# Innovative prognostic methodology for pipe defect detection leveraging acoustic emissions analysis and computational modeling integration

Ahmad Braydi, Pascal Fossat, Mohsen Ardabilian, Olivier Bareille

## ► To cite this version:

Ahmad Braydi, Pascal Fossat, Mohsen Ardabilian, Olivier Bareille. Innovative prognostic methodology for pipe defect detection leveraging acoustic emissions analysis and computational modeling integration. Applied Ocean Research, 2025, 158 (4), pp.104521. 10.1016/j.apor.2025.104521. hal-05419101

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https://hal.science/hal-05419101v1

Submitted on 23 Jan 2026

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Research paper

# Innovative prognostic methodology for pipe defect detection leveraging acoustic emissions analysis and computational modeling integration

Ahmad Braydi<sup>a,b,c</sup>,*, Pascal Fossat<sup>a</sup>, Mohsen Ardabilian<sup>b,c</sup>, Olivier Bareille<sup>a,c</sup>

<figure><img src="image_2.png" /></figure>

## ARTICLE INFO

### Keywords:

Prognostic and health monitoring

Predictive maintenance

Machine learning

Pipe clogging

Bubble-induced acoustic emissions

Finite element analysis

Acoustic emission testing

## ABSTRACT

Pipelines play a crucial role in transporting essential resources such as water, oil, and gas across industrial, urban, and environmental infrastructures. Clogging remains a persistent challenge, potentially resulting in catastrophic failures, operational disruptions, increased maintenance costs, and serious safety risks. This study presents a novel prognostic and health monitoring approach that utilizes bubble-induced acoustic emissions to detect and characterize pipeline blockages. An analytical model is developed to capture the acoustic signatures of detaching bubbles, revealing features highly sensitive to clogging. Finite element simulations using Abaqus further investigate how different clogging conditions affect acoustic wave propagation. These insights drive the development of a machine learning-based predictive maintenance strategy, validated on real-world datasets. The results demonstrate exceptional accuracy, with most classifiers achieving 100% detection rates for clogging presence, shape, and severity. Additionally, model generalization tests show that machine learning algorithms adapt more effectively to varying clogging thickness than clogging shape. This research paves the way for a highly accurate, non-destructive monitoring solution, enhancing predictive maintenance and ensuring the reliability of industrial pipelines.

## 1. Introduction

Pipes play a fundamental role in efficiently transporting essential resources like water, oils, and gases across extensive distances and diverse environments, including urban centers, residential neighborhoods, and industrial zones. In industrial settings, pipes facilitate the manufacture of products and provide energy for production and heating. Their robust construction is purposefully designed to withstand high-pressure environments, making them essential for industrial operations.

As a consequence, it is important to protect pipes from potential malfunctions, such as cracks and blockages. These issues can arise due to various factors, including the rigorous nature of industrial operations, challenging environmental conditions, prolonged usage, and human errors.

In 2019, the Orano/LA HAGUE site reported a total of 3449 instances of pipe clogs. To address this issue, the site's maintenance department deployed teams of two people, with each intervention taking around 30 min to unclog the pipes. This operation consumed a total of 3449 h of labor, resulting in a significant loss of productivity, along with associated energy and financial expenditures. Furthermore,

there was a potential risk of reduced fluid flow in the pipe systems due to partial blockages.

In the pursuit of optimizing plant performance and ensuring the continual reliability of critical pipelines, it is essential to thoroughly investigate and analyze pipe-clogging phenomena. The primary objective is to develop comprehensive solutions that integrate advanced, non-destructive, and non-curative approaches, using cutting-edge technologies for the early detection and characterization of potential pipeline blockages. Prioritizing proactive maintenance, including predictive measures, is vital for addressing issues before they escalate into major disruptions. This approach not only enhances operational efficiency but also reduces the use of resources and strengthens the long-term resilience of industrial systems.

A variety of conventional techniques have been developed for identifying defects in pipelines. These methods encompass thermography (Kafieh et al., 2011; Tong et al., 2020), magnetic approaches (Khodayari-Rostamabad et al., 2009; Feng et al., 2017), flow pressure monitoring (Eastvedt et al., 2022; Chen et al., 2007), radiographic methods (Suyama et al., 2019; Li et al., 2017), and other

<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>* 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), mohsen.ardabilian@ec-lyon.fr (M. Ardabilian), olivier.bareille@ec-lyon.fr (O. Bareille).</footnote>
approaches (Wong and McCann, 2021; Datta and Sarkar, 2016). Despite the value they bring to defect detection, these established methods often carry significant drawbacks, including high costs, time-intensive procedures, and potential risks to pipeline integrity (Ghidaoui et al., 2005; Murvay and Silea, 2012).

In response to these challenges, this research introduces an innovative approach that utilizes vibroacoustic signals generated by the conveyed fluid as a predictive maintenance tool for pipe clogging detection using machine learning. By leveraging principles from fluid dynamics and acoustics, this approach offers continuous monitoring, cost-effectiveness, and remote operation capabilities for monitoring pipe systems and identifying potential obstructions. With these advantages, this approach effectively overcomes some limitations associated with conventional methods, especially in challenging environments where sensor placement at the clogging level is not feasible. This technology holds the potential to significantly enhance the efficiency and reliability of pipeline monitoring and maintenance, particularly in scenarios where traditional approaches may fall short.

The integration of machine learning with passive vibroacoustic techniques is gaining recognition as a pivotal advancement for pipeline defect detection (Baronti et al., 2022; Hefft and Alberini, 2020; Merizio et al., 2021; Banjara et al., 2020). Machine learning's proficiency in processing extensive datasets offers the potential to significantly enhance the capabilities of vibroacoustic methods for defect detection. This integrated system, fusing machine learning with passive vibroacoustic measurements enables automated analysis of complex vibrational and acoustic data from pipelines, improving defect detection speed and accuracy while identifying specific defect patterns associated with various types of defects. Furthermore, these systems can learn and adapt over time, enhancing anomaly detection and adapting to changing conditions. Additionally, machine learning facilitates predictive maintenance by forecasting defect occurrences using historical data and real-time measurements, allowing proactive issue resolution and reducing the risk of costly pipeline failures.

