© The Author(s), Published by EDP Sciences, 2024

1 Introduction

With the rapid development of industrialization, as an important carrier of modern chemical industry, the problems of safe production, environmental protection and resource utilization efficiency of chemical parks are increasingly prominent [1]. As the key infrastructure of material transportation, wastewater discharge and energy supply in the chemical industry park, the operation state of underground pipeline is directly related to the overall safety and production efficiency of the park [2]. However, due to the complexity of underground pipe network, involving the transportation of various media, pipeline aging, corrosion and external environmental impact, pipeline leakage incidents occur from time to time, bringing serious economic losses, environmental pollution and even safety accidents to the park [3]. Therefore, how to accurately locate the leakage point of underground pipeline in chemical industry park has become an important issue to be solved urgently [4]. As an advanced nondestructive testing technology, ultrasonic creeping wave flaw detection technology has shown great application potential in the fields of material defect detection and structural health monitoring in recent years [5]. This technology uses the reflection, refraction, scattering and other phenomena when ultrasonic waves encounter defects or interfaces when propagating in the medium. By measuring and analyzing the changes of these ultrasonic signals, the internal structural state and defect position of the inspected object can be accurately judged [6]. Ultrasonic creeping wave has the characteristics of strong propagation ability in complex structures and high sensitivity to tiny defects, and is suitable for leak detection of underground pipelines in chemical industry parks. Based on this, it is of great significance to accurately locate the leakage point of underground pipeline in chemical industry park.

In reference [7], to achieve the target location and quickly determine the target location, based on the radio frequency identification (RFID) tag, combined with AoA (Angle of Array) hologram and hash table, accurately determine the target location; Affected by the characteristics of AoA positioning technology, each positioning base station covers a small area, which leads to the need to deploy a large number of base stations when it needs to achieve high positioning accuracy, in order to increase the complexity and cost of the positioning system. In addition, this positioning technology is vulnerable to multipath effects in complex environments, resulting in jitter in the positioning results and decreased accuracy. At the same time, the data in the hash table are out of order, which means that the hash table may not be the best choice when data needs to be accessed in a specific order. In reference [8], to realize the active location of pipeline leakage, based on the propagation signal of low-frequency sound waves in the pipeline, the signal is decomposed and processed, and the signal characteristics are extracted to achieve the leakage location. However, the low-frequency acoustic signal used in this method is vulnerable to interference from environmental noise. The background noise may mask the acoustic signal generated by the leakage, leading to a decline in the positioning accuracy or even an inability to locate it. In addition, the low-frequency acoustic signal is affected by absorption, scattering, reflection, and other factors in the transmission process, leading to the attenuation of signal strength and the inability to achieve accurate positioning of the leakage point. In reference [9], in order to achieve pipeline leakage location, starting from the assumption that the leakage may be related to soil deformation, the differential interferometric synthetic aperture radar (DInSAR) method is used to identify soil deformation in non-urban areas that may be related to the leakage location. By analyzing soil satellite images, the evolution of soil is determined, and then the leakage along the pipeline is judged. However, DInSAR technology may not be sensitive to small scale and subtle leakage, and its positioning accuracy is vulnerable to the influence of factors such as the performance of the radar system and the complexity of surface deformation characteristics. In reference [10], in order to ensure the management level of pipelines and realize real-time monitoring of pipeline health status, optical fiber cables embedded in textiles are used to monitor the health status of pipelines, and a Brillouin optical time domain reflectometer (OTDR) is used to obtain the sensing signal of pipelines, measure the change of strain distribution on pipelines, and locate the location of pipeline leakage points according to the change in strain distribution; However, in the application process of this method, the monitoring effect of the Brillouin OTDR is not ideal for many small damages. Moreover, the operation of Brillouin OTDR requires certain professional knowledge and skills, and incorrect operation or parameter setting may lead to inaccurate or invalid measurement results. In reference [11], the experimental tests of pressure change and leakage location during oil pipeline leakage were carried out, and the effects of different leakage point distances, inlet pressures and leakage hole diameters on pipeline pressure were analyzed. The accuracy of leakage location is calculated. Wavelet analysis is used to denoise the experimental negative pressure wave signal, and the principle of convolution wavelet transform is used to analyze the abrupt point of pressure signal. The results show that the pressure change is inversely proportional to the distance of the leakage point, and directly proportional to the input pressure and the diameter of the leakage hole. The negative pressure wave attenuates more obviously with the distance from the leakage point. When the inlet pressure increases from 0.5 MPa to 2 MPa, the corresponding average error of leakage location decreases from 18.97% to 12.15%. Comparing the two cases where the diameter of the leakage hole is 1.5 mm and 3 mm, the average error difference of the leakage hole position in the two cases is 0.68%. However, this method needs to dig the road surface for detection, which will cause interference to the surrounding environment. In reference [12], a nonconvex sparse regularization method is proposed to detect ultrasonic defects in noise signals. In order to improve the safety of long-span bridges, prolong their service life and reduce maintenance costs, it is expected to adopt a fast and reliable method to detect the damage. In recent years, more and more attention has been paid to dynamic damage detection technology. Dynamic damage detection strategy based on energy is a new topic in this field. Based on the relationship between frequency response function and vibration mode of acceleration response, a damage detection strategy based on acceleration response energy is proposed. Using this strategy and the traditional mode curvature strategy, a long-span cable-stayed bridge is numerically analyzed. In addition, the damage quantitative analysis and robustness analysis of noise pollution are also carried out. The analysis results show that the damage detection strategy based on acceleration response energy not only has accurate damage location ability, but also has good damage quantification ability and noise pollution resistance. However, this method can not adapt to the complexity and diversity of modern pipeline system, and it can not accurately detect the leakage of pipelines with new materials and new structures.

