Leakage detection method of natural gas pipeline combining improved variational mode decomposition and Lempel

Abstract

With the continuous development of pipeline transportation industry, pipeline leakage often occurs, posing a great threat to people’s lives and property safety. In order to improve the detection accuracy of natural gas pipeline leakage, a pipeline leakage detection method based on improved variational mode decomposition algorithm and Lempel–Ziv complexity analysis is proposed. In this work, the normalized mutual information is used to determine the decomposition level K of variational mode decomposition, and the Lempel–Ziv complexity analysis algorithm is used to extract pipeline signal feature. The results show that the proposed leakage detection method has higher classification accuracy than other methods, which verifies the effectiveness of this method in the process of pipeline leakage detection.

Keywords

Variational mode decomposition normalized mutual information K value determination Lempel–Ziv complexity feature pipeline leakage detection

Introduction

With the increasing demand for oil and gas and the vigorous development of pipeline transportation industry, more and more long-distance pipelines are gradually being put into use (Liu et al., 2019a). However, leakage occurs from time to time (Wang et al., 2019b), resulting in resources waste, environmental pollution, and even serious threat to people’s lives (Wang et al., 2017). In order to avoid frequent leakage accidents, the methods commonly used in pipeline leakage detection include dynamic pressure wave method (Liu et al., 2017), acoustic method (Yu et al., 2016), model-based detection method (Rui et al., 2017), and leakage detection method based on wireless sensor network (Okpare et al., 2018) and so on. Among them, the acoustic detection method can meet the requirements of wide frequency response range, high sensitivity, low false alarm rate, and good real-time detection, so it has been widely used (Quy et al., 2019; Wang et al., 2016c).

Because the sensor is interfered by the noise generated by the pipeline leak detection system itself and the complex environment, it directly affects the application effect of the acoustic wave detection method (Xiao et al., 2016). Therefore, in order to improve the accuracy of leakage detection (Xiao et al., 2017), the pipeline signal must be pre-processed for noise reduction. In 2014, Dragomiretskiy and Zosso (2014) proposed the variational mode decomposition (VMD) algorithm. It has a good processing effect on nonlinear and non-stationary signals, and can adaptively decompose the signal into a series of intrinsic mode functions (IMFs). Hausdorff distance was used to distinguish the effective and non-effective components of image after two-dimensional VMD (Gao et al., 2020), then used wavelet denoising to process non-effective modes, so as to achieve the purpose of pipeline image denoising. Although VMD has the advantages of high accuracy and strong noise robustness in signal decomposition, it has the disadvantage that the number of decomposition layer K needs to be determined in advance and it will directly affect the decomposition effect of VMD on the signal (Wang et al., 2019a). In order to determine the K of VMD, many scholars have carried out in-depth research (Li et al., 2020). Particle swarm optimization algorithm (PSO) was used to optimize the parameters of VMD (Wang et al., 2020), and applied it to detect the pipeline leakage signal. However, this method has the disadvantage of long time-consuming in parameter optimization process. Lu et al. (2020b) used the empirical mode decomposition (EMD) method to select K value, and combined VMD with the improved Bhattacharyya distance to denoise the leakage signal of natural gas pipeline, but due to the problem of mode aliasing in EMD algorithm, VMD will appear over-decomposition phenomenon. So, it is necessary to design an efficient and accurate K value determination method.

In addition, in the process of acoustic leakage detection, feature extraction is also very important to improve the accuracy of detection (Jin et al., 2014). Therefore, how to extract leakage characteristics from the signal has a great influence on reducing the false alarm rate of leakage detection. VMD was combined with variance contribution rate to denoise the pipeline signal, and extracted feature parameters, such as standard deviation, absolute mean, and information entropy, then input them to support vector machine (SVM) for classification, with the detection accuracy of 98.33% (Zhou et al., 2020). Markov feature and statistical features were extracted to detect the leakage of crude oil pipeline, and the results showed that the final accuracy can reach 99.17% (Liu et al., 2019a). Wavelet transform was used to preprocess the natural gas pipeline signal, and the features were selected through Relief-F algorithm, and then combined with SVM to identify the leakage. The accuracy was 99.4%, indicating that this method is an effective pipeline leakage detection method (Xiao et al., 2019). Although the above methods have achieved good detection results, there are also a small amount of detection errors, so the extraction of a more effective feature that is beneficial to leakage identification needs further study. For non-stationary signals, the Lempel–Ziv index was calculated to characterize the rate of generating new patterns when the signals changed, then measured the complexity of time series (Tang et al., 2019). The results showed that the Lempel–Ziv index can quantitatively measure the complexity of nonlinear signals and effectively distinguish different signals. Therefore, the Lempel–Ziv complexity analysis algorithm was used in this paper to extract the feature of pipeline signals.

