An Improved Convolutional Neural Network for Pipe Leakage Identification Based on Acoustic Emission

Abstract

Oil and gas pipelines are the lifelines of the energy market, but due to long-term use and environmental factors, these pipelines are prone to corrosion and leaks. Offshore oil and gas pipeline leaks, in particular, can lead to severe consequences such as platform fires and explosions. Therefore, it is crucial to accurately and swiftly identify oil and gas leaks on offshore platforms. This is of significant importance for improving early warning systems, enhancing maintenance efficiency, and reducing economic losses. Currently, the efficiency of identifying leaks in offshore platform pipelines still needs improvement. To address this, the present study first established an experimental platform to simulate pipeline leaks in a marine environment. Laboratory leakage signal data were collected, and on-site noise data were gathered from the “Liwan 3-1” offshore oil and gas platform. By integrating leakage signals with on-site noise data, this study aimed to closely mimic real-world application scenarios. Subsequently, several neural network-based leakage identification methods were applied to the integrated dataset, including a probabilistic neural network (PNN) combined with time-domain feature extraction, a Backpropagation Neural Network (BPNN) optimized with simulated annealing and particle swarm optimization, and a Long Short-Term Memory Network (LSTM) combined with Mel-Frequency Cepstral Coefficients (MFCC). Corresponding models were constructed, and the effectiveness of leak detection was validated using test sets. Additionally, this paper proposes an improved convolutional neural network (CNN) leakage detection technology named SART-1DCNN. This technology optimizes the network architecture by introducing attention mechanisms, transformer modules, residual blocks, and combining them with Dropout and optimization algorithms, which significantly enhances data recognition accuracy. It achieves a high accuracy rate of 99.44% on the dataset. This work is capable of detecting pipeline leaks with high accuracy.

1. Introduction

Marine oil and gas pipelines are critical components of the global energy supply chain, playing an essential role in the safe and efficient transportation of oil and natural gas. With the increasing global demand for energy, the significance of marine oil and gas pipelines has become increasingly prominent. However, these pipelines are often exposed to harsh marine environments, leading to gradual material degradation and corrosion over extended periods of service, making them highly susceptible to leaks [1]. Therefore, timely and effective leak detection is crucial for ensuring energy supply security, preventing environmental pollution, and avoiding economic losses. There are various pipeline leak detection techniques, including flow monitoring [2,3], pressure testing [4,5], vibration testing [6,7], visual inspection [8,9], and acoustic detection [10,11]. Current research mainly focuses on the following areas:

(1)

Leak Detection Methods Combining Models and Mechanisms

These methods primarily integrate actual operating conditions with theories such as fluid dynamics and heat transfer to analyze and locate leak points. For example, Jesús Peralta [12] explored the use of directional signal diagram processing techniques to detect and locate damage in pressurized pipelines, particularly focusing on the identification of transient patterns in faulty main pipelines. The study was based on a linearized model of the healthy part of the pipeline and a dual-port lumped model for leaks and blockages, deriving and transforming the directional signal diagrams of sound source signals under single- and dual-fault scenarios using graphical tools. Wasiu Yussuf Oseni [13] studied a first-order differential leak detection model based on the first-order differential method, using COMSOL Multi-physics for finite element simulation. The study considered the axial leak coefficient KL and incorporated turbulence kinetic energy transfer and kinetic energy rate models. By calculating the eigenvalues of velocity and pressure and observing their behavior in time diagrams across different pipeline sections, the model can assess system stability and detect leaks. Xuan Yang [14] investigated the impact of interference and environmental noise on leak detection in water pipelines. By combining experimental and numerical simulation methods and focusing on acceleration signals, the study analyzed the characteristics of leak signals under varying pressures and leak orifice sizes. Keramat [15] addressed the multi-leak localization problem in Transient-Based Leak Detection (TBLD) by introducing Metaheuristic and Gradient-Based Optimization (MGBO) techniques. Using a multidimensional nonlinear objective function, the method was optimized through two initialization algorithms for scenarios involving single, double, and triple leaks. Experimental results demonstrated that this approach performed excellently in situations with single, double, and triple leaks, particularly standing out in triple-leak localization, where more than 96% of cases had an error rate below 15%.

(2)

Methods Combining Machine Learning or Deep Learning Techniques

In recent years, with the advancement of artificial intelligence technology, the application of machine learning and deep learning in pipeline leak detection has been increasingly adopted. These methods extract complex feature patterns from historical data through training, which are then used for leak detection. Liu [16] proposed a Bayesian network model-based method for probabilistic simulation of natural gas pipeline leak orifice diameters. By constructing a Bayesian network, this method integrates prior knowledge, observational data, and uncertainty analysis to achieve precise assessment of leak orifice diameters. Wenhao Xie [17] introduced a pipeline leak detection algorithm that combines pressure and flow information with a discount factor BPA and an SVM classifier. This method utilizes wavelet packet decomposition of signals, integrates multi-sensor decision results, and ultimately enhances detection accuracy through a discount factor and D-S evidence theory. Chengsan Zhang [18] proposed a neural network model for a natural gas pipeline leak detection system named mCNN-LFLBs. The mCNN captures features from different frequency bands of the signals through multi-scale convolution kernels, while LFLB enhances the model’s ability to express local features and improves the quality of feature mining. Experimental results show that the mCNN-LFLBs model achieves a classification accuracy as high as 98.6%, with a test response time of approximately 10 ms, demonstrating excellent performance in convergence speed. Pengchao Chen [19] explored the importance of surface defect detection in long-distance oil and gas pipelines and the limitations of existing magnetic flux leakage detection methods. Using a dataset containing various simulated defects generated in a laboratory, the model was trained, and an algorithm combining YOLOv5 and Vision Transformer (ViT) was proposed to achieve accurate detection and classification of pipeline defects.

(3)

Methods Combining Various Sensors

To enhance the accuracy and reliability of leak detection, researchers have recently developed various sensor-based leak detection technologies. Jing Xie [20] proposed a pipeline leak detection technique that combines infrared thermography (IRT) with the Faster Region Convolutional Neural Network (Faster R-CNN). This method collects data through a designed pipeline network system and constructs a Faster R-CNN model based on an improved VGG16 network, achieving automated and high-precision leak detection in complex backgrounds. Xingyuan Miao [21] proposed a novel semi-supervised domain generalization leakage diagnosis method based on laser optical sensing technology and an Improved Auxiliary Classifier Generative Adversarial Network (IACGAN). This method achieves accurate diagnosis of leakage conditions in both source and unseen target domains by optimizing the network structure and loss functions, combined with a Capsule network improved via DenseBlocks. Experiments have shown that this model has an average recognition accuracy exceeding 95% in cross-domain leakage diagnosis and potential leakage risk identification, outperforming existing methods. Mingjiang Shi [22] proposed a detection and diagnosis method for internal leaks in ball valves of buried pipelines. This method first collects and denoises valve chamber pressure signals using pressure sensors, then inputs these signals into a constructed CSSOA-BP neural network for leak rate prediction and failure mode diagnosis. Experimental comparisons show that this method significantly outperforms other algorithms, such as SSA-BP and BP neural networks, in terms of prediction error and diagnostic accuracy. The maximum prediction error is reduced to 13.6%, and the diagnostic accuracy reaches as high as 83.3%.

