Abstract
The leakage of the ship’s pipeline system will bring great risks to the engine equipment and seriously threaten the vitality of the ship. In this paper, the pipeline leakage detection and localization research are carried out based on the vibration signal generated by pipeline leakage. First, the finite element model of the pipeline is constructed to obtain the variation law of the vibration signal when the pipeline leaks are carried out. Second, the vibration signal is processed based on the variational mode decomposition (VMD) and radial basis function (RBF) neural networks. The wavelet packet threshold noise reduction is conducted before signal decomposition to improve the signal-to-noise ratio. Then, the denoised signal is decomposed by VMD. The effective component is identified by analyzing the correlation coefficient between the component and the denoised signal. The center frequency and energy of the effective component are used as feature vector to train the RBF neural network to identify and locate leakage. Finally, a pipeline leakage test platform is built under laboratory conditions. After processing the data samples collected from the test, the RBF neural network is trained to identify and locate leaks. The test sample identification results show that the leak identification and localization method based on VMD-RBF has a high accuracy.
1. Introduction
The pipeline system of ships is used to transport various media such as oil, water, and gas. Due to the harsh working environment and the inconvenient maintenance, leakages of ship pipeline often occur. At present, there are few measures for leakage identification and location of warship pipeline system, mainly through inspection to find leakage or infer from pressure changes and mechanical failures. However, in practical engineering, the above measures have the following shortcomings: (1) the pipelines of ships are all over the corners and the working space is very small. Therefore, some pipeline leaks cannot be detected by inspection; (2) when the leakage is small; the change of pipeline pressure is not obvious. There are many factors that cause pressure changes, so the method of relying on pressure changes for leakage judgment has a situation of false detection; and (3) the method of inferring pipeline leaks from mechanical failure requires extensive field work experience. Therefore, there is an urgent need to study the intelligent leak detection and positioning method for ship pipelines.
Initially, the processing of the vibration signal generated by the leakage was limited by the signal processing method and computer technology. The frequency-domain characteristic analysis or the time-domain characteristic analysis method was adopted. Cheng et al. continuously monitored the leakage signal of boiler pipes, and then judged leakage by analyzing the frequency spectrum of the pipe signal [1]. In the experiment, Hunaidi and Chu simulated the leakage of plastic pipes under different conditions. The frequency components of the leakage vibroacoustic signal and the influence of pipe diameter and pressure were studied [2]. Ahadi et al. obtained the pipeline leakage signal by experimental method [3] and distinguished the leakage from other signals such as background noise and the natural vibration of the pipeline. Gao et al. combined the propagation model of acoustic and vibration signals in plastic pipes with the cross-correlation function to calculate the time delay [4], which improved the effectiveness of correlation detection in leak location of plastic pipes. Davoodi et al. collected the leaked signal and decomposed it with the wavelet transform, de-noised it by filtering, and then reconstructed the signal. The reconstructed signal was estimated by the cross-correlation method to locate the leak point [5]. Lang et al. proposed an improved local mean decomposition signal analysis method [6]. The results show that the method can identify the leakage point effectively under different working conditions. In view of the shortcomings of pipeline state monitoring, Hu et al. [7] proposed a tnGAN-based leak detection method. This method can realize different incomplete data recovery situations to obtain pipeline leak detection results. Finally, the experimental results on the pipeline network demonstrate the effectiveness of the method. Yang et al. [8] established a new ensemble model of support vector machine and one-dimensional convolutional neural network. Compared with existing models, the developed ensemble model can extract features of pipeline data faster and more accurately, and has better robustness during pipeline processing. Yang et al. [9] proposed a denoising algorithm based on variational mode decomposition (VMD), Manhattan distance (MD), and a one-dimensional convolutional neural network (1DCNN) to solve the problem of recognition error caused by noise interference in oil and gas pipeline signals.