Ultrasonic creeping wave flaw detection technology using ultrasonic propagation characteristics in a pipeline wall can detect small leaks. Owing to the high sensitivity of ultrasound to material defects, it can accurately identify small cracks, corrosion, and other defects on the pipeline wall surface, thereby realizing the precise positioning of the leakage point. Data integration involves a variety of inspection data (such as ultrasonic creep wave flaw detection data, pressure data, flow data, etc.) for clustering and analysis, to obtain a complete data model, to help engineers better understand the pipeline operating conditions and identify potential leakage risks. Therefore, in order to realize the accurate positioning of leakage points of underground pipelines in chemical parks, an accurate positioning method of leakage points of underground pipelines in chemical parks based on ultrasonic creep wave detection and data integration is proposed. The innovations of this method are as follows:

1. Using the ultrasonic creeping wave flaw detector to detect the underground pipeline in the chemical industry park, and obtain the status signal of the underground pipeline in the chemical industry park.

2. Using the improved K-means algorithm to fuse the collected signals to obtain abnormal signals.

3. The ultrasonic abnormal signals obtained by clustering are processed by wavelet transform, and the local time energy density characteristics of frequency bands are extracted, and the images are superimposed.

4. By introducing the image enhancement factor, the leakage area can be located centrally, and the coordinates of pipeline leakage points can be determined, and the leakage degree can be determined by calculating the sum of the damage probabilities of each leakage point.

2 Precise localization of leakage points of underground pipelines in chemical parks

2.1 Detection of underground pipelines in chemical parks based on ultrasonic creep wave flaw detection

2.1.1 Principles of ultrasonic crawl wave flaw detection

Ultrasonic creeping wave flaw detection is a technology that utilizes ultrasound for the non-destructive inspection of materials or mechanical components to identify internal defects and scars. To reliably pinpoint the leakage location in underground pipelines within chemical parks, the use of an ultrasonic creeping wave flaw detector is essential. The principle behind this method is that as ultrasound propagates through the material being inspected [13], changes in the acoustic properties and internal structure of the material will have a definite effect on the ultrasound propagation. By detecting the degree and condition of the influence of ultrasound, one can comprehend the material properties and structural alterations.

During the detection process, when the ultrasonic longitudinal wave travels from the first medium (plexiglass) towards the second medium (underground pipe) at an angle close to the first critical angle (27.6° ± 3°), not only does the surface longitudinal wave exist within the underground pipe material, but a diagonal transverse wave is also present. Typically, the wavefront of a transverse wave is referred to as the head wave. The wave that propagates along the surface of the medium at a certain distance between the peak of the transverse wave and the surface longitudinal wave is called a creeping wave. The distribution of the ultrasonic creeping waves is illustrated in Figure 1.

Figure 1 Distribution status of ultrasonic creeping waves.

In Figure 1, the dotted line represents the creeping wavefront. The creeping wave is not susceptible to surface conditions because its propagation is minimally affected by scratches, corrosion depressions, oil droplets, and other surface states [14]. This makes it advantageous for detecting surface and near-surface damage, contributing to improved accuracy of injury discernment. To address the issues encountered in conventional ultrasonic flaw detection processes, a curved surface creeping wave probe has been designed, considering the structure of the head-waist and waist-bottom arc areas and the characteristics of damage in underground pipelines. The arc-crawler probe employs a dual-chip format, with one chip for sending and another for receiving, effectively minimizing the detection of blind spots. The contact surface is curved, accommodating the curvature of the head-waist and waist-bottom arcs to ensure optimal coupling for flaw detection. Different frequencies are utilized, and the optimal echo frequency is determined through experimentation, ensuring that both the detection sensitivity and signal-to-noise ratio are maintained.