Despite the advantages of these sensor-based methods, their practical application is often limited by operational constraints and environmental factors. Among these technologies, acoustic-based leak detection is considered one of the most effective methods due to its efficiency and accuracy. Acoustic emission (AE) technology, for instance, detects leaks by capturing the high-frequency sound waves generated by the leak. The propagation characteristics of these sound waves through the pipeline material can be used to accurately detect leaks. The AE-based method not only enables early detection of pipeline leaks but also allows for inspection without interrupting pipeline operations, significantly enhancing the practicality and efficiency of the detection process. Ozevin [23] studied the impact of aging over time and instantaneous threats on pipelines and proposed a novel two-dimensional layout pipeline network leak localization method based on AE principles. This method utilizes sensors to detect elastic waves generated by leaks and precisely identifies the leak location by calculating time differences and incorporating geometric connectivity. Mostafapour [24] proposed a method that combines wavelet analysis and modal localization theory for continuous leak source localization in gas pipelines and noisy environments using a single sensor. By denoising and reconstructing signals through wavelet decomposition, the method analyzes the modal characteristics of signals within the 0–250 kHz frequency band using wavelet packet decomposition, determines modal arrival times, and calculates group velocity to achieve high-precision leak localization. Butterfield [25] researched the use of vibration acoustic emission (VAE) signal processing technology to quantify leakage flow rates in water distribution pipelines. The study found a strong correlation between the RMS of VAE signals and leak flow rates, leading to the construction of a flow prediction model. Zahoor Ahmad [26] proposed a leak detection and localization technique for industrial fluid pipelines. This technique utilizes pipeline AE signals, combined with a multi-scale Mann–Whitney test and AE event tracking method, to achieve high-precision leak detection and localization. By applying a constant false alarm rate algorithm based on the variance index and wave propagation theory to filter out AE events related to leaks, the method reduces false alarm rates and improves localization accuracy.

Some scholars have also proposed methods combining acoustic emission signals with machine learning or deep learning techniques. Ali [27] addressed the resource scarcity and economic losses caused by the increasing non-revenue water in Water Distribution Networks (WDNs) by introducing an innovative leakage detection system. This system integrates acoustic emission components, signal processing, and machine learning (ML) techniques. It was field-tested over two years in a real-world WDN in Hong Kong, employing wireless noise loggers to collect acoustic emission signals and exploring various ML algorithms to develop detection models suitable for operational and buried WDNs. The research involved extracting acoustic signal features from both the time and frequency domains, constructing a rich feature set to support ML model training. Sajjad [28] introduced a new pipeline leakage detection technique that first transforms acoustic emission signals into acoustic images (AE images) using continuous wavelet transformation and then applies a convolutional autoencoder and a convolutional neural network; the former extracts global features, while the latter focuses on local feature extraction. These features are then merged into a single feature vector for classification via a shallow artificial neural network to determine the presence of leaks. Experimental results show that this algorithm performs excellently under various leak sizes and fluid pressures, achieving high classification accuracy. Niamat [29] proposed an innovative pipeline leakage detection and analysis method utilizing acoustic emission (AE) signal technology and time-series deep learning algorithms. The study designed an AE-based automatic detection system incorporating deep learning models such as LSTM, Bi-LSTM, and GRU, which identify the normal state of pipelines, minor leaks, moderate leaks, and severe ruptures by detecting subtle changes in AE signals. The experiments used three AE sensors to optimize sampling rates and validated the model’s performance with various evaluation metrics, with the BiLSTM model performing excellently in most cases, achieving a classification accuracy of up to 99.78%.

For the pipeline systems of offshore oil and gas platforms, monitoring methods that can detect leakage accurately and timely are crucial. Extracting pipeline leakage information precisely and efficiently from complex signals with significant noise interference has become a core technological challenge that needs to be addressed urgently. Against this research backdrop, this study first established a laboratory pipeline model in the Ocean Engineering Mechanics Laboratory at Harbin Engineering University using a Z4DSY type electric pressure self-control testing pump manufactured by Shanghai Luoji Pump Industry Co., Ltd., seamless steel pipes, PCI-2 acoustic emission detection equipment produced by American Physical Acoustics Corporation, and other experimental setups to simulate and collect leakage signals. Additionally, it gathered on-site noise data from the landmark offshore facility—the Liwan 3-1 natural gas integrated processing platform in the South China Sea. To better reflect real-world conditions, the on-site noise was merged with the laboratory leakage signals to create a dataset. Subsequently, three neural network-based leak identification methods—TDF-PNN, SA-PSO-BPNN, and MFCC-LSTM—were applied to model the dataset, and their effectiveness was validated on a test set. Furthermore, this paper introduces an improved end-to-end convolutional neural network-based leak recognition technology called SART-1DCNN. This network incorporates attention mechanisms and transformer modules, enabling it to perform adaptive feature learning directly from raw acoustic emission signals. The results from the test set show that the recognition accuracy of this method exceeds 99%, outperforming the other methods discussed in this study by providing more accurate identification of pipeline leakage signals.

2. Acoustic Emission and Pipeline Leak Research

Acoustic emission (AE) technology, as a crucial non-destructive testing method, requires the collection of AE signals generated by pipelines. In the application to offshore oil and gas pipelines, AE technology can effectively monitor minute changes and damage in the pipeline, thereby providing early warnings of potential leaks. When applying AE technology to actual marine environments, the primary challenge to be addressed is environmental noise interference. The complex and dynamic conditions of offshore platforms, coupled with high-intensity background noise, pose significant challenges to the capture and analysis of AE signals.

To thoroughly investigate and validate the effectiveness of AE technology in leak detection for oil and gas pipelines, this Section will conduct two experiments. First, a pipeline leak model will be constructed in the laboratory, where leaks will be artificially induced to collect clear AE signals of pipeline leaks. Additionally, real environmental noise signals will be collected from the actual environment of an offshore platform. By combining these two types of signals, we will simulate the AE signals produced during pipeline leaks in real-world conditions. Subsequently, these signals will be compared in both the time and frequency domains, analyzing the characteristics of the leak AE signals to provide a foundation for subsequent leak detection research.

2.1. Pipeline Leak Simulation Experiment

During the experiment, the PCI-2 acoustic emission detection equipment provided by the Beijing representative office of Physical Acoustics Corporation (PAC), located in Chaoyang District, Beijing, was utilized. This equipment is a high-sensitivity, multi-channel synchronous acquisition device with a sampling frequency that ranges from 1 kHz to 3 MHz, capable of storing acoustic emission waveform information to the hard disk at a speed of 10 million points per second. The experiment employed R15 sensors, which have a central frequency of 150 kHz. During the data acquisition phase, the PCI-2 acoustic emission detection equipment was operated and controlled through AEwin^TM software (Standard Edition). To enhance signal quality, the experiment was also equipped with preamplifiers featuring 2, 4, and 6 channels, with adjustable gain settings of 20, 40, and 60 dB, respectively.

The pipeline leakage experiment is conducted in a specially designed laboratory pipeline leakage simulation system, where natural gas is used as the fluid in the pipeline. The system includes pressure gauges, pressure pipelines, pressure pumps, and multiple control valves. The pressure pipeline adheres to the GB/T 8163-2018 [30] national standard, made of seamless steel with a wall thickness of 0.5 cm, a diameter of 10.5 cm, and an overall length of 620 cm. The system is divided into two main sections: the experimental section, which is 500 cm long and equipped with several high-pressure welded needle valves to simulate and control leaks, and the buffer section, which is 120 cm long and connected to the pressurizing device via flexible rubber tubing. The pressurizing device used is a Z4DSY-type electric pressure self-control testing pump. Figure 1 illustrates the laboratory pipeline structure model, and Figure 2 shows the composition and principle of the pipeline AE detection system.