The vibration signal analysis method is one of the most important leakage detection and localization methods in the industry. It has great advantages of strong practicability, high accuracy, and easy implementation. In order to prevent the major safety hazards caused by pipeline leakage and improve the leakage detection of pipeline systems, this paper conducts research on the characteristics of leakage pipeline vibration signals, leakage feature extraction, intelligent identification, and location of leakage.
The organization of this paper is as follows. In Section 2, the finite element model of the pipeline is established. In Section 3, pipeline leak identification and location method based on the VMD-RBF neural network are presented. In Section 4, the finite element simulation of electromagnetic positive and electromagnetic negative stiffness devices is carried out and a pipeline leakage test platform is manufactured and experimental tests are conducted. Finally, conclusions are presented in Section 5.
2. Finite Element Simulation
2.1. A Model of the Leaking Pipeline
A model of the leaking pipeline is built by using ANSYS Workbench software. The simulation model is shown in Figure 1. The leakage pipeline model is a curved pipe with irregular leakage ports. The inner diameter is 50 mm. The wall thickness is 5 mm. In order to simulate the actual pipeline leakage situation, the leakage port is designed with an irregular shape. The position of the leakage port is assumed to be at the turning point of the pipeline. The fluid medium is water, and the pipeline is the material of structural steel.
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2.2. Numerical Simulation Results and Analysis
When the pipeline leaks, the pressure distribution and velocity distribution of the flow field are shown in Figure 2. It can be seen that when the pipeline leaks, the fluid in the pipe will be ejected along the leakage port, and the flow velocity of the jet is higher than that of the fluid in the pipe. At the same time, due to the frictional resistance of the leakage port wall to the fluid, the fluid near the pipe wall has a lower flow rate than the fluid in the middle part of the leakage port. This frictional resistance reacts to the pipeline and causes the pipeline to vibrate.
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The inlet pressure of the flow field is set to 50 kPa, and the pressure of the pipeline outlet and leakage port is 0 kPa. The radius of the leak hole is set to 5 mm. The vibration amplitude-frequency curve and power spectrum of the pipeline at different leakage positions are obtained, as shown in Figure 3.
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It can be seen that when the leakage position is different, the amplitude and power spectrum of the vibration signal will change. This change is mainly affected by two factors. The first is the attenuation of the vibration signal during the pipeline propagation process, and the second is the effect of the fixed constraint on the vibration signal. Since the length of the pipeline model is 1000 mm, the propagation attenuation of vibration is very small, so the main reason for the above changes is the effect of fixed constraints. At the same time, the change in leakage position did not change the frequency distribution of the vibration signal.
Through the above analysis, it can be seen that the changes in pipeline vibration signals can reflect the situation of pipeline leakage. The simulation results demonstrate the effectiveness of the leak detection scheme. Simulation data can also be used as leakage fault samples for neural networks.
3. Research on the Vibration Signal Processing Method
3.1. Basic Principles of VMD
In the VMD algorithm, the eigenmode function (IMF) is redefined and the concept of bandwidth-limited eigenmode function (BIMF) is proposed [10], which is defined as follows:where is the band-limited eigenmode function, is the instantaneous amplitude and envelope, , is the phase function of , and is the instantaneous angular frequency of , that is, the phase is nonmonotonically decreasing. The envelope of the signal and the instantaneous angular frequency change at a much slower rate than the phase .
The bandwidth of BIMF can be estimated by Carlson’s principle as follows:where is the bandwidth estimate of the BIMF, is the highest frequency of the envelope, is the offset rate of the instantaneous frequency, and is the maximum error of the instantaneous frequency.
Before decomposing the signal, it is necessary to preset the number of components K, and decompose the original signal into K BIMF components to minimize the sum of the bandwidth estimates of the components. The specific steps of decomposition are as follows:(1)Hilberting transforms each BIMF component to obtain the analytical signal, so the unilateral spectrum can obtain(2)Estimating the center frequency of each IMF component, multiplying it by an exponential signal, and moving the spectrum of to the corresponding baseband(3)The bandwidth of each component is estimated by calculating the square norm of the gradient of equation (4), thereby constructing the expression of the constrained variational problem where represents the time partial derivative of the function, is a unit impulse function.
