A distributed optical fiber sensing technique employs a novel sensing technology that directly uses the monitoring optical cables laid in the same trench as pipelines as sensors. It fully exploits the characteristics of continuous spatial distribution in fiber, forming the integration of “transmission” and “sensing,” and enabling the acquisition of physical parameter information at any point along the fiber. It can be used for applications in the fields of various industries including petroleum, petrochemicals, electric power, transportation, and bridge construction. Compared with traditional detection technologies, this technique has the advantages of long measurement distance, continuous distributed measurement, accurate positioning, simple installation, high safety and strong scalability.

There are three types of scattered light that occur when light is transmitted within the fiber, which are Rayleigh scattering, Brillouin scattering, and Raman scattering. Based on these scattering types, the optical fiber can realize the detection of vibration, temperature and other signals. Figure 1 shows the typical architecture of a common distributed optical fiber sensing system.

The DVS system is founded on the principles of Rayleigh scattering and ϕ-OTDR (phase-sensitive optical time domain reflectometry). The optical modulator modulates the continuous light emitted by the narrow linewidth laser with strong coherence into pulsed light in this system. The pulsed light continuously generates coherent back-Rayleigh scattering light modulated by external vibration signals when propagating in the fiber. When the fiber is in a stable state, the variation law of Rayleigh scattering intensity is basically unchanged. But when a certain section of the fiber vibrates, the refractive index and length of the corresponding position will change, leading to a change in the phase of the scattered light from the point of scattering. The change of the relative phase relation of the scattered light will lead to the fluctuation of the intensity of the back-Rayleigh scattered light under the action of light interference, and the change frequency is highly related to the external vibration frequency. Therefore, the vibration information can be obtained by calculating the intensity change of the scattered light, and the optical power can be obtained by the photodetector to detect sensing signals of DVS.

The DTS system is based on the Raman scattering and ϕ-OTDR principles. The properties of Raman scattering are used to measure ambient temperature. After Raman scattering, the incident light can produce two different frequencies of light. The frequency of Stokes light is lower than incident light and its intensity is independent of temperature, while anti-Stokes light possesses a greater frequency compared to incident light and its intensity is affected by temperature. Therefore, the temperature of the region can be obtained by measuring the intensity proportion of Stokes light vs. anti-Stokes light. By using OTDR technology, different temperature change points can be located according to the time difference between the incident light and the backward Raman scattering light and the transmission rate of light in the fiber.

The Artificial Neural Network (ANN) serves as a crucial cornerstone within artificial intelligence and machine learning, mirroring the functionality of biological neural networks. To simulate the role of neurons and synapses in biological neural networks, ANN is composed of a large number of nodes, and these nodes transfer information through connections. Each connection has a weight that indicates the strength of the signal transmission. The main goal of ANN is to solve complex problems through learning and training, such as image recognition, object detection, pattern recognition, text classification and so on.

The Convolutional Neural Network (CNN), a prominent deep learning architecture, has emerged as the predominant artificial neural network for leakage monitoring applications due to its hierarchical feature extraction capability through successive convolutional, activation, pooling, and fully-connected layers (Le Cun et al., 1989; Gu et al., 2018).

The convolutional layer employs trainable kernels that convolve with input data for hierarchical feature extraction. The filters slide over the input, calculating the dot product between their weights and local areas of the input, resulting in a feature map containing different aspects of the data. The activation function typically follows each convolutional operation. By using the activation function, nonlinear operations can be introduced into the network model, so as to learn more complex features. Pooling layers perform dimensionality reduction via down-sampling while preserving salient features, thereby enhancing computational efficiency, preventing overfitting, and improving model robustness and generalization. The network architecture terminates with fully connected layers that leverage the extracted feature representations to execute final classification or regression operations.

Because CNN is able to automatically extract and learn features from inputs, this makes it well suited for applications that require high accuracy and robustness, including pipeline leak detection, where the presence or absence of leaks can be discovered by extracting features and patterns in sensor data.