In the constructed laboratory pipeline leak simulation system, two R15 sensors were installed at both ends of the pipeline in the experimental section, positioned 10 cm from the edge. To ensure close contact between the sensors and the pipeline surface, industrial-grade white petroleum jelly was used as a coupling medium between the sensors and the pipeline surface. The sensors were then secured with adhesive tape, and the acquisition parameters were preset and optimized in the AEwin^TM software To verify the coupling effectiveness of the sensors with the pipeline and the stability of signal transmission, as well as to confirm that the data recording equipment was functioning correctly without any storage issues, a pencil lead break (PLB) test was conducted. After confirming that all adjustments were accurate, the pipeline leak AE experiments were carried out, and multiple sets of pipeline leak AE data were collected.

2.2. On-Site Noise Collection Experiment

A noise measurement experiment was conducted on the Liwan 3-1 offshore platform in the South China Sea. As shown in Figure 3, the platform’s vertical height (jacket section) reaches 196 m. The platform’s foundation structure is designed with eight jacket legs, which are securely connected and fixed to the seabed by 16 skirt piles, with an underwater depth of 191 m. The main structure consists of three main decks, with elevations of 19, 29, and 41 m, respectively. The platform is constructed entirely of steel, with a float-over weight of 32,000 tons.

For the on-site noise measurement experiment on the site of the oil pipelines, a detailed site survey was first conducted to select representative monitoring points for testing. Subsequently, acoustic emission sensors of the same specifications and parameters were uniformly installed at predetermined locations, which were chosen to be less affected by external weather conditions, and the sensor setup was strictly aligned with laboratory standards. Next, long-term automatic sampling was initiated, and a large amount of noise signal data from 16 to 27 June 2024 was collected, which was saved for subsequent research. Figure 4 illustrates the installation of some of the AE sensors on the offshore platform pipelines.

2.3. Analysis of Noise Signal Injection in Offshore Platform Pipelines

In the laboratory pipeline leak experiment described in Section 2.1, multiple sets of pipeline leak signals were collected. Figure 5 shows the waveform of one such segment.

During the operational phase of offshore platforms, the pipeline system is subject to various disturbances due to equipment operation and the dynamic behavior of the pipelines themselves, leading to a range of noise phenomena. However, the noise levels in a laboratory environment are relatively low and do not accurately reflect the actual conditions on an offshore platform. Therefore, in this study, the measured on-site noise was integrated with the leak signals collected in the laboratory to validate the pipeline leak detection methods based on AE technology. Since both are continuous signals, the signal power [31] was used to determine the percentage of noise, with the following calculation formula:

$$\epsilon =\sqrt{{\displaystyle \frac{P_Z}{P_X}}}=\sqrt{{\displaystyle \frac{RM{S}_Z^2}{RM{S}_X^2}}}={\displaystyle \frac{RM{S}_Z}{RM{S}_X}}$$

(1)

where $P_Z$ represents the noise power, $P_X$ represents the signal power, and $RM{S}_Z$ and $RM{S}_X$ are the root mean square (RMS) values of the noise and leak signals, respectively. The leak signal $F$ with the fused noise can be obtained using the following equation:

$$F=L+{\displaystyle \frac{RM{S}_X}{\epsilon \cdot RM{S}_Z}}\cdot N$$

(2)

where $L$ is the collected leak signal, and $N$ is the measured noise signal.

A segment of the collected signals was extracted for visualization. Figure 6a shows the waveform of the noise signal measured on the platform, while Figure 6b displays the waveform after randomly selecting and injecting noise collected from different pipeline locations into the leak signal. As can be seen from the figures, the amplitude differences between the two signals are minimal. Subsequently, the spectrum and time–frequency diagrams of these signals were plotted, as shown in Figure 7 and Figure 8. In the spectrum diagrams, it is evident that both the platform-measured noise signal and the noise-infused leak signal exhibit a very prominent peak at the low-frequency end (near 0 Hz), indicating a high concentration of energy in the low-frequency range. Additionally, as the frequency increases, the power density generally decreases, meaning that the energy of the signal is mainly concentrated in the low-frequency range, with less energy in the high-frequency range. In the time–frequency diagrams, strong signal intensity can also be observed in the mid-to-low frequency range (where the red–orange regions are more concentrated), indicating that these frequency components dominate the signal.

In summary, after infusing the measured noise into the leak signal, the noise-infused leak signal closely resembles the measured noise signal. Therefore, identifying this signal solely from the time or frequency domain is challenging.

To facilitate subsequent research, the dataset was created after completing the signal data collection. First, the noise-infused segments were evenly divided into non-overlapping sections of 1024 sampling points in length, resulting in 900 samples of leak signals infused with measured noise. Additionally, from the on-site noise collection experiment described in Section 2.2., raw noise signals were collected from the offshore platform pipelines. These signals were also divided into non-overlapping sections of 1024 sampling points in length, yielding 900 noise signal samples. Finally, the two types of signal samples were combined to form the original dataset for the subsequent deep learning network training process.

3. Pipeline Leak Detection on Offshore Platforms Using Existing Neural Network Methods

Traditional methods for pipeline leak detection on offshore platforms include pressure monitoring, flow rate monitoring, gas detection, and visual inspection. However, these methods have certain limitations in practical applications. For instance, pressure and flow rate monitoring respond slowly to leaks and are easily influenced by environmental changes; although gas detection has high sensitivity, it is prone to false alarms in complex noise environments; visual inspection relies heavily on lighting conditions and the clarity of the camera equipment, presenting significant limitations. Over the past few years, with the rapid development of information technology and artificial intelligence, data-driven pipeline leakage detection methods have gradually become a research hotspot [32]. These methods identify leakage events by collecting various data during pipeline operations and applying data analysis techniques, offering advantages such as real-time detection, high accuracy, and low cost [33]. Among the many data-driven approaches, neural network-based methods have garnered significant attention due to their powerful nonlinear fitting capabilities and robustness.

This part focuses on analyzing and researching the aforementioned dataset using several neural network-based leak detection methods. These include Tan’s method, which employs time-domain features and a probabilistic neural network (PNN) for pipeline leak detection [34]; Zhou’s method, which combines simulated annealing (SA) and particle swarm optimization (PSO) with a BP Neural Network (BPNN) for leak detection [35]; and Zhang’s method, which integrates Mel-Frequency Cepstral Coefficients (MFCC) with a Long Short-Term Memory (LSTM) network for pipeline leak detection [36].

3.1. Pipeline Leak Detection Based on Time-Domain Features—Probabilistic Neural Network

Time-domain features (TDFs) directly reflect the variations in a signal over time. By monitoring the time-domain characteristics of a signal, it is possible to identify anomalies or sudden changes within the signal. In Tan’s study, the characteristics of natural gas leaks were first analyzed, and certain TDFs of methane concentration and temperature were selected as feature vectors extracted from the raw signal data. The specific features extracted are shown in

Table 1. Extracted TDFs of methane gas and their calculation formulas.

