Using Hybrid LSTM Neural Networks to Detect Anomalies in the Fiber Tube Manufacturing Process

Abstract

The production process of tubes for fiber optic cables is a complex process, where proper execution is crucial to the quality of the final product. This process has a complex state vector whose structure and coordinates dynamically change during the tube extrusion process. Small fluctuations in process parameters, such as temperature, extrusion pressure, production speed, and optical fiber tension, affect the optical attenuation of the final product. Such defects necessitate the withdrawal of the product. Due to the high number of process coordinates and the technological inability to automatically label those segments of the production process that cause anomalies in the final product, the authors used data clustering methods to create a training set that enabled the use of neural tools for anomaly detection. The system proposed in the main part of the paper includes a hybrid Long short-term memory (LSTM) network model, which is fed with data streams recorded on the tube extrusion production line. The input module, which performs preprocessing of input data, conducts multiresolution analysis of recorded process parameters, and recommends the process state’s belonging to a set of classes describing individual production anomalies to appropriate LSTM network modules. The learning process of the three–channel network allowed effective recognition of five classes of the monitored tube production process. The fit level of the proposed network model reached R2 values of ≥0.85.

1. Introduction

Fiber optic cables in modern civilization are the primary medium used for efficient and reliable information transmission. The continuous expansion of computer network infrastructure drives a growing demand for such products. Solutions are expected to include both long segments of optical medium as well as multi–core and multi–mode solutions, which allow for parallelization and thus acceleration of information transmission. The basic raw material is usually optical fiber, which has specific parameters describing its attenuation, rigidity, and physical dimensions. It is obtained by process of drawing the fiber in special towers from prepared glass billets of high chemical purity, which ensures appropriately low optical attenuation. Typically, at this stage, the fiber is coated with a dedicated polymer that ensures light confinement within it. The polymer layers can be combined with a color that ensures proper separation of fibers already at the stage of digital network construction. The next stage of optical cable manufacturing in industrial conditions is the extrusion process of the tube, which involves continuous heating and extrusion of plastic or metal materials to form hollow tubes that serve as a hydrophobic coating surrounding bundles of optical fibers. The subsequent step is the twisting of tube assemblies, and the final product of this process is an optical cable.

As can be seen, the above process is complex, with many different state coordinates, and each stage of production can potentially be a source of defects in the final product. In this context, predicting process anomalies using data from production equipment and taking preventive action is crucial. This is a key leitmotif that motivates many research teams around the world [1,2,3] to seek solutions and tools for monitoring this process and preventing defects that degrade the quality of the final product. Typically, the anomaly detection process involves collecting and analyzing data from sensors that monitor temperature, pressure, vibrations, chemical parameters, diameter, ovality, and other indicators specific to a given production line’s state. In recent years, statistical algorithms (e.g., linear regression), machine learning algorithms (e.g., decision trees, Support Vector Machines (SVM), neural networks [2,4]), and deep learning algorithms (e.g., Recurrent Neural Networks (RNN), Autoencoders) have been used for this purpose. The primary task of these algorithms is to monitor the given process in real–time, maintain predictive maintenance [5], and ensure quality control. Currently, companies in the fiber optic cable manufacturing sector are developing various solutions to minimize the percentage of products manufactured out of specification. Among the challenges they face are the scalability and adaptability of algorithms, their ability to integrate with production systems, and their effectiveness in minimizing waste and downtime [6,7,8,9,10,11,12].

By reviewing the latest literature, State-of-the-Art Review on Anomaly Detection in Various Domains [13], several leading themes can be distinguished. The detection of anomalies has emerged as a critical focus across diverse domains, particularly within the Internet of Things (IoT), biomedical signal processing, industrial processes, and satellite telemetry data. This review synthesizes recent advances in methods and approaches, highlighting their unique characteristics, applications, and associated challenges. Anomaly detection in IoT systems often employs dual-view mechanisms, combining time reconstructors, frequency reconstructors, and dual-view adversarial learning [14,15]. These methods aim to analyze data streams comprehensively, addressing both temporal and spectral dimensions to enhance detection accuracy. Biomedical data, such as signals related to Parkinson’s disease, are processed using unsupervised deep networks. These methods focus on uncovering latent patterns within data without labeled training samples, providing significant insights into disease recognition while addressing specific anomaly types. The use of singular value decomposition (SVD) in deep neural network (DNN) models aids in encrypting hidden features of signals. Techniques incorporating Fourier transforms allow for robust analysis of anomalies while maintaining data integrity [16]. Recent developments include the implementation of self-adversarial variational autoencoders (VAEs) integrated with contrastive learning to enhance anomaly detection capabilities [16]. These architectures excel in capturing nuanced differences between normal and anomalous states. Multi-node knowledge graphs fused with expert knowledge and Bi-directional Long Short-Term Memory (Bi-LSTM) networks have been proposed [17] as powerful tools for local feature extraction in anomaly detection. This approach leverages both structural and temporal relationships within the data. The multi-scale sparse attention module effectively extracts global features across scales, preserving pattern information critical for detecting process disturbances [18]. This approach is particularly adept at handling data from industrial monitoring systems [19]. For multidimensional processes, local feature masking can amplify state differences to visually highlight anomalies [20]. Similarly, mechanisms for identifying highly divergent patterns based on data density help streamline the detection process [21]. A knowledge distillation approach [22], transferring insights from large models to smaller, more efficient models, has proven effective in speeding up anomaly detection. Stochastic approaches utilizing partial Markov chains are employed to mask irrelevant process features, such as in image data [23]. These methods improve reconstruction quality and focus anomaly detection efforts on significant features. An imbalance in training datasets is a persistent issue, especially in industrial processes where generating anomalies artificially is infeasible [24]. Few-shot anomaly detection using positive-unlabeled learning addresses this by preparing well-structured datasets, albeit with challenges in real-world implementation [25]. Preprocessing transformations, such as Kalman filtering, are used to simplify input data for anomaly detection in diverse systems, including ECG signals and cooling devices [26]. Additionally, federated learning enhances defect detection, achieving high accuracy, precision, recall, and F1 scores in certain industrial settings [24]. Frequency-domain techniques generate augmented pseudo-anomalous images, allowing for the discovery of key anomaly characteristics [27]. Analyzing short video sequences of industrial processes has achieved notable success, such as the MSTE environment yielding $90.7\%$ accuracy [28]. However, video-based methods face limitations due to measurement constraints and environmental variability. In satellite telemetry anomaly detection, deep learning algorithms contend with significant noise and data gaps [29]. To address data scarcity in anomaly states, mechanisms such as feature injection and heterogeneous spatiotemporal graphs have been developed [30]. These techniques enable artificial supplementation of training datasets, improving detection accuracy in processes with high anomaly deficits. In unsupervised scenarios, attributed networks leveraging graph-based models enhance the differentiation between normal states and anomalies by reducing interference [31].