For instance, in the study by Baronti et al. (2022), researchers used passive acoustic emissions from pipeline systems to predict their condition. The acoustic signals underwent initial preprocessing through Fourier analysis, leading to the creation of two distinct datasets. The first dataset contained the average and variance of Fourier transform amplitudes, while the second involved segmenting the data into 100 non-overlapping frequency intervals, a technique referred to as data binning. Notably, the study highlighted the superior effectiveness of the latter approach, data binning, in detecting pipeline clogs. Another study by Hefft and Alberini (2020) explores the utilization of a single passive acoustic emission sensor for detecting obstructions in a water recirculation system. This study visualizes the flow field around each obstruction using 2D particle image velocimetry and processes the acoustic emission signals employing supervised machine learning algorithms. Results indicate that various obstructions produce distinct acoustic signals and flow fields, with the acoustic signals demonstrating variation based on flow rate. Moreover, the study employs supervised machine learning to predict the type of obstruction with over 95% accuracy. Furthermore, a study by Banjara et al. (2020) explores the use of acoustic emission technology for detecting pipeline leaks through experimental trials. Simulating pipeline leakage involved releasing pressure through valves at identified locations and measuring signals from sensors attached to the pipeline. The results indicated that signal strength and cumulative energy were sensitive parameters for indicating leakage in the pipelines. Employing support vector machine (SVM) and Relevance Vector Machine (RVM) pattern recognition algorithms, the study classified the leakage. The findings demonstrated that the SVM and RVM-enabled acoustic emission features are highly effective in detecting and localizing leaks in pipelines.

Following a review of the literature, it is evident that the detection of blockages within pipeline systems remains a gray area. Despite numerous studies on the subject, there has been a notable

lack of focus on using acoustic pressure generated by bubbles during specific detachment mechanisms for effective blockage detection and characterization across varying flow rates. Furthermore, there is a need for a more in-depth examination to accurately characterize the acoustic signals emitted by bubbles, laying the groundwork for a robust machine-learning approach to improve blockage detection and characterization.

Within this framework, the present study explores the detection of pipe blockages by analyzing the vibroacoustic signals emanating from bubble formations. By leveraging computational simulations, real experiments, and machine learning methodologies, the study unveils a robust approach for accurately predicting the severity and geometry of pipe obstructions. This investigation constitutes a notable progression in the field of pipeline monitoring and upkeep, offering a proactive strategy to mitigate the adverse effects of clogging incidents on industrial processes.

To facilitate understanding and coherence, this paper is structured as follows: Section 2 introduces the acoustic signal model concerning underwater bubbles. Section 3 delves into finite element analysis for the propagation of acoustic waves in air-filled pipes. Subsequently, Section 4 outlines the testbench setup and problem definition. In Section 5, the development of the prognostic approach is elaborated upon. Furthermore, Section 6 investigates the model's generalization across different clogging levels and shapes, and finally, Section 7 offers conclusive remarks on the research findings.

## 2. Acoustic signal dynamics of underwater bubbles

Gas bubble detachment from an underwater pipe can produce significant sound pressure. As bubbles detach and rise through the water, they oscillate and resonate, emitting distinct acoustic signals that can be detected and analyzed. Variations in the acoustic signals generated by bubbles can serve as valuable indicators of changes in the flow dynamics within the pipe. As clogging begins to occur, the characteristics of the acoustic signals and the induced vibrations in the structures may exhibit discernible alterations. By monitoring and analyzing these variations over time, it becomes possible to develop predictive models for pipe clogging.

When gas bubbles detach from underwater pipes, they emit acoustic signals characterized by sinusoidal oscillation with exponential decay, as described by the Eq. (1) (Strasberg, 1956):

$$P(t) = P_0 e^{-\pi \delta f t} \cos(2\pi f t - \theta) \quad (1)$$

Here $P(t)$ represents the acoustic pressure at a given time $t$ [s], while $P_0$, $\delta$, $f$, and $\theta$ denote the peak acoustic pressure [Pa], dissipation parameter, oscillation frequency [Hz], and phase angle [rad], respectively.

The peak acoustic pressure $P_0$ at a reference distance $d$ [m] from the source is calculated using Eq. (2):

$$P_0 = \frac{D_b}{d} \sqrt{\frac{2k P_{amb} S}{D_b}} \quad (2)$$

where $D_b$ stands for the bubble diameter [m], $k$ is the specific heat of the gas inside the bubble, $P_{amb}$ is the ambient pressure [Pa], and $S$ is the surface tension [mN/m].

The dissipation parameter $\delta$, which accounts for signal attenuation, is given by Eq. (3) and is specifically adapted for air bubbles with a diameter larger than 0.01 cm in water, as (Strasberg, 1956):

$$\delta = 0.014 + 4.5 \times 10^{-4} \sqrt{f} \quad (3)$$

Additionally, the phase angle $\theta$ adjusts for phase shift and is determined by Eq. (4):

$$\theta = \arctan\left(-\frac{P_{amb}}{\pi f \sqrt{\frac{2}{3} S \rho D_b}}\right) \quad (4)$$
<figure><img src="image_3.png" /><figcaption>Fig. 1. Acoustic pressure profile generated by a single bubble.</figcaption></figure>

Here $\rho$ represents the density of the liquid [kg/m³].

The ambient pressure $P_{amb}$ is computed based on the depth of the pipe in the tank $h$ [m] and gravitational acceleration $g$ [m/s²], given by Eq. (5):

$$P_{amb} = \rho g h. \qquad (5)$$

The oscillation frequency $f$ of the bubbles, which directly corresponds to the frequency of the generated acoustic sound, is given by Eq. (6). This relationship highlights the effects of the oscillation of the bubble walls on generating acoustic sound, with the frequency depending on the bubble diameter $D_b$, ambient pressure $P_{amb}$, and liquid density $\rho$:

$$f = \frac{1}{\pi D_b} \sqrt{\frac{3k P_{amb}}{\rho}} \qquad (6)$$

Moreover, the bubble diameter $D_b$ depends on parameters such as gas flow rate $Q$ [m³/s] inner diameter of the pipe $d_o$ [m], surface tension $S$ [mN/m], and medium density $\rho$ [kg/m³], It is given by Eq. (7):

$$D_b = \sqrt[6]{\left(\frac{6Sd_o}{\rho g}\right)^2 + (0.54(Qd_o^{0.5})^{0.289})^6} \qquad (7)$$

Lastly, the bubble detachment frequency $f_d$ is defined by Eq. (8) (Luty and Prończuk, 2020):

$$f_d = \frac{6Q}{\pi D_b^3} \qquad (8)$$

The acoustic wave generated from a single bubble in a pipe immersed 0.5 m in water, with an inner diameter $d_o$ = 15 mm, and an airflow rate of $Q$ = 6 l/h is depicted in Fig. 1. This illustration is based on numerical simulations performed using the mathematical formulations introduced earlier in this section. The results reveal that the bubble's acoustic signal has a short duration and particular attenuation properties, consistent with the sinusoidal oscillation with exponential decay described in Eq. (1).