Object	Feature	Calculation Formula
Methane Concentration and Temperature	Mean	${\mu }_x={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}{x}_i$
	Standard Deviation	${\sigma }_x=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^N(x_i-{\mu }_x{)}^2}{N-1}}}$
	Square Root Amplitude	$x_r=(\sqrt{{\displaystyle \frac{{\sum }_{i=1}^N\sqrt{\left|x_i\right|}}{N}}}{)}^2$
	Root Mean Square	$X_{mis}=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}{x}_i^2}$
	Peak Value	$X_p=\mathrm{m}\mathrm{a}\mathrm{x}\left(x_i\right)$
	Impulse Factor	$I_p={\displaystyle \frac{\mathrm{m}\mathrm{a}\mathrm{x}\left|x_i\right|}{\frac{1}{N}{\sum }_{i=1}^N{x}_i}}$
	Skewness	$a={\displaystyle \frac{{\sum }_{i=1}^N(x_i-{\mu }_x{)}^3}{(N-1){\sigma }_x^3}}$
	Kurtosis	$\beta ={\displaystyle \frac{{\sum }_{i=1}^N(x_i-{\mu }_x{)}^4}{(N-1){\sigma }_x^4}}$
	Waveform Factor	$W={\displaystyle \frac{\sqrt{\frac{1}{N}\sum _{i=1}^N{x_i}^2}}{\frac{1}{N}\sum _{i=1}^N\left|x_i\right|}}$
	Crest Factor	$C={\displaystyle \frac{\mathrm{m}\mathrm{a}\mathrm{x}\left(\right|x_i)}{\sqrt{\frac{1}{N}{\sum }_{i=1}^N{x}_i^2}}}$
	Correlation Coefficient	$r={\displaystyle \frac{{\sum }_{i=1}^n(X_i-{\mu }_x)(Y_i-{\mu }_y)}{\sqrt{{\sum }_{i=1}^n(X_i-{\mu }_x{)}^2}\sqrt{{\sum }_{i=1}^n(Y_i-{\mu }_y{)}^2}}}$
Methane Concentration	Marginal Factor	$L={\displaystyle \frac{\mathrm{m}\mathrm{a}\mathrm{x}\left(\right|x_i\left|\right)}{{\left(\frac{1}{N}\sum \frac{N}{i=1}\sqrt{\left|x_i\right|}\right)}^2}}$

:

The feature vectors derived from the table above are then input into the PNN model. A PNN is a special type of feedforward neural network primarily used for classification tasks. It is based on Bayesian decision theory and kernel estimation theory, allowing it to provide a theoretically optimal solution during classification. The structure of a PNN typically consists of four layers: the input layer, the pattern layer (also known as the hidden layer), the summation layer, and the output layer [37]. The basic structure is illustrated in Figure 9.

The pattern layer, also known as the hidden layer, contains nodes where each node represents a training sample. Each neuron in the pattern layer calculates the Euclidean distance between the input vector and the training sample it represents. This distance is then processed through a radial basis function (RBF), which outputs a value indicating the similarity between the input vector and the training sample.

$$G(x)=e^{-\beta ·|x-x_i|{|}^2}$$

(3)

where $x$ is the input vector, $x_i$ is the training sample corresponding to the neuron in the pattern layer, and $\beta$ is the smoothing parameter, which determines the width of the radial basis function. In the summation layer, each neuron corresponds to a category and is responsible for summing the outputs of all pattern layer neurons that belong to the same category. The purpose of this step is to accumulate the probability scores for each category. The output layer typically contains a single neuron, which selects the category with the highest probability as the final classification result.

In this section, Tan’s method [34] is used to identify the fused data. Since the experiment only involves AE signals during pipeline operation, the correlation coefficient is excluded from the feature set. Therefore, the features extracted from the raw AE signals and used as input feature vectors for the PNN include the following: mean, standard deviation, square root amplitude, RMS, peak value, impulse factor, skewness, kurtosis, waveform factor, crest factor, and marginal factor.

To proceed with the analysis, 80% of the dataset from Section 2 (1440 samples) is used as the training set, while 20% (360 samples) is reserved as the test set. A PNN model is then defined, applying the Gaussian function to calculate the density. The density is computed as the average of the Gaussian function values based on the distance between each sample and the same-class training samples. Each test sample is classified into the category with the highest density value. Figure 10 illustrates the recognition results for 25% of the test set (90 samples).

The confusion matrix in Figure 11 illustrates the recognition results. Out of 360 test cases, the method identified 143 noise signals and misclassified 37 noisy leak signals as noise signals (false negatives). It correctly identified 163 noise signals and incorrectly classified 17 noise signals as noisy leak signals (false positives). The recognition accuracy is (143 + 163)/360 = 85%, indicating that the method performs poorly in terms of both false positives and false negatives, particularly with a higher rate of false negatives, which leads to a lower overall recognition accuracy.

3.2. Pipeline Leak Detection Based on Simulated Annealing–Particle Swarm Optimization–BP Neural Network

The simulated annealing (SA) algorithm is an optimization technique inspired by the annealing process in statistical physics. The core idea is to simulate the behavior of a material in a high-temperature state where its particles move freely, and then gradually cool it down until it reaches its lowest energy state, thus finding the global optimal solution [38].

$$T_{k+1}=\alpha \cdot T_k$$

(4)

The temperature update formula is given by Equation (4), where $T_k$ represents the temperature at the $k$-th iteration, and $\alpha$ is the cooling rate ($0<\alpha <1$). The algorithm starts at a high temperature, allowing for a large random search step. As the “temperature” gradually decreases, the step size is reduced, narrowing the search range until the global optimal solution is reached. Particle swarm optimization (PSO) is a population-based optimization algorithm that simulates the foraging behavior of bird flocks to search for the optimal solution. Each particle represents a potential solution, and the particles adjust their positions and velocities by following both their own historical best positions and the global best position of the swarm [39].

$$v_i(t+1)=w\cdot v_i\left(t\right)+c_1\cdot r_1\cdot (p_i-x_i)+c_2\cdot r_2\cdot (p_g-x_i)$$

(5)

$$x_i(t+1)=x_i\left(t\right)+v_i(t+1)$$

(6)

The speed and position update formulas are shown in Equations (5) and (6), where $v_i\left(t\right)$ represents the velocity of particle $i$ at the $t$-th iteration, $w$ is the inertia weight, and $c_1$ and $c_2$ are the cognitive and social acceleration constants, respectively. $r_1$ and $r_2$ are random numbers ($0<r_1$,$r_2<1$), $p_i$ is the historical best position of particle $i$, $p_g$ is the global best position of the swarm, and $x_i$ is the current position of particle $i$. The algorithm iteratively updates the positions and velocities of the particles, causing the swarm to gradually converge to the optimal solution.

A Backpropagation Neural Network (BPNN) is a type of multi-layer feedforward neural network that is trained using the error backpropagation algorithm.

$${\delta }^l=\left({\theta }^l\right)\prime \cdot ({\delta }^{l+1}\cdot W^{l+1})$$

(7)

The error backpropagation formula is given by Equation (7), where ${\delta }^l$ represents the error term of a layer, ${\theta }^l$ is the activation function, and $W^{l+1}$ is the weight matrix of the layer. A BPNN calculates the error between the output and the target and then backpropagates this error through the network layers. The weights and biases are updated to minimize the error. By iteratively adjusting these parameters, the network learns complex mapping relationships, enabling it to perform tasks such as classification and regression.

In Zhou’s study [35], two optimization algorithms—particle swarm optimization (PSO) and simulated annealing (SA)—are combined with the Backpropagation Neural Network (BPNN). While PSO can effectively optimize various functions, it often gets trapped in local minima during multi-objective optimization. SA, on the other hand, can escape the original state by accepting some suboptimal solutions with a certain probability, continuing the search process. During computation, these two algorithms iterate alternately, and by comparing the values of the objective function, the optimal result is obtained. The implementation steps are summarized as follows:

(1)

Initial Optimization via PSO Algorithm

(1)

Initialize particle swarm: in the PSO algorithm, each particle represents a potential solution. After initializing the particle swarm, the iteration process begins;

(2)

Update position and velocity: each particle updates its position and velocity based on its own best position and the global best position;

(3)

Fitness evaluation: evaluate the fitness of each particle, which is the loss function value of the BPNN.

