# A new hybrid data and model-centric predictive approach dedicated to industrial pipe maintenance

Ahmad Braydi, Pascal Fossat, Alessandro Casaburo, Victor Pernet, Cyril Zwick, Mohsen Ardabilian, Olivier Bareille

## ► To cite this version:

Ahmad Braydi, Pascal Fossat, Alessandro Casaburo, Victor Pernet, Cyril Zwick, et al.. A new hybrid data and model-centric predictive approach dedicated to industrial pipe maintenance. Engineering Applications of Artificial Intelligence, 2025, 153 (3), pp.110821. 10.1016/j.engappai.2025.110821. hal-05419053

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Submitted on 23 Jan 2026

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Research paper

# A new hybrid data and model-centric predictive approach dedicated to industrial pipe maintenance

Ahmad Braydi<sup>a,b,c</sup>, Pascal Fossat<sup>a</sup>, Alessandro Casaburo<sup>a,c</sup>, Victor Pernet<sup>d</sup>, Cyril Zwick<sup>a,c</sup>, Mohsen Ardabilian<sup>b,d</sup>, Olivier Bareille<sup>a,c,d</sup>

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## ARTICLE INFO

### Keywords:

- Prognostic and Health Monitoring

- Hybrid approach

- Data-centric

- Model-centric

- Predictive maintenance

- Artificial Intelligence

- Machine learning

- Pipe clogging

- Vibroacoustic

- Bubble-induced vibrations

- Passive instrumentations

## ABSTRACT

Predictive Maintenance (PdM) for pipe clogging is a critical challenge in the industrial sector, particularly with the increasing adoption of Artificial Intelligence (AI) and the Internet of Things (IoT). Frequent clogging incidents, such as those faced by Orano/La Hague, lead to energy waste, operational inefficiencies, financial losses, and potential safety hazards, highlighting the critical need for effective maintenance solutions to protect both assets and personnel. This study proposes a novel hybrid approach that combines the strengths of data-centric and model-centric methodologies for Prognostic and Health Monitoring (PHM) of pipeline systems in constrained industrial environments. The approach utilizes passive acceleration measurements to predict clogging occurrences and quantify clogging severity under varying airflow rates. Experimental results indicate that the proposed method achieves up to 100% accuracy in clogging detection and robust performance across diverse operational conditions. This integrated methodology represents a significant step forward in predictive maintenance, offering scalable and adaptable solutions to enhance safety, operational efficiency, and cost-effectiveness in industrial settings.

## 1. Introduction

Industrial facilities are transitioning profoundly to meet the recent technological advancements associated with AI and the IoT, enabling companies to enhance productivity and improve quality.

Orano/LA HAGUE is one of these plants that seek to make the most of the latest technology. In 2019, 3449 pipe cloggings were reported in the Orano/LA HAGUE site. At the rate of 2 people per team for a duration of intervention of 30 min, the site maintenance department carried out the pipe-blowing operations (pipe unclogging). This resulted in 3449 h of non-productive human time, leading to a waste of energy and financial resources, as well as a potential decrease of the fluid flow in the pipe systems due to partial clogging.

Therefore, in order to optimize the plant's effectiveness and reduce the waste of its resources, it is critical to detect and characterize pipeline clogging quickly and reliably so that it can be dealt with as early as possible. In this context, the non-destructive, non-curative solutions and predictive, preventive maintenance capabilities are the main objectives of the future solution.

Several traditional methods are available for detecting clogs in pipelines, including thermographic analysis (Joung and Kim, 2006), magnetic induction (Layouni et al., 2017), flow pressure monitoring (Gong et al., 2018), and radiographic techniques (Boaretto and Centeno, 2017). Thermographic analysis involves capturing thermal images during controlled heating and cooling cycles to identify structural irregularities through temperature variations (Donets et al., 2024; Manekiya and Arulmozhivarman, 2016). Convolutional neural networks are often employed to analyze these thermal images (Nasiri et al., 2019). Despite its effectiveness, this method has several limitations: it is sensitive to surface cleanliness, struggles with detecting minor or deep defects, requires significant temperature gradients, and relies heavily on reference data. Additionally, it is expensive and not universally applicable.

Magnetic induction uses coils to generate and detect magnetic fields, allowing for robust monitoring of underground pipelines by overcoming soil interference (Sun et al., 2011). However, this method faces challenges such as complex magnetic backgrounds (Song et al., 2017;

<footnote><sup>a</sup> Laboratory of Tribology and System Dynamics (LTDS), Ecole Centrale Lyon, 69130, Ecully, France</footnote>

<footnote><sup>b</sup> Computer Science Laboratory for Image Processing and Information Systems (LIRIS), Ecole Centrale Lyon, 69130, Ecully, France</footnote>

<footnote><sup>c</sup> Laboratoire de Mécanique de Normandie (LMN), INSA Rouen Normandie, 76800, Rouen, France</footnote>

<footnote><sup>d</sup> Heverett Group, 69006, Lyon, France</footnote>

<footnote>* Correspondence to: École Centrale de Lyon, 36 Avenue Guy de Collongue, 69130 Écully, France.
*E-mail addresses:* ahmad.braydi@ec-lyon.fr (A. Braydi), pascal.fossat@ec-lyon.fr (P. Fossat), alessandro.casaburo@ec-lyon.fr (A. Casaburo), v.pernet@axeal.com (V. Pernet), cyril.zwick@ec-lyon.fr (C. Zwick), mohsen.ardabilian@ec-lyon.fr (M. Ardabilian), olivier.bareille@insa-rouen.fr (O. Bareille).</footnote>
Li et al., 2017), high path loss, and material dependency (Sun et al., 2011).

Flow pressure monitoring detects pipe defects by measuring deviations in pressure and flow using sensors and hydraulic models (Gong et al., 2018; Wang et al., 2001). Significant deviations can indicate potential clogs. However, this method is less effective for detecting small leaks due to noise and requires frequent calibration and maintenance, making it costly to install and maintain (Ayadi et al., 2017).

Radiographic techniques, which use gamma rays or X-rays to create images, reveal variations in absorption that indicate clogs (Shafeek et al., 2004a). This method requires radiographic films and processing to visualize the internal conditions of pipes (Shafeek et al., 2004a,b).

In this context, vibroacoustic techniques offer an alternative solution. Vibroacoustic measurements provide a noninvasive and remotely operated approach to detecting pipeline blockages (Jiao et al., 2011; Gaponenko et al., 2016). However, their effectiveness diminishes with increasing pipe diameter and distance from the leak, making them less suitable for large-diameter or long-distance pipeline networks (Xiao et al., 2021; Butterfield et al., 2017).

Vibroacoustic techniques enable the precise measurement of vibrations and acoustic emissions from distinct points along the pipeline, even in aggressive environments (Monteiro et al., 2021; Che et al., 2019). These techniques utilize both active and passive sensors. Passive sensors detect emissions generated by the process itself, while active sensors employ an emitter-receiver system to measure changes in introduced acoustic waves, commonly known as slot waves, over the distance between the emitter and receiver. Moreover, these techniques provide valuable insights where the environment may pose challenges for other detection methods, making them a valuable asset in pipeline maintenance and monitoring.

These advancements in vibroacoustic technology have led to an increased emphasis on digitization, including the widespread deployment of sensors. As a result, a massive volume of energy data is generated every day, making Machine Learning (ML) a promising approach for implementing PdM in pipe systems. Numerous studies have been conducted that highlight the effectiveness of ML in PdM of pipe systems, and many publications have focused on this topic (Mustapha et al., 2017; Sen et al., 2019).