Furthermore, Fig. 2 presents the Fourier transform of the acoustic pressure waveform in Eq. (1), illustrating the oscillation frequency $f$ derived from Eq. (6). This figure demonstrates how the frequency spectrum shifts downward as the gas flow rate and pipe diameter increase. These frequency shifts are critical for characterizing both the leak hole diameter and the gas flow rate.

This first observation provides some insight into the behavior of the acoustic signals generated by underwater bubbles and highlights the relationship between gas flow rate, leak hole diameter, and the resulting frequency spectrum. It provides a foundation for the subsequent development of the calculations in the next section, which focuses on the effect of blockages on acoustic wave propagation.

<table><caption>Table 1
Studied case of various blocking profiles.</caption><thead><tr><td>Case No.</td><td>Blockage thickness</td><td>Blockage length</td><td>Location</td></tr></thead><tbody><tr><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>1</td><td>3.75 mm</td><td>0.1 m</td><td>0</td></tr><tr><td>2</td><td>3.75 mm</td><td>0.2 m</td><td>0</td></tr><tr><td>3</td><td>1.875 mm</td><td>0.1 m</td><td>0</td></tr><tr><td>4</td><td>3.75 mm</td><td>0.1 m</td><td>0.1 m</td></tr></tbody></table>

### 3. Blockage effects investigations on acoustic wave propagation in air-filled pipes using finite element analysis

In this section, finite element analysis (FEA) with Abaqus software is employed to investigate the influence of blockages on acoustic wave propagation in air-filled pipes. The focus is on simulating acoustic wave behavior within a 3 m-long pipeline model, incorporating various blockage characteristics. Fig. 3 illustrates a 2D schematic of the clogged air-filled pipe, presenting an inner diameter of 15 mm and an outer diameter of 21 mm, matching the dimensions of the pipe used in the experimental setup. The blockage is positioned at one end, reflecting typical conditions found in industrial applications. This numerical study aims to unravel the intricate changes in acoustic pressure characteristics induced by these blockages, encompassing features in both the time and frequency domains. These insights contribute to enhancing engineering diagnostics, offering significant implications for fault detection and condition monitoring in pipeline systems.

#### 3.1. Modeling intact and clogged pipe systems

Within the Abaqus Computer-Aided Engineering (CAE) module, a 3D numerical model was developed to simulate both the intact and clogged pipe systems. The pipe structure was modeled as a hollow cylindrical shell, while the air volume inside the pipe cavity was represented as a solid cylinder to account for acoustic wave propagation. To simulate blockages, the pipe thickness was locally increased at one end, as illustrated in Fig. 3. A series of configurations were analyzed, varying the blockage length, thickness, and position to comprehensively assess their impact on the acoustic pressure distribution within the pipe. The details of the studied cases are summarized in Table 1, providing insights into the parametric variations considered in this study.

To represent the acoustic properties of the air medium, fundamental parameters were defined, including a bulk modulus $B$ of 142 000 N/m² and a density $\rho_{air}$ of 1.225 kg/m³, yielding an acoustic velocity of 340.47 m/s ($c = \sqrt{\frac{B}{\rho_{air}}}$). For the pipe structure, steel material properties were assigned, with a density $\rho_{steel}$ = 7860 kg/m³, a Young's modulus of 190 GPa, and a Poisson's ratio of 0.3.

To model the interaction between the air medium and the pipe structure, a Tie constraint was employed in Abaqus CAE. This method ensures a rigid coupling between the acoustic and structural domains, effectively preventing relative motion at the interface. The Tie constraint was chosen for its ability to enforce a seamless transfer of acoustic pressure fluctuations from the air domain to the pipe wall, capturing both wave propagation and structural response without introducing spurious reflections or numerical instabilities.

In this implementation, the acoustic surface, representing the air domain, was designated as the main surface, while the pipe structure surface was defined as the secondary surface, ensuring proper enforcement of the constraint, as the pipe structure provides the boundary conditions for the acoustic medium. The discretization method was set to Analysis Default, and a position tolerance of 5 was applied to allow for slight geometric discrepancies while maintaining physical consistency. Additionally, the “Adjust Secondary Surface Initial Position” option was enabled to correct any initial misalignment, ensuring that the pipe and acoustic domains remained perfectly coupled throughout the simulation.
<figure><img src="image_4.png" /><figcaption>Fig. 2. Frequency spectrum comparison for different gas flow rates and leak sizes.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. 2D schematic drawing for a clogged pipe.</figcaption></figure>

## 3.2. Loading and boundary conditions configuration

Utilizing the developed model described in Section 2, a sinusoidal acoustic wave with exponential attenuation, as depicted in Fig. 1, was generated to represent the acoustic pressure emitted by the bubble. This waveform, characterized by an oscillation frequency of 161.45 Hz and a maximum amplitude of 300 Pa, served as the excitation signal applied to the air at the blocked end of the pipe. The direction of the acoustic wave propagation was guided by the pressure boundary condition $P_{in}$, as illustrated in Fig. 3. The excitation was applied continuously for a duration of 0.6 s, providing sufficient time to observe the dynamic response of the system. To ensure precise experimentation, the second end of the pipe was designated as a non-reflecting boundary, effectively mitigating any undesired echoes while maintaining the fidelity of the excitation.

In this analysis, a general dynamic implicit step was implemented for the air-filled pipe, with a time period set to 1 s longer than the excitation signal duration of 0.6 s. This adjustment was crucial for achieving convergence, given the time-dependent nature of the excitation signal.

For meshing the computational model, an acoustic 3D solid element AC3D6 (6-nodes triangular prism element) was chosen to discretize the geometry of the air within the pipe. Simultaneously, the geometry of the pipe structure was meshed using a C3D6 element type. Fig. 4 provides an overview of the meshed air-filled pipe, showcasing the discretization of the computational domain for subsequent analysis and evaluation.

## 3.3. Blockage-driven changes in acoustic pressure features

An extensive FEA was conducted to accurately model the propagation of acoustic waves in a 3-meter-long air-filled pipe, accounting for both blocked and unblocked scenarios. Response was meticulously recorded at the unblocked end of the pipe, designated as point S in Fig. 3, to capture the effects of blockages on acoustic wave dynamics. Fig. 5 presents an Abaqus visualization depicting the propagation of acoustic

<figure><img src="image_6.png" /><figcaption>Fig. 4. Mesh representation of the air-filled pipe model.</figcaption></figure>

waves within the pipe, offering a visual representation of the results and insights derived from the simulations.

To ensure the fidelity of the simulations, the time-of-flight approach was utilized, which not only measured the time taken for acoustic waves to traverse the pipe but also provided a robust means of assessing simulation accuracy by comparing computed travel times with theoretical expectations. This comprehensive analysis offers valuable insights into the intricate behavior of acoustic waves in the presence of blockages within pipeline systems.