(2)

Improved Optimization via SA Algorithm

(1)

Accept suboptimal solutions: in each iteration, the SA algorithm accepts suboptimal solutions based on a temperature probability, allowing it to escape local optima;

(2)

Temperature update: as the iterations proceed, the temperature gradually decreases, reducing the probability of accepting suboptimal solutions.

(3)

Collaborative Optimization

(1)

Alternate iterations: the SA and PSO algorithms alternate. The PSO phase focuses on global search, while the SA phase handles local search and escaping from local optima;

(2)

Particle update: if the SA algorithm finds a better solution, a random particle is selected and its position is updated to increase the diversity of the particle swarm;

(3)

Initial position setting: if the PSO algorithm finds a better solution, the SA algorithm uses that solution as the initial position for further search, improving search efficiency. The SA-PSO parameter optimization process is illustrated in Figure 12.

In this part, Zhou’s method is applied for modeling and predictive analysis on the dataset. The process begins with data preprocessing, including normalization and matrix formation. The dataset is then split into training, validation, and test sets in a 5:3:2 ratio. A three-layer BPNN is constructed, comprising two hidden layers with 512 and 256 neurons, respectively, followed by a Sigmoid activation function.

To optimize the parameters of the BPNN model, the PSO algorithm is initially used to simulate the movement of particles in the search space to find the optimal solution. The swarm size for PSO is set to 100, with 100 optimization iterations. Next, the SA algorithm is employed for further optimization, with an initial temperature of 100, a cooling rate of 0.9, and 100 training iterations. PSO is then used again to refine the model parameters further. Finally, the optimized model is evaluated on the test set, with the accuracy calculated and the confusion matrix plotted to visualize the classification performance.

Figure 13 shows the recognition results of this method. The method identified 143 leak signals and misclassified 37 noisy leak signals as noise signals (false positives). It correctly identified 177 noise signals and misclassified 3 noise signals as noisy leak signals (false negatives). The recognition accuracy is (143 + 177)/360 = 88.9%. Compared to the TDF-PNN method, this approach has improved the issue of false positives but still has a high rate of false negatives. This indicates that the method is better at avoiding the misclassification of noise signals as noisy leak signals but still requires improvements in accurately identifying noisy leak signals.

3.3. Pipeline Leak Detection Based on Mel-Frequency Cepstral Coefficients–Long Short-Term Memory Network

Mel-Frequency Cepstral Coefficients (MFCCs) is a feature extraction method introduced from speech recognition. MFCCs are coefficients derived from a linear transformation of the logarithmic energy spectrum based on the nonlinear Mel scale of frequency. These coefficients effectively reflect the spectral characteristics of a speech signal [40]. The steps for extracting MFCCs are as follows:

(1)

Pre-emphasis: the input sound signal is filtered to enhance high-frequency components, resulting in a smoother spectrum;

(2)

Framing and windowing: the continuous sound signal is segmented into multiple frames, with each frame containing a fixed number of samples. To reduce edge effects, each frame is multiplied by a window function;

(3)

Fast Fourier transform (FFT): a fast Fourier transform is applied to each frame to convert the time-domain signal into a frequency-domain signal, resulting in a spectrum. The FFT formula is given by Equation (8):

$$X\left[k\right]=\stackrel{N-1}{\sum _{n=0}}{x}_w\left[n\right]e^{-j{\displaystyle \frac{2\pi }{N}}kn}$$

(8)

where $X\left[k\right]$is the FFT result, N is the number of points in the FFT, $x_w$ is the input signal, and $k$ is the index of the frequency bin;

(4)

Mel-frequency filtering and summation: the spectrum is weighted and summed using a Mel-frequency filter bank, which converts the spectrum to the Mel-frequency scale. The conversion formula to the Mel-frequency scale is given by Equation (9):

$$Mel(f)=2595·{\mathrm{l}\mathrm{o}\mathrm{g}}_{10}(1+{\displaystyle \frac{f}{700}})$$

(9)

where $f$ is the linear frequency in Hertz (Hz), and $Mel\left(f\right)$ is the corresponding frequency on the Mel scale;

(5)

Discrete Cosine Transform (DCT): the output energies of the filter bank are subjected to a Discrete Cosine Transform (DCT) to generate the MFCC features. The DCT formula is given by Equation (10):

$$C_n=\stackrel{M}{\sum _{m=1}}\mathrm{l}\mathrm{o}\mathrm{g}(E_m)\mathrm{c}\mathrm{o}\mathrm{s}({\displaystyle \frac{\pi n}{M}}(m-{\displaystyle \frac{1}{2}}))$$

(10)

where $C_n$ is the $n$-th MFCC coefficient, $M$ is the number of filters in the filter bank, and $E_m$ is the energy of the $m$-th filter. The main process of MFCC extraction is shown in Figure 14.

A Long Short-Term Memory Network (LSTM) is a specialized type of Recurrent Neural Network (RNN) that effectively learns and remembers long-term dependencies in sequence data. Figure 15 depicts the internal structure of an LSTM neuron. An LSTM unit comprises three gate units: the forget gate, the input gate, and the output gate, as well as a memory cell [41]. The computation at each time step involves the following steps:

(1)

Forget gate: the forget gate decides how much of the previous time step’s cell state needs to be forgotten. The calculation for the forget gate is given by Equation (11):

$$f_t=\sigma (W_f\cdot \left[h_{t-1},x_t\right]+b_f)$$

(11)

where $f_t$ is the forget gate’s output. $\sigma$ is the Sigmoid activation function. $W_f$ is the weight matrix of the forget gate. $b_f$ is the bias term of the forget gate. $h_{t-1}$ is the hidden state from the previous time step. $x_t$ is the input at the current time step;

(2)

Input gate: the input gate determines how much of the current time step’s input needs to be remembered. The input gate’s calculation is divided into two steps: first, the part that needs to be updated is calculated using Equation (12):

$$i_t=\sigma (W_i\cdot \left[h_{t-1},x_t\right]+b_i)$$

(12)

Then, the candidate cell state is calculated using Equation (13):

$${\tilde{C}}_t=\mathrm{t}\mathrm{a}\mathrm{n}h(W_C\cdot \left[h_{t-1},x_t\right]+b_C)$$

(13)

where $i_t$ is the input gate’s output. ${\tilde{C}}_t$ is the candidate cell state. $\mathrm{t}\mathrm{a}\mathrm{n}h$ is the activation function. $W_i$ is the weight matrix for the input gate. $b_i$ is the bias term for the input gate. $W_C$ is the weight matrix for the candidate cell state. $b_C$ is the bias term for the candidate cell state;

(3)

Cell state update: the cell state is updated by combining the previous time step’s cell state and the current time step’s input information, as shown in Equation (14):

$$C_t=f_t\cdot C_{t-1}+i_t\cdot {\tilde{C}}_t$$

(14)

where $C_t$ is the current time step’s cell state, and $C_{t-1}$ is the previous time step’s cell state;

(4)

Output gate: the output gate determines how much of the current time step’s cell state should be output as the hidden state. The output gate’s calculation is given by Equation (15):

$$o_t=\sigma (W_o\cdot \left[h_{t-1},x_t\right]+b_o)$$

(15)

The hidden state at the current time step is then calculated using Equation (16):

$$h_t=o_t\cdot \mathrm{t}\mathrm{a}\mathrm{n}h\left(C_t\right)$$

(16)

where $o_t$ is the output gate’s output. $h_t$ is the hidden state at the current time step. $W_o$ is the weight matrix for the output gate. $b_o$ is the bias term for the output gate.