2.1.2 Signal acquisition of underground pipes in chemical parks

When the gas pipeline leaks, sound waves of a certain frequency are generated at the leakage hole owing to the pressure difference between the inside and outside of the pipeline. The acoustic frequency generated at the leakage hole is generally between 10 and 100 kHz, and the energy is mainly distributed between 10 and 50 kHz. Because the energy difference between the 40 kHz ultrasonic and ambient noise is the largest, we choose a 40 kHz ultrasonic signal as the detection signal [15].

Owing to the difference between the acoustic properties of the material and its defects, the ultrasonic wave propagation and reflection waveforms and the energy of penetration are different. Therefore, the ultrasonic method can be used to detect underground pipes. Based on the ultrasonic wave propagation in the waveguide, the waveguide boundary on the ultrasonic propagation of ultrasound is the basis for obtaining and analyzing the ultrasonic echo signal under the influence, and then detecting a variety of underground pipe states, including pipe bursts, pipe corrosions, and pipe damage and defects, etc.

After the ultrasound transmitter transmits the ultrasound signal [16], the signal is divided into two parts: one part of the signal for the reflection signal, the reflection occurs at the interface between the reference medium and the measurement chamber, and the reflected signal is received by the reflection receiver; the other part of the signal for the propagation of the signal, received by the propagation of the receiver, the signal propagation is accomplished by the interface between the reference medium and the measurement chamber; and, in the propagation of the receiver, the received signal is reflected again and transmitted back to the reflection receiver. Based on this, the formula for the acquired signal x(t) of the state of the underground pipe is:

$$x\left(t\right)=A\sin (\omega t+\phi )$$(1)

where: A denotes the acquired signal amplitude of the defective signal of the underground pipeline, where φ indicates the ultrasonic phase.

The acquired underground pipeline status signal shall meet the Dirichlet condition, therefore, the x(t) computational procedure can be converted to:

$$x\left(t\right)={\vartheta }_0\sin \left(\omega t\right)+{\vartheta }_1\cos \left(\omega t\right)$$(2)

Expanding equation (5) yields:

$$x\left(t\right)=A\cos \left(\phi \right)A\sin \left(\omega t\right)+A\sin \left(\phi \right)A\cos \left(\omega t\right)$$(3)

where: ϑ₀ = Acos(φ); ϑ₀ = Asin(φ).

Based on this, the ultrasonic phase φ and amplitude A can be obtained. The formulas for both are:

$$\phi =\arctan \left(\frac{{\vartheta }_1}{{\vartheta }_0}\right)+\left[1-\mathrm{sgn}\left({\vartheta }_0\right)\right]\frac{\pi }{2}$$(4)

$$A=\sqrt{{\vartheta }_0^2+{\vartheta }_1^2}.$$(5)

Based on the above steps can complete the acquisition of the chemical park underground pipeline status signaling x(t) = [x₁(t), x₂(t), …, x_n(t)], and the signal is used in leakage localization.

2.2 Underground pipeline status signal fusion method based on improved K-means clustering algorithm

Based on the state signals of the underground pipelines in the chemical park obtained from the above vignettes, the x(t) exists a certain time series, and x(t) contains the data of different pipeline positions [17]. Therefore, in order to ensure the accurate location of underground pipeline leakage points in the chemical industry park, the improved K-means algorithm is used to complete the clustering of x(t), obtain the anomalous signals in the signal.

The improved K-means algorithm is based on the K-means algorithm. To optimize the clustering performance of the algorithm, the location of its cluster center is optimized through the quantum particle swarm optimization algorithm to reduce the impact of the initial cluster center, reduce the possibility of falling into the local optimal solution, and improve the clustering performance. If the scale of x(t) is n, each signal has p characteristic attributes, the number of clusters is k, and the cluster center is c_j(j = 1, 2, …, k), and N particles are generated. The position of each particle is composed of k cluster centers. The position coding structure $B_i^x$ of the underground pipeline state signal x(t) in the chemical industry park is:

$$B_i^x=[{\overline{x}}_{c_1}, {\overline{x}}_{c_2},\dots ,{\overline{x}}_{c_k}]$$(6)

where: ${\overline{x}}_{c_j}$ is the cluster center of the underground pipeline state signal in class j chemical industry park, is a p dimensional vectors.

The formula for velocity coding structure $B_i^v$ is:

$$B_i^v=\left[v_1, v_2,\dots ,v_k\right].$$(6)

The fitness of each particle is a real number, fitness is denoted by φ, the relevant formula is:

$$\{\begin{array}{c}\phi =\mathcal{l}{\sigma }^2\\ {\sigma }^2=\sum _{j=1}^k\sum _{o\in C_j}^{}\Vert x-{\overline{x}}_{c_j}\Vert \end{array}$$(8)

where: ℓ denotes a normal number. C_j indicates the j class; and σ² denotes the sum of squared errors.