Employing the time-of-flight methodology, case 0, representing the intact pipe, underwent meticulous analysis. The dynamic pressure amplitude at $P_{out}$ initiated from zero, marking the commencement of the time-of-flight evaluation, as visually depicted in Fig. 6. Concurrently, oscillations in the waveform indicated the propagation of acoustic pressure to the pipe's second end.

The simulated time-of-flight $ToF_s$ was determined by measuring the time difference between the initial peak of the measured wave $P_{out}$ and
<figure><img src="image_7.png" /><figcaption>Fig. 5. Abaqus visualization of acoustic wave propagation in a 3-meter-long air-filled pipe.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 6. Temporal profiles of $P_{in}$ and $P_{out}$ across cases.</figcaption></figure>

the first peak of the excitation wave $P_{in}$, resulting in $ToF_s = 10.6–1.5 = 9.1$ ms. Considering the actual speed of sound in the air $c = 340.47$ m/s and the pipe’s length $l = 3$ m, the actual time of flight $ToF_a$ was calculated as $ToF_a = l/c = 8.81$ ms.

This comparison between simulated and actual time-of-flight values allowed for the assessment of the accuracy of FEA. The FEA accuracy was computed as follows:

$$ Accuracy = \left(1 - \frac{Error\_Percent}{100}\right) \times 100 = \left(1 - \frac{|ToFa - ToFs|}{ToFa}\right) \times 100 = 96.71\% \quad (9) $$

The influence of blockages on acoustic waves was thoroughly analyzed by examining both inlet and outlet acoustic pressures, crucial for developing effective prognostic and real-world monitoring strategies for pipeline health. Throughout the analysis, the fixed $P_{in}$ functioned as the consistent excitation source across varied scenarios, enabling the identification of changes in outlet pressure resulting from alterations in clogging characteristics.

An analysis was conducted on the outlet pressure, $P_{out}$, for all studied cases, revealing notable shifts in amplitude fluctuations, as shown in Fig. 6. Additionally, detailed examination of $P_{out}$ characteristics across different cases was performed, considering metrics such as maximum and minimum values, standard deviation, $L^2$ norm, energy, RMS, kurtosis (kurt), skewness (skew), crest factor (cf), magnitude at resonant frequency ($M_r$), and other relevant parameters.

Various combinations of these characteristics were graphically represented in Fig. 7, aiming to visualize relationships between features and uncover patterns distinguishing the cases. By understanding the interactions between these features, important features can be selected for machine learning models, improving predictive accuracy and supporting data-driven decision-making. The clear separation between cases, as shown in Fig. 7, underscores the importance of all the features in the analysis.

This thorough numerical investigation reveals essential features for the detection and characterization of pipe clogging. These insights serve
<figure><img src="image_9.png" /><figcaption>Fig. 7. Combined characteristics analysis of $P_{out}$.</figcaption></figure>

as the foundation for refining prognostic and health monitoring strategies, leveraging acoustic signals generated by bubbles for improved diagnostics and proactive maintenance protocols.

## 4. Experimental studies on acoustic signal analysis for pipeline health monitoring

In this section, a case study application is introduced, featuring a test bench consisting of four pipes. The design of the experiment and subsequent analysis are informed by the numerical results and conclusions drawn from the previous sections. The available data is thoroughly described and analyzed, alongside a formal presentation of the problem.

### 4.1. Experiment description

At the Orano/LA Hague factory, specialized monitoring equipment plays a crucial role in accurately assessing liquid level and density within a designated tank, with safety being paramount. This equipment includes four metallic pipes partially submerged at different depths within the liquid, allowing for the measurement of air pressure within them to determine liquid properties. To ensure stability, the pipes are securely anchored through a 100 mm-thick concrete block and reinforced with metallic stiffeners before being welded onto the tank's upper cover. The pipes have inner and outer diameters of 15 mm and 21 mm, respectively. Fig. 8 provides a visual representation of the monitoring equipment setup.

The air emitted from the submerged pipe ends creates bubbles, generating acoustic vibrations within the pipes. Given the small diameter of the pipes and the presence of impurities in the liquid, there is a risk of partial or complete blockage at their lower ends. This obstruction compromises the accurate measurement of critical parameters, poses a significant operational hazard to the plant, and disrupts both the vibrations and the acoustic pressure. Therefore, regular monitoring of the pipes and proactive implementation of preventive measures are essential to ensure uninterrupted flow and precise readings. To facilitate prognostics and health monitoring of the pipe system, one pipe has been equipped with a microphone positioned above the concrete

<figure><img src="image_10.png" /><figcaption>Fig. 8. 2D schematic drawing for the test bench with attached microphone location.</figcaption></figure>

(highlighted in red in Fig. 8), enhancing safety measures and yielding comprehensive data on the pipe's condition.

A series of experiments were conducted, exploring various configurations such as different airflow rates, blockage shapes and thicknesses, types of liquid, liquid levels, and the number of active pipes. Fig. 9 provides a 3D schematic depicting the polymer blockages under investigation, including an oblique blockage and a circular blockage. The oblique blockage, characterized by a cylinder with one elliptical end, was positioned at the submerged end of the equipped pipe with its elliptical end facing upwards. The blockages were installed at varying
<figure><img src="image_11.png" /><figcaption>Fig. 9. 3D schematic representation of blockages and their placement within the pipes.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 10. Insights into measured bubble acoustic signals.</figcaption></figure>

<table><caption>**Table 2**
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 blockage</th><th>Blockage thickness</th><th>Clogging material</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<br/>Circular</td><td>0%</td><td rowspan="3">Polymer</td></tr><tr><td>6 l/h</td><td>50%</td></tr><tr><td>10 l/h</td><td>75%</td></tr></tbody></table>

severity in the pipe, simulating different degrees of clogging by adjusting the blockage position and extent within the 15 mm inner diameter pipe. Additional details regarding the experimental setups can be found in Table 2.

## 4.2. Data description

Analysis was conducted on a dataset collected over a 20-s period using the precise Supervised Control and Data Acquisition (SCADA) system, renowned for its accuracy (NI 9234). The data, sampled at a uniform frequency of 10240 Hz, exhibited minimal errors in both sampling frequency and synchronization, with deviations well below acceptable thresholds.

The data collection process involved capturing acoustic signals at various times throughout the day, corresponding to different experimental setup parameters outlined in Table 2. Specifically, signals were gathered at 9 o'clock, 14 o'clock, and 19 o'clock, resulting in either 3 or 6 acoustic signals per time slot and a total of 9 or 18 signals for each experimental configuration. The selection of sampling times was driven by the aim to explore temperature fluctuations across the day. An example of the signal is presented in Fig. 10.

