· Home · Table of Contents · Fundamental & Applied Research | ## The application of wavelet transform in magnetic flux leakage test of pipelineYang-Lijian, Fong-Haiying and Wong-YumeiSchool of Information Science and Engineering, Shenyang University of Technology,Shenyang, China. Contact |

The paper describes the principle and methods of detecting localized flaws in oil and gas pipeline by measuring magnetic flux leakage. The theory of wavelet transform is applied to the processing of detected signals. We use biorthogonal wavelet to decompose actual signals; the result shows that the wavelet analysis has high performance in the feature extraction of flux leakage signals of pipeline.

**Indexterms:** Magnetic flux leakage test, Flaw discrimination, Wavelet transform, Resolution, Feature extraction,

At present, the majority of oil and gas pipelines have been used several decades in the world. Because of erosion, fray, accidental impairment and so on, the leaking accidents of pipeline frequently happen. These not only bring huge damage in economic, but also pollute the environment badly and harm people's health. So, that has very considerable economic and social significance to test the pipeline erosion termly and carry out its maintenance according to the fact.

The method of magnetic flux leakage is the most widely used means of pipeline's on-line detecting now, and flaw discrimination is the purpose of detecting magnetic flux leakage. Early flaw discrimination is mostly finished by professional non-destructive testing men. The result lies on lots of human factors and wastes a great deal of time. The wavelet transform has a time-frequency window altering with scale; its time-frequency window has a character of the filter having a constant quality factor. So the waveform signal can be well decomposed by wavelet in time-scale field, and it can show the character of signal's time-scale (i.e. time-frequency character) [1]. The paper gets some flaw's time-frequency character using signal's distribution in time-scale field decomposed by wavelet, which provides instructing direction for intellectualized discrimination of pipeline's flaw.

The method of magnetic flux leakage is one of the means of non-destructive testing. It judges the size of workpiece's flaw by measuring magnetic strength leaking from a ferromagnetic material workplace's surface after it is magnetized. If workpiece's surface is slick and has no flaw and inside inclusion, magnetic flux will all pass by workpiece tested according to the principle, the case is described in figure 1(a). If there is flaw, the reluctancy at the flaw and nearby will increase, then the magnetic field round flaw becomes distortion, the case is shown in figure 1(b), it can be fell into three parts: 1. A majority of magnetic flux bypass flaw inside workpiece. 2. A few magnetic flux can pass through flaw. 3. Other magnetic flux leave workpiece`s up and down surface and bypass flaw by air. The later is magnetic flux leakage that is said, it can be tested by Hall element or induction coil moving.

Fig 1: The principle of testing by Magnetic flex index. |

Suppose x(t) is a squareintegrable function(noted as x(t)ÎL^{2}â),y(t) is a basic wavelet or mother wavelet and meets with allowing condition: C_{y}=òR(1/2y(w)1/2^{2}/1/2w1/2)dw<¥,here y(w) is the Fourier transform of wavelet function y(t), thus [1][3]:

WT_{x}(a,b)=a^{-1/2}ò_{R}x(t)y^{*}((t-b)/a)dt = <x(t),y_{a,b}(t)>
| (1) |

Formula 1 is called the wavelet transform of x(t), a(>0)is scale multiplier; b reflects translocation and it's value can be positive or negative, superscript * represents conjungation, y_{a,b}(t)=a^{-1/2}y((t-b)/a) is translocation and scale telescopic motion of basic wavelet. In formula 1, t is continuous variable, a and b can continuously change (called continuous wavelet transform (CWT)) or discontinuously (called discrete wavelet transform (DWT)).

Wavelet transform analyses signal by the scale telescopic motion and the translation at time field of y(t), wavelet transform's result may have good locality in time and frequency field if we select wavelet function properly, so wavelet transform is called mathematics microscope of analyzing signal. Wavelet transform's resolution can change with frequency at time and frequency field compared with short time Fourier transform (STFT) supplying localized observation character [3], it's character is described in figure 2. At high frequency, it uses small scale a, here time axis' observation scope is small but it is equivalent to observe finely with high frequency wavelet at frequency field. At low frequency, it uses big scale a, then time axis' observation scope is big but it is equivalent to observe general picture with low frequency wavelet. Analysis frequency is high or low but analysis' quality factor keeps constant in every analysis frequency range. Which is a character according to actual demand, because if we hope to observe more finely at time field, we more compress observation scope and increase analysis frequency.

Fig 2: Resolution analysis of wavelet transform in time-frequency field |

- Signal's decomposition:
- Signal's reconstruction:

**3.1 Analysis of many resolution
**

Wavelet transform's character shows that it is very good to analysis jiggly signal such as magnetic flux leakage signal of pipeline. To the signal meeting with Nyquist sampling rate, we use ideal lowpass and high-pass filter having equal frequency band to decompose it into low frequency and high frequency reflecting respectively signal's general picture and detail. Similar process can be repeatedly done to low frequency part after every time decomposition, then [2][4]:

Here h_{0},h_{1} and g_{0},g_{1} are respectively the coefficients of lowpass and high-pass filter made by basic wavelet used for signal's decomposition and restruction, A_{k} and D_{k }are respectively approximate and detail signal of every time decomposition. Which is the idea of much resolution analysis.

**3.2 Many resolution Decomposition of magnetic flux leakage of pipeline**

In wavelet transform, it is very important for signal process' result to select seemly wavelet base. The following factors need thinking over: orthogonality, having tight defines area, symmetry and regularity. Because of the excellent character of tight supporting biorthogonal wavelet, here it is chosen as basic wavelet for many resolution decomposition of magnetic flux leakage signal of pipeline [2].

Figure 3 is fourth order decomposition of magnetic flux leakage signal of pipeline based on tight supporting biorthogonal wavelet. Detail signal D_{1},D_{2},D_{3} and D_{4}'s variation rate and peak value provide better character in frequency field; however, A_{4} keeps the outline of original signal. D_{1} and D_{2}'s strangeness very sharp, they can be seen as high frequency interfere. Seeing reconstruction signal taken off D_{1 }and D_{2} we find that it basically provides the same information as actual measurement does, thus it also approves that wavelet decomposition is correct. It also shows that inclined weld's peak-to-peak value is smaller than circumferential weld's, and circumferential weld's detail signal is all behaving in D_{2}, D_{3} and D_{4} but inclined weld's is just put up distinctly in D_{4.} Which shows that two kinds of flaw signal's energy and frequency are different, thereby we get to the purpose of feature extraction for different flaw signals.

Fig 3:
fourth order decomposition of magnetic flux leakage signal of pipeline based on tight supporting biorthogonal wavelet.
X-axis is distance, unit: mm, y-axis is amplitude. |

Making a comprehensive view of above elaboration, analysis of many resolution based on tight supporting biorthogonal wavelet is an ideal analysis method for signal processing of magnetic flux leakage signal of pipeline. At Shenyang University of Technology, commercial measurement and control center has been developing an intelligent on-line tester by magnetic flux leakage for pipeline; it can detect 36 channels' magnetic flux leakage signal of a circuit at one time. Here just one of test signals was processed, if we do with other channels' signal with same means and then comprehensively consider the information provided by every channel's signal decomposed, we may accurately distinguish the type, location and area of pipeline's flaw. Wavelet analysis will get broader application in magnetic flux leakage test of pipeline.

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