In the study [6], anomaly detection in smart factories was explored using machine learning techniques, particularly addressing challenges related to diverse sensors and their transferability across different production lines. A combination of machine learning algorithms, including neural networks and transfer learning, was employed to facilitate knowledge transfer between production lines. The authors achieved high accuracy in anomaly detection using datasets from various sensors, and the knowledge transfer between sensors enhanced system effectiveness in new, unfamiliar production environments. The study [10] proposed the creation of a digital twin for a production line, enabling improved monitoring and real-time anomaly prediction. This approach integrated digital twin modeling with machine learning algorithms, such as Long Short-Term Memory (LSTM) networks and autoencoders. The system demonstrated high accuracy in anomaly prediction, while the digital twin allowed for dynamic production parameter adjustments, reducing defects by $40\%$ compared to standard methods. In [5], the authors introduced a system for predicting production costs in the context of Industry 4.0. This system integrated data from multiple sources, including industrial sensors and ERP systems, to forecast changes in production costs. Advanced ML models, such as LSTM networks and decision trees, were applied to analyze time-series data from various sources. The model achieved a $92\%$ accuracy rate in production cost predictions, significantly reducing financial losses from unplanned downtimes and production defects. The study [7] focused on anomaly detection in optical fiber networks using machine learning algorithms. The primary application involved monitoring the integrity of optical cables and detecting damages in communication networks. Support Vector Machines (SVM) and neural networks, including LSTM models, were used to process sensor data and detect cable irregularities. The LSTM model excelled in real-time anomaly detection, achieving $94\%$ accuracy, and effectively identified both minor and major damages. Finally, Ref. [12] investigated automatic anomaly detection in manufacturing machines based on sensor data, aiming to minimize machine failures and downtimes by predicting potential issues. Statistical algorithms such as linear regression and k-Nearest Neighbors (k-NN) were combined with advanced machine learning methods, including LSTM networks. These models successfully identified anomalies in $87\%$ of cases, leading to a $25\%$ reduction in production process downtimes.

Table 1. Summary of key elements, applied models, and results for selected works on anomaly detection in production processes.

Authors (Year)	Research Description	Applied Models	Key Results
Abdallah et al. (2023) [6]	Anomaly detection in smart factories with sensor-to-sensor transfer	LSTM, Transfer learning, Neural networks	High anomaly detection accuracy, effective knowledge transfer between sensors
Kakavandi et al. (2023) [10]	Digital twin for real-time production line monitoring	Digital twin, LSTM, Autoencoders	40% defect reduction, dynamic adjustment of production parameters
Soleimani et al. (2023) [5]	Production cost prediction in Industry 4.0	LSTM, Decision trees	92% prediction accuracy for costs, reduction of defect-related losses
Abdelli et al. (2022) [7]	Anomaly detection in fiber optic monitoring	LSTM, SVM	94% anomaly detection accuracy, effective detection of optical cable damages
Pittino et al. (2020)  [12]	Automatic anomaly detection in production machines	LSTM, Linear regression, k–NN	87% anomaly detection accuracy, 25% downtime reduction

presents a summary of the technologies employed and the performance of the models in the context of research on anomaly detection and production process monitoring.

Regarding above, the industry practice shows, that often heuristic strategies are needed to overcome these industrial challenges, which frequently hinder effective detection [32,33]. Emerging trends such as federated learning, knowledge graphs, and advanced neural architectures offer promising directions for overcoming these challenges. By integrating domain expertise with sophisticated computational techniques, anomaly detection continues to evolve, bridging gaps across diverse applications. Although the recent reviews have attempted to unify diverse methods to facilitate objective comparisons, but unfortunately significant challenges persist due to process-specific measurement differences and the unique nature of anomalies across domains, which often hinder generalization [34,35,36,37,38,39,40].