The objective of the improved quantum particle swarm clustering algorithm in this study is to search for the global optimal position, i.e., the clustering center, which minimizes the adaptation of particles. When the global optimal solution (clustering center) is determined, the clustering is determined by the nearest-neighbor rule, i.e., each chemical park underground pipeline state signal is preferentially divided into the nearest class [18], and the state signal of the underground pipeline in the chemical park and the clustering centroid satisfy equation (9):

$$\Vert x-{\overline{x}}_{c_j}\Vert =\underset{j=\mathrm{1,2},\dots ,k}{\min }\Vert x-{\overline{x}}_{c_j}\Vert .$$(9)

The K-means clustering center can be determined according to the above steps. According to the clustering principle of the K-means algorithm, using quantum particle swarm optimization to optimize the clustering center, the clustering division under different clustering numbers can be obtained. The quantum particle swarm optimization algorithm is not interfered with by the initial solution, and has a strong global search ability and fast convergence speed. A clustering center that makes the clustering objective function as small as possible can be obtained in the entire search space, which can effectively avoid the dependence of the K-means clustering algorithm on the initial center and improve the clustering accuracy of the algorithm [19]. Each particle represents a state signal of the underground pipeline in the chemical industrial park, as described in Section 2.1. The algorithm uses the global optimal location (i.e., the cluster center) as the K-means cluster. When clustering the signal set, it is divided according to the principle that the Euclidean distance between the sample and the cluster center is the nearest. The detailed steps of underground pipeline defect signal clustering based on the improved K-means clustering algorithm are as follows:

• Step 1: Input parameters. The number of x(t)n, sample characterization dimensions p, number of clusters k.

• Step 2: Initialize the particle swarm: Randomly select k clustering center of underground pipeline state signals in a chemical park used as the initial position of a particle, and the process is repeated N times, generating a total of N particles; calculating the initial particle encoding, containing the population size N, dimensions D, maximum number of iterations T_max, maximum positional boundaries X_max, the minimum positional boundary X_min, parameters such as random positions of all particles in D dimensional space.

• Step 3: The average value of the individual optimal positions of all particles and local attractors is calculated, and the population contraction-expansion factor and random variables are designed. The average value of the individual optimal position represents the average value of the clustering center of the optimized underground pipe condition signal in the industrial park found by the particles in previous iterations, which can help the algorithm to understand the distribution of the better solution in the search space and be used to guide the particles to move to the next step. The local attractor indicates the tendency of particles to converge to their historical optimal clustering centers of underground pipeline status signals in industrial parks and the global optimal clustering centers, which are used to balance the ability of global search and local fine search to find the optimal clustering centers in the complex search space more efficiently. A population contraction-expansion factor is used to determine the step size and search range of particles moving towards the optimal clustering center in each iteration.

• Step 4: In D dimensional space, calculate the particle x_i for the current fitness f(x_i), which is used to evaluate the degree of superiority of each particle location (clustering center).

• Step 5: Update the individual optimum and global optimum, compare the current particle fitness f(x_i) with the particle’s individual optimal fitness f(p_i), population-optimal fitness $\tilde{f}\left(pi\right)$, and update the individual and group optimal positions, i.e., the local optimal clustering centers and the global optimal clustering centers of the underground pipeline state signals in the chemical park.

• Step 6: Update the positions of all the particles and perform boundary variation processing. When dealing with complex and variable underground pipe state signals, boundary variation processing can cause the particles to jump out of the current search area and explore a wider search space, which is crucial to prevent the algorithm from falling into the local optimal solution.

• Step 7: Check whether to meet the end conditions: If the exit conditions cannot be met (not reached the maximum number of iterations), then return to step 3 for the next iteration; otherwise, go to step 8, the output of the global optimal fitness and the global optimal position (the final clustering center).

• Step 8: Find out the clustering results: for each chemical park underground pipeline state signal, calculate the distance to the final clustering center, according to the nearest-neighbor rule to determine the clustering division of the state signal, and finally assign all chemical park underground pipeline state signals to k clustering centers, complete the clustering of underground pipeline signals in industrial parks, obtain the anomalous signals therein [20], and output the clustering results $\widehat{x}\left(t\right)$.