In order to find the optimal solution of expression (5), Lagrange multipliers and quadratic multiplication factor are introduced. Then, the constrained variational problem to be solved will become an unconstrained variational problem. The Lagrangian expression expands to
The alternating direction multiplier algorithm (ADMM) is used to alternately update , , and , and to search for the “saddle point” of equation (6), thereby completing the solution to the constrained variational problem. The specific process of solving is as follows:(1)Initialize the values of , , and to 0(2)Execute the loop, (3), for all , update the functional sum and with equations (7) and (8) until (4)For all , update with the following formula: where is the noise tolerance parameter.(5)Repeat steps 2 to 4 until the following constraints are satisfied, and the iteration stops.
The pipeline vibration signal is decomposed into K components with a certain center frequency. When the pipeline leaks, the center frequency of each signal component will change. So the center frequency of each component of the vibration signal can be used as a eigenvector to identify pipeline leakage. Under the same working condition, when the leakage location is different, each energy distribution of the frequency band will change. So the energy corresponding value of each component can be used as the eigenvector, and the change in leakage position is reflected as the change in the vibration signal energy. The specific steps of feature extraction are as follows:(1)Using wavelet packet threshold to denoise the signal obtained by the sensor to perform preliminary noise reduction(2)Performing VMD decomposition on the denoised leakage signal and use the observation center frequency method to determine the parameter K(3)Calculating the correlation coefficient between the K BIMF components and the denoised signal, and select N effective components(4)Arranging the center frequencies of the selected N BIMF components from small to large to construct eigenvectors . Due to the large value, it is inconvenient for the processing of the neural network, so the eigenvectors of all samples are normalized and normalized. The method is where is the center frequency of the BIMF component of the sample, and are the maximum and minimum values of the center frequency of the component, and the normalized vector is used for leakage identification.(5)Calculating the energy of each effective component where represents the amplitude of the discrete points of each BIMF component.(6)Construct the eigenvectors of the vibration signal with the energy values of the N BIMF components
Normalizing the feature vector where is the sum of the energy of all BIMF components, and the eigenvector is used to reflect the change of the leak point position.
3.2. Principle of RBF
The radial basis function (RBF) neural network [11, 12] is a forward nonfeedback, local approximation neural network proposed by Moody and Darken The vector is directly mapped to the latent space. When the center point of the RBF is determined, the mapping relationship is also determined. The output layer of the network is the linear weighting of the output of the hidden layer. The structure of the RBF neural network is shown in Figure 4, which consists of input layer, hidden layer, and output layer.
The number of nodes in the input layer, hidden layer, and output layer are , , and , respectively. The input layer of the neural network just inputs the signal into the network. Let the model input vector be = , the neuron activation function of the hidden layer is composed of radial basis functions, and its output is composed of nonlinear activation functions is expressed aswhere is the center vector of the node of the hidden layer, representing the Euclidean distance between the two, and is a positive scalar, representing the width of the Gaussian basis function. In order to improve the network accuracy and reduce the number of hidden layer nodes, the activation function can also be changed to a multivariate normal density function.
The expression iswhere is the inverse of the input covariance matrix.
The output layer of the network is a linear weighting of the output of the hidden layer, and the expression iswhere is the weight from the hidden layer to the output layer, ( = 1, 2, …, ) is the output of the network.