In this study, the authors refer to the concept of anomalies as a set of various disturbances that may accompany the production process. These deviations from the correct process, which has its proper signature representing a normal and unthreatened production state, can become, in the absence of corrective actions, a potential source of defects in the final product. This may result in either a reduction in the product’s final quality or, in a worst-case scenario, render it unusable for further application.

This paper presents the results obtained from monitoring the tube extrusion process based on actual measurements recorded on the production line at the industrial plant FIBRAIN Sp. z o.o. This company specializes in the production and delivery of fiber optic technology solutions and is one of the leading manufacturers of fiber optic cables and telecommunication components in Central and Eastern Europe. The designed anomaly detection system allows for the reduction of disposal and repair costs for tube sections produced out of specification on the tube extrusion production line. The system described in the main section of the paper incorporates a hybrid Long Short-Term Memory (LSTM) network model, designed to process data streams collected from a tube extrusion production line. The input module, responsible for preprocessing, performs multiresolution analysis of the recorded process parameters. It subsequently assigns the current process state to one of the predefined classes, representing specific production anomalies, and directs it to the appropriate LSTM network modules. The three-channel network’s training process enabled the effective identification of five distinct classes within the monitored tube production process.

2. Materials and Methods

Given the current and continuously growing scale of production, the number of occurrences of various defects disqualifying a given fiber optic cable is a source of significant financial losses for the manufacturer in the form of wasted resources, the cost of disposing of defective cables, or their potential repair. The entire research work encompassed three different production lines, as shown in Figure 1: the RLR line for tube extrusion (a), the RLV line for coating extrusion on the cable core (b), and the RLM line for twisting cable cores from tubes (c).

These are stages where both the number and type of sensors used make it impossible to implement a uniform system that, in a hybrid form, would simultaneously record and detect anomalies from different processes. Therefore, at the current stage of work, the considerations presented by the research team focus on the production stage involving a single RLM production line.

In this paper, a hybrid LSTM network model is presented, which pertains to measurements from the RLM line. The other production lines are subjects of ongoing research and will be discussed in future works focusing on the engineering applications of AI tools. The RLM line is responsible for the production of micro–module cables with fiberglass rods (FRP) (MDC–FM, AERO–FM), aerial cables (ADSS, AERO–AS), road cables reinforced with fiberglass or metal rods in the cable sheath (AERO–DDF, Burry, VC–Tx), easy access cables (EAC), duct cables (BDC), micro cables (MK–LX), central tube cables (EXO), and steel tape armored cables (SST).

2.1. Factory RLM Line Data Acquisition

As part of the conducted work, the line was equipped with devices that allow for monitoring and recording the tension of individual modules or tight tubes, as well as the temperature of the process water located directly in the cooling baths. Based on the recommendations of tube manufacturing technology experts, 232 measurement points were designated, where the production process was recorded at a frequency of $1\left[s\right]$. This set included both the established process recipe parameters and process variables. The complete data set contained 180 randomly recorded production sessions lasting from 30 min to 150 min, corresponding to different working hours of the line and the teams of operators handling it. An example fragment of measurement data from a single session is presented in

Table 2. Sample of process data recorded for RLM line.

Time Stamps 29 November 2023	BAZ1 _iTens	BAZ2 _iLoad	BAZ2 _iMetLo	BAZ2 _iSpeed	EXT1 _iLoad	EXT1 _iSpeed	⋯	SPE2 _iLoad	SPE2 _iSpeed
22:17:14	0.274658	6.427	11	53.9844	33.5266	30.957	⋯	15.4602	55.0488
22:17:15	0.219727	6.38428	21	53.9844	33.783	30.957	⋯	17.218	55.0879
22:17:16	0.183106	6.49414	30	53.9941	33.5205	30.9961	⋯	16.5955	54.7461
22:17:17	0.146484	6.46973	39	54.043	33.5571	30.957	⋯	15.5945	54.6094
22:17:18	0.164795	6.51245	48	53.9941	33.7036	30.9473	⋯	16.9556	54.4238
22:17:19	0.201416	6.5918	59	54.0234	33.7341	30.957	⋯	16.1804	54.209
22:17:20	0.201416	6.5918	68	54.0234	33.5022	30.9668	⋯	16.6687	54.209
22:17:21	0.274658	6.37817	77	53.9551	33.5449	30.9668	⋯	17.4622	54.1406
22:17:22	0.274658	6.50024	86	53.9844	33.8196	30.918	⋯	16.2292	54.3359
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
22:25:29	0.128174	6.79321	4644	54.9609	34.4177	31.6602	⋯	3.62549	−0.2929
22:25:30	0.366211	6.86035	4654	54.9707	34.1492	31.6113	⋯	3.62549	−0.2929
22:25:31	0.1	7.00073	4663	54.9902	34.2896	31.6113	⋯	3.62549	−0.2929
22:25:32	0.1	6.98242	4673	54.9707	34.1919	31.6016	⋯	3.62549	−0.2929
22:25:33	0.146484	7.04346	4682	54.9707	34.3018	31.5723	⋯	3.62549	−0.2929
22:25:34	0.146484	6.92749	4691	54.9805	34.0881	31.6211	⋯	3.62549	−0.2929
22:25:35	0.146484	6.88477	4701	55.0293	34.3445	31.6309	⋯	3.62549	−0.2929
22:25:36	0.128174	6.88477	4711	54.9805	34.0271	31.6504	⋯	3.62549	−0.2929
22:25:37	0.1	6.89697	4721	55.0098	34.1125	31.5723	⋯	3.62549	−0.2929
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
22:53:52	0.347901	7.88574	23544	79.9707	38.7207	46.8945	⋯	3.62549	−0.2929
22:53:53	0.347901	7.72095	23558	80.0195	38.4277	46.8945	⋯	3.62549	−0.2929
22:53:54	0.347901	7.72095	23571	80.0195	38.4277	46.9531	⋯	3.62549	−0.2929
22:53:55	0.219727	7.73315	23585	80.0586	38.269	46.9336	⋯	3.62549	−0.2929
22:53:56	0.219727	7.69043	23599	79.9805	38.855	46.9922	⋯	3.62549	−0.2929
22:53:57	0.366211	7.67212	23612	79.9902	38.3606	46.9629	⋯	3.62549	−0.2929
22:54:03	0.146484	7.59277	23696	80	38.8367	47.002	⋯	3.62549	−0.2929
22:54:04	0.347901	7.45239	23710	80.0391	38.6475	46.9336	⋯	3.62549	−0.2929
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
23:16:44	0.109863	6.75659	40728	53.9746	33.252	31.3477	⋯	3.62549	−0.2929
23:16:45	0.238037	6.71997	40737	53.9941	33.4595	31.3086	⋯	3.62549	−0.2929
23:16:46	0.384522	6.79932	40746	54.0137	33.3801	31.2598	⋯	3.62549	−0.2929
23:16:47	0.1	6.93359	40755	54.0039	33.5266	31.2598	⋯	3.62549	−0.2929
23:16:48	0.1	6.92749	40766	53.9941	33.1848	31.2012	⋯	−0.00610	−0.1464