2.3 Accurate localization of underground pipeline leakage points in chemical parks based on wavelet transform

According to the clustering results of the underground pipeline signals in the chemical park obtained from the summary of Section 2.2, to locate the leakage points of the underground pipelines in the chemical park, the wavelet transform was used to transform the underground pipe ultrasonic anomalous signal of the cluster into a function of f(a, b) about the scale parameters a and the time parameters b, which is calculated by the following formula:

$$f\left(a,b\right)=\frac{1}{\sqrt{a}}{\int }_{-\infty }^{+\infty }\widehat{x}\left(t\right){\psi }^{*}\left(\frac{t-b}{a}\right)\mathrm{d}t$$(10)

where: ψ(t) denotes the wavelet basis function, the ψ^*(t) represents the complex conjugate of ψ(t).

According to the isometric property of wavelet transform, i.e., ultrasonic anomaly signal of underground pipeline $\widehat{x}\left(t\right)$ of the wavelet transform is energy-conserving, then:

$${\int }_{-\infty }^{+\infty }{\left|\widehat{x}\left(t\right)\right|}^2\mathrm{d}t=\frac{1}{{\xi }_{\psi }}{\int }_{-\infty }^{+\infty }\frac{1}{a^2}{d}_a{\int }_{-\infty }^{+\infty }{\left|f\left(a,b\right)\right|}^2{d}_b$$(11)

where: ξ_ψ denotes the wavelet function tolerance condition; the scale interval d_a indicates the energy of the time interval d_b.

Equation (11) is transformed to form:

$${\int }_{-\infty }^{+\infty }{\left|\widehat{x}\left(t\right)\right|}^2\mathrm{d}t={\int }_{-\infty }^{+\infty }E\left(b\right)d_b$$(12)

$$E\left(b\right)=\frac{1}{{\xi }_{\psi }}{\int }_{-\infty }^{+\infty }\frac{{\left|f(a,b)\right|}^2}{a^2}{d}_a$$(13)

where: E(b) indicates the energy value for the ultrasonic anomaly signal of the underground pipeline at the moment b, expressed as a function of time-energy density, reflects the distribution of the time-dependent energy parameters b of all frequencies of the ultrasonic anomaly signal of the underground pipeline. In order to overcome the disadvantages of strong attenuation of sound waves by soil, a series of comprehensive strategies are needed.

1. Select appropriate sound wave frequency: Because the attenuation of low-frequency sound wave in soil is relatively small, low-frequency ultrasonic wave is given priority for flaw detection to ensure that sound wave can penetrate the soil and effectively spread to the target pipeline area.

2. Optimizing the transmitting and receiving technology of ultrasonic wave is also very important: by enhancing the power of ultrasonic wave transmitter, the energy of acoustic wave signal can be increased, so that it can overcome soil attenuation and reach a longer distance.

3. In data processing, noise interference can be removed by signal amplification and filtering technology, and the signal-to-noise ratio of the signal can be improved, so that the signal at the leakage point can be more prominent.

Based on equation (13) to obtain the time interval in which of [a₁, a₂], the local time-energy density function is expressed as follows:

$$E_1\left(b\right)=\frac{1}{{\xi }_{\psi }}{\int }_{a_2}^{a_1}\frac{{\left|f(a,b)\right|}^2}{a^2}{d}_a$$(14)

where: E₁(b) indicates that in the time interval [a₁, a₂], the local time-energy density function. By changing the upper and lower limits, the distribution of the energy of the signal over time in different frequency ranges can be obtained.

Gabor wavelet basis function is used to transform the signal without leakage of underground pipeline in the chemical industry park, extract the local time-energy density characteristics of the frequency band, compare the signal difference before and after leakage, and define the damage index ψ_D in time-frequency domain, which is calculated by the following formula:

$${\psi }_D=\left|\frac{{\int }_{b_1}^{b_2}{E}_{1x^{″}\left(t\right)}\left(b\right)d_b}{{\int }_{b_1}^{b_2}{E}_{1x^{\text{'}}\left(t\right)}\left(b\right)d_{\mathit{b}}}\right|$$(15)

where: x′(t) indicates the reference signal in the no-leakage condition. x″(t) indicates the detection signal in the state with leakage. The larger the leakage ψ_D, the closer the leakage is to the sensing path, and vice versa.