Zhang et al. [36] proposed a method combining MFCC and LSTM for pipeline leak detection. This method extracts MFCC features from AE signals through steps including pre-emphasis, framing, FFT, mapping and filtering, and DCT. The extracted MFCC features are then input into an LSTM network for training and testing. In this section, Zhang’s method is applied to construct an MFCC-LSTM model, which is then used for analysis and prediction.

First, for the MFCC feature extraction method, the sampling frequency is set to 1 MHz, the MFCC dimension is set to 96D as in Zhang’s paper, the FFT window size is set to 1024, and the number of Mel filters is set to 48. MFCC features are then extracted from all samples in the dataset, and the resulting feature vectors are divided into training and test sets.

As can be seen from Figure 16, the method identified 172 leak signals and misclassifying 8 noisy leak signals as noise signals (false negatives). It correctly identified 167 noise signals and misclassified 13 noise signals as noisy leak signals (false positives). The recognition accuracy is (167 + 172)/360 = 94.16%. Compared to the SA-PSO-BPNN method, this approach shows better performance in reducing false negatives, but the number of false positives has increased. Overall, the recognition accuracy has improved by about 5%.

3.4. Limitations of the above Neural Network-Based Detection Methods

For pipeline leaks, the risk of false negatives (missed leaks) is greater than that of false positives (false alarms), so more attention needs to be paid to reducing false negatives in models. Although the pipeline leak detection methods for ocean platforms have demonstrated varying degrees of effectiveness in theory and experiments, there are the following shortcomings in the analysis process and identification results of pipeline leak signals:

(1)

TDF-PNN method: the TDF method only extracts time-domain features, ignoring frequency-domain and time–frequency domain characteristics. Pipeline leak signals may manifest significant characteristics not only in the time domain but also in the frequency and time–frequency domains. Extracting only TDFs may fail to comprehensively capture all critical information of the signal. Additionally, the use of a probabilistic neural network (PNN) model, which has a relatively simple structure, might not be able to capture complex patterns and nonlinear relationships within the data, leading to low classification accuracy and a notable incidence of false negatives;

(2)

SA-PSO-BPNN method: firstly, when searching for optimal solutions in the parameter space, both simulated annealing (SA) and particle swarm optimization (PSO) algorithms have high computational complexity, resulting in longer training times. Secondly, both SA and PSO algorithms have several hyperparameters that need to be adjusted, such as initial temperature, cooling rate, swarm size, and inertia weight. These parameters significantly impact the final optimization results, yet tuning them often requires repeated experimentation, increasing the difficulty of use. Despite iterating one hundred times each, neither parameter optimization algorithm led to a significant improvement in accuracy compared to the TDF-PNN method, nor did they improve the situation with false negatives;

(3)

MFCC-LSTM method: MFCC features are primarily used in speech signal processing, and the extracted features are static. When applied to pipeline leak signals, some important frequency or time-domain information might be lost, along with the dynamic characteristics of the leak signal over time. Although there was an improvement in overall accuracy and the rate of false negatives compared to the previous two methods, there remains room for enhancement in the identification performance.

4. Leak Detection for Offshore Platform Pipelines Based on Improved End-to-End Convolutional Neural Networks

Convolutional neural networks (CNN) are a type of feedforward neural network that includes convolutional computations and has a deep structure. CNNs effectively extract and classify features from input data by mimicking the operation mechanisms of the human visual system, particularly by utilizing properties such as local receptive fields and weight sharing [42]. The early concept of this network originated from the research conducted by Hubel and Wiesel [43] on the visual cortex of cats in the 1960s, while the modern framework of CNNs was mainly proposed and refined by LeCun [44] in the early 1990s.

4.1. Convolutional Neural Network

CNNs can be categorized into one-dimensional (1D-CNN), two-dimensional (2D-CNN), and three-dimensional (3D-CNN) based on the dimensionality of the data they process. 1D-CNNs are primarily used for analyzing one-dimensional time series, 2D-CNNs are widely applied in computer vision and image processing, while 3D-CNNs are mainly used for the recognition and analysis of medical images and video data. In this paper, a 1D-CNN is employed to analyze and process the one-dimensional AE signals generated during pipeline operation.

One-Dimensional Convolutional Neural Network

The basic structure of a 1D-CNN includes an input layer, convolutional layers, pooling layers, fully connected layers, and an output layer. In a 1D-CNN, the convolutional layers are responsible for extracting temporal or sequential features from the input data. This process is carried out using one or more convolutional kernels to generate transformed feature maps. During the convolution operation, the kernel begins at one end of the input data and slides along the length of the data, computing the dot product of the kernel and the input data at each step. Assuming there is an input sequence $x$ and a convolutional kernel $k$, where the length of $x$ is $L$ and the length of $k$ is $M$, the length of the output $y$ will depend on the input length, the kernel size, and the stride $S$. The calculation for each element in the output $y$ is given by the following formula:

$$y\left[t\right]=\stackrel{M-1}{\sum _{i=0}}x\left[t·S+i\right]\cdot k\left[i\right]+b$$

(17)

where $t$ is the index of the output sequence, and b is the bias term. Commonly used pooling layers include max pooling and average pooling. Average pooling reduces the size of the feature map by calculating the average value of each small region in the input feature map. During average pooling, a window is selected, which slides over the input feature map according to the window size. The pixel values within the covered region of the window are averaged, and this average value replaces the original pixel values in the window region. Assuming the operation is performed over a region of size $n\times n$, the average pooling operation can be expressed as follows:

$$Y_{\mathrm{a}\mathrm{r}\mathrm{g}}(x)={\displaystyle \frac{1}{n^2}}\sum _{i=1}^n\sum _{j=1}^n{x}_{ij}$$

(18)

where $Y_{\mathrm{a}\mathrm{r}\mathrm{g}}\left(x\right)$ is an element in the output feature map, and $x_{ij}$ is the value at position $(i,j)$ in the input feature map. Average pooling helps the network reduce the spatial dimensions while preserving background information and less prominent features in the image, making the network more robust to small positional changes. Even if there are slight shifts in the object’s position within the image, the features extracted through average pooling can maintain consistency.

Max pooling is used to reduce the size of the feature map, decrease computational load, and provide a certain degree of translation invariance. Max pooling achieves this by selecting the maximum value within a given window. For a feature map region, the max pooling operation can be expressed as follows:

$$Y_m\left(x\right)=\mathrm{m}\mathrm{a}\mathrm{x}\left(X\right)$$

(19)

where $X$ is the set of elements in the feature map region covered by the pooling window, and $Y_m\left(x\right)$ is the maximum value extracted from $X$. The introduction of max pooling and average pooling in CNNs allows for the extraction of key features while simultaneously reducing the dimensionality of the feature map and the number of parameters. This reduction in complexity helps decrease computational load and prevents overfitting.

In a 1D-CNN, the fully connected layer plays a crucial role in integrating the features extracted by the previous layers and in performing classification or regression tasks. The fully connected layer is a form of a traditional neural network layer, where each input node is connected to every output node. This layer is typically located at the end of the network and receives the output of the previous convolutional or pooling layers, which has been flattened as input. Through the weights in the fully connected layer, the network learns how to extract useful information from the combined features to make decisions. The computation in the fully connected layer is essentially a linear transformation followed by a nonlinear activation function. The expression for the regression in the fully connected layer is as follows:

$$y\left(x^m\right)=f\left(\omega x^{m-1}+b\right)$$

(20)

where $x^{m-1}$ is the input from the previous layer to the fully connected layer, $\omega$ and $b$ represent the weights and biases of the neuron, respectively, and $f$ is the activation function, commonly ReLU, Sigmoid, or Tanh. As shown in Figure 17, the 1D-CNN uses one-dimensional convolution to extract local one-dimensional segments from the time series and performs convolution and pooling operations to extract sequence features.