. This includes a small range of approximately a one–hour measurement session in which 20 km of optical cable was produced.

During the conducted work related to recording measurement data, the team observed random gaps in the process data. These gaps were caused either by improper operator handling of the production line or by malfunctions in individual sensors. Naturally, there are fundamentally different strategies to counteract such issues, ranging from simple methods of discarding damaged data sequences to advanced strategies for repairing them using sophisticated statistical methods, machine learning, or interpolation and extrapolation techniques. Each approach has a specific level of accuracy and computational complexity, which can be crucial when selecting the appropriate method for various industrial applications.

For the experiments involving the RLM line, the method of extrapolating missing data (“gaps”) was adopted, when the size of the gaps did not exceeded 10 s. In cases where the negative effect was more pronounced, the affected data packets were discarded. Considering the strict technological conditions, the occurrence of missing data or abrupt changes in the recorded values was extremely rare.

These data were subsequently analyzed using a sliding window with sizes of [64, 128, 256, 512, 1024]. Considering the dynamics of the manufacturing process, it was determined that the most optimal window size, from a technological standpoint and accounting for the possible reaction time of the line operator in the hypothetical event of an anomaly presence, would be approximately 4 min, corresponding to a 256-element window. Other time intervals might also highlight interesting properties of the process; however, for the purposes of this study and its limited scope, they were excluded from further consideration.

2.2. Preprocessing of Input Data for Training Set

A fundamental problem faced by research teams working on anomaly detection is the inability to precisely construct a training sequence, due to the fact that the vast majority of defects caused by anomalies are detected only after the completion of the production process during the final product quality checks. Usually, determining the precise temporal coincidence of a specific moment in the production process is either impossible or associated with a large spatial localization error. To address this, an initial assessment of the input data was performed by analyzing the significance of features in the recorded process state vector using the Discrete Wavelet Transform (DWT) with a Haar wavelet basis function, applying a 4–octave wavelet decomposition level. This resulted in sets of 32 features for successive windows, which illustrate different process states. For the purposes of further discussion, the following mathematical notation have been assumed. Let $x_i\left(t\right)$ represent the discrete input signal registered from the i-th sensor channel of the RLM production line, where: $i=1,2,\dots ,S_N$, $t=0,1,2,\dots ,W_s$, $S_N=232$—denotes the number of mounted sensors in RLM line, $W_s=256$—denotes the window size, (i.e., 256 time stamps in the moving window of length 256). The matrix representation of the complete signal data from all sensors of consecutive channels within the moving window can be represented as a matrix:

$$X\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ \dots \\ x_{S_N}\left(t\right)\end{array}\right]$$

(1)

where $X\left(t\right)\in R^{S_N\times W_S}$. The moving window mechanism we assume respectively: $t_w$ denote the moving window size (here $t_w=W_S$). For every sensors channels i, the windowed segment can be expressed to as: $x_i\left(t\right)=\left\{x_i\left(k\right)\mid k=t,t+1,\dots ,t+t_w-1\right\}$. The initial research assumptions were that a pyramidal wavelet decomposition would be performed on the process coordinates so recorded, which, due to the absence of constraints on the periodicity and continuity of the signal characteristic of Fourier frequency decomposition, allows the extraction of selected components of the transformed signal into complementary components. For this purpose, we used the algorithm proposed by [41] which uses signal decomposition $x_i\left(t\right)$ into approximations and details at various levels j: $j:DWT\left\{x_i\left(t\right)\right\}={\left\{A_j,D_j\right\}}_{j=1}^J$, where $A_j$ is the approximation coefficients at level j, $D_j$ is the detail coefficients at level j and J is the maximum decomposition level, depending on the length of $x_i\left(t\right)$. Taking into account the technological requirements determined by the size of the analyzed window, it was assumed for the purposes of the preliminary analysis that the $J\in \left\{2,3,4,5,6\right\}$. The multi-sensor processing with DWT is applied to each feed individually:

$$DWT\left\{X\left(t\right)\right\}=\left[\begin{array}{c}DWT\left\{x_1\left(t\right)\right\}\\ DWT\left\{x_2\left(t\right)\right\}\\ \dots \\ DWT\left\{x_{S_N}\left(t\right)\right\}\end{array}\right]$$

