six welds securing the tubes around their circumferences and eight straight welds attaching the front square surfaces. A typical welding process for these paths was split into single events of varying durations, with the duration of a single event typically not exceeding 6 s.

The Open Platform Communications Unified Architecture (OPC-UA) communication protocol was used to collect data from the welding source, enabling manufacturer-independent data exchange between the machines used in industrial systems. The protocol serves as a base for integrating devices in IoT and implementing Industry 4.0 approaches. The Fronius welding source had an option that allowed real-time recording of the required information into a text file, which was later analyzed. The industrial signals collected are presented in the time domain (Figure 2). As shown, the recorded data clustered into dominant areas, with some outliers which could be considered undesirable. For example, in Figure 2a, there are five dominant regions (“islands”) of data, displayed in detail in the zoomed view of Figure 2b. Additionally, two significant regions appear: one at the beginning of the recording (time = 0), where non-zero values of current are observed, and another with zero-value currents below the islands, recorded for time > 70,000. Other points exhibit a random behavior, indicating abnormal data.

2.2. Preliminary Data Clustering

A deeper analysis of the measured parameters can be conducted by excluding the time domain—a standard step in clustering analysis. Modified results are shown in Figure 3. While other combinations of datasets are possible, the presented relations are representative for further analysis. However, this presentation alone does not provide comprehensive insight into undesirable production moments, which is crucial for making corrections during the technological process.

The following section will focus on the relationship observed in Figure 3a, specifically the dependence of energy on the current.

2.3. Methods of Data Analysis

2.3.1. K-Means Algorithm

The classical k-means clustering method divides data into sub-areas by determining a specific number of clusters and their centers, minimizing the sum of distances from individual points to their cluster centers. In this method, the number of centers and the distance metric must be specified by the user. For the presented analysis, the Euclidean quadratic distance $d_{ki}$ between the position of the actual i-th data point ${\overrightarrow{r}}_{ki}$ and the k-th cluster ${\overrightarrow{c}}_k$ was used, defined as

$$d_{ki}\left({\overrightarrow{r}}_{ki}, {\overrightarrow{c}}_k\right)={\left({\overrightarrow{r}}_{ki}-{\overrightarrow{c}}_k\right)}^2,$$

(1)

and the total sum of distances within all k-clusters is minimized as follows

$$\underset{{\overrightarrow{c}}_k}{\min }\left(\sum _k\sum _i{d}_{ki}\left({\overrightarrow{r}}_{ki}, {\overrightarrow{c}}_k\right)\right).$$

(2)

Figure 4 (left panel) shows an example of a k-means clustering result between normalized energy and current data. Although normalization is unnecessary, it is commonly applied, especially for data from unrelated subject areas. In the right panel, the choice of four clusters is justified using the overall silhouette value (SV) parameter, which indicates how effectively data points are grouped. For the i-th data point from a dataset of N points, the individual silhouette value is defined as

$$SV(i)={\displaystyle \frac{{\overline{D}}_i-{\overline{d}}_{ki}}{max\left\{{\overline{D}}_i,{\overline{d}}_{ki}\right\}}},$$

(3)

where ${\overline{D}}_i$ is the mean distance of the i-th data point to all points in other clusters, and ${\overline{d}}_{ki}$ is the mean distance within the k-th cluster. Thus, the overall SV is then calculated as

$$SV={\displaystyle \frac{1}{N}}\sum _{i=1}^{i=N}SV\left(i\right).$$

(4)

The first minimum in the relationship between SV, and the number of clusters typically determines the optimal cluster count. Our intention was not to review clustering outcomes across different algorithms but rather to focus on identifying noisy data from other data points. For comprehensive reviews of various approaches in this field, readers are directed to [78,79].

Clusters also provide meaningful interpretations, as shown in Figure 5, which demonstrate the relationship between consumed energy, applied currents, and welding durations (welding_time_n) across clusters.

While k-means produces clear cluster boundaries (Figure 4)—an advantage of the method—its graphical representation may not quickly convey information about undesirable situations to an operator. Although cluster center observations can offer hints about production quality, they may rely too heavily on human recognition and reflex.

2.3.2. DBSCAN Algorithm

In the next step, we focus on testing the effectiveness of monitoring the production process. This can be achieved using an algorithm that excludes outlier results from clusters, treating these as undesirable noise indicative of problematic technological situations. The DBSCAN approach is an example of such a solution. This algorithm allows the user to define a minimum number of data points, within an assumed range of influence (epsilon), required for a point’s coordinates to be classified as part of a given cluster.

The algorithm classifies data points into three categories: core points, directly reachable points, and non-reachable (noise) points [73]. Core and directly reachable points form data clusters. In our case, the clusters generated by DBSCAN may overlap entirely, and the density at a given position remains unknown.

2.3.3. HDBSCAN Algorithm

While the DBSCAN algorithm offers the basic advantage of distinguishing outlier data (noise) from dominant clusters, the closely related HDBSCAN approach [7,80] extends this capability by identifying variable densities within local clusters. In HDBSCAN, the classification of clustered points versus noise relies not only on the epsilon range but also on the assumed density threshold for data points to be considered cluster members. The density of clustered points provides a useful way to graphically inform an operator about the degree of overlap (density). For example, a point in the figure may have a size proportional to its density.

However, we propose an important enhancement in data presentation: generating figures in real time, where the time-dependent number of noisy points serves as a key indicator of the welding process’s stability or instability. Detailed information extracted from such an approach will be discussed in the subsequent paragraphs.