3.3. Leak Identification and Localization Steps of VMD-RBF by Vibration Signal
In this paper, the pipeline vibration signal is extracted, and the feature vector constructed by the center frequency is used to train the neural network to identify the leakage. The specific steps for establishing an RBF neural network are as follows:(1)Obtaining sample data: This paper simulates the pipeline of the ship, builds a leaking pipeline test platform in the laboratory, and obtains the samples by measuring the vibration signal of the pipeline without leakage and leakage at different positions(2)Determine the input and output of the network: use the feature extraction method in the previous section to perform feature extraction on the sample data, and the extraction result is used as the input vector of the neural network, and the output vector is determined according to the purpose of establishing the neural network(3)Initialize the neural network: set various parameters of the neural network, including the number of input layer, hidden layer, output layer nodes, training accuracy target, and training speed(4)Training the neural network: randomly select some samples as training samples and input them into the neural network, and the RBF neural network will continuously adjust the weights between neurons until the error reaches the set accuracy, and the training of the neural network is completed(5)Test neural network: use the trained network to test the remaining data samples to identify and locate leaks.
4. Experimental Studies
4.1. Design of the Test Platform
In order to verify the effectiveness of the method, a pipeline leakage test platform is built in the laboratory. The method based on VMD-RBF neural network is used to identify and locate the leakage. The overall schematic diagram of the ship pipeline leakage identification test platform is shown in Figure 5.
The test platform consists of two parts: a pipeline system and a data acquisition system. On the pipeline, round holes of different sizes are set at different positions to simulate leakage. The boundary conditions of the pipeline are changed by adjusting the opening of the inlet valve and the outlet valve. The pressure signal and flow signal of the pipeline are measured by the pressure sensor and the flow sensor. After the vibration signal is collected by the acceleration sensor, it is transmitted to the computer through the data acquisition module through the network cable for analysis and processing.
The physical diagram of the test piping system is shown in Figure 6. The pipeline system is mainly composed of four parts: water tank, water pump, pipeline, and accessories.
4.1.1. Water Tank
The water tank is used to provide water for the entire pipeline system and collect the water flowing out of the pipeline, thus forming a cycle and reducing the waste of water resources. There is an outlet valve at the bottom of the water tank for discharging the water in the water tank, which is convenient for cleaning the water tank and replacing the water.
4.1.2. Piping and Accessories
The pipe material used in this test is stainless steel, which is commonly used in ship pipelines. The pipe diameter is 32 mm, the thickness is 3 mm, and the length is 13 m. The parameters of each part of the pipeline system are shown in Table 1. Both the inlet and the outlet of the pipeline are provided with manually adjustable stop valves, and the pressure and flow rate of the fluid can be adjusted by opening of the stop valve. Leakage holes are arranged in the AB and CD sections, and each leakage hole is equipped with a plugging bolt of the corresponding size. This kind of bolt has a good plugging effect and is easy to operate.
The vibration signal acquisition system used in this test is the B&K system, which mainly includes three parts: an acceleration sensor, a data acquisition module, and a computer. The sensor is a 4534B general-purpose accelerometer, which has the characteristics of a wide measurement frequency range, low noise, and low sensitivity to environmental factors. Due to its light weight, strong, and well-sealed titanium shell, it can perform well in complex and harsh environment. The technical parameters are shown in Table 2.
The neural network method is used to identify and locate the leakage of the pipeline, but it requires a large number of training samples. In order to obtain the samples, the AB section of the pipeline is selected as the object, and four leakage holes with a diameter of 4 mm are arranged in different positions. The distances to the inlet valve are 0.25 m, 1.75 m, 3.25 m, and 4.75 m.