(2)

Presented above mathematical framework ensures clarity in processing, accommodating the 232 sensor channels, 256—sample moving window, and 1—second sampling interval. Below (Figure 2) are sample fragments of the signal recorded from the RLM production line for wavelet decomposition using the Haar mother wavelet with 2 and 4 octave sizes, respectively.

For all waveforms in Figure 2, the designations , and stand for: the waveform of the components $\left\{A_j,D_j\right\}$ of the DWT transform, the waveforms of the leading 40 components of the production process, and the membership of the RLM line signal to the different classes extracted in the clustering process. The left column (Figure 2a,c,e,g,i,k) corresponds to the decomposition of the signal recorded during the measurement session from the RLM production line using a 4–octave Haar–based DWT, while the right column (Figure 2b,d,f,h,j,l) corresponds to the decomposition of the same signal using a 2–octave Haar–based DWT. The waveforms (Figure 2a–d) show example sections of RLM line acceleration, in which the time interval $〈S_B,\dots ,S_E〉$ is marked with a rectangular area. The symbols $S_B$ and $S_E$, denote the start of the fiber twisting process and the end of the twisting process of a given tube section, respectively. Graphs (Figure 2e–h) contain waveforms for the ongoing basic production process also for two different randomly selected sessions. The recorded process data from the RLM line $X\in R^{S_N\times W_S}$, were normalized $\left\{a=0,b=1\right\}$ for each signal channel data independently:

$$x_{i,j,\mathrm{norm}}=a+\left(b-a\right)·{\displaystyle \frac{x_{i,j}-min\left(X_{i,:}\right)}{max\left(X_{i,:}\right)-min\left(X_{i,:}\right)}}$$

(3)

where: $X_i$ is the i-th row of X. The plots (Figure 2i–l) show sample stages of the finalization of the fiber twisting process for a given tube section, marked as $〈C_B,\dots ,C_E〉$, where the symbols $C_B$ and $C_E$ denote the start and end of the production completion process for the given tube section, respectively. All plots marked with the number represent an attempt to visualize the potential membership of the production process state to a priori selected number of classes.

Subsequently, a univariate feature selection algorithm for classification using the Chi–square test was applied. This allowed for the visualization and assessment of the importance of individual leading features in the recorded data stream, represented as a cluster structure corresponding to 32 different process states, as shown in Figure 3. The 

Table 3. Corresponding process coordinates names.

Column Indexes	Name
{[ 4]}	{’BAZ1_iSpeed’}
{[30]}	{’KAP1_iTens17_20’}
{[31]}	{’KAP1_iTens21_24’}
{[32]}	{’KAP1_iTens5_8’}
{[57]}	{’POF1_iDancMode_N’}
{[58]}	{’POF1_iFltCodeTrav’}
{[59]}	{’POF1_iLoad’}
{[60]}	{’POF1_iReelDiam’}
{[61]}	{’POF1_iSpeed’}
{[63]}	{’QSD2_ValDel’}
{[49]}	{’MES_MeterCnt’}
{[56]}	{’POF1_iDancerPos’}
{[50]}	{’MES_MeterCnt2’}
{[52]}	{’MES_OKaltRe’}
{[40]}	{’MES_DWarmY’}

contains the coordinates and names of the individual leading components of the process.

In the course of observing the impact of individual process characteristics on cluster distribution, it was found that it is possible to use an automatic clustering mechanism to construct a training set for Deep Neural Networks (DNN). At the same time, it was noted that the DWT showed high sensitivity to momentary impacts of some parameters, such as the state of the cable length counter when changing the winding drum. Such a phenomenon caused strong interference, which negatively affected the segmentation process of individual process states. In addition, for analytical purposes, the authors attempted to graphically interpret the distribution of individual clusters and the distance between them, using the Hierarchical Clustering with Binary Clustering Tree method. Assuming that the given is a dataset with n observations, where each observation is represented as a d-dimensional vector ${\mathbf{x}}_i=(x_{i1},x_{i2},\dots ,x_{id})$, the steps for agglomerative hierarchical clustering we obtained by iterative merging: by serching for the pair of clusters $(C_i,C_j)$ with the smallest distance $d(C_i,C_j)$. Then merging clusters $C_i$ and $C_j$ into a new cluster $C_{ij}$ and eventually update the distance matrix to reflect the distance between consecutive new cluster $C_{ij}$ and all other. As the linkage criteria we assumed the average distance method to measure the distance between clusters:

$$d(C_i,C_j)={\displaystyle \frac{1}{|C_i\left|\right|C_j|}}\sum _{{\mathbf{x}}_a\in C_i}\sum _{{\mathbf{x}}_b\in C_j}d({\mathbf{x}}_a,{\mathbf{x}}_b)$$

(4)

By the repetition of merging loop we obtained a Binary Clustering Tree of the monitored process clusters. This preliminary preprocessing of RLM line data we performed for all sessions and the resulting dendrogram and 3D view of the most significant components are shown on the Figure 4 respectively.