4.2. Framework of the Proposed Method

Traditional fault diagnosis techniques rely on the expertise and experience of technicians and generally involve data processing and signal conversion. However, these conventional methods may suffer from issues such as low accuracy and poor robustness. In contrast, a 1D-CNN can directly perform pipeline leak detection from raw signal data. Compared to traditional methods, it not only eliminates the need for complex data preprocessing and signal transformation but also significantly improves the accuracy of fault diagnosis. Building upon the 1D-CNN framework, this paper incorporates spatial attention mechanisms, residual modules, and transformer modules. According to the characteristics of the model, the improved 1D-CNN network is named the Spatial Attention-Residual-Transformer 1D Convolutional Neural Network (SART-1DCNN).

4.2.1. Improvement Approach

(1)

Spatial Attention Mechanism

The goal of the spatial attention mechanism is to assign attention weights to different spatial positions in the input feature map based on their importance. These weights reflect the regions that the model should focus on when processing the feature map. Attention weights are usually calculated using the global information of the feature map.

Assume the input feature map is $X$ with dimensions $H\times W\times C$, where $H$ is the height, $W$ is the width, and $C$ is the number of channels. The main calculation process of the spatial attention mechanism is as follows: first, global information is extracted from the feature map through average pooling and max pooling. Then, the results of the average pooling and max pooling are concatenated to generate a two-dimensional feature map:

$$A(x,y)=\left[A_{avg}(x,y),A_{\mathrm{m}\mathrm{a}\mathrm{x}}(x,y)\right]$$

(21)

where $A_{\mathrm{m}\mathrm{a}\mathrm{x}}(x,y)$ and $A_{avg}(x,y)$ represent the results of max pooling and average pooling at position $(x,y)$, respectively; $A(x,y)$ has a size of $H\times W\times 2$, meaning that each spatial position has two channels.

Next, a convolutional layer with a kernel size of $k\times k$ is applied to the concatenated feature map, resulting in a single-channel attention map:

$$M(x,y)=\sigma (W\ast A(x,y)+b)$$

(22)

where $W$ represents the convolution kernel, $\ast$ denotes the convolution operation, $b$ is the bias term, $\sigma$ is the activation function, and $M(x,y)$ is the final spatial attention map.

Finally, the generated spatial attention map $M(x,y)$ is element-wise multiplied with the original input feature map $X$, resulting in a weighted feature map:

$$X_{out}(x,y,c)=M(x,y)\cdot X(x,y,c)$$

(23)

where $X_{out}$ is the feature map after being weighted by the spatial attention. The spatial attention mechanism enables the model to focus on important regions while suppressing less relevant parts. Introducing this mechanism is highly effective in enhancing the model’s ability to recognize target objects.

(2)

Residual Connections

Residual connections are primarily used to address the issue of vanishing or exploding gradients as the number of network layers increases. The core idea is to allow the output of one layer to be directly connected to a later layer, typically through a “shortcut connection”, making the training of deep networks more efficient. Residual connections were first proposed by Kaiming He et al. [45]. In a residual network, a basic residual block can be expressed as follows:

$$y=F(x,\{W_i\left\}\right)+x$$

(24)

where $x$ is the input to the residual block, $F(x,\{W_i\left\}\right)$ represents the mapping function passed through the weights $\left\{W_i\right\}$ in the block, and $y$ is the output of the residual block. The above equation indicates that if $x$ is already a good output, the network only needs to learn the residual part from $x$ to $y$, rather than learning the entire $y$. This approach allows for more effective gradient propagation, even as the network depth increases, because the direct path provided by the shortcut connection preserves the strength of the gradient, thereby mitigating the issue of vanishing gradients. In this study, by adding residual connections between convolutional layers, the model is able to maintain stability and efficiency in training as the depth increases. This design enables the network to learn more complex and abstract feature representations.

(3)

Transformer Module

The transformer module is based on the self-attention mechanism, which was originally proposed by Vaswani et al. in their 2017 paper [46]. The self-attention mechanism allows the model to consider all positions in the entire sequence simultaneously when calculating the representation of each position in the sequence. Specifically, for each element in the input sequence, three vectors are generated through linear transformations: the Query vector, the Key vector, and the Value vector. The calculation formulas for these vectors are as follows:

$$Q=X{W}_Q,K=X{W}_K,V=X{W}_V$$

(25)

where $X$ represents the input sequence, and $X{W}_Q,X{W}_K,X{W}_V$ are the parameter matrices used for the linear transformations. In the transformer layer, the output of the self-attention mechanism is passed through a feedforward neural network. This is a position-wise fully connected network that independently operates on each position within the sequence. The calculation formula for the feedforward neural network is as follows:

$$FFN\left(x\right)=\mathrm{m}\mathrm{a}\mathrm{x}(0,x{W}_1+b_1)W_2+b_2$$

(26)

where $W_1$ and $W_2$ are the weight matrices, $b_1$ and $b_2$ are the bias terms, and $\mathrm{m}\mathrm{a}\mathrm{x}(0,x)$ represents the ReLU activation function. To prevent gradient vanishing and accelerate training, the transformer uses residual connections and layer normalization in each sublayer.

Overall, the transformer architecture consists of an encoder and a decoder. Each layer of the encoder includes a self-attention mechanism and a feedforward network. The decoder has a similar structure to the encoder, but in addition to the self-attention mechanism, it also includes a cross-attention mechanism with the encoder’s output. This structure effectively captures long-range dependencies within sequences.

(4)

Application of Dropout and Optimization Algorithms

Dropout is a regularization technique used to prevent overfitting in neural networks, first proposed by Hinton et al. [47]. During training, Dropout randomly drops a portion of the neurons in the network (i.e., sets their output to zero). This can be represented as follows:

$$y_o=m\otimes x$$

(27)

where $x$ is the input vector to a neuron, $m$ is a randomly generated 0−1 (Obey Bernoulli distribution) vector with the same dimension as $x$, and $\otimes$ denotes element-wise multiplication. The working principle of Dropout is that during each forward pass, some neurons in the hidden layer, along with their corresponding connections, are temporarily removed from the network at random. This means that these neurons do not participate in the current forward and backward propagation calculations or in gradient updates. By doing so, the model effectively trains with different network architectures on each pass, reducing dependency on specific training samples and improving the model’s generalization ability.

In addition, the Adam optimization algorithm is used to adjust the network weights. Adam is an adaptive learning rate optimization algorithm proposed by Diederik P. Kingma and Jimmy Ba in 2014 [48]. It calculates an adaptive learning rate for each parameter, which can be expressed as follows:

$${\theta }_{t+1}={\theta }_t-{\displaystyle \frac{\eta }{\sqrt{{\widehat{v}}_t+\mathsf{ϵ}}}}{\widehat{m}}_t$$

(28)

where $\theta$ represents the parameter, $\eta$ is the learning rate, ${\widehat{m}}_t$ and ${\widehat{v}}_t$ are bias-corrected estimates of the first and second moments, respectively, and $\mathsf{ϵ}$ is a small constant added for numerical stability. These improvements work together to enhance the performance of the improved 1D-CNN model in the task of offshore platform pipeline leak detection.

4.2.2. Structure of SART-1DCNN Model

The CNN model is an 8-layer lightweight CNN framework, composed of several core components. The main structural parameters of this network are shown in

Table 2. Structural parameters of the SART-1DCNN model.