Machine learning techniques have proven successful in the detection and classification of both damage and clogging in pipe systems. In the context of damage detection in pipe systems, a wide range of approaches have demonstrated considerable success. For example, in Sen et al. (2019), guided ultrasonic waves were generated and detected using a piezoelectric transducer in active mode to detect the presence of damage on the pipe and locate it. Two approaches were proposed: a semi-supervised learning-based approach that uses the hierarchical clustering-based algorithm to detect the damage, and a supervised learning-based approach that performs the damage localization. In their study, they proved that the angle between the actuator and sensor strongly affects damage detection and localization. Another study (Zajam et al., 2019) investigated the use of the support vector machine (SVM) and wavelet analysis on vibration response to identify defects within the pipeline. The study simulated the pigging process using ANSYS to generate measurements, which underwent wavelet analysis to extract spectral components of frequency. Subsequently, the SVM was employed to detect and locate pipeline defects. In Ahn et al. (2019), a machine-learning approach was developed to improve the classification of faults in pipe systems using support vector machines. To process the raw input data, various steps were employed to transform it into a format suitable for the machine learning models. In the signal preprocessing step, two methods were explored: envelope analysis and intensified envelope analysis. In addition, genetic algorithm and principle component analysis were evaluated for feature selection and reduction. The study found that the combination of genetic algorithm and intensified envelope analysis performed better than principle component analysis and simple envelope analysis in improving the model's performance.

ML techniques have also been successfully employed to detect and recognize blockages in pipe systems, playing a crucial role in PdM. For instance, a PdM method proposed in a study (Baronti et al., 2022) leveraged passive acoustic emissions produced by pipe systems to detect obstructions. The acoustic emission patterns were pre-processed using Fourier analysis, and two data sets were created: the first containing the average and variance of the Fourier transform amplitudes, and the second containing data binning of 100 non-overlapping frequency intervals. The study found that the latter approach, which employed data binning, was the most effective for detecting pipeline clogging. Another study (Zhu et al., 2022) presented a method for identifying multiple blockages in pipe systems using the acoustic signature model and convolutional neural network (CNN). The acoustic signature model was utilized to extract distinct acoustic signatures or sound patterns from the raw measurements. These sound patterns are then used to train and test a deep CNN, specifically SqueezeNet. The study concluded that the proposed method is effective for recognizing multiple blockages. Furthermore, a study (Panda et al., 2018) focused on SVM for detecting blockages in centrifugal pumps via vibration signals while considering different blockage thicknesses. Two models, namely binary and multinomial classifiers, were developed and evaluated. Results demonstrated that the binary classifier outperformed the multinomial classifier in terms of prediction accuracy for all blockage conditions.

The field of machine learning is a rapidly evolving one, with ongoing discussions around the most effective methods for improving the performance of machine learning models (Zhan et al., 2022; Ramponi and Plank, 2020). Three main approaches have emerged: model-centric, data-centric, and hybrid approaches. In the model-centric approach, the focus is on upgrading the model itself to optimize its performance, while keeping the quality and quantity of the data used to train the model fixed. In contrast, the data-centric approach centers on improving the quality of the training data used to train the model.

The hybrid approach, on the other hand, combines both the model-centric and data-centric approaches. It recognizes that both the quality of the data and the performance of the model are equally important factors in achieving optimal machine learning performance.

Over the last thirty years, model-centric artificial has been the dominant approach used in both research and industry. In research, for instance, over 90% of published research projects have employed a model-centric approach (Hamid, 2023). However, there has been a recent shift in focus towards the data-centric approach (Zajam et al., 2019; Anik and Bunt, 2021). The importance of high-quality training data has become increasingly apparent, and developers are recognizing that model-centric approaches are limited by the quality and quantity of the training data. Despite this, the hybrid approach that combines both model-centric and data-centric methods is relatively underutilized.

In contrast to existing methods, this paper introduces a hybrid model that combines the data-centric and model-centric approaches for PHM of industrial pipeline systems. In this context, the data-centric approach is used to preprocess the data and extract useful features, and then the model-centric approach is used to optimize the model architecture, parameters, and hyperparameters to achieve the best possible performance. Moreover, most existing studies focus on prognosis using numerous sensors and when the experiment is well-isolated from the environment, this study puts forward a robust approach that can operate on a low signal-to-noise ratio.

Key contributions of this study include:

* Introduction of a hybrid approach that combines data-centric and model-centric methodologies to enhance PHM performance.

* Development of a robust feature extraction framework using a sliding window approach to enhance the predictive capabilities of machine learning models.

* Validation through experimental data, demonstrating up to 100% accuracy in clogging detection under various airflow conditions and different blockage severities.
* Scalability and adaptability of the approach, making it suitable for diverse industrial environments beyond pipeline systems.

For ease of comprehension, the paper is structured as follows: Section 2 outlines the PHM and hybrid approaches. Section 3 describes the test bench, analyzes the available data, and defines the problem. In Section 4, we detail the development of the hybrid approach. Finally, Section 5 provides the research conclusions.

## 2. Hybrid model and prognostic approaches

This section presents the hybrid model approach for PHM of pipe systems, which combines both data-centric and model-centric methods. The methodology entails involving the data-centric approach for data preprocessing and feature extraction, followed by the model-centric approach to optimize the model parameters and hyperparameters.

### 2.1. Hybrid model approach

In the field of machine learning, a hybrid model represents a powerful approach that combines data-centric and model-centric methods to achieve superior results (Ramponi and Plank, 2020).

In this approach, the data-centric component plays a vital role in preprocessing the data and extracting valuable features (Miranda, 2021). It involves tasks such as gathering and refining data from diverse sources, ensuring its quality through cleaning and transformation, engineering relevant features, selecting the most informative ones, reducing dimensionality when needed, and augmenting the dataset to make it suitable for analysis.

The model-centric aspect of the hybrid approach focuses on selecting the appropriate machine learning algorithm and optimizing the model's parameters and hyperparameters to attain optimal performance. Techniques like cross-validation, grid search, and hyperparameter optimization are employed to identify the best combination of settings for the model (Garan et al., 2022).

By combining the strengths of the data-centric and model-centric approaches, the hybrid model excels in creating a robust and accurate machine-learning model capable of handling complex and diverse datasets. Leveraging the advantages of both paradigms, this hybrid model surpasses the results obtained by using either approach in isolation.

### 2.2. Prognostics and health monitoring approach

PHM is a field of study that involves the development of algorithms and models to monitor the state and performance of a target machine or system over time. Prognostics is used in PdM to estimate the remaining useful lifetime of a system or component (Baptista et al., 2024). The goal of PHM is to detect potential faults or failures in the system as early as possible and provide actionable insights for maintenance and repair (Tsui et al., 2015).

In machine learning, PHM typically relies on data from sensors and other sources to monitor system behavior and identify patterns or anomalies (Rezaeianjouybari and Shang, 2020). The key advantage of PHM is that it allows for proactive maintenance, which can prevent costly downtime and repairs, and avoid replacement. By monitoring a system's state in real-time and predicting potential failures before they occur, maintenance teams can perform preventive maintenance and repairs before a breakdown occurs.

In the context of pipe system clogging, PHM focuses on developing algorithms and models specifically tailored for monitoring the state and performance of pipe systems over time. The objective is to detect early signs of pipe clogging, enabling prompt actions for maintenance and repair. Extensive research has demonstrated the efficacy of machine learning models in PHM techniques for effectively monitoring pipe systems and identifying patterns or anomalies indicative of potential

<figure><img src="image_3.png" /><figcaption>Fig. 1. 2D schematic drawing for the test bench with attached sensor locations.</figcaption></figure>

clogging incidents (Zhu et al., 2022; Panda et al., 2018). By leveraging machine learning algorithms and utilizing data from sensors and other sources, PHM enables real-time monitoring and predictive analysis, empowering maintenance teams to proactively address clogging issues before they lead to severe disruptions or costly repairs.