The periodicity observed in the waveform depicted in Fig. 10 aligns with the formation of individual bubbles, each contributing a distinct

acoustic signature. Notably, the number of peaks within the waveform serves as a direct indicator of the quantity of bubbles generated over the observed timeframe.

## 4.3. Problem context and formulation

The dataset under consideration holds significant promise for the application of machine learning techniques and the evaluation of data-driven approaches since it contains identifiable distinct clogging scenarios. Its relevance extends to prognostics and health management due to its provision of diverse blockage characteristics, which serve as valuable indicators for potential identification. Moreover, leveraging this dataset ensures operational safety by preempting hazards to individuals and properties. The overarching objective is to develop a precise prognostics and health management framework capable of effectively predicting blockage incidents within the designated system, thereby enabling proactive maintenance strategies.

In formulating the prognostics and health management problem for this specific system, the focus lies on the following: given a new datapoint $d_i$ obtained from pipe $p_i$, the goal is to predict whether pipe $p_i$ is obstructed. If the prediction indicates a blockage, the subsequent step is to predict the severity of the obstruction. This formulation
<figure><img src="image_13.png" /><figcaption>Fig. 11. Proposed pipeline for prognostics and health monitoring strategy.</figcaption></figure>

aims to enable timely intervention and decision-making, enhancing the efficiency and reliability of the system's operations.

# 5. Prognostics and health monitoring with bubble acoustic signals: methodology and implementation

The proposed approach for prognostics and health monitoring is designed to predict pipe system defects and characterize them by utilizing clogging information extracted from bubble acoustic signals. This comprehensive approach encompasses two fundamental and complementary phases: training and testing, illustrated in Fig. 11.

The process typically begins with problem definition and targeted raw data collection. Following data acquisition, preprocessing and cleaning are critical to ensure the data's readiness for utilization by machine learning algorithms. Subsequently, the dataset is partitioned into training and testing sets, facilitating model development and evaluation.

## 5.1. Training phase

In this phase, the raw acoustic pressure generated from the bubbles is utilized to develop a robust machine learning model that accurately predicts the occurrence, severity, and form of pipe clogging. This process involves four essential steps: data preprocessing, feature engineering, feature selection, data labeling, and model development. Each step plays a crucial role in the overall effectiveness of the process.

### 5.1.1. Data preprocessing

The proposed strategy initiates with data preprocessing, a pivotal step influencing the accuracy and performance of ensuing ML models. Raw data often contains missing values, outliers, or errors, which can detrimentally impact model efficacy. Through the application of data preprocessing techniques, such issues can be identified and rectified, culminating in enhanced data quality.

Upon meticulous examination of the available dataset, it was discerned that no missing values or outliers were present, indicating the high quality of the acoustic pressure signals.

<table><caption>**Table 3**
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>√<span style="text-decoration: overline;">Σ(x<sub>i</sub> - μ)<sup>2</sup></span>/n</td><td>Mean</td><td><sup>1</sup>/<sub>N</sub> Σ<sub>i=1</sub><sup>N</sup> x<sub>i</sub></td></tr><tr><td>Energy</td><td>Σ<sub>i=1</sub><sup>n</sup> |x<sub>i</sub>|<sup>2</sup></td><td>L<sub>2</sub> norm</td><td>√<span style="text-decoration: overline;">Σ<sub>i=1</sub><sup>n</sup> |x<sub>i</sub>|<sup>2</sup></span></td></tr><tr><td>Kurtosis</td><td><sup>1</sup>/<sub>n</sub> Σ<sub>i=1</sub><sup>n</sup> (<span style="text-decoration: overline;">x<sub>i</sub> - μ</span><sup>2</sup>)/σ<sup>4</sup></td><td>Skewness</td><td><sup>1</sup>/<sub>n</sub> Σ<sub>i=1</sub><sup>n</sup> (<span style="text-decoration: overline;">x<sub>i</sub> - μ</span><sup>2</sup>)/σ<sup>3</sup></td></tr><tr><td>RMS</td><td>√<span style="text-decoration: overline;"><sup>1</sup>/<sub>n</sub> Σ<sub>i=1</sub><sup>n</sup> x<sub>i</sub><sup>2</sup></span></td><td>Crest factor</td><td>max(x)/√<span style="text-decoration: overline;"><sup>1</sup>/<sub>n</sub> Σ<sub>i=1</sub><sup>n</sup> x<sub>i</sub><sup>2</sup></span></td></tr><tr><td>Second maximum</td><td></td><td>Second minimum</td><td></td></tr><tr><td>M<sub>r</sub></td><td></td><td>F<sub>r</sub></td><td></td></tr><tr><td>PF<sub>2</sub></td><td></td><td>F<sub>2</sub></td><td></td></tr></tbody></table>

In this phase, the signals were divided into non-overlapping, 1-s segments, resulting in 20 parts from each signal. Fig. 12 depicts the segmentation of the acoustic signal acquired at an airflow rate of 3 l/h. The adoption of 1-s segments ensures that even at the lowest airflow rate (3 l/h), at least one acoustic pressure generated by the bubbles is captured.

### 5.1.2. Feature engineering

This step involves extracting pertinent features or patterns from preprocessed data, with the goal of constructing a feature set that accurately encapsulates crucial data characteristics for precise predictions. Machine learning programmers strive to identify and extract features crucial for addressing the specific problem. The significance of each feature lies in its contribution to categorizing the data.

Consequently, an in-depth analysis was conducted on the acoustic emissions of the bubbles (Sections 2 and 3) to discern the impact of blockages on pipe emissions, with the goal of identifying blockage-sensitive acoustic wave features. Section 2 analysis reveals that acoustic pressure emissions resulting from bubble formation are influenced by the pipe's inner diameter, leading to shifts in resonant frequency and changes in associated amplitude. Additionally, Section 3 analysis demonstrates how bubble emissions' characteristics change as they propagate within the pipe.

Drawing from these analyses, 16 features in both time and frequency domains were extracted from each one-second segment. Table 3 outlines these features and their corresponding formulas. Within this table, $M_r$ and $PF_2$ denote the magnitude at the resonant frequency and the second-highest peak in the frequency domain, while $F_r$ and $F_2$ represent their frequencies.

To ensure uniformity in feature scale and magnitude, the extracted features underwent scaling. This step is critical as certain machine learning models are particularly sensitive to feature scales, and variations in feature ranges can introduce bias into results. A commonly employed technique for this purpose is standard scaling, which adjusts features to possess a zero mean and unit variance (Feature, 2024). This process enhances model performance by mitigating the impact of differing feature scales.