As we can observe a binary clustering tree is as a kind of dendrogram, where each node represents a cluster, and each leaf node represents an individual observation. The height of the nodes in the tree corresponds to the distance (or dissimilarity) at which consecutive clusters are merged. A spatial visualization of the location of the leading features of the clusters is provided in Figure 4b. As can be seen, there is a classic “energy leakage effect” causing the extracted classes of process states to interpenetrate and individual clusters to differ to a very small degree. Therefore, a multi–resolution K—means Clustering mechanism was adopted in later part of this work to cluster the input data at different resolutions of the space of feature channels $C{h}_j\in \left\{8,16,32\right\}$, for $j=1,2,3$. So, having an RLM line dataset with $n=256$ observations for each stepping window, where each observation is represented as a d-dimensional vector we have:

$${\mathbf{x}}_i^{C{h}_j}=(x_{i1}^{C{h}_j},x_{i2}^{C{h}_j},\dots ,x_{id}^{C{h}_j})$$

(5)

Then we performed K—means clustering in each of the channels to partition the observations into channel independent clusters:

$$K^{C{h}_j}\in \left\{C_1^{C{h}_j},C_2^{C{h}_j},\dots ,C_K^{C{h}_j}\right\}$$

(6)

such that sum of squared distances between observations and their corresponding cluster centroids is minimized. Given ${\mathit{\mu }}_1,{\mathit{\mu }}_2,\dots ,{\mathit{\mu }}_k$, as initial cluster centroids we assign each observation ${\mathbf{x}}_i^{C{h}_j}$ to the cluster:

$$C_k^{C{h}_j}=\left\{{\mathbf{x}}_i^{C{h}_j}\mid arg\underset{k}{min}\parallel {\mathbf{x}}_i^{C{h}_j}-{\mathit{\mu }}_k{\parallel }^2\right\},k=1,\dots ,C{h}_j$$

(7)

where $\parallel {\mathbf{x}}_i^{C{h}_j}-{\mathit{\mu }}_k\parallel$ is the Euclidean distance between observation ${\mathbf{x}}_i^{C{h}_j}$ and centroid ${\mathit{\mu }}_k$. The update of the centroid for each cluster in a given channel $C{h}_j$, is calculated as a mean of the observations assigned to that cluster:

$${\mathit{\mu }}_k={\displaystyle \frac{1}{|C_k^{C{h}_j}|}}\sum _{{\mathbf{x}}_i^{C{h}_j}\in C_k^{C{h}_j}}{\mathbf{x}}_i$$

(8)

where $|C_k^{C{h}_j}|$ is the number of observations in cluster $C_k^{C{h}_j}$. This way of preprocessing the input data was intended to maximize the disparity of the process states in order to facilitate the task of building a training set for the LSTM network. One of the key difficulties that arises in anomaly detection tasks is that technological limitations do not allow precise labeling of training set classes. Therefore, an analysis of individual measurement sessions was carried out in cooperation with RLM line technologists. As a result of it, it was indicated after which sessions the quality procedure checks showed any defects in the final product. In this way, it was possible to estimate the index of potential defect for each measurement session: $p=1$ for normal production, $p=0$ for the interval of the production process in which any defects were detected during the post manufacturing quality control in a given measurement session. A dendrogram and a spatial visualization of the most relevant features were constructed again for such a completed input data set, see Figure 5.

By incorporating this additional indicator for the rough spatial localization of defects, a sufficiently effective mechanism for distinguishing anomalies responsible for defects in the final product was achieved. The described data preprocessing stage was used to construct the training dataset.

2.3. Hybrid LSTM Network Model for Anomaly Detection

To process the data stream recorded during the manufacturing of fiber optic cables, which are subjected to K—means clustering in three channels simultaneously, a dedicated model of a hybrid LSTM network has been proposed. Its task is to analyze the states of the production line in each of the channels, see Figure 6. The integrating module of the network is an aggregating layer along with a set of auxiliary layers, whose task is to detect anomalies based on the recommendations of the three predictors operating in each of the channels.

Considering the three–channel architecture of the LSTM network, the following single cell model was used, see Figure 7.

Assuming that the input data of a single cell at time step t is the input vector $x_t$, the mathematical model for a fixed time step enabling the update of the memory state $c_t$ is as follows:

$$f_t^{Ch}=\sigma \left(u_f{h}_{t-1}+w_f{x}_t+b_f\right)$$

(9)

$$i_t^{Ch}=\sigma \left(u_i{h}_{t-1}+w_i{x}_t+b_i\right)$$

(10)

$${\tilde{c}}_t^{Ch}=tanh\left(u_c{h}_{t-1}+w_c{x}_t+b_c\right)$$

(11)

$$o_t^{Ch}=\sigma \left(u_o{h}_{t-1}+w_o{x}_t+b_o\right)$$

(12)

$$h_t^{Ch}=tanh\left(o_t\odot c_t\right)$$

(13)

$$c_t^{Ch}=f_t\odot c_{t-1}+i_t\odot \widetilde{c_t}$$

(14)

and the generalized matrix is written in the form:

$$W^{Ch}={\left[w_f,w_i,w_c,w_o\right]}^T$$

(15)

where: $\sigma$—is the sigmoid activation function, $h_{t-1}$—previous hidden state and $tanh$ is the hyperbolic tangent activation function and $W^{Ch}$ denotes the given channel weights set. Figure 8 represents the structure of a single LSTM layer operating in each of the channels.