While conventional deep convolutional neural networks theoretically achieve enhanced feature extraction through sequential stacking of convolutional and activation layers, practical implementations often encounter optimization challenges including gradient vanishing and explosion phenomena as network depth increases. As the networks advance to a fairly deep layers, model training becomes more difficult. The phenomenon of gradient disappearance means that during the backpropagation of gradient information, the gradient gradually becomes smaller, resulting in the weight update of the earlier layer becomes very slow, which may cause the network convergence speed to slow down, and even the training failure. To solve these problems, researchers have proposed the residual network (ResNet). Based on the original CNN, the concepts of residual block and skip connection are introduced, in which residual block is the basic building block and core architecture of ResNet. K. He believes that the core idea of the residual network is to directly transfer information from the previous layer to the subsequent layer through skip connection (He et al., 2016). Therefore, the input is added directly to the output through the proposed skip connection, so that the gradient can be propagated more easily through the network. The residual block consists of the mapping part and the residual part, and the mathematical expression is as follows:

Where, h(x_l) represents the mapping part, which is used to raise or decrease dimension, usually in the form of direct mapping or 1 × 1 convolution operation, and F(x_l, W_l) represents the residual part.

The structure of the residuals block is shown in Figure 2a. After the introduction of jump joins, the residual function can be expressed as F(x) = f(x)−x, and when F(x) = 0, an identity map f(x) = x is formed. When the neural network layer is an identity mapping, the residual function to be learned is 0, which reduces the difficulty of model learning, and the identity mapping also alleviates the problem of model degradation.

The residual architecture facilitates direct feature propagation from input to weight layer outputs through skip connections, effectively mitigating signal attenuation in deep networks. This structural design not only alleviates gradient vanishing during backpropagation—thereby preventing model degradation—but also reduces parametric complexity while enabling effective training of deep neural architectures. As illustrated in Figure 2b, conventional residual blocks employ this mechanism to achieve substantial performance improvements through optimized information flow and gradient propagation pathways.

In the actual network construction, by stacking multiple residual blocks, the network can train the deep structure more easily, thus improving the performance of the model.

To ensure model generalization and prevent overfitting, substantial training datasets are essential for machine learning algorithms. But the fiber optic system in the actual pipeline has few signals in this study. Thus, it is necessary to build an experiment platform with DTS and DVS systems on the pipeline to simulate the operating state (normal operation and leakage state) of the actual pipeline. The DTS and DVS systems are used to collect sufficient temperature and vibration signals of the pipeline under normal operation and leakage state, and fuse these two types of signals in the machine learning model, carry out feature extraction, and complete the classification and regression tasks to obtain the pipeline operation state. The experimental test bench enables controlled leakage simulations to generate extensive datasets, ensuring sufficient training samples for neural network models while minimizing statistical uncertainties.

The DTS and DVS used in this experimental platform are based on an Advantech as their mainboards. The finished product is manufactured by Herch Opto Electronic Technology Co., Ltd. This research employs dual distributed fiber optic sensing systems: a Raman scattering-based temperature monitoring system and a Rayleigh scattering-based vibration detection system, with the experimental setup illustrated in Figure 4.

The DTS system adopts the temperature calibration algorithm, the steps of which are shown in Figure 5. This algorithm can reduce the influence of light scattering and transmission loss, thereby improving the accuracy of this DTS system. The technical specifications of DVS and DTS are respectively shown in Tables 1, 2.

The experimental setup consists of a 20-meter-long steel pipeline with 60 mm diameter (Figure 6), featuring multiple artificially created leakage orifices of 2 mm and 3 mm diameters sealed by threaded fasteners along the pipe wall at varying intervals. By changing the diameter and spacing of leakage holes, the influence of pipeline leakage on the monitoring results can be reduced, and the resolution of leakage location of the model can be easily determined. The distributed temperature fiber and the vibration fiber are fixed to the pipeline through cable ties. A water pump is connected to the inlet of the pipeline, and a valve and pressure gauge are installed at the outlet. The water flow pressure in the pipe can be adjusted through the valve to the maximum of 1MPa. During the experiment, the non-leakage state of the pipeline was simulated by sealing the nut at the leak hole, and the leakage of different diameters could be simulated by unscrewing the nut of the leak hole. In addition, in order to enable the model to monitor multiple leaks, a series of experiments with two sets of leak holes were also conducted. Taking into account the temperature variation, the duration of each set of experiments was 120 s.