According to the damage imaging algorithm requirements to divide the detection area into a collection of points, and superimposed imaging. Ultrasound in the propagation path of the energy distribution has a certain width, the propagation path of the damage index ψ_D, mapped to each point of the underground pipeline inspection area in the chemical park through a distribution function. The formula for the spatial distribution function R(x, y) of the damage index ψ_D is:

$$R(x,y)=\{\begin{array}{cc}\frac{1}{L_k},& 1\le L_k\le D\\ 0,& L_k>D\end{array}$$(16)

$$L_K=\frac{L_a+L_s}{L_{\mathrm{as}}}=\frac{\sqrt{{\left(x_a-x_k\right)}^2+{\left(y_a-y_k\right)}^2}+\sqrt{{\left(x_t-x_k\right)}^2+{\left(y_t-y_k\right)}^2}}{\sqrt{{\left(x_a-x_t\right)}^2+{\left(y_a-y_t\right)}^2}}$$(17)

where: L_a denotes the distance from the imaging point to the generator. L_s denotes the distance from the imaging point to the receiver, the L_as denotes the distance from the generator to the receiver. (x_a, y_a) denotes the coordinates of the ultrasonic emission. (x_i, y_i) indicates the receiving coordinates, i.e., the coordinates of any point in the detection area of the underground pipeline in the chemical park. L_k denotes the ratio of the sum of the distances from any point in the detection region to the excitation and receiver to the distance of the propagation path, the D is a parameter indicating the size of the area affected by the ultrasonic energy. The smaller D, The ultrasound signal is affected in the smaller area. The probabilistic damage imaging algorithm describes the relationship between any point in the detection region and the propagation path position using equation (17), with, the sum of L_a and L_s takes different values, the affected area will be distributed in an ellipse, and the focus of the ellipse will be the generator and the receiver.

When L_k = 1, the imaging point lies on the propagation path; when L_k = 0, the imaging point is located at the edge of the ellipse. When the sum of L_a and L_s is the same value, the imaging points are on the same elliptical trajectory, and then the same leakage probability estimate exists.

First, the damage probability values on each propagation path were superimposed, and the coordinates of the point with the highest probability values were the leakage locations of the underground pipelines in the chemical park. Subsequently, the damage probabilities of the multiple propagation paths are superimposed. Finally, to solve the phenomenon of dispersed localization results, an image enhancement factor is introduced to realize the centralized localization of the leakage area and determine the coordinates of the leakage point, at the same time, the calculation formula of the damage probability sum P(x, y) at each point is:

$$P\left(x, y\right)={\left[\sum _{k=1}^n{\psi }_{\mathrm{Dk}}R\left(x,y\right)\right]}^n$$(18)

where: n denotes the number of communication paths involved in the convergence. u denotes the image enhancement factor; at the place (x, y), the larger the leakage point P, the greater the probability of leakage, based on the above content to complete the precise positioning of the leakage point of the underground pipeline in the chemical park, and at the same time to determine the severity of the leakage point.

3 Analysis of results

To verify the application effect of the method in this study, a chemical industrial park in a region is taken as an example to carry out relevant tests. By simulating the pipeline leakage under actual working conditions, the clustering effect, separability measurement index, positioning error and applicability of this method in the actual complex environment are evaluated. The experimental area is located in the chemical industry park, with an area of about 20,000 m², a length of about 160 m and a width of about 125 m. The functional zoning in the park is clear, with functional zoning such as oil depot, workshop, warehouse, office building, sewage pump room and outdoor parking lot. There are dangerous gases such as hydrogen and ammonia in chemical plants, which put forward higher requirements for experimental safety. The distribution of each area in the park is shown in Figure 2.

Figure 2 Distribution plan of testing and chemical industrial park.

The experimental object is the hydrogen pipeline made of seamless steel pipe, DN200 specification, with a total length of 4500 m. These pipelines are laid along the public pipe gallery without buried pipe sections, which is convenient for non-contact detection. The designed hydrogen transport capacity is 28,500 m³/h, the working pressure is 2.7 MPa, and the controlled flow range is 13.05~13.56 m/s. The pipeline is equipped with electrostatic grounding device every 80–100 m to ensure safety.

Install ultrasonic sensors at key positions along the hydrogen pipeline (such as bends, branch points, flange joints, etc.) in advance to capture acoustic signals in the pipeline and the surrounding environment. Sensors should be selected with high sensitivity and strong anti-interference ability to ensure the accuracy of data. Establish a data acquisition system, receive the data transmitted by each sensor in real time, and carry out preliminary processing (such as filtering and denoising). The system should have data storage and remote transmission functions for subsequent data analysis and processing. At the same time, environmental parameter monitoring stations are set up in the park to monitor environmental factors that may affect sound wave propagation, such as temperature, humidity and wind speed, so as to provide a basis for data correction. Equipped with high-performance ultrasonic flaw detector, it is used to generate and receive ultrasonic signals and detect internal defects of pipelines by creeping wave technology. Set up a data processing center, equipped with high-performance computers and data analysis software, to deeply process and analyze the collected ultrasonic signals, identify the characteristics of leakage signals, and determine the location of leakage points. Combined with the safety monitoring system in the park, the whole process of the experiment is monitored to ensure the safety of the experiment. Focus on the inspection of pipeline connection parts (such as flanges, welds, etc.), which are high-risk areas for leakage accidents. At the same time, carefully check the parts that are prone to stress concentration, such as pipeline elbows and tees. Using ultrasonic creeping wave flaw detection technology, combined with data analysis software, the interior of the pipeline was scanned in all directions. By comparing the difference between the ultrasonic signal in normal state and the signal in leakage state, the position of the leakage point can be identified.