Overall, PHM is gaining new momentum thanks to AI-oriented solutions that enhance the reliability and performance of pipe systems, reduce downtime and maintenance costs, and ultimately improve the bottom line.

## 3. Case study application and problem formulation

In this section, a case study application is introduced, which involves a test bench comprising four pipes. The available data is thoroughly described and analyzed, and the problem is also formally presented.

### 3.1. Experiment description

The Orano/LA Hague factory utilizes specified monitoring equipment to estimate the liquid level and density in a particular tank. This equipment is designed to provide precise and real-time monitoring of the target liquid, while also prioritizing safety, which is of utmost importance to the plant.

Fig. 1 depicts a 2D schematic drawing for the monitoring equipment. This test bench comprises four metallic pipes that are partially submerged in a liquid at varying levels. The liquid level and density are determined by measuring the pressure of the air flowing within the pipes.

To ensure stability, the metallic pipes are mounted through a 100 mm-thick block of concrete and are supported by two metallic stiffeners. Finally, they are welded onto the upper cover of the tank. The inner and outer diameters of the pipes are 15 mm and 20 mm, respectively.

Due to the tiny diameter of the pipes and the impurities in the liquid, there is a risk of partial or complete blockage at the bottom ends of the pipes. This can lead to inaccurate measurements of the target parameters, which can be detrimental to the plant's operations. Therefore, it is crucial to monitor the pipes regularly and take appropriate action to prevent blockage and ensure accurate readings.
Oblique blockage

<figure><img src="image_4.png" /><figcaption>Fig. 2. 3D schematic drawing for blockage.</figcaption></figure>

<table><caption>**Table 1**
The settings selected for the experiment.</caption><thead><tr><th>Liquid</th><th>Air flow rate</th><th>Liquid level in the tank</th><th>Number of pipes in operation</th><th>Shape of blockaque</th><th>Blockage thickness</th></tr></thead><tbody><tr><td rowspan="3">Water</td><td>3 l/h</td><td rowspan="3">350 mm</td><td rowspan="3">1</td><td rowspan="3">Oblique</td><td>0%</td></tr><tr><td>6 l/h</td><td>50%</td></tr><tr><td>10 l/h</td><td>75%</td></tr></tbody></table>

The air flowing out of the submerged ends of the pipes creates bubbles, which generate an acoustic sound and make the pipes vibrate. However, if there is a blockage inside the pipe, it can affect both the pipe vibrations and the acoustic pressure.

The Orano/LA HAGUE plant recognized the importance of condition-based maintenance and set its sights on the benefits of PHM. By implementing PHM, the plant can proactively monitor the pipes and detect any blockages or other issues before they cause significant damage or downtime. This approach can help to optimize maintenance schedules and minimize costs while ensuring the safety and reliability of the plant's operations.

For that purpose, one of the pipes was equipped with sensors as shown in red in Fig. 1, that provide a great amount of data about its state through different parameters such as acceleration, acoustic pressure, static pressure, temperature, etc. The acceleration was recorded at three locations: one three-axis accelerometer directly above the tank's cover that provides the acceleration in cylindrical coordinates (noted by: Acc_LR, Acc_LTh, and Acc_LZ), and two one-axis accelerometers above the concrete that provides the acceleration in the radial direction (noted by: Acc_C and Acc_H). Whereas, the acoustic pressure and the static pressure were recorded at one location above the concrete.

It should be noted that Acc_H is the one chosen for PHM, and as a result, all the analyses presented in this study are centered around the use of Acc_H.

Numerous experiments were carried out under various configurations, including different airflow rates, blockage shapes and thicknesses, liquid types and levels in the tank, and the number of pipes in operation. Throughout the experiments, sensor measurements were gathered.

Fig. 2 depicts a 3D schematic of the polymer blockage that was considered, a cylinder with one elliptical end. The blockage was placed at the immersed end of the equipped pipe, with the elliptical end oriented upwards. The blockage diameter is equal to the inner diameter of the pipe (15 mm) and was installed in the equipped pipe at varying rates to regulate the rate of pipe clogging. The other setup options for the experiment are summarized in Table 1.

<figure><img src="image_5.png" /><figcaption>Fig. 3. Measurements from an intact pipe.</figcaption></figure>

## 3.2. Data description

Analysis was performed on a real dataset. One of the pipes was equipped with several sensors that collect measurements about the state of the pipe, as indicated in red in Fig. 1.

The data has been collected at a uniform sampling frequency of 10 240 Hz using one supervised control and data acquisition (SCADA) system (NI 9234). This system is extremely precise. In each time period, the uniform sampling frequency error for 10 240 Hz is less than 12.5 ns, and the synchronization error between measured variables is less than 1 ns. Furthermore, the synchronization error caused by differing cable lengths connecting sensors to (SCADA) systems is too small. In general, the total error is negligible.

The data collection process involved gathering subsets using the SCADA system at different times of the day for each combination of experiment setup parameters listed in Table 1. Specifically, at 9 o'clock, 14 o'clock, and 19 o'clock, 3 (or 6) subsets were collected, resulting in a total of 9 (or 18) subsets for each experimental configuration. The choice of sampling times was motivated by the desire to investigate the impact of temperature, which varies at different times of the day. Each subset was collected over a 20-s interval at a sampling frequency of 10 240 Hz, producing a total of 204 800 samples per subset. Considering the 9 distinct parameter combinations in Table 1, the minimum number of subsets collected was 81 (i.e., 9 × 9). An example of the signals is presented in Fig. 3.

The airflow inside the pipe induces the formation of bubbles at the submerged end, resulting in sound generation and pipe vibration. The subfigure labeled "microphone (V)" on the y-axis represents the recorded acoustic waves over a 20-s timeframe. The periodicity in the waveform corresponds to the formation of individual bubbles, with each bubble producing a unique acoustic signature. The number of peaks in the waveform indicates the count of bubbles generated during the observed timeframe.
All the generated bubbles exhibit remarkably similar acoustic
sounds, as depicted in the subfigure. However, upon synchronizing the
acoustic measurements with other signals, namely *Acc_LR*, *Acc_LT*,
*Acc_LZ*, and comparing the vibrations attributed to the bubbles in
these signals, it becomes evident that the vibrations are not exactly
identical. These variations can be attributed to the presence of noise
affecting the measurements.

Additionally, when examining the *Acc_H* signal, variations can be
observed over time, as depicted by the two ellipses. This implies that
the signal exhibits fluctuations over time, suggesting the influence of
varying factors or noise sources impacting the measured acceleration.

3.3. Data analysis

Data analysis involves the process of examining and interpreting
data to identify valuable information and gain insights that can be
used to improve operations. In machine learning, the quality of the
data used to train models has a significant impact on the accuracy
and robustness of the resulting models. Therefore, data analysis is
essential in identifying and resolving issues such as missing values and
outliers, as well as selecting relevant features for a given task, which
can enhance the performance of the models. By leveraging data analysis
techniques, machine learning models can be trained on high-quality
data, leading to more accurate and effective predictions.

3.3.1. Null values

In Pandas, a powerful data manipulation library in Python, missing or undefined data is represented as a null value, denoted by “NaN” (not a number). These NaN values must be treated before the model can be built since the machine learning algorithms do not deal with this data automatically.

There are different methods to deal with missing values including
dropping the whole sample, replacing them with the mean or median,
using interpolation, or using machine learning algorithms to predict the
missing values based on the other variables in the dataset.

3.3.2. Outliers

Outliers are data points that are significantly different from the
other values in a dataset. A commonly used definition of outliers is
values that lie more than three standard deviations away from the
mean (Outliers, 2024). According to the definition, the percentage of
outliers in particular datasets is around 1.1012%. The percentage of
outliers can vary depending on the specific dataset and its distribution.