For the method of determining the VMD parameter K value by EMD, here are obvious limitations of this method because the EMD algorithm has the problem of mode mixing, which can directly lead to the over-decomposition of VMD. Using intelligent optimization algorithm to select VMD parameter value will consume a lot of time and seriously reduce the use efficiency of VMD. In addition, the traditional time–frequency domain features are non-stationary, resulting in poor leakage identification. To improve the pipeline leakage recognition rate, the main contribution of this paper is to propose an improved VMD algorithm that solves the problem of K value selection and improves the leakage detection accuracy by extracting the Lempel–Ziv complexity feature (LZC). First, the preliminary K value is obtained by EMD decomposition, and the K value is continuously updated by the normalized mutual information between the original signal and each IMF until the final VMD decomposition layer K value is obtained. Next, the effective modes after VMD decomposition are selected using dispersion entropy and reconstructed to denoise the pipeline signal. Finally, the Lempel–Ziv complexity analysis algorithm is used to analyze the denoised pipeline signal to extract the Lempel–Ziv complexity feature, and the effectiveness of the proposed feature for leakage detection is verified by SVM classifier.

The rest of this paper is organized as follows. Section “Theory” introduces the principle of VMD and Lempel–Ziv complexity analysis algorithm. Section “Proposed method” presents the method of determining the K value, the VMD-based denoising method, and the Lempel–Ziv complexity feature extraction method. Section “Experimental processing results and discussion” introduces the experimental device and data, and uses the proposed method to detect the pipeline leakage. Finally, section “Conclusion” draws a conclusion.

Theory

VMD

As a new adaptive decomposition algorithm, VMD can decompose signals into multimodal components with different center frequencies (Dragomiretskiy and Zosso, 2014). The original signal $f$ is assumed to be a multi-component signal and decomposed by VMD. Then, the following constraint variational model can be established

\begin{matrix} min_{{u_{k}, ω_{k}}} {\sum_{k} ‖ \partial_{t} [(δ (t) + \frac{j}{π t}) * u_{k} (t)] e^{- j ω_{k} t} ‖_{2}^{2}} \\ s . t . \sum_{k} u_{k} = f \end{matrix}

(1)

where $u_{k}$ represents K mode components ${u_{1}, u_{2}, \dots, u_{k}}$ . $ω_{k}$ is the center frequency of each component ${ω_{1}, ω_{2}, \dots, ω_{k}}$ . * is convolution, $δ (t)$ represents unit impulse function, and $\partial_{t}$ is partial derivative to $t$ .

The optimal solution of constraint variational model is obtained based on the introduction of quadratic penalty factor $α$ and Lagrange multiplier $λ$ , that is

\begin{matrix} L ({u_{k}}, {ω_{k}}, λ) = α \sum_{k} {‖ \partial_{t} [(δ (t) + \frac{j}{π t}) * u_{k} (t)] {e^{- j}}^{ω_{k} t} ‖}_{2}^{2} \\ + ‖ f (t) - \sum_{k} u_{k} (t) ‖_{2}^{2} + 〈 λ (t), f (t) - \sum_{k} u_{k} (t) 〉 \end{matrix}

(2)

Using the alternating direction method of multipliers (ADMM) to solve the above variational model, K IMFs are finally obtained. The specific operation of VMD is shown in Algorithm 1.

Algorithm 1. Pseudocode for VMD.
1. Initialize ${{\hat{u}}_{k}^{1}}, {ω_{k}^{1}}, {\hat{λ}}^{1}, n \leftarrow 0 .$
2. Repeat $n = n + 1, k = k + 1 until k = K,$ update ${\hat{u}}_{k}^{n + 1} (ω) \leftarrow \frac{\hat{f} (ω) - \sum_{i \neq k} {\hat{u}}_{i} (ω) + (\hat{λ} (ω) / 2)}{1 + 2 α {(ω - ω_{k})}^{2}} (ω \geq 0), ω_{k}^{n + 1} \leftarrow \frac{\int_{0}^{\infty} ω {\| {\hat{u}}_{k}^{n + 1} (ω) \|}^{2} d ω}{\int_{0}^{\infty} {\| {\hat{u}}_{k}^{n + 1} (ω) \|}^{2} d ω} .$
3. Update ${\hat{λ}}^{n + 1} (ω) \leftarrow {\hat{λ}}^{n} (ω) + τ [\hat{f} (ω) - \sum_{k} {\hat{u}}_{k}^{n + 1} (ω)], until convergence \sum_{k = 1}^{K} (‖ {\hat{u}}_{k}^{n + 1} - {\hat{u}}_{k}^{n} ‖_{2}^{2} / ‖ {\hat{u}}_{k}^{n} ‖_{2}^{2}) < ε .$

From the VMD decomposition process, it is known that the K value is crucial to the decomposition effect of VMD. And according to the analysis in references (Yang et al., 2017), the setting of the mode number K directly determines the performance of VMD decomposition, and the selection of K value by human experience often leads to the over-decomposition or under-decomposition. Therefore, the K value is chosen to be studied in this paper. For the two key parameters of VMD, decomposition layer K and penalty factor α: the value of α is set to 2000 according to Lu et al. (2020b), and the value of K is discussed and analyzed in this study.