Although the sampling frequency of distributed fiber is 1 KHz, due to the need for filtering and preprocessing of optical fiber signals, as well as temperature calibration of optical fiber temperature signals, these operations lead to a decrease in the signal output speed of the distributed optical fiber system. Finally, during the experiment, the time length of vibration signal obtained from the distributed fiber vibration system for each sample is 800, and the time length of temperature signal read from the distributed fiber temperature system is 54.

Figure 7 shows the temperature signal and vibration signal of a sampling time point read through the distributed fiber system. The results show simultaneous temperature increase and vibration amplification at the leak location. However, since leakage is a long-time process, the introduction of time dimension enables the model to extract more characteristic quantities of leakage signals and judge the pipeline state more accurately. Interference events caused by changes in temperature and vibration signals caused by human and environmental factors can be better identified from the perspective of data samples. Figure 8 presents the distribution characteristics of different leakage holes along the pipeline length through two dimensions of amplitude and temperature. Different color layers correspond to different combinations of leakage holes (such as single-hole leakage, multiple-hole simultaneous leakage), and can be used to analyze the influence patterns of leakage on the vibration and temperature field of the pipeline. In the vibration amplitude distribution under different leakage hole conditions, the higher the peak value, the stronger the vibration caused by the leakage at that position. The temperature change triggered by the leakage will lead to an abnormal increase in local temperature. For multi-pore leakage, the range and intensity of amplitude and temperature enhancement can be increased.

As RO1 stated, this study collected a total of 3,530 sets of usable signal samples. Table 3 lists the number of signal samples and related parameters. This study collected 1,813 sets of normal operating data and 1,717 sets of leakage operation data. Under the leakage condition, two different diameters of leakage holes were set up, and each leakage hole was equipped with a mechanical nut. The mechanical nut could adjust the size of the leakage volume, and different leakage situations ranging from slight leakage to heavy leakage were collected. This enables a more comprehensive assessment of the model's identification and classification capabilities. Additionally, datasets of single-hole leakage and simultaneous multi-hole leakage were also collected. By locating the leakage holes, the positioning accuracy of the model can be further tested.

The experimental dataset was constructed by extracting all 3,530 synchronized temperature and vibration signal pairs from the distributed optical fiber system's TDMS output files, which were subsequently normalized to consistent dimensions and integrated into a unified JSON format suitable for deep neural network training. Following standard machine learning protocols, the compiled dataset underwent randomized partitioning into three distinct subsets (training, validation, and test sets) as detailed in Table 4, where the training set facilitates model parameter learning, the validation set enables hyperparameter optimization and interim performance assessment, while the held-out test set provides an unbiased evaluation of the model's generalization capability on previously unseen data. This systematic data preparation and partitioning approach ensures rigorous model development and reliable performance estimation.

In this study, the model construction is based on the Pytorch platform. Due to the temporal and spatial characteristics of fiber optic data, the ResNet model architecture consisting of two-dimensional convolution layer is used to extract the features of the data and complete the task of pipeline status identification and location.

Because the signals collected in this study include vibration signal and temperature signal, and the sampling frequency and sampling point interval between the two signals are different, the decision-level fusion is selected for the fusion level when constructing the residual block of the residual neural network, so as to analyze and monitor the two groups of signals in real time and reduce the extra computing resources as much as possible. Finally, the specific model structure is shown in Figure 9.

Numerous hyperparameters and algorithmic components are fine-tuned throughout model architecture design and training to enhance predictive performance.

Batch normalization layers can not only accelerate the training process, but also reduce overfitting by adjusting the inputs for each layer to keep the mean stays close to 0 and the variance stays close to 1.