There are different methods to handle outliers: clipping, keeping, or deleting. In signal processing, clipping is the process of limiting the values into the predefined range [lower limit, upper limit] by replacing the values beyond the bounds with the corresponding limit values (Clipping, 2024).

When a dataset contains a large number of outliers with anomalous
values, the definition of outliers based on three standard deviations
from the mean may not be effective. This is because the presence of
many outliers can significantly increase the standard deviation of the
signal, making it difficult to distinguish between true outliers and noise.
The highest outliers can still be identified using the definition and the
lowest outliers may be considered as a component of the signal.

3.3.3. Obvious surround effect

In the context of an industrial facility, the vibration of a pipe is influenced by its supports, as well as other structures and facilities. However, these external factors may experience unexpected vibration and noise during operation, leading to an impact on the pipe system and potentially causing the SCADA system to report inaccurate information regarding the pipe's status.

Pipe systems can be affected by various types of sources that in-
troduce vibrations into the system. These sources can be broadly cat-
egorized into three types: mechanical, fluid, and natural sources. The

vibrations can be divided into two forms: regular and random. Regular
vibrations are usually caused by mechanical and fluid sources, while
random vibrations are introduced by the natural environment.

In some cases, certain subsets of the data exhibit odd signals that
can be separated from those caused by normal pipe system activities.
To avoid poor training and testing of machine learning algorithms,
these subsets must be treated before building the model. Fig. 4 depicts
some of the anomalous vibrations that were observed. They have an
amplitude comparable to the signal amplitude and occur for a time
period shorter than the observed time. These anomalies correspond to
human interaction with the machine more than the influence of the
machine itself, making them easily detectable.

3.4. Problem formulation

It is worth noting that this dataset is interesting for machine learn-
ing and evaluating data-driven approaches, and it is suitable for PHM
since it provides different blockage characteristics that may be iden-
tified. In addition, it ensures safety and avoids endangering people
and properties. The ultimate aim is to design a precise PHM approach
capable of predicting blockage incidents within the designated system.

Therefore, the PHM problem for the specified system can be formal-
ized as follows: for a new datapoint *d*<sub>*l*</sub> which was measured from the
pipe *p*<sub>*l*</sub>, predict if the pipe *p*<sub>*l*</sub> is clogged or not, if yes, then predict the
blockage severity.

4. Development of a hybrid model for prognostics: methodology and implementation

The machine-learning process typically starts with defining a prob-
lem and gathering data that helps to address it. Once the data is
collected, it must be preprocessed and cleaned to ensure that it is
suitable for machine learning algorithms. Then, the data is divided into
training and testing sets, and a model is selected and trained using the
training data.

<figure><img src="image_6.png" /><figcaption>Fig. 4. Abnormal variations in some *Acc_H* signals.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 5. A graphical representation highlighting the stages of a model-centric machine learning pipeline.</figcaption></figure>

## 4.1. Model-centric approach

The conventional approach to machine learning typically focuses on a model-centric perspective, where the primary objective is to optimize the performance of the machine learning model itself. This involves selecting an appropriate algorithm, fine-tuning its hyperparameters, and designing its architecture to achieve the best possible results on the test dataset. The stages of this process, as depicted in Fig. 5, are structured in a sequential manner, starting with data collection and progressing through data preprocessing, feature selection, and data splitting, before culminating in model training and deployment.

In the model-centric approach illustrated in the figure, the process begins with the collection of raw data, which undergoes minimal preprocessing to make it suitable for the chosen machine learning algorithm. Feature selection is then carried out to identify and retain the most relevant attributes from the dataset, while data splitting divides the dataset into training and testing subsets. The subsequent step of model training involves iterative refinement of the model parameters and hyperparameters to optimize its performance on the test dataset. Once this optimization is achieved, the trained model is deployed to make predictions on new, unseen data.

The figure highlights the emphasis placed on the model training stage, which is treated as an independent and pivotal component of the pipeline. However, the fixed nature of the earlier stages, such as data preprocessing and feature selection, often results in their limited influence on the overall outcome. While this approach is effective for many applications, it assumes that the data provided to the model is of sufficient quality, which may not always be the case.

One of the critical drawbacks of the model-centric approach, as reflected in the figure, is its limited focus on the quality of the input data. This can lead to suboptimal results, particularly in scenarios involving noisy, incomplete, or inconsistent datasets. Addressing these challenges often requires additional efforts in data refinement and preprocessing, which are not fully integrated into the conventional model-centric pipeline.

## 4.2. Data-centric approach

In recent years, the focus has progressively shifted towards a data-centric approach, emphasizing the importance of high-quality data for effective model training (Miranda, 2021). Unlike the model-centric approach, which prioritizes the optimization of machine learning models, the data-centric approach aims to enhance the quality and representativeness of the input data to improve overall system performance.

Fig. 6 presents a graphical representation of a data-centric machine learning pipeline. This figure illustrates the iterative nature of the data-centric approach, where the primary efforts are directed at refining the data through processes like preprocessing, feature engineering, and feature selection. The pipeline begins with the collection of raw data, which undergoes rigorous data processing to ensure it is clean, accurate, and free from noise or anomalies. Techniques such as noise reduction, and outlier detection are applied to prepare the data for analysis. The emphasis on data quality ensures that even relatively simple models can achieve high performance and generalize well to unseen datasets.

The subsequent step, feature engineering, involves extracting meaningful attributes from the processed data to capture the essential characteristics relevant to the problem domain. Various transformations, such as scaling, dimensionality reduction, or the creation of composite features, are applied to enhance the data's informativeness. Feature selection then narrows down the attributes to those most relevant to the task, improving model interpretability and efficiency.

Unlike the model-centric approach, the data-centric pipeline maintains a fixed model architecture throughout the process. The model is trained only once, allowing the iterative improvement of the data itself to drive performance gains. This approach is particularly advantageous in domains where data availability and quality are critical constraints, as it focuses on optimizing the input to achieve better outcomes without necessitating complex or resource-intensive models. The figure underscores the central role of the data in determining the success of machine learning applications. By iteratively refining the dataset, the data-centric approach reduces the reliance on model complexity and ensures robust performance even in challenging scenarios.

## 4.3. Proposed approach: hybrid machine learning methodology for PHM of the pipe system

Although both model-centric and data-centric approaches have their advantages and disadvantages, the hybrid model approach seeks to integrate the benefits of both approaches. This entails using a more intricate model architecture and supplementing it with more features to enhance its performance.

The proposed hybrid machine learning methodology for PHM of pipe systems, which leverages clogging information from the *Acc_H* signals to predict the pipe state and characterize blockages when they occur, involves two distinct and complementary phases: training and testing, as presented in Fig. 7. In contrast to the pipelines depicted in Figs. 5 and 6, the process employed here combines both data-centric and model-centric approaches. Data preprocessing and feature engineering steps are executed multiple times, and for each iteration, the model is fitted with the best hyperparameters tuned during the model development step.

### 4.3.1. Training phase

In this phase, the raw training data, precisely *Acc_H*, from Heverett Group is utilized to develop a robust machine learning model that can accurately predict the occurrence of pipe clogging and its severity. This phase involves four essential steps: data preprocessing, feature engineering, data labeling, and model development, each of which plays a crucial role in the overall process.

#### 4.3.1.1. Data preprocessing.
The proposed strategy begins with data preprocessing, which plays a crucial role in the accuracy and performance of the resulting ML models. Raw data may contain missing values, outliers, or errors that can negatively affect model performance. By employing data preprocessing techniques, such issues can be identified and addressed, leading to improved data quality.

After careful examination of the available dataset, any signals with aberrant effects were removed (as shown in Fig. 4).

