·Table of Contents ·Computer Processing and Simulation | ## Wavelet Analysis of MFL Signal for Steel Wire Rope TestingV.Barat, D.Slesarev, V.LuninMoscow Power Engineering Institute (TU), Russia S.Belitsky INTRON Plus, Moscow, Russia Contact |

In-situ inspection of steel wire ropes is an actual problem of modern Non-destructive testing. Today this inspection is realized by magnetic flux leakage (MFL) method. When using this technique, magnetic head magnetically saturates a rope specimen. While rope is passing through magnetic head, the instrument inspects the rope. Any changes in inspected rope area such as discontinuities, like broken wires or strands, pits of corrosion etc., cause changes in leakage magnetic field. These changes are detected by field sensors, which are placed close to the rope midway between the pole pieces of magnetic head [1]. Signals from field sensors consist information to be extracted about defects of the rope. The task of signal analysis is to register number and characteristics of broken wires and to measure the loss of metallic cross-section area. Conventionally, narrow band or optimized filtration is used for analyzing signal.

One of typical features of the problem consists in a strong influence of such factors as rope vibrations, gap changes, twisted rope structure, etc. As a result of this influence, diagnostic signal has a lot of interference, which form wide band (white) and narrow band noises. This reduces significantly sensibility of the method and reliability of broken wire detection and increases requirements to operating personnel. Even by using optimized filtration one can increase signal-to-noise ratio to no more than 2 - 2.5 times. Therefore, a problem of effective signal analysis is really actual.

Diagnostic signal of steel wire rope MFL testing consists of impulses with different magnitude and duration, depending on depth and dimension of the wire defects. However, all such impulses have approximately the same form, which is caused by distribution of magnetic flux leakage around a broken wire. This particular feature allows us to suppose that application of Wavelet transformation for the purpose of signal analysis can significantly increase sensibility and reliability of defect detection.

It is known, that Wavelet Transform (WT) as a time-scale signal representation, has a property of good localization of time events in different scales. Continuous WT is given by formula [2]:

(1) |

where *s(t)* - an analyzed signal, *t* and t
- independent variables (time or spatial coordinate), *a* - scale parameter, y
(t
) - a mother wavelet. It can be viewed as a filtration with a changing of time scale. So, if a mother wavelet has a form of informative signal (in our case, impulse), then WT acts as a matched filtration with changing time scale, which should ensure defect impulse detection. It can be seen from formula (1), that WT is a kind of two-dimensional signal representation, therefore, algorithms of image processing can be used for its analysis. Our approach assumes a similarity of mother wavelet y
(t
) to a form of defect impulse.

As already mentioned, the magnetostatic transducers (based on Hall-effect sensor) are usually used for inspection of steel wire ropes. This sensor measures the distribution of leakage field caused by defect. Using differential measurement scheme, signal of a typical defect has a form of smooth two-polar impulses with duration depending on depth and size of the defect.

We need to select such mother wavelet which similar to form of typical defect impulse. For this, application of several types of mother wavelets was tested in the frame of this study: Haar-wavelet, Symmetrical wavelet and Daubechies-wavelet. They are all widely used in signal and image processing and provide good impulse localization in different scales. A range of scale parameter *a* should be chosen considering the rope diameter and transducer construction - appropriate values of *a* can be calculated from impulse characteristics [3].

Figure 1 shows one of a typical test signal that contains the impulses influenced by 14 defects of different size and location.

Fig 1: Example of signal for rope area containing 14 defects |

The signal was sampled with a step of 2 mm along rope. Test signal provides estimation of defect impulse duration - in this case, it lies in the range from 28 to 42 mm. Considering impulse form and duration, we can estimate its frequency spectrum shown in Figure 2.