In addition, regularization can also control model complexity to prevent overfitting. Both L1 and L2 regularization operate by incorporating parameter magnitude (either absolute values or squared terms) into the loss function as penalty terms, effectively constraining model weights to control complexity. In this study, the L2 regularization method, also known as weight decay, was chosen, and the penalty term adopted in this method is the square of the parameter, which is able to make the weight of the model gradually approach 0, as shown in Equation 2.

Where, J(θ) is the loss function with regularization, L(θ) is the original loss function, α is the regularization intensity, and w_i is the weight of the model.

The loss function plays a critical role in neural networks by measuring the discrepancy between model predictions and actual target values. Selecting an appropriate loss function significantly enhances both training effectiveness and model performance. For classification problems, cross-entropy loss is widely adopted due to its effectiveness in quantifying inter-class prediction errors and facilitating efficient parameter optimization. The cross-entropy loss is defined as follows:

Where, L(y, p) represents the cross-entropy loss, and p_i is the probability that the model prediction output belongs to category i.

The evaluation metrics of the regression model are different from those of classification tasks. Regression analysis deals with continuous numerical predictions, and traditional accuracy metrics are not applicable in this case. The standard evaluation criteria for regression performance include mean squared error (MSE), mean absolute error (MAE), and coefficient of determination (R²). In this study, MAE is adopted as the main loss function, which calculates the arithmetic mean of the absolute differences between the predicted values and the actual values. Its mathematical formula is as follows:

The choice of optimization method significantly impacts parameter adjustment efficiency and convergence speed during model training. Among various optimizers like stochastic gradient descent (SGD), RMSprop, and AdaGrad, this research employs the Adam algorithm. Adam integrates momentum-based gradient descent with RMSprop's adaptive learning rate approach, dynamically modifying individual parameter learning rates through first-order (momentum term) and second-order (RMSprop term) gradient moment estimations.

The parameter update method of Adam algorithm is as follows (Kingma and Ba, 2014; Zaheer et al., 2018):

Where, θ is the model parameter, η is the learning rate, and ϵ is a constant that usually takes the value of 1e−8.

Model optimization is achieved through iterative training. The learning process essentially minimizes the objective function through an iterative process. Training begins with parameter initialization, followed by alternating forward and backward calculation cycles. In the forward calculation process, the input data propagates through the network layers to generate prediction results. Subsequently, the backward calculation computes the gradients of the loss with respect to all parameters, enabling the adjustment of weights, gradually reducing errors and improving model performance. The complete training algorithm is as follows.

Where, a_l denotes the output of the l_th layer, ω_l refers to the weight of the l_th layer, b_l refers to the bias of the l_th layer, and g(·) is the activation function. The common activation functions are Tanh, Sigmod, and ReLu functions.

Where, m represents the number of samples, L(·) refers to the loss function, y⁽ⁱ⁾ and ŷ⁽ⁱ⁾ represents the actual label and predicted result of the i_th sample, respectively.

During model training, steps (2)–(5) are executed cyclically until either loss convergence or predefined termination conditions are satisfied. This iterative optimization process systematically improves the model's ability to learn from training data.

This study evaluated various neural network architectures, with their respective accuracies presented in Table 5. As can be seen from Table 5, when the fused signal is the dataset, the classification accuracy of ResNet is the highest. When the single-source signal is the dataset, the classification accuracy of the same model with the fused signal is slightly higher. It can be concluded that the input of the fused signal into the ResNet model is the optimal model for this study. The comparative analysis reveals that the ResNet-based fusion model achieved superior performance, reaching a peak classification accuracy of 92.16%.

Model optimization effectiveness and computational efficiency are highly dependent on the selected training algorithm. To select the most appropriate optimizer, this study compared the performance of different optimizers during the training of the same model for 100 epochs, as shown in Figure 10.

Comparative results in Table 6 demonstrate that the Adam optimizer achieves superior performance in both accuracy and computational efficiency for the ResNet fusion model among various optimization algorithms tested.

Through validation set evaluation, the fusion model's optimal architecture and parameters were determined, with results presented in Table 7.