Lempel–Ziv complexity analysis

Lempel and Ziv put forward an algorithm for measuring the complexity of a finite length signal, Lempel–Ziv complexity analysis, which can characterize the rate of generating new patterns when the signal changes (Ziv and Lempel, 1977). Algorithm 2 shows the procedure for calculating the Lempel–Ziv complexity of the signal sequence $X (n)$ , and the specific steps are as follows (Tang et al., 2019):

Step 1: Coarse graining of numerical sequences.

Algorithm 2. Procedure for Lempel–Ziv complexity analysis.
1. Coarse graining $X (n) \to S_{n} = {s_{1}, s_{2}, . . ., s_{n}}$ .
2. Initialize $Q_{0} = {}, S_{v, 0} = {}, C_{(n)} (0) = 0, i = 1$ .
3. Update if $(Q_{i} \in S_{v, i - 1}), C_{(n)} (i) = C_{(n)} (i - 1)$ ; else, $C_{(n)} (i) = C_{(n)} (i - 1) + 1, Q_{i} = {}, i = i + 1$ , until $i = n$ .
4. Normalize $C = C_{(n)} (n) \log_{k} n / n$ .

$X (n)$ represents a numerical sequence consisting of ${x (1), x (2), . . ., x (n)}$ , and every element in $X (n)$ is treated as $x (i)$ . Coarse graining is used to study the complexity of the whole sequence from a macro perspective. Here, binary coarse graining is adopted to encode $X (n)$ into a series of binary symbol sequences consisting of 0 and 1, $S_{n} = {s_{1}, s_{2}, . . ., s_{n}}$ , where, $s_{i} \in S_{n}$ . If $x (i) \geq mean (X (n))$ , then $s_{i} = 1$ ; otherwise, $s_{i} = 0$ . Where, $mean (X (n))$ is the average value of the sequence.

Step 2: Parameter initialization.

Sequences $Q_{0} = {}$ and $S_{(v, 0)} = {}$ , two subsequences of $S_{n}$ , are initialized, and Lempel–Ziv complexity value is $C_{(n)} (0) = 0, i = 1$ .

Step 3: Calculate the Lempel–Ziv complexity value of the sequence.

Let $Q_{i} = Q_{i - 1} s_{i}, S_{v, i} = S_{v, i - 1} s_{i} = {s_{1}, s_{2}, . . ., s_{i}}$ . Determine whether $Q_{i}$ belongs to $S_{v, i - 1}$ . If so, then $C_{(n)} (i) = C_{(n)} (i - 1)$ ; if not, then $C_{(n)} (i) = C_{(n)} (i - 1) + 1, Q_{i} = {}$ . Both have $i = i + 1$ , and repeat step3 for $n$ times until the last bit of $S_{n}$ .

Step 4: Normalized Lempel–Ziv complexity value.

For the convenience of data analysis, the normalized reference formula is used to calculate the complexity of the signal sequence. The value of $C_{(n)}$ will be defined between [0, 1], and the final complexity $C$ can be expressed as

C = C_{(n)} (n) \log_{k} n / n

(3)

where, since $S_{n}$ is a binary sequence, so $k = 2$ . The size of Lempel–Ziv complexity value indicates the randomness of sequence, and they are in direct proportion.

Proposed Method

Improved VMD based on EMD and normalized mutual information

For determining the VMD decomposition layer number K, the improved VMD method shown in Figure 1 is proposed in this section, and the specific steps are as follows:

Step 1: EMD is applied to decompose the signal $f$ , and K mode components, IMFs, are obtained.

Step 2: The mode number K obtained from EMD decomposition is initially set as the decomposition layer K of VMD.

Step 3: Use VMD to decompose $f$ and get K IMFs.

Step 4: Calculate the normalized mutual information (MI) between IMF and $f$ according to equation (4)

{\begin{matrix} I (f, IMF) = \sum_{f} \sum_{imf \in IMF} p (f, imf) \log (p (f, imf) / p (f) p (imf)) \\ MI (f, IMF) = 2 I (f, IMF) / (H (f) + H (IMF)) \end{matrix}

(4)

where $p (f), p (imf)$ are the probability densities of $f, IMF$ , respectively, and $p (f, imf)$ is the joint probability density. $H (f), H (IMF)$ are the information entropy of $f, IMF$ . If the mutual information between the two variables is larger, it means that they are similar; otherwise, they are more independent and represent different information sources.

Step 5: After a large number of experiments, the threshold value of ΔMI (the difference between adjacent MIs) is determined as 0.001. Compare the ΔMI(i), if equation (5) holds, it means that two modes of frequency aliasing are generated. There is over-decomposition phenomenon in VMD decomposition, reset K = K – 1, and repeat Step 3, Step 4 until equation (5) does not hold, then the loop ends, and the optimal K of VMD decomposition is obtained. On the contrary, if equation (5) does not hold at the beginning, then there is no need to carry out the loop step, and the mode number K obtained by EMD decomposition is the final decomposition layer K of VMD. In addition, the mode number of EMD decomposition is taken as the maximum upper limit of the layer number K of VMD decomposition, since the K value is set from large to small, so the situation of under-decomposition of VMD is avoided to some extent

Δ MI (i) = | M I_{i + 1} - M I_{i} | < 0.001, (1 \leq i < K)

(5)

Figure 1.