Assuming the clustering mechanism described by Equation (7), we obtain the relationship for the expected values of the signature at time t of the industrial process on the RLM line:

$$y^{C{h}_j}\left(t\right)=C_{C{h}_j}^k\left(X\left(t\right)\right)$$

(16)

As in the supervised training model the goal of the LSTM model is to learn a function $f:R^{S_N\times W_S}\to \left\{1,2,\dots ,C_k^{C{h}_j}\right\}$ such that the output ${\widehat{y}}^{C{h}_j}\left(t\right)$ predicted by the model is as close as possible to the true label $y^{C{h}_j}\left(t\right)$. This we achieved by minimizing the loss function $L\left(W^{Ch}\right)$:

$$L\left(W^{Ch}\right)=-{\displaystyle \frac{1}{N}}\sum _{i=1}^N\sum _{k=1}^{C_k^{C{h}_j}}{y}^{C{h}_j}log\left({\widehat{y}}^{C{h}_j}\left(W^{Ch}\right)\right)$$

(17)

where $W^{Ch}$ represents the weight set collection sought and N denotes the number of samples in the learning set.

Individual channels of $LST{M}^{C{h}_{\left(8,16,32\right)}}$ have the following numerical details, see

Table 4. Hybrid LSTM networks parameters Channels 1–3.

Name	Type	Activations	Learnables
Seq 1	Sequence input	232	–
Seq 1	LSTM	512	Input Weights	2048 × 232
			Recurrent Weights	2048 × 512
			Bias	2048 × 1
Seq 3	Full Connected	8/16/32	Weights	8/16/32 × 512
			Bias	8/16/32 × 32
Seq 4	Softmax	8/16/32	–
Seq 5	Classification Output	8/16/32	–

and 

Table 5. Hybrid LSTM networks parameters Aggregation Pipeline.

Name	Type	Activations	Learnables
Channel 16	Feature input	1	–
Channel 32	Feature input	1	–
Channel 8	Feature input	1	–
Aggregation	Concatenation	3	–
Anomalies-organiser	Full Connected	50	Weights	50 × 3
			Bias	50 × 1
Anomalies-recognizer	Full Connected	5	Weights	5 × 50
			Bias	5 × 1
Softmax	Softmax	5	–
Anommaly	Classification Output	5	–

.

For the chosen LSTM network model, a training set was constructed with parameters summarized in

Table 6. Training data set information.

Name	Data
Production line	RLM
Session measurement dates	Start time	End time
	1 June 2021	1 December 2023
Total measurement time	688,896 [s], ∼191 [h]
Number of measurement points	232
Size of the moving window	256 [s]
Window shift step	5
Number of samples in the learning set	2691
Training set size	70%
Test set size	30%

. They represent the time interval from which individual measurement sessions originate. In total, recorded coordinates of the production process and extracted classes corresponding to individual diagnostic states and the actual production state were used.

3. Results and Discussion

The training process of the hybrid LSTM network was conducted independently in each of the submodules $LST{M}^{C{h}_{\left(8,16,32\right)}}$. Subsequently, for the frozen weight sets $W^{C{h}_{\left(8,16,32\right)}}$, a convergent learning process of the aggregating module was carried out using the Anomalies labeler block (see Figure 6). The course of this process and the achieved degree of model fit for the entire LSTM network are shown in Figure 9. The proportion of the training set split into training and testing sets was set at $70\%$ and $30\%$, respectively. The obtained model fit coefficient $R^2>0.85$ demonstrates the high efficiency of the model on the tested data set.

RLM production line

Root Mean Squared Error: 0.475

F-statistic vs. constant model: 6.62 × 10³, p-value = 0

R =

1.0000 0.9442

0.9442 1.0000

Obtained Pearson correlation coefficients: 0.9442

Obtained R2 determination coefficient: 0.892

Figure 9. Pearson coefficient (a) and Confusion matrix (b).

Figure 9. Pearson coefficient (a) and Confusion matrix (b).

To evaluate the effectiveness of anomaly detection, a detailed experimental study was conducted using identical data sets, with models: Random Forest, SVM, and a simple RNN as benchmarks. The performance of each of these models was evaluated using standard metrics, including Precision, Recall, F-1 Score, and $R^2$, which allow an objective assessment of the quality of anomaly detection and prediction [42]. Detailed results are shown in

Table 7. Summary of results for each forecasting model, taking into account Precision, Recall, F-1 Score and $R^2$ indicators (the higher the values, the better the performance).

Metric	LSTM	Random Forest	SVM	RNN
Precision	>0.94	~0.85	~0.88	~0.87
Recall	>0.96	~0.83	~0.85	~0.86
F–1 Score	>0.91	~0.84	~0.86	~0.86
$R^2$	>0.86	~0.85	~0.85	~0.85

.

The obtained results show that LSTM significantly outperforms other models, particularly in the context of detecting complex temporal and sequential dependencies. The Precision and Recall metrics for LSTM exceed 0.94 and 0.96, respectively, while the F1-score is >0.91, indicating a balance between the model’s accuracy and sensitivity. To thoroughly evaluate the effectiveness of the proposed model, a detailed performance analysis for individual classes was conducted using Precision, Recall, and F1-score metrics. The results, presented in

Table 8. Performance indicator results for each class.