Under the same working conditions, 10 sets of data were collected for the vibration signal of the pipeline when there was no leakage and the vibration signal when leakage occurred at the four leak points, respectively. The same working condition means that the pressure and flow of the pipeline are the same during each measurement. The collected data samples are used for training and validation of neural networks.. The collected vibration signal is processed by the method mentioned in the previous chapter.(1)After analysis and attempt, the method of denoising by soft threshold is selected. The wavelet base used is db4 wavelet, and the number of decomposition layers is 3. The time domain waveforms of the leakage pipeline vibration signal before and after noise reduction are shown in Figures 7 and 8.(2)Select the appropriate K value by observing the center frequency of the denoised signal. When K = 2–7, the denoised signal is decomposed by VMD, and the center frequency of each BIMF component of a set of sample data is shown in Table 3. It can be found that when K = 7, the center frequencies of the BIMF4 and BIMF5 components are 1264 Hz and 1385 Hz, which are in the frequency range of 1200−1400 Hz. There is an overdecomposition phenomenon, so the number of decomposition layers is K = 6. All the leakage signal data are analyzed, and it is found that K is the most suitable for 6.(3)The denoised signal is performed by 6-layer VMD decomposition, and the result is shown in Figure 9. The center frequency of each BIMF component is arranged from small to large. The correlation coefficient between each component and denoised signal is calculated. Table 4 shows the correlation coefficient between the BIMF component l and the denoised signal.
It can be found from Table 4 that the correlation coefficient between BIMF1–BIMF4 and the signal before decomposition is greater than the set threshold of 0.1, and the degree of correlation with leakage is relatively large. Therefore, these four components are selected as effective signal components of center frequency and energy value.
4.2. Research on Pipeline Leakage Identification Based on RBF Neural Network
When the leak occurs, the excitation sources such as turbulence, friction, and cavitation will be generated near the leak hole. Therefore, the frequency distribution of the vibration signal of the pipeline will change. Table 5 shows the center frequency of the effective BIMF components obtained after some data samples are processed. The corresponding pipeline health status is expressed as 0 or 1, where 0 means no leakage and 1 means leakage.
In order to facilitate observation, the table is made into Figures 10 and 11. Figure 10 is the center frequency distribution of the vibration signal of the leaking pipeline, and Figure 11 is the center frequency distribution of the vibration signal of the leak-free pipeline.
It can be found that when the pipeline leaks, the center frequencies of the data samples BIMF1, BIMF2, BIMF3, and BIMF4 are mainly distributed in the 25−50 Hz, 500−750 Hz, 850−1100 Hz, and 1200−1400 Hz frequency bands. The center frequency of each BIMF component of the vibration signal is lower than that of the leaking pipeline.
The RBF neural network is used to identify the pipeline leakage state. The specific operation steps are as follows:(1)The center frequencies of the four effective components of each group of data , , , and , form a feature vector , and the normalized vector is used as the input layer of the neural network. The expected output for the normal state of the pipeline is 0, and the expected output for the leaking state is 1.(2)In order to improve the training effect of neural network, 32 groups of leakage signals and 8 groups of nonleakage signals are selected as data samples. The newrb function was used in the MATLAB environment to establish the neural network, and the mean square error index is GOAL = 0.001. The error convergence curve for training is shown in Figure 12.(3)Inputting 10 groups of test samples into the trained neural network for testing, and the results of leak state recognition are shown in Table 6.
It can be seen from Table 6 that the output result of the neural network is not a simple 0 or 1, but the actual output value is close to the expected output, except for one recognition result that cannot be judged. Therefore, the RBF neural network can be effective. The identification of leakage status is carried out, and the accuracy rate is 90%.
4.3. Research on Location of Pipeline Leakage
For the location of the leak point, the cross-correlation method is currently the most used method. The sensor is placed to collect pipeline vibration signals at the same time, and the cross-correlation calculation of the two signals is performed. In this paper, this method is used to locate the leak point 2. Two sensors are placed at both ends of the pipeline AB and the leak signals are collected at the same time. The distances between the leak point 2 and the sensors 1 and 2 are 1.75 m and 3.25 m, respectively, as shown in Figure 13.
The vibration signal generated by the hammer knocking propagates along the pipeline and is received by the sensor 1. The knocking signal and the signal received by the sensor are amplified, as shown in Figure 14.