Flowchart of the improved VMD.

The proposed pipeline leakage detection method

To ensure good classification performance, the noise reduction preprocessing should be carried out for the pipeline signal first and then use the Lempel–Ziv complexity algorithm to analyze the complexity of the denoised signal. Based on the improved VMD, dispersion entropy, Lempel–Ziv complexity analysis, and SVM, a novel pipeline leakage detection method is proposed as follows:

Step 1: Use the improved VMD proposed in section “Improved VMD based on EMD and normalized mutual information” to decompose pipeline signal and obtain K IMFs.

Step 2: Calculate the dispersion entropy of each IMF, select the IMFs with significantly smaller values as the effective IMFs, and the other IMFs are considered as noisy IMFs.

Step 3: Reconstruct the effective IMFs to get the denoising signal.

Step 4: Binarize the denoised signal, and change the signal into a binary sequence of 0 and 1.

Step 5: Initialize the parameters and iteratively loop to find the Lempel–Ziv complexity value of the sequence.

Step 6: The normalized Lempel–Ziv complexity value is regarded as the final complexity value of the pipeline signal.

Step 7: Take the Lempel–Ziv complexity value as the feature vector and input it to the SVM classifier for training and classification. Figure 2 shows the overall process of pipeline leakage detection method.

Figure 2.

Flowchart of pipeline leakage detection method.

Experimental processing results and discussion

Data source

The experimental data in this paper were collected from the natural gas pipeline leakage detection simulation platform. The platform parameters are shown in Table 1, and Figure 3 shows the HD-II pipeline leakage detection system and experimental pipeline diagram. The total length of the pipeline is 160 m, the pipe diameter is DN50, and the wall thickness is 1 cm. Fifteen leakage points are installed in the pipeline, one leakage point every 10 m, and each leakage point is linked with the quarter ball valve to simulate the leakage of the natural gas pipeline in the field. The pipeline fluid is air and powered by the air compressor. The pressure range in the pipeline is 0.1–0.5 MPa, and the flow rate is 60 m³/h.

Table 1.

The parameters of simulation platform for fault detection.

Total length of pipe (m)	Pipe wall thickness (cm)	Flow rate (m³/h)	Air pressure (MPa)	Sampling frequency (kHz)
160	1	60	0.5	1

Figure 3.

Natural gas pipeline leakage detection platform.

The experiment software adopted the LabVIEW programming environment, through the National Instruments NI-9215 acquisition board card for data acquisition, and the sampling frequency was 1 kHz. When collecting data, the piezoelectric acoustic sensor was used to turn the signal in the pipeline into an electrical signal, and then through the data acquisition board card for signal sampling and transmitted to the computer (the experimental process through compressed air to simulate the natural gas pipeline, and the influencing factors such as medium and pipeline material were not considered temporarily).

The pipeline signals used in this study were collected at 0.3 MPa pressure, including the following three categories: normal signals, leakage signals, and knocking signals, among which, normal signal was the signal collected when the pipeline natural gas was transported normally, knocking signal was an interference signal simulated by knocking the pipeline, and leakage signal was obtained by quickly switching the quarter ball valve. The time-domain waveforms of the three pipeline signals collected by the experimental platform are shown in Figure 4, and the number of sampling points for each signal is 10,324.

Figure 4.

Three time-domain waveforms of sample signals.

From the above figures, three time-domain waveforms contain obvious noise signal, which is not conducive to the feature extraction and leakage detection of the pipeline signal. Therefore, the next main work is to first denoise the signal, highlight the signal feature, and then extract the feature to distinguish three working condition signals and finally carry out classification and identification.

Determination method of K value based on EMD and MI

Before the VMD decomposition of pipeline signal, the decomposition layer K value of VMD must be set first. For the leakage signal, the EMD algorithm was used to decompose it adaptively, as shown in Figure 5, and 10 IMFs was obtained. Next, formula (4) is used to calculate MIs between IMF component and leakage signal to obtain the results of Table 2. From the table, ΔMI between IMF6 and IMF7 is 0.0001 (marked in bold) and less than 0.001, which is considered as over-decomposition. Therefore, according to the method of determining K value in section “Proposed method,” reset K = K – 1, that is, decomposed leakage signal into nine IMFs. MIs of IMFs and leakage signal are calculated again and compared ΔMI between adjacent IMFs, and they are shown in Table 3. It can be observed from the table that ΔMI between IMF3 and IMF4 is 0.0004 (marked in bold), which is less than 0.001. Similarly, over-decomposition has occurred again. Therefore, it is necessary to reset the value of K, let K = 8, repeated the above operations, shown in Table 4. From Table 4, the ΔMIs between all adjacent IMFs are greater than 0.001, indicating that there is no over-decomposition phenomenon in this decomposition. So, the VMD decomposition layer K of leakage signal was finally determined to be 8.