Block Name	Layer Type	Input Channels	Output Channels	Kernel Size	Stride	Padding
Convolutional Block	Conv1d	1	16	5	1	2
	BatchNorm1d	-	-	-	-	-
	ReLU	-	-	-	-	-
Attention Block	Conv1d	2	1	7	-	3
	Sigmoid	-	-	-	-	-
Residual Block	Conv1d	16	16	5	1	2
	BatchNorm1d	-	-	-	-	-
	ReLU	-	-	-	-	-
	Conv1d	16	16	5	1	2
	BatchNorm1d	-	-	-	-	-
Pool	AvgPool1d	-	-	2	2	-
Transformer Block	Dimension	Feature Dimension = 16
	Heads	Number of Attention Heads = 2
Residual Block	Conv1d	16	16	5	1	2
	BatchNorm1d	-	-	-	-	-
	ReLU	-	-	-	-	-
	Conv1d	16	16	5	1	2
	BatchNorm1d	-	-	-	-	-
Convolutional Block	Conv1d	16	16	5	1	2
	BatchNorm1d	-	-	-	-	-
	ReLU	-	-	-	-	-
Fully Connected Block	Linear	8192	1024	-	-	-
	ReLU	-	-	-	-	-
	Dropout	P = 0.4
	Linear	1024	2	-	-	-

.

First, preliminary features are extracted through a convolutional layer, followed by a spatial attention mechanism layer to enhance important features. The features then enter the first residual block for further processing and are down-sampled through an average pooling layer. Subsequently, the features pass through a transformer encoder layer to capture global dependencies within the sequence. Next, the features go through the second residual block, and after being processed by another convolutional layer, they are flattened and passed through a fully connected layer for final classification. The improved 1D-CNN structure is illustrated in Figure 18.

4.2.3. Diagnostic Process

The diagnostic process for the SART-1DCNN for offshore platform pipeline leak detection is illustrated in Figure 19. The process begins with the collection of AE signals from the pipeline to create the dataset, which is then divided into 60% training set, 20% validation set, and 20% test set. The training phase involves building the improved 1D-CNN model and tuning the model parameters until the training is completed and results are output.

The process then follows two possible directions: If the model’s accuracy meets the requirements, the model is output and saved, and the test set is used for prediction result evaluation, after which the process ends. If the accuracy is insufficient, adjustments are made, and the process is repeated.

4.3. Model Training and Prediction Results Analysis

The CNN was trained and tested using the dataset consisting of 1800 sets of data as described in Section 2. These sets of data were randomly divided, with 1080 sets used as the model training set, 360 sets as the validation set for assisting in model parameter tuning, and 360 sets as the test set.

4.3.1. Network Training

All data were input into the improved one-dimensional CNN model with a batch size of 128 and a learning rate set to 10-5. The model was trained for 100 epochs. After training, the accuracy and loss functions for both the training and validation datasets were visualized. The accuracy and loss function curves are shown in Figure 20. In the figure, the data points on the accuracy and loss curves represent the results at the 1st, 50th, and 100th epochs. It can be seen that after 100 epochs of training, the accuracy for both the training and test datasets reached over 99%.

After completing the model training and validation, the trained model was used to extract high-dimensional features from the test data. The t-SNE (t-distributed Stochastic Neighbor Embedding) algorithm was then applied to reduce the dimensionality of these high-dimensional features into a two-dimensional space, generating the t-SNE plot shown in Figure 21. In the t-SNE plot, distinct clusters of data can be observed, with clear boundaries between them. This indicates that the model performs well in feature extraction and can effectively distinguish between different categories.

Figure 22 shows the confusion matrix obtained from the predictions made by the trained model on the test set. From this confusion matrix, we can observe that the model successfully identified all noise-containing leakage signals, while misclassifying two actual noise signals as noise-containing leakage signals (false negatives). The identification accuracy is (178 + 180)/360 = 99.44%. Compared to the three methods discussed in Section 3, this method significantly reduces both false negatives and false positives, resulting in a notable improvement in accuracy.

4.3.2. Comparative Analysis

Two typical CNNs, LeNet and AlexNet, were used to analyze the AE leak data. LeNet is a classic CNN structure proposed by Yann LeCun et al. [44] in 1998, originally designed for handwritten digit recognition tasks (MNIST dataset). AlexNet, proposed by Alex Krizhevsky et al. [49] in 2012, is a CNN that achieved significant success in the ImageNet image classification competition. When applying these two CNN architectures to the leak analysis in this study, the original 2D convolutional and pooling layers in both networks were replaced with 1D convolutional and pooling layers, respectively. The frameworks of the two models are shown in Figure 23.

The batch size for training LeNet and AlexNet was set to be the same as that of the network used in this study, and the same number of training epochs was applied. A comparison was made between the three methods from Section 3 and the method presented in this Section, with the results shown in

Table 3. Performance comparison of different network models.

Network Name	Epochs	Parameters	Accuracy (%)
TDF-PNN	-	-	85.00
SA-PSO-BPNN	Simulated Annealing = 100 Particle Swarm Optimization = 100	656,385	88.90
MFCC-LSTM	100	230,658	94.16
LeNet	100	498,666	78.28
AlexNet	100	50,075,748	93.12
Improving SART-1DCNN	100	8,467,265	99.44

.

It can be seen that the accuracy obtained using the LeNet model is the lowest, likely due to the network structure being too simple to effectively learn the features of the data. The SA-PSO-BPNN method performs better than the TDF-PNN method, indicating that the use of optimization algorithms can improve the network’s recognition performance to some extent. Both the MFCC-LSTM and AlexNet methods achieve accuracy rates above 90%, but the MFCC-LSTM network has significantly fewer parameters than AlexNet and also achieves higher accuracy. Finally, the SART-1DCNN method has a number of parameters between those of LeNet and AlexNet, and it achieves an accuracy of 99.44% on the test set, higher than all other methods mentioned in this study.

5. Conclusions

This paper first designs and sets up a pipeline leakage model, formulates corresponding experimental protocols, collects pipeline leakage signals and noise signals from marine platform pipelines, and integrates the leakage signals with actual measured noise signals to simulate real-world leakage scenarios. Subsequently, several existing network-based leakage identification methods were trained and validated on the dataset, and their shortcomings were identified. Finally, it proposes an improved method based on CNN—named SART-1DCNN—and compares it with other methods. The specific conclusions are as follows:

(1)

It implements and compares three pipeline leakage identification methods: TDF-PNN, SA-PSO-BPNN, and MFCC-LSTM. Among these, the TDF-PNN method extracts time-domain features of the signal and classifies them using a probabilistic neural network (PNN), but its recognition performance is poor under noisy conditions (85.00%). The SA-PSO-BPNN method optimizes the parameters of the BP neural network via simulated annealing (SA) and particle swarm optimization (PSO) algorithms, thus enhancing recognition performance (88.90%). In contrast, the MFCC-LSTM method exhibits the best performance, achieving a recognition accuracy rate of 94.16%;

(2)

The 1D-CNN model can directly take the original acoustic emission signal as input for training and testing, effectively addressing the complexities of data preprocessing and feature extraction during the fault diagnosis of gas pipelines, achieving accurate end-to-end fault diagnosis. This paper introduces the SART-1DCNN method for processing original acoustic emission signals. This improved model combines attention modules, residual modules, and convolutional modules. After 100 training epochs, it achieves a high accuracy rate of 99.72% on the test set, demonstrating the efficiency and accuracy of this model compared to others.