### 5.1.3. Feature selection

Feature selection is a critical step in the proposed methodology, ensuring that only the most informative and relevant features are retained while reducing dimensionality. This process enhances model interpretability, optimizes computational efficiency, and improves generalization performance. Several well-established techniques exist for feature selection and dimensionality reduction, including manual selection, recursive feature elimination (Darst et al., 2018), principal component analysis (Abdi and Williams, 2010), feature importance ranking (Hussain et al., 2021), mutual information selection, independent component analysis, and high-correlation filtering, etc. Among
<figure><img src="image_14.png" /><figcaption>Fig. 12. Partitioning acoustic data into time segments.</figcaption></figure>

these techniques, Recursive Feature Elimination with Stratified Cross-Validation (RFESCV) stands out as one of the most reliable, effective, and powerful feature elimination techniques (Misra and Yadav, 2020). Consequently, it was selected as the optimal choice for this purpose.

Recursive Feature Elimination (RFE) is an iterative feature elimination method that evaluates feature importance by training a machine learning estimator and recursively removing the least important features until an optimal subset is identified. The process begins by training the model on the full set of features and computing feature importance scores. The least significant feature(s) are then removed, and the model is retrained with the reduced feature set. This elimination process is repeated until a predefined stopping criterion is met, such as achieving a specified accuracy threshold or reducing the feature set to a minimum number of attributes. The inclusion of stratified cross-validation (SCV) ensures that the evaluation remains statistically reliable across different data folds by maintaining the same proportion of classes in each training and validation split.

SVC enhances the stability of feature selection by distributing data points across multiple folds, mitigating biases that may arise from class imbalances. This ensures that feature rankings remain robust and consistent across different training subsets. Integrating SCV with RFE involves multiple iterations of training and evaluating the estimator on different folds, enhancing the robustness of the feature selection process.

To implement RFESCV, a random forest model comprising 10,000 trees was selected as the base estimator due to its robustness in handling non-linear relationships and its inherent ability to rank feature importance. A four-fold stratified cross-validation scheme was employed, ensuring that each fold maintained class distribution consistency while allowing a comprehensive evaluation of feature significance. Fig. 13 illustrates the random forest accuracy across outer folds of the stratified cross-validation process, demonstrating how the model's performance remained stable as less relevant features were eliminated. The analysis was conducted on the dataset generated from measurements at an airflow rate of 6 L/h, capturing the impact of feature selection on classification performance. The blue horizontal line represents the mean test accuracy across the four-folds, while the red vertical line indicates the standard deviation.

This analysis demonstrates that not all extracted features contribute equally to prediction accuracy. Some features exhibit negligible influence when combined with more dominant ones, highlighting the importance of systematic elimination. The RFESCV process determined that the feature set could be reduced to 15 by excluding the mean from the feature list, while still achieving 100% prediction accuracy across all outer folds. Furthermore, 99.8% ± 0.02 accuracy was attained using only three features, underscoring the efficiency of RFESCV in identifying the most impactful attributes. These results validate the necessity of feature selection in optimizing model performance, ensuring that only the most relevant features contribute to pipe clogging detection.

### 5.1.4. Data labeling

In the proposed strategy, the fourth step involves data labeling, a fundamental aspect of supervised learning. This process entails assigning descriptive labels or tags to each data instance within a dataset, essentially providing the model with ground truth for the output variable. By systematically labeling the data, machine learning models uncover patterns and correlations, enabling them to generalize insights and make accurate predictions on unseen test data. In this scenario, distinct labels were thoughtfully applied to ensure clarity and precision in analysis.

### 5.1.5. Model development

Upon completing the preprocessing of data to ensure compatibility with machine learning algorithms, the focus shifts to the crucial step of model development. This stage involves the design, training, and evaluation of both machine and deep learning models, essential for accurately predicting the condition of the pipeline system and characterizing blockages.

Depending on the characteristics of the pipeline data, a variety of machine and deep learning algorithms can be applied. Options include decision trees, support vector machines, and neural networks. Illustrated in Fig. 14, the model development step for prognostics and health monitoring of the piping system, leveraging acoustic emissions from bubbles, provides a comprehensive depiction of the process.

The reduced datasets underwent a two-stage division process. Initially, they were split into two sets: one comprising 70% of the subsets for training and inner testing, and the other containing the remaining 30% for outer testing. Here, a “subset” refers to the features and information extracted from a signal measured over a 20-s period. This division mirrors the GroupKFold technique, ensuring that each subset is exclusively present in either the training or testing set.

Subsequently, the first set underwent further division into the training set and the inner test set. The training set encompassed 70% of the data selected randomly, while the inner test set held the remaining 30%. Importantly, the class distribution was maintained at 50%–50% in both subsets, a practice known to mitigate bias in machine learning algorithms.

Afterward, six distinct multi-classifiers including decision trees, random forests, AdaBoost, extra trees, support vector machines, and neural networks, underwent training on the training set. Their performance was then evaluated on the inner test sets to identify the best-performing classifier(s) based on prediction accuracy. Finally, the selected classifier(s) underwent comprehensive evaluation on the unseen outer test set.

## 5.2. Testing phase

Following the training phase, the developed multi-classifiers progress into the testing phase, where their efficacy in predicting the
<figure><img src="image_15.png" /><figcaption>Fig. 13. RFESCV performance analysis with random forest at 6 l/h airflow rate.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 14. Model development step for proposed prognostic and health monitoring methodology.</figcaption></figure>

pipeline system's condition and characterizing blockages undergoes validation. This step involves subjecting the multi-classifiers to new unseen datasets. By encountering these unfamiliar inner and outer datasets, the models apply their learned patterns and insights to novel scenarios. This process serves as a demonstration of their capability to make accurate predictions in real-world applications.

Selecting an appropriate evaluation metric to assess the model's performance is crucial. In this context, the accuracy metric, derived from the confusion matrix, serves as a fundamental measure of the model's effectiveness. The confusion matrix provides a comprehensive summary of the model's predictions versus the actual outcomes across different classes or categories. From this matrix, the accuracy metric quantifies the proportion of correctly predicted instances relative to the total number of instances. It offers a concise yet informative assessment of the model's overall predictive accuracy, making it a valuable tool for evaluating classification models.

Fig. 15 illustrates the inner and outer testing accuracy of the multi-classifiers for experiments conducted with an airflow of 6 l/h. “Ob” denotes obliquely clogged pipes, while “Cr” indicates circularly clogged pipes, with the percentage representing the severity of clogging. Remarkably, the multi-classifiers achieved identical accuracy in both the inner and outer test sets. They successfully predicted the pipe state with 100% accuracy across both sets, except for AdaBoost. AdaBoost

misclassified 75% of obliquely clogged data as 50% obliquely clogged in both the inner and outer test sets.