Figure 5.

IMFs of leakage signal after EMD decomposition.

Table 2.

MIs value of IMFs and ΔMI(i) between adjacent IMFs (leakage signal, when K = 10).

IMFs	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	IMF7	IMF8	IMF9	IMF10
MIs	0.3611	0.1903	0.1170	0.1196	0.1237	0.1329	0.1330	0.1314	0.1405	0.1461
ΔMI(i)	0.1708	0.0733	0.0026	0.0041	0.0092	0.0001	0.0016	0.0091	0.0056

IMF: intrinsic mode function.

Table 3.

MIs value of IMFs and ΔMI(i) between adjacent IMFs (leakage signal, when K = 9).

IMFs	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	IMF7	IMF8	IMF9
MIs	0.3610	0.1916	0.1180	0.1176	0.1406	0.1360	0.1399	0.1455	0.1412
ΔMI(i)	0.1694	0.0736	0.0004	0.0230	0.0046	0.0039	0.0056	0.0043

IMF: intrinsic mode function.

Table 4.

MIs value of IMFs and ΔMI(i) between adjacent IMFs (leakage signal. when K = 8).

IMFs	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	IMF7	IMF8
MIs	0.3611	0.1916	0.1176	0.1156	0.1387	0.1503	0.1384	0.1401
ΔMI(i)	0.1696	0.0740	0.0020	0.0231	0.0116	0.0119	0.0017

IMF: intrinsic mode function.

The validity of a newly proposed method needs to be verified by repeated experiments. This study then briefly describes the application of the improved VMD method in processing knock signal and normal signal.

Figure 6 shows EMD decomposition diagram of knocking signal, and Tables 5 –7 show the determination process of K value for knocking signal. Figure 7 shows the EMD decomposition diagram of normal signal, and Tables 8 and 9 show the determination process of K value for normal signal. The K values of VMD for knocking signal and normal signal are 9 and 10, respectively. The effective modes are selected and reconstructed using the dispersion entropy. Compared with the noisy pipeline signal shown in Figure 4, the three signals shown in Figure 8 have significant denoising effects.

Figure 6.

The modes of the knocking signal decomposed by EMD.

Table 5.

MIs value of IMFs and ΔMI(i) between adjacent IMFs (knocking signal. when K = 11).

IMFs	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	IMF7	IMF8	IMF9	IMF10	IMF11
MIs	0.0881	0.2663	0.0708	0.0828	0.0786	0.0888	0.0690	0.0733	0.0732	0.0778	0.0709
ΔMI(i)	0.1782	0.1955	0.0120	0.0042	0.0102	0.0198	0.0043	0.0001	0.0046	0.0069

IMF: intrinsic mode function; MI: mutual information.

Table 6.

MIs value of IMFs and ΔMI(i) between adjacent IMFs (knocking signal. when K = 10).

IMFs	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	IMF7	IMF8	IMF9	IMF10
MIs	0.0882	0.2691	0.0711	0.0852	0.0897	0.0633	0.0650	0.0707	0.0716	0.0677
ΔMI(i)	0.1809	0.1980	0.0141	0.0045	0.0264	0.0017	0.0057	0.0009	0.0039

IMF: intrinsic mode function.

Table 7.

MIs value of IMFs and ΔMI(i) between adjacent IMFs (knocking signal. when K = 9).

IMFs	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	IMF7	IMF8	IMF9
MIs	0.0890	0.2679	0.0700	0.0916	0.0903	0.0687	0.0723	0.0812	0.0679
ΔMI(i)	0.1789	0.1979	0.0216	0.0013	0.0216	0.0036	0.0089	0.0133

IMF: intrinsic mode function.

Figure 7.

The modes of the normal signal decomposed by EMD.

Table 8.

MIs value of IMFs and ΔMI(i) between adjacent IMFs (normal signal. when K = 11).

IMFs	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	IMF7	IMF8	IMF9	IMF10	IMF11
MIs	0.2353	0.2642	0.1986	0.2331	0.1756	0.2000	0.1929	0.2167	0.2173	0.2133	0.2152
ΔMI(i)	0.0289	0.0656	0.0345	0.0576	0.0244	0.0071	0.0238	0.0006	0.0040	0.0019

IMF: intrinsic mode function; MI: mutual information.

Table 9.

MIs value of IMFs and ΔMI(i) between adjacent IMFs (normal signal. when K = 10).

IMFs	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	IMF7	IMF8	IMF9	IMF10
MIs	0.2358	0.2647	0.1890	0.2328	0.2141	0.2091	0.2060	0.2264	0.2078	0.2140
ΔMI(i)	0.0289	0.0756	0.0438	0.0187	0.0051	0.0030	0.0204	0.0187	0.0063

IMF: intrinsic mode function; MI: mutual information.

Figure 8.

Denoised pipeline signals l of normal, leakage and knocking signal.