Outliers (as detailed in the earlier Section 3.3.2) are particularly important as they may contain valuable information related to clogging. Therefore, selecting an appropriate threshold to exclude noisy data while retaining as much relevant information as possible is crucial. To accomplish this, different thresholds were tested, such as 93%, 95%, 97%, 98%, and 100%, and the accuracy of the model was used as the metric for selecting the optimal threshold.
<figure><img src="image_8.png" /><figcaption>Fig. 6. A graphical representation highlighting the stages of a data-centric machine learning pipeline.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. Innovative hybrid machine learning approach for PHM methodology.</figcaption></figure>

### 4.3.1.2. Feature engineering.
This step involves the extraction of relevant features or patterns from the preprocessed data. The objective of this step is to create a set of features that can effectively capture the essential characteristics of the data and contribute towards precise predictions. In this step, machine learning programmers aim to extract relevant features that are important for solving the problem at hand. The importance of each feature is determined by its weight in separating the different categories. ML classifiers then detect the patterns and use the information provided by the features to differentiate between the various categories.

In this step, the sliding window was used to extract meaningful features from the Acc_H data. The sliding window is a signal processing technique that involves dividing data into consecutive fixed-size segments or windows, and analyzing them as they slide over the data. The aim of this technique is to extract relevant information or features from the signal, which may be useful for various tasks such as pattern detection, anomaly detection, or change detection over time (as shown in Fig. 8). The sliding window is a commonly used method for online signal monitoring, allowing the changes in the signal to be tracked by comparing the estimated features with either a known reference or the same features extracted over a different time window (Daigle et al., 2010).

The size of the window is an important parameter that can affect the performance of the analysis and should be chosen based on the characteristics of the signal and the specific task that needs to be performed. The size of the window refers to the number of data points that are included in each segment or window. A larger window size may capture more information but may also lead to more computational complexity, while a smaller window size may miss critical details. Therefore, determining the optimal window size is essential to ensure accurate and effective results. In this context, various window sizes, including 500, 1000, 2000, 2500, 3000, 3500, and 4500, were evaluated, and the accuracy of the model was used as the criterion for selecting the optimal size.

To ensure that the proposed framework can be applied in various scenarios and to address the challenge of extracting a single “super

<figure><img src="image_10.png" /><figcaption>Fig. 8. Illustration of the sliding window technique for feature extractions.</figcaption></figure>

<table><caption>Table 2
Extracted features and their equations.</caption><thead><tr><th>Parameters</th><th>Equations</th><th>Parameters</th><th>Equations</th></tr></thead><tbody><tr><td>Maximum</td><td>max(x)</td><td>Minimum</td><td>min(x)</td></tr><tr><td>Std</td><td>√<sup>Σ(x<sub>i</sub> - μ)<sup>2</sup></sup>/<sub>n</sub></td><td>Energy</td><td>Σ<sup>n</sup><sub>i=1</sub> |x<sub>i</sub>|<sup>2</sup></td></tr><tr><td>Curve length</td><td>Σ<sup>n</sup><sub>i=2</sub> |x<sub>i</sub> - x<sub>i-1</sub>|</td><td>L<sub>2</sub> norm</td><td>√<sup>Σ<sup>n</sup><sub>i=1</sub> |x<sub>i</sub>|<sup>2</sup></sup></td></tr><tr><td>Kurtosis</td><td><sup>1</sup>/<sub>n</sub> Σ<sup>n</sup><sub>i=1</sub> (x<sub>i</sub> - μ)<sup>4</sup></td><td>Skewness</td><td><sup>1</sup>/<sub>n</sub> Σ<sup>n</sup><sub>i=1</sub> (x<sub>i</sub> - μ)<sup>3</sup></td></tr><tr><td>RMS</td><td>√<sup>1</sup>/<sub>n</sub> Σ<sup>n</sup><sub>i=1</sub> x<sub>i</sub><sup>2</sup></td><td>Crest factor</td><td>max(|x|)/√<sup>1</sup>/<sub>n</sub> Σ<sup>n</sup><sub>i=1</sub> x<sub>i</sub><sup>2</sup></td></tr><tr><td>Second maximum</td><td></td><td></td><td></td></tr></tbody></table>

feature” that can effectively detect various types of clogging while being robust to environmental effects in SHM, a multitude of features were extracted from the Acc_H signal using a sliding window approach. Table 2 provides a summary of 11 key features. Additionally, the mean of these features was computed to reduce noise and enhance the accuracy of the results (as shown by the ellipsis in Fig. 3). Consequently, a total of 22 features were extracted.

In this context, distinct subsets were created for each configuration. After excluding signals with aberrant effects, the number of subsets provided varied for each configuration. Consequently, the subsets differed in size. The size of each subset is (204 800 × number of remaining subsets) * 22, where 204 800 represents the base data points per subset and 22 refers to the number of extracted features.

To ensure that the features are at the same scale and magnitude, the extracted features were subjected to scaling. This is crucial because some machine learning models are highly sensitive to the scale of the features, and having features with varying ranges can lead to biased results. One widely used technique is applying a standard scaler, which scales the features to have zero mean and unit variance (Feature, 2024). This step helps to enhance the performance of the models by reducing the effect of differences in the scale of the features.

### 4.3.1.3. Data labeling.
The third step in the proposed strategy involves data labeling, which is the process of assigning a label to each data point in the dataset. This label describes the category or class to which the data point belongs and is crucial for supervised machine learning algorithms. By assigning labels to each data point, the model can identify patterns and relationships between the input data and the desired label, allowing it to learn and generalize from the labeled data to new, unseen data. In this context, the available datasets were labeled using distinct labels.
<table><caption>**Table 3**
Parameter grid for Decision Trees and Random Forests.</caption><thead><tr><th>Algorithm</th><th>Parameter</th><th>Values</th></tr></thead><tbody><tr><td rowspan="3">Decision Tree</td><td>max_depth</td><td>[1, 2, 3, ..., 15, None]</td></tr><tr><td>Criterion</td><td>['gini', 'entropy', 'log_loss']</td></tr><tr><td>Splitter</td><td>['best', 'random']</td></tr><tr><td>Random Forest</td><td>n_estimators</td><td>[100, 500, 1000]</td></tr></tbody></table>

#### 4.3.1.4. Model development.
In this step of the training phase, the focus shifts to a model-centric approach. The goal is to fine-tune the hyperparameters to achieve the best possible performance of the model. To accomplish this, a combination of nested cross-validation and grid search techniques are employed to search for the optimal hyperparameters.

Grid search is a technique used in machine learning to find the optimal hyperparameters for a model. It involves defining a range of possible values for each hyperparameter, and then exhaustively exploring all possible combinations of these values to find the one that results in the best performance of the model. The process involves evaluating the model's performance using a validation set for each combination of hyperparameters and selecting the set of values that yields the highest performance.

For this analysis, Decision Trees and Random Forests were the machine learning algorithms developed. Table 3 summarizes the parameter grid for both Decision Trees and Random Forests.

The max_depth parameter in Decision Trees controls the maximum depth of the tree, with tested values ranging from 1 to 15 and None, which allows nodes to expand until all leaves are pure or contain fewer than the minimum required samples to split (DecisionTreeClassifier, 2023). The criterion parameter determines the function to measure the quality of a split, including 'gini' for Gini impurity, which indicates the likelihood of misclassification with values between 0 and 0.5 (Gini Impurity, 2023), 'entropy', which quantifies disorder or uncertainty in the data and aims to minimize it (Decision Trees, 2023; ML, 2023), and 'log_loss' (logistic loss or cross-entropy loss), which measures the difference between predicted and true probabilities (Understanding, 2023). In Random Forests, the n_estimators parameter defines the number of trees in the forest (RandomForestClassifier, 2023), with values tested at 100, 500, and 1000. More trees generally improve model performance and stability by averaging predictions, thus reducing variance, but also increasing computational requirements.