The proposed strategy then underwent thorough evaluation across a spectrum of airflow rates, including 3 l/h and 10 l/h, providing detailed insights into its adaptability to various operational conditions. Impressively, the multi-classifiers exhibited outstanding effectiveness, achieving flawless prediction accuracy of 100% across all classes, even with the challenging AdaBoost classifier. This exceptional performance facilitated precise predictions of the pipe state and accurate characterization of clogging severity, enhancing the strategy's utility. These findings underscore the robustness and reliability of the proposed strategy.

## 6. Exploring model generalization through partial fit and evaluation across differing clogging levels and shapes

In a real implementation, beyond the confines of experimental settings, instances of clogging often vary in shape and severity. It is uncommon for clogs to strictly conform to circular or oblique formations. Thus, implementing an analysis that assesses the model's generalization capabilities becomes imperative.

This section undertakes an in-depth investigation into the model's generalization capabilities using partial training and testing. This
<figure><img src="image_17.png" /></figure>

(a) The inner and outer test accuracy of AdaBoost multi-classifier.

(b) The inner and outer test accuracy of other multi-classifiers.

<caption>Fig. 15. Comprehensive inner and outer testing accuracy analysis for multi-classifiers under airflow rate of 6 l/h.</caption>

<table><caption>**Table 4**
Datasets configuration for model generalization analysis.</caption><thead><tr><td>Case No.</td><td>Train set</td><td>Inner test set</td><td>Outer test set</td></tr></thead><tbody><tr><td>1</td><td>Healthy & 50% Ob</td><td>Healthy & 50% Ob</td><td>Healthy & 75% Ob</td></tr><tr><td>2</td><td>Healthy & 75% Ob</td><td>Healthy & 75% Ob</td><td>Healthy & 50% Ob</td></tr><tr><td>3</td><td>Healthy & 75% Ob</td><td>Healthy & 75% Ob</td><td>Healthy & 75% Cr</td></tr><tr><td>4</td><td>Healthy & 75% Cr</td><td>Healthy & 75% Cr</td><td>Healthy & 75% Ob</td></tr></tbody></table>

method provides valuable insights into the model's adaptability to diverse scenarios beyond its original training data. By training the model on a subset of classes and assessing its performance on a separate set, the aim is to determine its effectiveness in generalizing across a spectrum of conditions.

In this context, the partial fit and evaluation method closely aligns with the proposed approach illustrated in Fig. 11, encompassing all extracted features. Unlike the data division depicted in the model development step (Fig. 14), multiple datasets were constructed, each leveraging a distinct clogging feature. Reflecting the diversity of classes, four distinct datasets were created as illustrated in Table 4. Among these, cases 1 and 2 were dedicated to studying the model's generalization concerning clogging thickness while maintaining a fixed shape, whereas cases 3 and 4 were devised to explore the model's generalization regarding clogging shape while keeping clogging thickness constant.

In this analysis, datasets were meticulously constructed to ensure comprehensive evaluation. The training and inner test set was meticulously crafted to incorporate 70% of the baseline data alongside a full representation (100%) of a designated clogging class. Conversely, the outer test set comprised the remaining 30% of the baseline data, accompanied by 100% inclusion of a novel clogging class absent from the training set. Subsequently, the training and inner test set underwent further partitioning into two subsets: the training set, encompassing 70% of the data selected randomly, and the inner test set, comprising the remaining 30%.

The inner test set mirrored the class distribution of the training set, which facilitated the analysis of model performance. In contrast, the outer test set introduced novel scenarios, enabling an assessment of the model's ability to generalize. The primary aim was to determine whether the model could accurately predict or classify instances from

the new, previously unseen clogging class, which was absent from the training data, as instances of clogging.

Table 5 provides a comparative evaluation of model performances concerning Case 1, illustrated in Table 4. The classifiers (ClS), denoted as DT, RF, AB, ET, SVM, and NN, correspond to Decision Trees, Random Forests, AdaBoost, ExtraTrees, Support Vector Machine, and Neural Network, respectively. Furthermore, abbreviations Tr, Acc, TP, TN, FN, FP, PR, and RE signify Train, Accuracy, True Positive, True Negative, False Negative, False Positive, Precision, and Recall, respectively.

In classification contexts, TP denotes instances accurately classified as clogged pipes, whereas TN represents instances correctly identified as healthy pipes. Conversely, FP indicates instances erroneously classified as clogged pipes when they are actually healthy, while FN represents instances incorrectly labeled as healthy pipes when they are truly clogged. Precision quantifies the accuracy of positive predictions by evaluating the ratio of correctly predicted positive instances to all instances predicted as positive. In contrast, recall assesses the completeness of positive predictions by determining the ratio of correctly predicted positive instances to all actual positive instances.

The TP, TN, FN, FP, PR, and RE metrics were computed based on the outer test set. Table 5 presents the performance of the classifiers in generalizing to different clogging thickness scenarios. The models were trained on a dataset comprising healthy and 50% oblique clogged pipes and tested on both the inner set (consisting of healthy and 50% oblique clogged pipes) and the outer test set (comprising healthy and 75% oblique clogged pipes). The results reveal that all classifiers achieved a remarkable 100% prediction accuracy on the unseen inner test set, indicating robust training. With the exception of the SVM, the classifiers accurately predicted the occurrence of clogging, achieving 100% prediction accuracy on the outer test set. The SVM exhibited satisfactory performance on the outer test set, achieving an accuracy of 98.3%. Overall, the classifiers showcased outstanding performance across this classification scenario.

Tables 6, 7, and 7 depict the classifiers' performance in adapting to varying clogging thicknesses and shapes for cases 2, 3, and 4, respectively, as outlined in Table 3. Across all cases, the classifiers demonstrated flawless prediction accuracy of 100% on both the train set and the unseen inner test set, showcasing robust training. The outer test accuracy provided insights into the classifiers' ability to generalize to different clogging thicknesses and shapes. Specifically, for generalization regarding clogging thickness, RF, AB, and NN exhibited
<table><caption>**Table 5**

Classifier performance comparison for case 1, highlighting accuracy and predictive capabilities.</caption><thead><tr><th></th><th>Cls</th><th>Tr. Acc.</th><th>Inner Acc.</th><th>Outer Acc.</th><th>TP</th><th>TN</th><th>FN</th><th>FP</th><th>PR</th><th>RE</th></tr></thead><tbody><tr><td rowspan="5">Case 1</td><td>DT</td><td>100.0%</td><td>100.0%</td><td>100.0%</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</td><td>100.0%</td><td>100.0%</td><td>100.0%</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>AB</td><td>100.0%</td><td>100.0%</td><td>100.0%</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>ET</td><td>100.0%</td><td>100.0%</td><td>100.0%</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>SVM</td><td>100.0%</td><td>100.0%</td><td>97.50%</td><td>96.7%</td><td>100.0%</td><td>3.3%</td><td>0%</td><td>100.0%</td><td>96.7%</td></tr><tr><td>NN</td><td>100.0%</td><td>100.0%</td><td>100.0%</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>