Lempel–Ziv complexity feature extraction of pipeline signal

As can be seen intuitively from Figure 4, three kinds of signals—normal, leakage, and knocking signal—have obviously different time-domain characteristics. The normal signal waveform of the pipeline is stable and disordered, without obvious shock or oscillating components. The leakage characteristics of the leakage signal are mainly manifested in the low frequency, and there are obvious leakage components at the moment when the valve is opened to simulate the leakage state. Over time, the magnitude of leakage signal decreases little by little and finally tends to be stable. The knocking signal appears obvious pulse component at the time of striking the pipe, then the signal is accompanied by a period of oscillation, and the signal waveform shows fluctuation.

It can be seen from the above analysis that the signals of different pipeline working conditions have different waveforms and show different degrees of complexity. Therefore, for improving the accuracy of pipeline leakage detection, this paper proposed a feature extraction method combining improved VMD and Lempel–Ziv complexity feature for pipeline signal. First, the noise reduction preprocessing was performed on the pipeline signal and then the complexity analysis was carried out for the denoised signal to extract Lempel–Ziv complexity feature. Table 10 shows the Lempel–Ziv complexity values of some test signals, and the higher the value is, the more complex the signal is and the stronger the randomness is. Observation results show that the normal signal has the highest complexity no matter before or after denoising, knocking signal is second, and the complexity of the leakage signal is lowest. Figure 9 shows the line chart of Table 10. From Figure 9, the complexity values of leakage signal and knocking signal before denoising are relatively close, which may have an impact on the result of the pipeline signal recognition.

Table 10.

Lempel–Ziv complexity values of part test data.

Signal status	Experiment groups	Normal	Leakage	Knocking
Before denoising	1	0.6600	0.3306	0.3655
	2	0.6574	0.3448	0.3565
	3	0.6290	0.3113	0.3642
	4	0.6690	0.3035	0.3592
	5	0.6509	0.3268	0.3733
After denoising	1	0.3642	0.0710	0.2105
	2	0.3655	0.0646	0.2157
	3	0.3410	0.0659	0.2351
	4	0.3345	0.0827	0.2544
	5	0.3539	0.0623	0.2273

Figure 9.

The Lempel–Ziv complexity value of pipeline signal (a) before denoising (b) after denoising.

In order to compare the complexity value of the signal before and after denoising more clearly, 30 groups of experimental samples for each working condition were randomly selected, that is, 90 groups of samples were selected in total, and Lempel–Ziv complexity value of each group was calculated. For the convenience of comparative analysis, the final results are presented in the box plots of Figure 10. Figure 10 shows that the complexity values of pipeline signals after denoising are significantly lower than that before denoising, which is due to the reduction of noise components after denoising, and the reduction of signal randomness, resulting in the reduction of signal complexity. At the same time, it can be observed that the complexity values of leakage signal and knocking signal before denoising overlapped. In contrast, the complexity values of three kinds of signals after denoising do not have any intersection, and the size of the values has obvious difference. The importance of denoising method is proved in this paper, and the Lempel–Ziv complexity index can be used as the characteristic parameter to distinguish different pipeline signals for the subsequent classification and recognition.

Figure 10.

Box plots of the Lempel–Ziv complexity value of pipeline signal before and after denoising (blue box represent the normal signal, red box represent the leakage signal, green box represent the knocking signal, and the circles represent the outliers).

Classification and recognition of pipeline signal based on SVM

For artificial neural network, its construction model requires a large number of sample data, which is not suitable for small samples of pipeline leakage. Decision tree and random forest are very easy to fall into over-fitting. Although a model is generated that fits the training set perfectly, the performance of the model on the test set is very poor (Ferreira et al., 2017). Cortes and Vapnik (1995) proposed the classification algorithm support vector machine (SVM) and compared with the above three pattern recognition methods; SVM adopts a structural risk minimization scheme, which has good generalization ability. In the environment of sparse learning samples, SVM can still maintain high multi-classification accuracy (Jan et al., 2021). In addition, SVM effectively avoids the problems of under-learning, over-learning and local minima, and its robustness is better than other similar related algorithms. It is not affected by external abnormal factors and has good classification effect. Therefore, SVM is used in this study to identify the extracted pipeline feature. Through the pipeline leakage detection platform, 60 groups of each kind of signal were gathered for experiment. Among them, 120 groups of pipeline signals were designed as training samples to train SVM, and the rest 60 groups as testing samples data were input to the trained SVM for prediction. In addition, in order to achieve better classification effect, according to Jia et al. (2019), this study used the PSO to optimally select the parameters (penalty factor c and kernel parameter g) of SVM, and the workflow of PSO-SVM method is shown in Figure 11. Finally, optimum parameters are obtained: penalty factor c = 1.2 and kernel parameter g = 2.17.

Figure 11.

The workflow of PSO-SVM training.