Name	Precision	Recall	F1-Score
Proper	0.9414	0.9695	0.9553
Anomaly 1	0.9180	0.9438	0.9307
Anomaly 2	0.8554	0.7513	0.7997
Anomaly 3	0.9185	0.9185	0.9185
Anomaly 4	0.6647	0.8248	0.7368

, reveal that Proper achieved the highest Precision (0.9414) and Recall (0.9695), indicating an excellent fit of the model to this class. In contrast, the lowest Precision (0.6647) and Recall (0.7513) values were observed for Anomaly 4, highlighting some challenges for the model in detecting anomalies in this class.

The experimental results confirm that the proposed hybrid LSTM model outperforms other approaches in terms of anomaly detection effectiveness in production processes. The application of advanced deep learning methods represents a significant step toward improving anomaly detection quality in data with complex temporal structures, which is critically important in the context of industrial process monitoring.

The resulting network model was implemented in the FIBRAIN industrial plant in a technological supervision system with the task of providing real–time support for RLM line operators during the production process. Figure 10 and Figure 11 show examples of the monitoring view during: normal process operation and the occurrence of an anomaly threatening a defect in the final product, respectively. The bar graph represents the probability values of the current process signature belonging to one of the classes: Proper, Anomaly 1–4. For the operator’s convenience, the values on this graph correspond to the output signals of the penultimate Softmax layer of the aggregating module. The system operator’s task was to control and tune the line’s working parameters so that the process state signature recognized by the LSTM network corresponded to its proper operation. The number of distinguishable anomalies for the RLM line was set at 4, based on heuristic assumptions and consultations with experts supervising the production technology on this line.

During the period from 1 January 2024, to 28 June 2024, the constructed LSTM network model was test–integrated into the production process monitoring system. Based on the observations made, the following coincidences between detected anomalies and corrective actions taken were identified:

• Anomaly 1: Excessive fluctuations in pressure and temperature alter the geometry and texture of the produced item. Significant pressure variations cause diameter changes within the range of 0.2 [mm] to 0.4 [mm], leading to the product being classified as non–compliant. In the cable coating extrusion process, large pressure changes result in discontinuities in the coating material, causing the final product to be divided into short segments, which are often unacceptable to customers.
• Anomaly 2: Excessive deviations in the pressure and temperature of the hydrophobic gel. Pressure changes lead to variations in the external and internal diameters of the semi–finished product. Changes in the external diameter result in weakened strength at the constriction points of the semi–finished product.
• Anomaly 3: Excessive production speed and the associated tension force of the production line and winding device. According to experts, this is a crucial anomaly that causes excess fiber in the tube, negatively affecting the transmission properties and strength of the finished fiber optic cable. Moreover, its frequent occurrence indicates wear and tear of the drive and consumable parts of the line.
• Anomaly 4: Temperature fluctuations in the cooling bath water affect the surface condition of semi–finished and finished products, as well as the dynamics of secondary shrinkage, which negatively impacts semi–finished and finished cables many days after their production.

During the analyzed period of the test implementation, a reduction in the amount of defective product by 66.3% was achieved, which should be considered a significant reduction in unnecessary production costs per unit length of the final product. A notable drawback of the developed approach is the relatively high sensitivity of the monitoring module to sterile measurement conditions that must be maintained when using such a large number of sensors. Its susceptibility to transient spikes or temporary loss of measurement values may pose a significant challenge in adapting the proposed method to similar production processes.

4. Conclusions

Combining statistical methods, machine learning, and sensor-based monitoring provides a robust approach to detecting and addressing anomalies. The proposed approach effectively integrates the multi-resolution K-means clustering method with recursive LSTM network architectures. The analysis conducted in this study on the available data from the monitored RLM production line identified key parameters determining product quality during technological processes: pressure and temperature of the material and gel, and constant production speed, which is crucial for maintaining the correct dimensions of the extruded product. The achieved results indicate the validity of using deep learning with LSTM networks for the analysis and classification of technological data.

This work makes a significant contribution to the field of anomaly detection by applying an innovative hybrid architecture that combines clustering techniques with LSTM networks, enabling the automatic creation of training datasets even in the absence of manually labeled data. The multi-channel temporal data analysis system from production lines provided a new perspective on real-time monitoring of industrial processes, which can also be adapted to other industries. However, certain limitations of the developed model should be noted. The high sensitivity of the system to input data disturbances, particularly when using multiple sensors, necessitates precise measurement conditions. Additionally, the scalability of the model presents a challenge when deploying it across production lines with differing characteristics. Despite these challenges, the proposed method significantly reduces the number of defects and allows for better management of the production process.

The ultimate application of the described system is full integration with production lines in real industrial facilities, enabling further monitoring and optimization of the manufacturing processes for optical fiber tubes. The system facilitates a significant reduction in waste and improvement in the quality of final products, making an essential contribution both economically and environmentally. The application of anomaly detection methods using LSTM in other manufacturing processes, especially within the Industry 4.0 framework, can enhance quality control across a wide range of technologies. Ultimately, the findings of this study demonstrate that further advancements in optical cable production technology and advanced machine learning techniques will continue to improve the precision and efficiency of anomaly detection methods, thus supporting better quality control and the advancement of industrial process automation.