3. Analysis of Results

3.1. DBSCAN Results

Figure 6 illustrates four cases of clustering using the DBSCAN algorithm, where the assumed minimum number of cluster members is set to 5, 10, 25, and 50 (described in the figure captions as the number of samples). These cases are presented for an exemplary energy–current dataset to determine the optimal value of the impact range (epsilon range). This analysis helps estimate a rational number of clusters for data visualization and assess the relevant number of noisy points, as evident in the figures.

By comparing these results with the earlier k-means analysis, we can conclude that setting epsilon = 10 and a minimum sample size of 25 or 50 (shown in the lower panels of Figure 6) offers a good balance. Too small an epsilon value causes numerical instability, while too large a value reduces the number of clusters, leading to information loss. Proper selection of these parameters (epsilon and minimum samples) ensures clear distinction between desired data and noise, enabling effective monitoring of production process stability. Figure 7 further demonstrates the clustering results for varying epsilon values (5, 10, 15, and 25), with a consistent minimum sample size of 50.

These results (compare Figure 4 and Figure 7), particularly for epsilon = 10, effectively highlight relevant regions of the welding process dynamics.

3.2. HDBSCAN Results

The HDBSCAN algorithm enables the identification of clusters with variable densities, graphically represented by circles of varying diameters proportional to the number of samples with identical coordinates. Like DBSCAN, this method uses a separation measure called “cut distance”, equivalent to epsilon in DBSCAN. Additionally, HDBSCAN incorporates an adjustable parameter for the minimum number of points needed to form a cluster’s nucleus. In Figure 8, various cases are presented, where the minimum cluster size is set to 15, 20, 25, 30, 40, and 80. The cut distance is fixed at 0.1 for consistency across analyses.

HDBSCAN Data Analysis

Choosing a minimum cluster size of 30 enables the detection of two clusters at zero-value current, a potentially significant observation about the welding process’s resting state. Additional relationships among data series are shown in Figure 9. Points with higher densities are represented by larger circles, though the uniformity of circle sizes indicates a relatively consistent density within the analyzed welding process.

While HDBSCAN provides more precise information compared to earlier methods, the real-time monitoring of process dynamics—specifically, variations in cluster counts and noisy points—remains ambiguous until the process conclusion. This limitation is addressed in Figure 10, which dynamically tracks these variations for a minimum sample size of 30. In the figure, the initial phase is clearly identifiable, marked by the formation of the first two clusters and a simultaneous drop in the number of noise points. Following this phase, the production process transitions to a four-cluster state, during which the number of noise points increases linearly at a relatively small growth rate of approximately 0.015 points per time step. However, toward the final stages of production, a sudden step in noise levels is observed.

To simulate a hypothetically more unstable production scenario, the minimum sample size was reduced to 15, as shown in Figure 11.

The number of clusters and noisy points reveals instabilities, such as at time = 600 and 660. In the latter case, the system transitions from four clusters to six, with an intermediate five-cluster state, as more clearly seen in the noisy data (right panel of Figure 11). Unlike the results in Figure 10, noise signals here exhibit nonlinear behaviors. However, from a practical standpoint, these instabilities have no adverse effects on the welded parts. Figure 11 primarily serves as a simulation of a hypothetical, undesirable situation.

Returning to the case with a minimum sample size of 30, Figure 12 shows noise patterns recorded in real time across different data series. Observing multiple datasets provides additional insights, such as process instabilities in the energy–power relationship around time = 600, which are not evident in other datasets.

To deepen this analysis, Figure 13 presents the first derivative of the noise signal, highlighting two significant instability periods: around time = 620 and nearing the process conclusion (time > 1000).

From this perspective, two significant instabilities were identified: the first occurring around the time-point 620 (clearly visible in Figure 13b) and the second near the end of the production process, at time-points exceeding 1000 (most apparent in Figure 13a,b). These two uncertain situations can be detected through direct (xy) dependency analysis, particularly in the energy vs. power relationships shown in Figure 14 and Figure 15. Both figures illustrate the state prior to the abrupt increase in noise levels (left panels) and during elevated noise levels (right panels).

In both cases, noise spikes correspond to scattered energy consumption values (0–15 kJ), while power fluctuates around 3500 W. These points remain unclassified within the clusters.

4. Conclusions

In this paper, we demonstrated the practical application of the unsupervised machine learning algorithm HDBSCAN for monitoring the arc welding process. A visually informative representation of the production process was developed, providing valuable insights for operators. The advantages of HDBSCAN were also highlighted in comparison to classical algorithms like k-means and DBSCAN, particularly for identifying potentially problematic situations during the production process.

Our findings underscore the importance of analyzing a combination of diverse data series to accurately assess process flow, especially when dealing with noisy data. In this case, the analysis focused on mechanical and energy-related time-dependent parameters. These two types of data, specific to arc welding process engineering, appear to form a reasonable minimum requirement for addressing the challenge of failure prediction.

By leveraging real-time information from HDBSCAN about the number of clusters and the volume of noisy data signals—as well as their first derivatives—it was possible to clearly identify process instabilities. We emphasize once more that such graphical representations should be simultaneously monitored across several selected combinations of data series for a more comprehensive analysis. Hence, we recommend using real-time data on the number of clusters and the number of noise points as a significant type of graphical information to be implemented in user interface screens.

We hope that the analysis of real industrial data presented here will contribute to broadening the use of practical machine learning (ML) and big data (BD) methodologies in industrial technological processes. In future work, we will aim to integrate supervised methods as a natural extension of the current unsupervised approach, addressing the additional challenge of labeling data, particularly for high-dimensional datasets representing complex technological processes.