To verify the effectiveness of the proposed method, comparative experiments are designed as shown in Table 11. It shows the comparison of methods, extracted features, and leakage detection recognition rates in the literature. Although these methods have achieved certain detection results, they also have their own shortcomings. For example, the leakage detection model proposed in El-Zahab et al. (2018) can identify the potential leakage size, but there is still the disadvantage that the quality of collected data can be improved by signal filtering. The method proposed in Pérez-Pérez et al. (2021) realized the prediction of leakage location, but the application scope of this method may be limited due to the requirements of pressure flow. As can be seen from the table, the proposed method has the highest recognition accuracy. Compared with other methods, the average identification accuracy is improved by 2.65%, indicating that the proposed pipeline leakage detection method based on improved VMD signal preprocessing and Lempel–Ziv complexity feature selection significantly improved the leakage identification accuracy.

Table 11.

Comparisons of methods, selected features and accuracy of leak detection with other research.

References	Working condition recognition methods	Extracted features	Accuracy (%)
Wang et al. (2016a)	RWSVM	Envelope spectrum entropy	91
Wang et al. (2016b)	PSO-VMD	Root mean square, average amplitude, amplitude of square root,clearance factor, kurtosis	96.5
El-Zahab et al. (2018)	SVM, Decision treesand Naïve Bayes	Monitoring index efficiency	98.25
Liu et al. (2019a)	LS-SVM	Markov feature and Statistical feature	99.17
Liu et al. (2019b)	SVM	Spectrum Density, Approximate entropy and Principal component analysis feature	98
Rui et al. (2017)	SVM	Standard deviation, Wavelet mean frequency, Absolute mean, Frequency centroid and Short-term energy	99.4
Lu et al. (2020a)	SVM	Cloud model characteristic entropy, Sample entropy, Root mean square and Centroid frequency	96
Zhou et al. (2020)	SVM	Standard deviation, Absolute mean, Center of gravity frequency, Instantaneous frequency mean, Exponential entropy and Information entropy	98.33
Pérez-Pérez et al. (2021)	Artificial neural networks	Friction factors and pressures	99.5
The proposed method	SVM	Lempel–Ziv complexity feature	100

PSO-VMD: Particle swarm optimization algorithm-variational mode decomposition; SVM: support vector machine.

Conclusion

The innovation of this study is to solve the problem of K value selection of VMD using EMD and mutual information, and extract the Lempel–Ziv complexity feature of pipeline signal for leakage detection. In order to solve the difficulty of selecting the K value of VMD by human experience, a method for determining K value based on EMD algorithm and normalized mutual information is proposed. To effectively distinguish the characteristic of the different pipeline signals, Lempel–Ziv index is introduced to measure the complexity of pipeline signals. Compared with other methods in the experiment, the proposed method can improve the detection accuracy and has the higher classification accuracy. Although the proposed leakage detection method effectively improved the accuracy of natural gas pipeline leakage identification, there are still some areas that need to be improved. For example, this study only solved the problem of K value selection and does not further analyze the influence of α value on VMD. Therefore, the main work and research direction in the future is to consider the influence of both K and α on VMD at the same time, and take measures such as studying the new swarm intelligence optimization algorithm and using it to adaptively select the optimal parameter pair [K, α], so that the VMD can achieve the best signal processing effect.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The Project Supported by The National Natural Science Foundation of China (NSFC61873058) and (NSFC 51575407), The Natural Science Foundation of Heilongjiang Province (LH2020F005), Youth science foundation project of northeast petroleum university (2018QNL-33), and The Open Fund of The Key Laboratory for Metallurgical Equipment and Control of Ministry of Education in Wuhan University of Science and Technology (MECOF2019B01).

ORCID iD

Jikang Yue

References

Cortes

Vapnik

(1995) Support-vector networks. Machine Learning 20(3): 273–297.

Dragomiretskiy

Zosso

(2014) Variational mode decomposition. IEEE Transactions on Signal Processing 62(3): 531–544.

El-Zahab

Abdelkader

Zayed

(2018) An accelerometer-based leak detection system. Mechanical Systems and Signal Processing 108: 58–72.

Ferreira

Carrano

Silva

, et al. (2017) Fault detection and diagnosis for solar-powered wireless mesh networks using machine learning. In: 2017 IFIP/IEEE symposium on integrated network and service management (IM), Lisbon, 8–12 May, pp. 456–462. New York: IEEE.

Gao

Dong

, et al. (2020) An improved two-dimensional variational mode decomposition algorithm and its application in oil pipeline image. Systems Science & Control Engineering 8(1): 297–307.

Jan

Lee

Koo

(2021) A distributed sensor-fault detection and diagnosis framework using machine learning. Information Sciences 547: 777–796.

Jia

Ren

, et al. (2019) Pipeline leakage identification and localization based on the fiber Bragg grating hoop strain measurements and particle swarm optimization and support vector machine. Structural Control and Health Monitoring 26(2): e2290.

Jin

Zhang

Liang

, et al. (2014) Integrated leakage detection and localization model for gas pipelines based on the acoustic wave method. Journal of Loss Prevention in the Process Industries 27: 74–88.

Liu

, et al. (2020) Application of optimized variational mode decomposition based on kurtosis and resonance frequency in bearing fault feature extraction. Transactions of the Institute of Measurement and Control 42(3): 518–527.