Fig 2: Frequency spectrum of test signal | Fig 3: Haar-wavelet transform of test signal |

Considering mother wavelet spectrum, we can evaluate the range of scaling parameter appropriate to defect impulses [3]. In our case this range is *a=* 1.5 - 4.5, Haar-wavelet transform of test signal is depicted in Figure 3. The rope defects are reflected as distinct vertical lines on the WT at given scale range. Length and profile of the lines on wavelet plane depend on defect features (its form and length) as well on mother wavelet features. In particular, Haar-wavelet has a broad frequency spectrum, therefore it gives lower localization in scale range comparing with Daubechies-wavelet, which has narrow frequency range (in this case - spatial frequency, because independent variable is a spatial variable). It should be noticed that impulse interference also has a form of vertical lines and they are presented in the same scale range. Therefore some special image processing techniques are necessary for effective defect detection.

Some known techniques of image processing can be used for line localization on wavelet plane. With the help of such techniques we can localize defects and estimate some of its parameters. Nevertheless, this techniques do not provide possibility to suppress impulse interference presented in signal, and therefore reduce reliability of diagnosis. Figure 4 shows WT of test signal with Symmetrical mother wavelet. As it follows from comparison of Figures 3 and 4, Symmetrical wavelet gives better scale resolution.

Fig 4: Symmetrical wavelet transform of test signal |

Good result, in sense of diagnosis reliability, can be achieved using weighted summation of wavelet values for some chosen scales *{a _{k}}_{1}^{K}*. Set of scale values should be chosen so, that all wire defects are presented. Signal-to-noise ratio (SNR) of linear weighted summation for Haar-wavelet is 3.1 and for Symmetrical wavelet - 4.5, SNR for input signal is 2.0 (optimal filtration gives 2.9). Better result can be achieved using nonlinear processing of WT. Figure 5 shows result of weighted summation with nonlinear noise elimination using Haar-wavelet, and Figure 6 shows the result for Symmetrical wavelet.

Fig 5: Result of weighted summation with nonlinear noise elimination using Haar-wavelet | Fig 6: Result of weighted summation with nonlinear noise elimination using Symmetrical wavelet |

If we calculate a value, that reflects relation of useful impulse energy to interference energy for different wavelet types (namely, square root of this relation), we get following data

Haar-wavelet | Symmetrical wavelet | Daubechies-wavelet |

11.9 | 3.4 | 6.4 |

We can see, that Haar-wavelet gives dramatic improvement of SNR, that is, in diagnosis reliability. It means that in practice such signal processing can detect really weak impulses. For example, in case of 24-mm rope inspection with instrument for 32-mm rope, it can be detected 12 from 14 defects. Figures 7 and 8 depict results of nonlinear processing of wavelet transform for test signal.

Fig 7: Result of nonlinear processing of Haar-wavelet transform for test signal | Fig 8: Result of nonlinear processing of Symmetrical wavelet transform for test signal |

Here is the data with the same signal to interference ratio as before for test signal

Haar-wavelet | Symmetrical wavelet | Daubechies-wavelet |

12.9 | 6.2 | 12.2 |

We should mention that obtained ratios do not reveal real ability of particular wavelet to be estimate characteristics of defects. So, Haar-wavelet is not so sensitive to defect's characteristics as Symmetrical wavelet. Depending on specific task, Haar-wavelet, Daubechies-wavelet or some other type of wavelet can be applied for analysis of diagnostic signals with the purpose to detect wire defects or estimate its characteristics.

Also, we would like to notice that described approach of signal processing with application of WT ensures significant increase of sensibility and reliability of steel rope inspection. Furthermore it provides a basis for automated rope diagnosis.

- Sukhorukov V., Steel Wire Rope Inspection: New Instruments. - The 7th ECNDT, Copenhagen, May, 26-29, 1998
- Daubechies I., Ten Lectures on Wavelets - Philadelphia: 1995
- Slesarev D., Barat V., Application of wavelet transformation to the analysis of signals with impulse components. - Izmeritelnaja Technika, M: 2000. - No 7

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