Nested cross-validation is a technique used in machine learning to evaluate the performance of a model and to tune its hyperparameters. It involves creating two nested loops, an outer loop, and an inner loop. Unlike standard k-fold cross-validation, which splits the data into one set for training and another for testing, nested cross-validation uses an additional layer to integrate optimization techniques such as hyperparameter tuning using grid search or some other technique.

In the outer loop, the data is divided into k-folds, each used exactly once as a test fold while the remaining folds are combined to form a training fold. The model is trained on the training fold and tested on the test fold. This process is repeated k times, with each fold used exactly once as a test fold.

In the inner loop, which is embedded within the outer loop, the training fold is further divided into n-folds. One is used as a validation fold while the remaining folds are combined to form a training fold. The model is trained on each combination of hyperparameters using the training folds and evaluated on the validation fold to obtain a set of performance estimates. The best hyperparameters are then selected based on the best performance on the validation set, and the model is then tested on the test fold.

Combining nested cross-validation with grid search is a very powerful training technique, however, it can be computationally expensive, particularly for large datasets or complex models with many hyperparameters.

<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Detailed illustration of the model-centric strategy in the model development step of the proposed hybrid machine-learning approach.</figcaption></figure>

The proposed approach's model development step is illustrated in Fig. 9. During this step, the available subsets are divided into two sets. The first set, which consists of 70% of the subsets, is used for training and inner testing and is balanced. The second set, which contains the remaining 30% of the subsets, is used for outer testing. A subset in this context refers to the features and information extracted from a signal measured over a 20 s period. This division is similar to the technique called GroupKFold, which ensures that the same subset is not present in both the training and testing sets. If the training and testing sets are created from the same subsets, the model may fail to generalize to new subsets, despite achieving high prediction accuracy on the unseen test set, due to the machine learning algorithm's flexibility in learning from specific information. This division allows the identification of such issues.

The original dataset was split into two subsets, specifically the training and inner test sets. The training set was created by randomly selecting 70% of the data, with the remaining 30% assigned to the inner test set. Notably, the class distribution was preserved at 50%-50% in both subsets. A balanced training set is generally beneficial in reducing the bias of machine learning algorithms.

In order to select the hyperparameter settings that yield the highest prediction accuracy, a combination of nested cross-validation and grid search was employed to train multiple machine learning algorithms on the training set. The outer loop of this process divided the training set into four folds, while the inner loop divided the training folds into three additional folds for each iteration. Stratified cross-validation was used in all divisions to maintain equal proportions of categories or classes in each fold, resulting in a balanced dataset for every fold. This approach ensured that the best hyperparameters were selected while preventing overfitting and bias in the models.

Once the optimal hyperparameter settings were selected, the machine learning algorithms were then trained on the entire training set and subsequently tested on two distinct test sets: the inner test set and the outer test set. Evaluating the accuracy of the model on these
test sets enables accurate detection of its generalization ability. This is crucial in ensuring that the model can effectively predict outcomes on previously unseen data, making it a reliable tool for real-world applications.

### 4.3.2. Testing phase

During this phase, the developed ML models, specifically decision trees and random forests, are deployed to predict pipe clogging and assess blockage severity on unseen test sets. Decision trees were prioritized due to their shorter training time of 2 h and 30 min, allowing for rapid model development and deployment. In contrast, random forests were selected for their higher accuracy and robustness. As an ensemble method, random forests average multiple trees to reduce variance and mitigate the risk of overfitting. Moreover, both decision trees and random forests have demonstrated high predictive performance in various applications (Raniprima et al., 2024). Their capability to handle complex relationships and interactions between features makes them particularly suitable for diverse datasets (Wang et al., 2018). These attributes render decision trees and random forests ideal for addressing the complexities of PdM tasks, ensuring reliable predictions on unseen data.

Selecting an appropriate evaluation metric to assess the model's performance is crucial. Accuracy is the most commonly used metric for classification problems, defined as the ratio of correct predictions to the total number of predictions (Eq. (1)). However, accuracy can overestimate the predictive model's effectiveness when dealing with skewed datasets. In machine learning, a skewed dataset refers to a dataset with unequal sample sizes for each category.

$$ \text{Accuracy} = \frac{\text{Number of correct predictions}}{\text{Total number of predictions}} \qquad (1) $$

In the case of real-world datasets collected by SCADA systems, PdM models often encounter skewed datasets, where there is a significantly larger number of healthy data points than faulty ones. As a result, using accuracy as the sole criterion to evaluate model performance may not be optimal. In such scenarios, evaluating model performance using metrics like true positive (TP), true negative (TN), false positive (FP), false negative (FN), precision, and recall becomes essential. Precision and recall, derived from these metrics, provide a more nuanced understanding of model performance, particularly in handling imbalanced datasets, thus offering a better assessment of the model's effectiveness.

**TP:** It refers to the true pipe cloggings that the model detected Eq. (2).

$$ \text{TP rate} = \frac{\text{Number of correct predictions for clogged data}}{\text{Total number of predictions for clogged data}} \qquad (2) $$

**TN:** It refers to the healthy pipe state that the model detected Eq. (3).

$$ \text{TN rate} = \frac{\text{Number of correct predictions for healthy data}}{\text{Total number of predictions for healthy data}} \qquad (3) $$

**FP:** It refers to the false prediction when there is no cloggings Eq. (4).

$$ \text{FP rate} = \frac{\text{Number of wrong predictions for healthy data}}{\text{Total number of predictions for healthy data}} \qquad (4) $$

**FN:** It refers to the false prediction when there is a clogging Eq. (5).

$$ \text{FN rate} = \frac{\text{Number of wrong predictions for clogged data}}{\text{Total number of predictions for clogged data}} \qquad (5) $$

Precision is the positive predictive value, calculated as the ratio of TP to the total number of samples classified as positive by the model (TP + FP) Eq. (6). It indicates the proportion of positive predictions that are actually correct. A higher precision means that the model is making fewer false positive predictions.

$$ \text{Precision} = \frac{\text{TP}}{\text{TP}+\text{FP}} \qquad (6) $$

<table><caption>**Table 4**
Models associated with the experimental setup.</caption><thead><tr><th>Models</th><th>Pipe state</th><th>Blockage rate</th><th>Shape of blockage</th></tr></thead><tbody><tr><td rowspan="2">M<sub>1</sub></td><td>Healthy</td><td>0%</td><td>–</td></tr><tr><td>Clogged</td><td>50%</td><td>Oblique</td></tr><tr><td rowspan="2">M<sub>2</sub></td><td>Healthy</td><td>0%</td><td>–</td></tr><tr><td>Clogged</td><td>75%</td><td>Oblique</td></tr><tr><td rowspan="2">M<sub>3</sub></td><td>Healthy</td><td>50%</td><td>Oblique</td></tr><tr><td>Clogged</td><td>75%</td><td>Oblique</td></tr></tbody></table>

Recall, also known as sensitivity, is the proportion of TP instances that are correctly identified by the model, calculated as the ratio of TP to the total number of positive instances (TP + FN) Eq. (7). A higher recall means that the model is better at detecting all positive instances.

$$ \text{Recall} = \frac{\text{TP}}{\text{TP}+\text{FN}} \qquad (7) $$

A set of machine learning predictive models has been developed to accurately predict the state of pipes and the severity of clogging. Three models were created for each of the three airflows (3 l/h, 6 l/h, and 10 l/h), resulting in a total of nine models. The testbench configuration settings for each airflow are detailed in Table 4.

The predictive models were specifically designed to detect clogging at different blockage thicknesses, with models $M_1$ and $M_2$ developed for clogged detection at blockage thicknesses of 50% and 75%, respectively, and model $M_3$ used for clogging severity detection. The models were trained and validated using the Acc_H data.