It can be seen from Figure 14 that the peak value of the received signal by the sensor is 0.0035 s later than the peak value of the tap signal. And the distance between the tap position and the sensor is 5 m, so the propagation speed of the vibration signal in the test pipeline can be obtained at about 1429 m/s. From the propagation speed and time difference, it can be calculated that the distance between the leak point and the two sensors is 2.43 m. So the distance between the leak point and the pipeline section A is about 1.29 m, which is 0.46 m away from the actual one. The test results verify the feasibility of the cross-correlation method for leak location. However, with the continuous development of artificial intelligence, intelligent detection has become the mainstream research direction of leak detection. In this paper, the RBF neural network is applied to the pipeline vibration signal data samples, and a new method is proposed. A method of leaking smart localization is put forward. The data samples of the collected leakage signal are processed by the previous method, and the energy distribution of the effective BIMF component of the pipeline vibration signal with leakage at different positions is obtained as shown in Figure 15.
As can be seen from Figure 15, when the pipeline leakage location is different, the energy distribution of each BIMF component of the vibration signal is different. Therefore, the energy is used as the feature vector to train and test the neural network to locate the location of the leak point. The specific steps are as follows:(1)The 40 groups of leaked signals are extracted and normalized by the above data processing method, and the feature vector is obtained as the input layer of the network. The expected outputs for leaks at leak point 1, leak point 2, leak point 3, and leak point 4 are (0, 0), (0, 1), (1, 0), and (1, 1), respectively. The energy eigenvectors of some data samples are shown in Table 7.(2)Among the 10 groups of data leaked from each leak point, 8 groups are randomly selected as training samples. A total of 32 groups of training samples, and the remaining 8 groups of data are used as test samples to test the network. The RBF neural network is trained using the same method as before.(3)The 8 sets of test samples are input into the trained neural network for training. The results are shown in Table 8.
It can be seen from Table 8 that the actual output results of the neural network are close to the expected output except for one that has a large deviation from the expected output. The final test result has an accuracy rate of 80%, which verifies the effectiveness of the designed intelligent positioning method.
5. Conclusion
This paper studies the identification and location methods of warship pipeline leakage based on variational mode decomposition (VMD) and radial basis function (RBF) neural networks. The center frequency of the effective BIMF component is used to construct the eigenvector for leakage identification. The RBF neural network is used to identify the pipeline leakage and locate the leakage point. In order to verify the accuracy of t the proposed method, a test pipeline platform is built in the laboratory. The pipeline vibration signals of different pressures, flow rates, and leak hole sizes are collected and analyzed. The vibration signal of the pipeline is used as the data sample of the RBF neural network, and the data is processed to extract the center frequency and energy of the effective BIMF component to construct the feature vector. The results show that the proposed method has high accuracy.
Based on the current research foundation [13], the future work can be divided into the following aspects: (1) How to extract weak signal features from strong background noise is the next problem to be saved. (2) The research on the identification and location of multiple leaks and complex pipeline leaks needs to be further strengthened.
Data Availability
The data that support the fndings of this study are available from the first author, [Pan Su], upon reasonable request.
Additional Points
Article Highlights. (1) The finite element analysis software is applied to conduct a numerical simulation of the pipeline leakage. (2) A pipeline leakage identification and location methods based on variational mode decomposition (VMD) and RBF neural network is proposed, and the effective component center frequency and energy value obtained by VMD are used to construct signal feature vectors, which are input into the RBF neural network to achieve the purpose of leakage identification and location. (3) The test platform of leakage pipeline is built to simulate the ship environment, and the vibration signals of leakage pipeline under different conditions are analyzed, and the diagnostic accuracy of the RBF neural network is verified.
Conflicts of Interest
The authors declare that there are no conflicts of interest.
Acknowledgments
This study was funded by the National Natural Science Foundation of China (grant numbers 51909267 and 51579242) and by the Naval University of Engineering Foundation (2022502040).