In this study, a GCT-8C ultrasonic creeping wave flaw detector is used for signal acquisition in underground pipelines. Detailed parameters of the equipment are shown in Table 1.

Using the aforementioned ultrasonic creeping wave equipment to analyze the signals from the underground pipelines in the chemical park, we obtained signal results for the hydrogen pipeline. In total, 20,000 signal samples were collected, encompassing normal signals, defective signals (such as pipeline scratches and corrosion points that have not yet caused leakage), and leakage signals. These signals are distributed in a time-series format and will be utilized as the text of the test signals for further analysis.

When the method in this study is used to locate the leakage points of underground pipelines in chemical parks, it is necessary to cluster and fuse the collected signals to accurately obtain the leakage signals in the signals, which provides the basis for the leakage point localization. Therefore, in order to verify the effect of the method on the acquisition of underground pipeline signals in chemical parks, the divisibility index is used $O_{C_i,C_j}$ as an evaluation index to measure the clustering and fusion effect of the method in the paper, this index can measure the clustering and fusion effect of different categories of signals. The formula for $O_{C_i,C_j}$ is:

$$O_{C_i,C_j}=\frac{{\chi }_0^2(\left\{C_i\right\}, \{C_j\left\}\right)}{{\chi }_0^2\left(\left\{C_i\right\}, \left\{C_i\right\}\right)+{\chi }_0^2(\left\{C_j\right\}, \{C_j\left\}\right)}$$(19)

where: ${\chi }_0^2$ indicates the coefficient of variation. C_i and C_j represent two different signals of underground pipeline defects in chemical parks, respectively.

This indicator takes values between 0 and 1, if the result of $O_{C_i,C_j}$ is larger, then it means that the signal clustering and fusion of this paper’s method is better, i.e., the C_i and C_j has significant separability; if the result of O_A,B is smaller, then it means that the signal clustering and fusion of this paper’s method is less effective, i.e., the separability between the C_i and C_j is poor.

According to the above formula, the different number of signals is calculated by analyzing the $O_{C_i,C_j}$ of the cluster fusion of various signals. The analysis results are shown in Table 2.

Based on the analysis results in Table 2, it is concluded that after using the method of clustering and fusion of different numbers of signals in the paper, for different categories of signals clustering and fusion of $O_{C_i,C_j}$, the results were all above 0.925, with a maximum value of 0.986, when $O_{C_i,C_j}$ approaching 1 means that the clustering result is almost perfect, and the signals of different categories are completely distinguished, with almost no confusion or overlapping. This is crucial for the localization of underground pipeline leaks, because accurate signal classification can help the subsequent methods to find the leak location accurately.

When leakage occurs in underground pipelines within a chemical park, it can manifest as either a single-point leakage or multi-point leakage. To verify the effectiveness of the method presented in this study, leakage point localization was performed based on the collected pipeline signals. This allowed us to obtain the results of the method for localizing both single-point and multi-point leakage points, as depicted in Figure 3.

Figure 3 Localization results of single point and multi-point leakage points. (a) Single point leakage localization results. (b) Multi point leakage localization results.

In Figures 3a and 3b, the x-axis represents the linear position on the pipeline; the y-axis represents the response value of the linear position. Based on the test results presented in Figure 3, the method proposed in this study not only accurately locates a single leakage point but also simultaneously identifies the locations of multiple leakage points. This capability is crucial for identifying leakage points in underground pipelines within complex environments, such as chemical industry parks. In practical applications, underground pipelines may exhibit multiple leakage points, and the inability to locate them simultaneously can significantly hinder and delay repair. Consequently, the multi-point location capability of the method in this paper offers an effective solution for leak detection in chemical industry parks. Furthermore, this method not only pinpoints the leak location but also calculates the damage probability of the leak point. This functionality is vital for assessing the severity of leakage and anticipating potential leakage risk in advance. By calculating the damage probability, engineers can gauge the extent of the damage at the leak point and devise appropriate repair strategies. Additionally, for regions with high damage probability, preemptive monitoring and early warning can be implemented to forestall or mitigate the occurrence or expansion of leakage incidents. In conclusion, the application of this method is commendable, satisfying the requirements for locating leak points in underground pipelines within chemical industry parks.

To further verify the positioning effect of the method in this study, the method is used to locate the pipeline leakage point at different flow rates of hydrogen, and the positioning error of the method for the location of the leakage point at different leakage distances (the expected standard is less than 15 mm) is obtained. The test results are shown in Table 3.