#### 4.3.2.1. Fine-tuning window width and outlier threshold.
The appropriate window width and outliers threshold were fine-tuned using the Acc_H vibration signals obtained at an airflow rate of 10 l/h. The developed strategy, incorporating these tuned parameters, was then evaluated on airflow rates of 3 l/h and 6 l/h. In this context, eleven datasets were created by applying a sliding window of different sizes and removing outliers at various thresholds, with the aim of extracting diverse and relevant features for model $M_1$ at an airflow rate of 10 l/h. Table 5 shows the decision tree prediction accuracy for the sliding window datasets, where SW(W, Th) refers to the sliding window of size W and outliers threshold Th. As the extracted information depends on the window size and outlier threshold, the performance of the decision tree is expected to differ among the sliding window datasets.

The training accuracy is computed based on the best hyperparameter settings chosen by grid search on the training set. The outer folds test accuracy is the average test accuracy obtained from the outer folds using nested cross-validation. The inner test set accuracy refers to the test accuracy on the previously unseen inner test set, while the outer test set accuracy refers to the test accuracy on the unseen outer test set.

The metric chosen to evaluate the optimal combination of window size W and threshold percentage Th is the prediction accuracy. The evaluation involved testing seven different window sizes (500, 1000, 2000, 2500, 3000, 3500, 4500) and five threshold percentages (93%, 95%, 97%, 98%, and 100%), and the combination that resulted in the highest prediction accuracy was selected as the best.

The ideal combination of threshold Th and window size W was evaluated based on prediction accuracy. The evaluation of threshold Th was performed on a fixed window size of W = 500, where the highest outer test set accuracy of 80.6% was achieved by excluding outliers at 97% thresholds. Additionally, the evaluation of window sizes at a fixed threshold of Th = 97% showed that prediction accuracy increases with increasing window size W. At a window size of W = 4500, the hybrid model of the proposed prognostic methodology achieved 100% prediction accuracy on the outer folds test sets, inner test sets, and outer test sets. Therefore, the combination of W = 4500 and Th = 97% was selected for the methodology and will be further evaluated on various predictive models with different airflow settings.
<table><caption>**Table 5**
Training and testing accuracies of the model $M_1$, at airflow of 10 l/h, for different window sizes and outliers thresholds.</caption><thead><tr><th>Datasets</th><th>Training accuracy</th><th>Outer fold test accuracy</th><th>Inner test set accuracy</th><th>Outer test set accuracy</th></tr></thead><tbody><tr><td>SW(500, 100%)</td><td>99.14%</td><td>99.2% ± 0.02</td><td>94.89%</td><td>55.63%</td></tr><tr><td>SW(500, 95%)</td><td>99.71%</td><td>99.71% ± 0.01</td><td>99.12%</td><td>75.96%</td></tr><tr><td>SW(500, 93%)</td><td>99.79%</td><td>99.82% ± 0.00</td><td>99.45%</td><td>60.77%</td></tr><tr><td>SW(500, 97%)</td><td>99.47%</td><td>99.52% ± 0.01</td><td>99.17%</td><td>80.6%</td></tr><tr><td>SW(500, 98%)</td><td>99.41%</td><td>99.47% ± 0.01</td><td>98.95%</td><td>67.71%</td></tr><tr><td>SW(1000, 97%)</td><td>99.90%</td><td>99.91% ± 0.00</td><td>99.49%</td><td>87.24%</td></tr><tr><td>SW(2000, 97%)</td><td>99.98%</td><td>99.98% ± 0.00</td><td>99.68%</td><td>94.01%</td></tr><tr><td>SW(2500, 97%)</td><td>99.99%</td><td>99.99% ± 0.00</td><td>96.89%</td><td>96.10%</td></tr><tr><td>SW(3000, 97%)</td><td>99.99%</td><td>99.99% ± 0.00</td><td>98.50%</td><td>97.32%</td></tr><tr><td>SW(3500, 97%)</td><td>100.0%</td><td>100.0% ± 0.00</td><td>99.53%</td><td>98.21%</td></tr><tr><td>SW(4500, 97%)</td><td>100.0%</td><td>100.0% ± 0.00</td><td>100.0%</td><td>100.0%</td></tr></tbody></table>

Despite achieving high accuracies on the training and inner test sets, the proposed hybrid models for the prognostic methodology provided low test accuracy on the outer test sets for datasets created using a sliding window with a small window size (W = 500). This observation highlights the fact that the inner test sets, which contain information derived from the same signals used for training the models, may not be sufficient for evaluating their performance. In contrast, the outer test sets contain information extracted from other signals.

The high accuracy observed on the inner test sets can be considered as an indicator of well-trained models. This is because these test sets contain information derived from the same signals used for training the models, which can help in capturing patterns that are very similar to the training set. However, the models may exhibit low accuracy on the outer test sets since they contain information extracted from other signals that are different from those used for training. This reflects the potential of ML algorithms to learn patterns that are similar to those in the training set but can fail to generalize. This failure of generalization can lead to poor performance on the outer test sets, as observed in this study.

Another reason for the observed differences in model performance may be related to the window size and the level of noise present in the vibration signal. A larger window size (W) may be more effective at suppressing noise than a smaller window, making the patterns in both datasets close to each other. In general, there are many different sources of noise that can significantly impact the vibration signal, particularly when the signal is weak and more susceptible to distortion.

The noise in vibration signals can come from various sources, and it can significantly impact the accuracy of the ML model. In some cases, using a larger window size may be necessary to suppress the noise and extract meaningful information from the signal. This is demonstrated in Table 5, where the decision tree model struggled to generalize when a small window size was used but performed well when a larger window size was employed.

The larger window size suppressed the noise to a level that allowed the decision tree model to effectively extract the relevant features in the data and make accurate predictions. As a result, the patterns observed in both the training and outer test sets become more aligned, indicating that the model can successfully generalize to new, unseen data.

Therefore, selecting an appropriate window size is crucial in optimizing the performance of ML models for the proposed strategy in analyzing vibration signals. For the best combination of window width and threshold SW (4500, 97%), the optimal hyperparameters for the decision tree were found to be: using the Gini impurity criterion, the 'best' splitter strategy, and setting the maximum depth of the tree to 14. However, the analysis demonstrates that this hyperparameter tuning can vary across test folds, with the maximum depth sometimes reducing to 12. This variability indicates that while the identified hyperparameters are generally effective, they may require adjustments based on specific dataset characteristics and noise levels.

<table><caption>**Table 6**
Training and testing accuracy at an airflow = 10 l/h.</caption><thead><tr><th>Cls MDLs</th><th>Training accuracy</th><th>Outer fold test accuracy</th><th>Inner test set accuracy</th><th>Outer test set accuracy</th></tr></thead><tbody><tr><td>M<sub>1</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>99.85%</td><td>100.0%</td></tr><tr><td>DT M<sub>2</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>100.0%</td><td>100.0%</td></tr><tr><td>- M<sub>3</sub>/M<sub>1</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>99.89%</td><td>100.0%</td></tr><tr><td>RF M<sub>2</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>99.32%</td><td>100.0%</td></tr><tr><td>M<sub>3</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>99.99%</td><td>100.0%</td></tr></tbody></table><table><thead><tr><th>Cls MDLs</th><th>TP</th><th>TN</th><th>FN</th><th>FP</th><th>PR</th><th>RE</th></tr></thead><tbody><tr><td>M<sub>1</sub></td><td>100.0%</td><td>100.0%</td><td>0%</td><td>0%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>DT M<sub>2</sub></td><td>100.0%</td><td>100.0%</td><td>0%</td><td>0%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>- M<sub>3</sub>/M<sub>1</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>99.92%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>RF M<sub>2</sub></td><td>100.0%</td><td>100.0%</td><td>0%</td><td>0%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>M<sub>3</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td></tr></tbody></table>