<table><caption>**Table 6**

Classifier performance comparison for case 2, highlighting accuracy and predictive capabilities.</caption><thead><tr><th></th><th>Cls</th><th>Tr. Acc.</th><th>Inner Acc.</th><th>Outer Acc.</th><th>TP</th><th>TN</th><th>FN</th><th>FP</th><th>PR</th><th>RE</th></tr></thead><tbody><tr><td rowspan="5">Case 2</td><td>DT</td><td>100.0%</td><td>100.0%</td><td>96.25%</td><td>95%</td><td>100%</td><td>5%</td><td>0%</td><td>100.0%</td><td>95%</td></tr><tr><td>RF</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100%</td><td>100%</td><td>0%</td><td>0%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>AB</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100%</td><td>100%</td><td>0%</td><td>0%</td><td>100.0%</td><td>100.0%</td></tr><tr><td>ET</td><td>100.0%</td><td>100.0%</td><td>99.58%</td><td>99.44%</td><td>100%</td><td>0.56%</td><td>0%</td><td>100.0%</td><td>99.44%</td></tr><tr><td>SVM</td><td>100.0%</td><td>100.0%</td><td>25.42%</td><td>0.56%</td><td>100%</td><td>99.44%</td><td>0%</td><td>100.0%</td><td>0.56%</td></tr><tr><td>NN</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100%</td><td>100%</td><td>0%</td><td>0%</td><td>100.0%</td><td>100.0%</td></tr></tbody></table>

<table><caption>**Table 7**

Classifier performance comparison for case 3, highlighting accuracy and predictive capabilities.</caption><thead><tr><th></th><th>Cls</th><th>Tr. Acc.</th><th>Inner Acc.</th><th>Outer Acc.</th><th>TP</th><th>TN</th><th>FN</th><th>FP</th><th>PR</th><th>RE</th></tr></thead><tbody><tr><td rowspan="5">Case 3</td><td>DT</td><td>100.0%</td><td>100.0%</td><td>100.0%</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</td><td>100.0%</td><td>100.0%</td><td>100.0%</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>AB</td><td>100.0%</td><td>100.0%</td><td>100.0%</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>ET</td><td>100.0%</td><td>100.0%</td><td>100.0%</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>SVM</td><td>100.0%</td><td>100.0%</td><td>25%</td><td>0%</td><td>100.0%</td><td>100%</td><td>0%</td><td>100.0%</td><td>0%</td></tr><tr><td>NN</td><td>100.0%</td><td>100.0%</td><td>100.0%</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>

<table><caption>**Table 8**

Classifier performance comparison for case 4, highlighting accuracy and predictive capabilities.</caption><thead><tr><th></th><th>Cls</th><th>Tr. Acc.</th><th>Inner Acc.</th><th>Outer Acc.</th><th>TP</th><th>TN</th><th>FN</th><th>FP</th><th>PR</th><th>RE</th></tr></thead><tbody><tr><td rowspan="5">Case 4</td><td>DT</td><td>100.0%</td><td>100.0%</td><td>94.17%</td><td>92.2%</td><td>100%</td><td>7.8%</td><td>0%</td><td>100.0%</td><td>92.2%</td></tr><tr><td>RF</td><td>100.0%</td><td>100.0%</td><td>68.75%</td><td>58%</td><td>100.0%</td><td>42%</td><td>0%</td><td>100.0%</td><td>58%</td></tr><tr><td>AB</td><td>100.0%</td><td>100.0%</td><td>100.0%</td><td>100%</td><td>100%</td><td>0%</td><td>0%</td><td>100.0%</td><td>100%</td></tr><tr><td>ET</td><td>100.0%</td><td>100.0%</td><td>25%</td><td>0%</td><td>100.0%</td><td>100%</td><td>0%</td><td>100.0%</td><td>0%</td></tr><tr><td>SVM</td><td>100.0%</td><td>100.0%</td><td>25%</td><td>0%</td><td>100.0%</td><td>100%</td><td>0%</td><td>100.0%</td><td>0%</td></tr><tr><td>NN</td><td>100.0%</td><td>100.0%</td><td>25%</td><td>0%</td><td>100.0%</td><td>100%</td><td>0%</td><td>100.0%</td><td>0%</td></tr></tbody></table>

excellent performance, achieving 100% accuracy in outer testing. In contrast, when considering generalization concerning clogging shape, Tables 7 and 8 highlighted AB as the most adept classifier.

## 7. Conclusion

The study introduces an innovative prognostic and health-monitoring methodology tailored for pipe systems, leveraging domain knowledge to anticipate clog occurrences and their specific shapes. The proposed approach capitalizes on acoustic emissions from bubbles, strategically located far from excitation points, thereby enhancing safety measures in potentially dangerous environments.

In this research, the acoustic emissions are induced by bubbles formed during the normal operation of the pipe system under consideration. Although this specific mechanism may not be present in all pipeline systems, the study effectively demonstrated the potential of using operational vibroacoustic signals for defect detection and characterization.

Initially, the study conducted an in-depth analysis of an analytical model for underwater bubble acoustic emissions. This analysis shed light on the dynamic nature of acoustic signals and identified crucial features sensitive to clogging events. Subsequent Abaqus simulations explored the influence of pipe configurations and clog formations on acoustic emission propagation within the pipe, revealing essential insights instrumental to the proposed methodology.

Drawing upon insights from the model analysis and Abaqus simulations, the study formulated a robust prognostics and health monitoring strategy to accurately forecast pipe blockages and assess their severity. The effectiveness of this strategy was evaluated using six multi-classifiers, including decision trees, random forests, AdaBoost, extra

trees, support vector machines, and neural networks, across various experimental scenarios.

Through rigorous experimentation and analysis, the study demonstrates the remarkable efficacy of the proposed methodology in precisely predicting the onset and severity of pipe blockages. Furthermore, the model's generalization capabilities were investigated through partial fit and evaluation, revealing its adaptability to diverse scenarios involving varying clogging levels and shapes. This comprehensive examination not only validates the robustness of the approach but also underscores its potential applicability in real-world settings beyond its original training data.

### Credit authorship contribution statement

Ahmad Braydi: Writing – original draft, Software, Methodology, Conceptualization. Pascal Fossat: Visualization, Validation. Mohsen Ardabilian: Writing – review & editing, Validation, Supervision, Conceptualization. Olivier Bareille: Writing – review & editing, Validation, Supervision, Conceptualization.

### 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.

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