10.

Liu

Fang

, et al. (2017) Leakage monitoring research and design for natural gas pipelines based on dynamic pressure waves. Journal of Process Control 50: 66–76.

11.

Liu

Zang

Liu

, et al. (2019a) A leak detection method for oil pipeline based on Markov feature and two-stage decision scheme. Measurement 138: 433–445.

12.

Liu

, et al. (2019b) Water pipeline leakage detection based on machine learning and wireless sensor networks. Sensors 19(23): 5086.

13.

Yue

Jiang

, et al. (2020a) Feature extraction based on variational mode decomposition and support vector machine for natural gas pipeline leakage. Transactions of the Institute of Measurement and Control 42(4): 759–769.

14.

Yue

Zhu

, et al. (2020b) Variational mode decomposition denoising combined with improved Bhattacharyya distance. Measurement 151: 107283.

15.

Okpare

Anyasi

Ebegba

(2018) Oil pipeline leak detection and localisation using wireless sensor networks. Current Journal of Applied Science and Technology 32: 1–9.

16.

Pérez-Pérez

López-Estrada

Valencia-Palomo

, et al. (2021) Leak diagnosis in pipelines using a combined artificial neural network approach. Control Engineering Practice 107: 104677.

17.

Quy

Muhammad

Kim

(2019) A reliable acoustic emission based technique for the detection of a small leak in a pipeline system. Energies 12(8): 1472.

18.

Rui

Han

Zhang

, et al. (2017) A new model to evaluate two leak points in a gas pipeline. Journal of Natural Gas Science and Engineering 46: 491–497.

19.

Tang

Lin

Zou

(2019) Complexity analysis of time-frequency features for vibration signals of rolling bearings based on local frequency. Shock and Vibration 2019: 7190568.

20.

Wang

Huang

, et al. (2019a) Early fault diagnosis for planetary gearbox base on adaptive parameter optimized VMD and singular kurtosis difference spectrum. IEEE Access 7: 31501–31516.

21.

Wang

Zhang

Song

, et al. (2019b) A novel optimized SVM algorithm based on PSO with saturation and mixed time-delays for classification of oil pipeline leak detection. Systems Science & Control Engineering 7(1): 75–88.

22.

Wang

Zhu

Yue

, et al. (2020) Application of variational mode decomposition based on particle swarm optimization in pipeline leak detection. Engineering Research Express 2(4): 045036.

23.

Wang

Lin

Liu

, et al. (2017) Pipeline leak detection by using time-domain statistical features. IEEE Sensors Journal 17(19): 6431–6442.

24.

Wang

Gao

Liu

(2016a) Gas pipeline small leakage feature extraction based on LMD envelope spectrum entropy and PCA–RWSVM. Transactions of the Institute of Measurement and Control 38(12): 1460–1470.

25.

Wang

Chen

Zhong

(2016b) Research on leak detection of water pipeline base on PSO-SVM. DEStech Transactions on Engineering and Technology Research 2016: 238–244.

26.

Wang

Tan

, et al. (2016c) The application research of the natural gas pipeline leakage detection based on adaptive time frequency analysis. International Journal of Signal Processing Systems 4(4): 334–338.

27.

Xiao

(2017) SVD-NMF based denoising algorithm for pipeline leak signal. Chinese Journal of Sensors & Actuators 30(1): 101–108.

28.

Xiao

Bai

, et al. (2016) A small leak detection method based on VMD adaptive de-noising and ambiguity correlation classification intended for natural gas pipelines. Sensors 16(12): 2116.

29.

Xiao

(2019) Leak detection of gas pipelines using acoustic signals based on wavelet transform and Support Vector Machine. Measurement 146: 479–489.

30.

Yang

Liu

Zhang

(2017) Adaptive estimation of VMD modes number based on cross correlation coefficient. Journal of Vibroengineering 19(2): 1185–1196.

31.

Liang

Zhang

, et al. (2016) Dual-tree complex wavelet transform and SVD based acoustic noise reduction and its application in leak detection for natural gas pipeline. Mechanical Systems and Signal Processing 72: 266–285.

32.

Zhou

Zhang

Yang

, et al. (2020) Pipeline signal feature extraction with improved VMD and multi-feature fusion. Systems Science & Control Engineering 8(1): 318–327.

33.

Ziv

Lempel

(1977) A universal algorithm for sequential data compression. IEEE Transactions on Information Theory 23(3): 337–343.

Leakage detection method of natural gas pipeline combining improved variational mode decomposition and Lempel–Ziv complexity analysis

Abstract

Keywords

Introduction

Theory

VMD

Lempel–Ziv complexity analysis

Proposed Method

Improved VMD based on EMD and normalized mutual information

The proposed pipeline leakage detection method

Experimental processing results and discussion

Data source

Determination method of K value based on EMD and MI

Lempel–Ziv complexity feature extraction of pipeline signal

Classification and recognition of pipeline signal based on SVM

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References