The performance of the optimized model is illustrated in Figure 11a, which displays both classification accuracy and loss for leak type identification, while Figure 11b depicts the regression loss results. In the classification task, as the number of training rounds increases, the classification loss drops rapidly, then fluctuates slightly at a lower level, the prediction error keeps decreasing, and eventually stabilizes, indicating that the model gradually converges in the classification task. The classification accuracy rose rapidly in the early stage of training and then gradually stabilized. As the number of training rounds increases, the regression loss drops rapidly and then fluctuates within a lower range. This indicates that the model's prediction accuracy in the regression task keeps improving, gradually optimizing from the initial large deviation, and stabilizing later, suggesting that the model also converges in the regression task.

The regression loss stabilizes near 1 after sufficient training iterations. Given that MAE measures the absolute difference between predictions and true values, this result suggests a mean positioning error of 1 meter, demonstrating the model's capability for meter-level leak detection. Implementing a helical fiber arrangement could enhance this accuracy even more.

We conducted a statistical test on the classification accuracy using the McNemar test. We sorted MAE results from 5-fold cross-validation and took the 2.5% and 97.5% percentiles as the 95% confidence interval. The specific results are as follows.

Based on the experimental data and through the McNemar test, the p-value is less than 0.05, indicating a significant difference between the two models. The MAE confidence interval of Resnet is [0.9107, 0.9526], while that of 1DCNN + LSTM is [1.0024, 1.1195]. Since the intervals do not overlap, it can be directly concluded that Resnet has better performance.

The single temperature signal has low sensitivity to minor leaks and is easily affected by environmental temperature variations, leading to incorrect judgments; the single vibration signal is susceptible to pipeline operation noise and difficult to distinguish between leakage vibrations and normal operating vibrations. Moreover, both single signal methods cannot fully extract the spatiotemporal correlation features of the leakage event, resulting in low accuracy of leakage identification. As RO2 pointed out, the core of integrating temperature signals with vibration signals lies in making these signals complement each other and work together to optimize. Through feature collaboration, leakage conditions can be identified, errors in individual signals can be avoided, and the integrity of feature extraction can be fundamentally improved.

In this study, residual networks were used to extract features from the original vibration signals and temperature signals separately, effectively learning and extracting the important features of the signals. The output of the residual network can yield two types of features: classification features and regression features. The classification features are used to classify the input signals, that is, to determine whether the signal belongs to the leakage category; while the regression features are used to locate the abnormal leakage points in the input signal, that is, to find the location where the leakage occurs. Through the decision-level fusion of the model, the classification features and regression features are concatenated to form a fused feature vector. The feature vector is classified through the fully connected layer to determine the state category of the signal. The fused feature vector is regressed through the linear layer to predict the final regression value, which is used for signal positioning. Through this deep learning model, this study can achieve intelligent state classification and positioning of the input signals without manual feature selection. However, the regression task usually does not use accuracy as an evaluation metric because the regression problem is the prediction of continuous numerical values and there is no concept of “correct” or “wrong” prediction. Therefore, the metric used to evaluate the performance of the regression model in this study is the mean absolute error. The output result of the regression task is the distance from the leakage location to the starting point of the pipeline. Figure 12 is the fitting graph for pipeline leakage location, which enables a clear visualization of the data distribution and the deviation between the model prediction and the actual values. In this study, the R² value is 0.9857, indicating that the model positioning accuracy is quite good.

The above model provides a foundation for the construction of the monitoring system, enabling real-time monitoring and early warning of pipeline leaks. Moreover, by further integrating blockchain technology (Ressi et al., 2024), it can achieve automated alerts and maintenance workflows, avoiding the aggravation of pipeline corrosion, medium loss and environmental pollution caused by leakage, extending the effective lifespan of the pipeline, and also predicting potential pipeline failures (Doshmanziari et al., 2020), achieving the upgrade from “repair after failure” to “prevention before failure.” Through the closed loop of “physical entity—digital model—data interaction—decision feedback,” the full state digital mapping of the physical pipeline is realized (Grieves, 2005; Zhou et al., 2024; Huang et al., 2023).