<table><caption>**Table 7**
Training and testing accuracy at an airflow = 6 l/h.</caption><thead><tr><th>Cls MDLs</th><th>Training accuracy</th><th>Outer fold test accuracy</th><th>Inner test set accuracy</th><th>Outer test set accuracy</th></tr></thead><tbody><tr><td>M<sub>1</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>100.0%</td><td>100.0%</td></tr><tr><td>DT M<sub>2</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>100.0%</td><td>100.0%</td></tr><tr><td>- M<sub>3</sub>/M<sub>1</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>99.92%</td><td>100.0%</td></tr><tr><td>RF M<sub>2</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>100.0%</td><td>100.0%</td></tr><tr><td>M<sub>3</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>100.0%</td><td>100.0%</td></tr></tbody></table><table><thead><tr><th>Cls MDLs</th><th>TP</th><th>TN</th><th>FN</th><th>FP</th><th>PR</th><th>RE</th></tr></thead><tbody><tr><td>M<sub>1</sub></td><td>100.0%</td><td>100.0%</td><td>0%</td><td>0%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>DT M<sub>2</sub></td><td>100.0%</td><td>100.0%</td><td>0%</td><td>0%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>- M<sub>3</sub>/M<sub>1</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>99.92%</td><td>100.0%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>RF M<sub>2</sub></td><td>100.0%</td><td>100.0%</td><td>0%</td><td>0%</td><td>100.0%</td><td>100.0%</td></tr></tbody></table>

#### 4.3.2.2. Proposed strategy performance at different airflow rates.
Table 6 provides a summary of the training and testing accuracies achieved by decision trees and random forest classifiers for the models $M_1$, $M_2$, and $M_3$ in predicting the state of the pipe and the severity of clogging under an airflow of 10 l/h. The datasets were created using the SW (4500, 97%) signal processing technique. The TP, TN, FP, FN, PR, and RE were computed on the outer test set, providing a more realistic estimation of model performance. The abbreviations CLs and MDLs refer to classifiers and models, respectively.

Both decision trees and random forests achieved a 100% accuracy in predicting the occurrence of clogging with thickness rates of 50% ($M_1$) and 75% ($M_2$) and distinguishing between severity ($M_3$) on the outer test set. However, on the inner test set, their prediction accuracy sometimes falls short of 100% due to the small part of the Acc_H signal that may be distorted. It should be noted that the proposed strategy was applied separately to random forests and decision trees, with different training sets for each inner and outer test set, due to the random splitting process. Both models performed well on these sets.

Overall, the proposed hybrid model for PHM techniques for the pipe system demonstrated strong prediction accuracy at an airflow of 10 l/h.

The performance of the proposed predictive methodology was assessed for two other airflows: 6 l/h and 3 l/h. The training and testing accuracies for the models $M_1$, $M_2$, and $M_3$ were determined using decision trees and random forests, and are presented in Table 7 for an airflow of 6 l/h, and Table 8 for an airflow of 3 l/h.

At an airflow rate of 6 l/h, both decision trees and random forests achieved a 100% prediction accuracy in determining the pipe state and clogging severity (50% or 75%) on both inner and outer test sets, as presented in Table 7. This highlights the effectiveness of the Acc_H signal in providing valuable features for machine learning-based clogging detection.

At an airflow of 3 l/h, the proposed methodology utilizing decision trees and random forests demonstrated promising results in predicting the occurrence of clogging ($M_1$ and $M_2$) with 100% prediction accuracy on both the inner and outer test sets. However, distinguishing between
<table><caption>**Table 8**
Training and testing accuracy at an airflow = 3 l/h.</caption><thead><tr><th>Cls MDLs</th><th>Training accuracy</th><th>Outer fold test accuracy</th><th>Inner test set accuracy</th><th>Outer test set accuracy</th></tr></thead><tbody><tr><td>M<sub>1</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>100.0%</td><td>100.0%</td></tr><tr><td>DT M<sub>2</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>99.97%</td><td>100.0%</td></tr><tr><td>- M<sub>3</sub>/M<sub>1</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>99.67%</td><td>74.64%</td></tr><tr><td>RF M<sub>2</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>100.0%</td><td>99.54%</td></tr><tr><td>M<sub>3</sub></td><td>100.0%</td><td>100.0% ± 0.00</td><td>100.0%</td><td>79.97%</td></tr></tbody></table><table><thead><tr><th>Cls MDLs</th><th>TP</th><th>TN</th><th>FN</th><th>FP</th><th>PR</th><th>RE</th></tr></thead><tbody><tr><td>M<sub>1</sub></td><td>100.0%</td><td>100.0%</td><td>0%</td><td>0%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>DT M<sub>2</sub>/M<sub>1</sub></td><td>100.0%</td><td>100.0%</td><td>0%</td><td>0%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>RF M<sub>2</sub></td><td>100.0%</td><td>99.81%</td><td>0%</td><td>0.19%</td><td>99.81%</td><td>100.0%</td></tr></tbody></table>

50% and 75% clogging thicknesses proved to be more challenging, with an accuracy of 74.64% for the decision tree and 79.97% for the random forest. This difficulty in distinguishing between clogging severity at lower airflow rates can be attributed to the greater impact of noise on the acceleration signal, which makes the signal-to-noise ratio decrease in amplitude as the airflow decreases.

The grid analysis for both the decision tree and random forest demonstrates that the best hyperparameter tuning varies with the experimental configurations. However, the high accuracy achieved on the outer test set indicates that the provided list of configurations is comprehensive and effectively covers all possible cases.

## 5. Conclusion

This study introduces a novel hybrid approach for the PHM of pipe systems, integrating both model-centric and data-centric techniques. The method leverages acceleration measurements taken from a safe distance, ensuring safety while maintaining high prediction accuracy. Implementing a sliding window technique, with precise tuning of window width and outlier thresholds, is critical for minimizing noise and extracting relevant data features.

One of the key strengths of this approach is its capability to safely analyze data from a distance, which is especially beneficial in hazardous environments such as nuclear plants. The hybrid method demonstrates robust performance in predicting clogging occurrences and assessing their severity under various airflow conditions, due to the integration of model-centric and data-centric methodologies and a focus on data quality and the model. Additionally, this approach is scalable and adaptable for use in diverse industrial applications beyond pipe systems, potentially benefiting sectors such as manufacturing, transportation, and infrastructure management. Its emphasis on data quality and model structure ensures high overall accuracy, and its support for real-time monitoring enhances its practical utility in dynamic and rapidly changing environments.

However, the proposed approach has certain limitations. It is sensitive to noise in the acceleration signals and outliers, which can affect the accuracy of the model. The feature extraction and parameter tuning process can be complex and resource-intensive. While fine-tuning can enhance model performance, it also introduces additional challenges. These challenges include increased computational requirements and longer processing times.

Future work will focus on several key areas to enhance the proposed approach's effectiveness and applicability. Expanding the methodology to different pipeline configurations and other industrial applications will validate its versatility and robustness across various contexts. Additionally, investigating and integrating more advanced noise reduction techniques can further improve model accuracy, particularly in low signal-to-noise ratio scenarios.

## CRediT authorship contribution statement

**Ahmad Braydi:** Writing – original draft, Methodology, Conceptualization, **Pascal Fossat:** Visualization, Supervision, **Alessandro Casaburo:** Visualization, **Victor Pernet:** Visualization, Validation, **Cyril Zwick:** Visualization, **Mohsen Ardabilian:** Writing – review & editing, Validation, Supervision, Project administration, **Olivier Bareille:** Writing – review & editing, Validation, Supervision, Project administration.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

Regarding the here-reported works, the authors would like to gratefully acknowledge the financial support to PSPC - Régions n°2 - HAGILY - a scientific project in the frame of a co-financed "Investissement d'Avenir" program, co-supported by the French government and its Regions.

## Data availability

The data that has been used is confidential.

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