According to the test results in Table 3, after the method in this paper is used to locate the leakage point of the hydrogen pipeline, the maximum value of the positioning error result of the method in this paper is 11.55 mm under different hydrogen flow rates, which is significantly lower than the standard error result. Because the method in this paper is based on the collected ultrasonic signal and makes full use of the collected signal information when locating the leakage point of the underground pipeline. This can significantly reduce the positioning error of the leakage point and ensure the accuracy of the positioning results.

In order to deeply verify the localization performance of the method in the paper, the Hamming loss is used in the paper h_loss as an evaluation indicator that measures the reliability of leak location results. The formula for h_loss is:

$$h_{\mathrm{loss}}=\frac{1}{N_{\mathrm{sample}}M}\sum _{I=1}^{N_{\mathrm{sample}}}\sum _{j=1}^M{\psi }_{\mathrm{or}}({\xi }_{\mathrm{ij}},P_{\mathrm{ij}})$$(20)

where: M indicates the number of labels. ξ_ij and P_ij both represent confidence levels, the former corresponding to the actual outcome and the latter to the localization outcome, and both belonging to the ith sample and the jth leakage results. ψ_or indicates heteroscedasticity, i.e., the value is equal to 0 if it is the same, and equal to 1 if it is not. The result of the index h_loss is required to be lower than 0.1, and the closer it is to 0, the higher the accuracy of the method of this paper for the localization of the leakage point of the underground pipeline.

References [7–10] four methods as a comparative method of the method in the text, using the above five methods were used to locate the leakage point of the underground pipeline, obtaining the test results of the five methods after locating the h_loss. In order to visualize the localization effect of each method, the test results are shown in Table 4 as an example of multi-leakage point localization.

Based on the test results in Table 4, it is concluded that, at different burial depths, four methods from references [7–10] were used to locate the leakage points of underground pipelines in chemical parks, the maximum values of h_loss after localization of the four methods were 0.16, 0.17, 0.21, and 0.19, respectively. After using the method in the paper to locate the leakage points of underground pipelines in chemical parks at different burial depths, the maximum value of h_loss is 0.096. Therefore, the positioning accuracy of the proposed method for the leakage point of underground pipeline in the chemical park is better than that of the other four comparative methods because the pipeline signals are better acquired by ultrasonic crawler flaw detection and the signal fusion with the fusion clustering algorithm improves the utilization rate of the signals and ensures the positioning accuracy of the leakage point of the underground pipeline.

4 Conclusion

Underground pipelines in chemical parks are used to transport dangerous goods, including gases and liquids. Therefore, once they leak, it will have a more serious impact. To accurately locate the leakage point of underground pipelines in chemical industry parks, an accurate location method for underground pipeline leakage points in chemical industry parks based on ultrasonic creeping wave detection and data fusion is proposed, and the leakage point location based on ultrasonic signal acquisition and pipeline state signal comprehensive acquisition is completed. The test results show that:

The main results are as follows:

1. In this paper, different signals are clustered and fused, and the results are all above 0.925, with a maximum value of 0.986.

2. This method can not only accurately locate the position of a single leak point, but also determine the positions of multiple leak points at the same time.

3. After using this method to locate the leakage point of hydrogen pipeline, the maximum positioning error of this method is 11.55 mm under different hydrogen flow rates, which is obviously lower than the standard error result.

4. The maximum value of this method is 0.096 after locating the pipeline leakage points in chemical sites with different burial depths, which improves the signal utilization and ensures the location accuracy of the underground pipeline leakage points.

Future research can be further developed and improved in the following ways:

1. With the continuous progress in ultrasonic detection technology, the performance of ultrasonic transducers should be continuously optimized to improve the sensitivity and resolution of detection. Explore new data processing algorithms, such as deep learning and machine learning, to further improve the accuracy and efficiency of leak location.

2. Combined with other non-ultrasonic detection technologies, such as infrared temperature measurement and pressure monitoring, the fusion and complementarity of multi-source information can be realized, and the comprehensiveness and reliability of leak detection can be improved. Through a comprehensive analysis of various sensor data, the location and cause of the leakage point can be determined more accurately.

Conflicts of interest

The authors have no competing interests to declare that are relevant to the content of this article.

Data availability statement

The data are available from the corresponding author on request.

References

All Tables

All Figures

	Figure 1 Distribution status of ultrasonic creeping waves.
In the text

	Figure 2 Distribution plan of testing and chemical industrial park.
In the text

	Figure 3 Localization results of single point and multi-point leakage points. (a) Single point leakage localization results. (b) Multi point leakage localization results.
In the text