Non-Destructive Detection of Wire Rope Discontinuities from Residual Magnetic Field Images Using the Hilbert-Huang Transform and Compressed Sensing
Abstract
:1. Introduction
2. RMF Detection
2.1. Platform Design
2.2. Data Acquisition
2.3. RMF Image
3. Signal Processing
3.1. Reprocessing Theory
- The average number of maxima and minima of an IMF component must be equivalent to the number of 0 crossings, or they differ by 1 at most.
- The average of the maxima and minima, as defined by the envelope, should be 0 at any given moment.
- (1)
- First, extend the raw signal to obtain , and initialize the residual signal , IMFs set as .
- (2)
- Add Gaussian white noise to :
- (3)
- Implement EMD for to obtain IMF :
- (4)
- Repeat steps (2) and (3) k times, obtaining an IMF set , and calculate the average of the IMFs. Update as follows:
- (5)
- If i > n or cannot be further decomposed, the decomposition is complete. Otherwise, i = i + 1, and return to step (2).
3.2. Compressed Sensing Theory
3.3. Description of the De-Noising Algorithm
- i
- The EEMD described in Section 3.1 is applied to the raw data, and the reprocessing signal is obtained.
- ii
- Apply CSWF to the re-processed signal of the i-th channel:
- (1)
- The Mallat decomposition algorithm is applied, and the sparse expression of signal is obtained for each scale .
- (2)
- Randomly generate a Gaussian matrix and calculate the linear measure under the matrix : .
- (3)
- Implement the OMP algorithm and reconstruct the most-sparse wavelet coefficient . These procedures are as follows:
- Step One: initialize residue, , and index set, (empty set);
- For each iteration t from 1 to K (here, K = 8);
- Begin;
- Step Two: the inner product is calculated ;
- Then, the column whose inner product is the maximum in is obtained: ; The subscript is stored, and the most orthogonal column of Φ: , the selected column of , is set to 0;
- Step Three: The least-squares method is implemented;
- Step Four: Approximation is updated;
- The residue, , is updated;
- End.
- (4)
- Utilize the inverse wavelet transform for the approximate coefficients , and the RMF signal is then re-established.
- iii
- If the channel number i < 18, return to step iv or end the process.
4. RMF Image Processing
4.1. Morphological Processing and Defect Location Detection
4.2. Normalization and Resolution Enhancement
- The position of the minimum of defect is obtained by searching the modulus maximum of a target region image in multiplied image. Then, the axial center is .
- In the target region, the defect image can be expressed as:
- If , is given as follows:If , is given as follows:
5. Detection of Broken Wires
5.1. Extracting Artificial Image Characteristics
5.2. Quantitative Defect Detection
6. Results and Discussion
7. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Number of Broken Wires | 1 | 2 | 3 | 4 | 5 | 7 |
---|---|---|---|---|---|---|
102 | 254 | 231 | 164 | 251 | 174 | |
17.3 | 4.12 | 20 | 19.4 | 15.4 | 28.57 | |
4.60 × 10−3 | 2.61 × 10−4 | 6.11 × 10−3 | 5.73 × 10−3 | 3.61 × 10−3 | 1.24 × 10−2 | |
−0.076 | −0.009 | −0.35 | −0.112 | −0.267 | −0.549 | |
0.023 | 0.947 | 0.071 | 0.02 | 0.758 | 0.068 | |
5.91 | 0.33 | 4.99 | 6.1 | 1.35 | 5.65 | |
M1 | 1.71 × 10−3 | 5.66 × 10−4 | 7.33 × 10−4 | 1.04 × 10−3 | 6.48 × 10−4 | 1.01 × 10−3 |
M2 | 7.42 × 10−9 | 1.89 × 10−11 | 8.08 × 10−11 | 1.72 × 10−10 | 5.39 × 10−12 | 3.18 × 10−10 |
M3 | 1.82 × 10−12 | 6.70 × 10−15 | 1.04 × 10−13 | 6.27 × 10−13 | 5.68 × 10−16 | 4.22 × 10−15 |
M4 | 2.62 × 10−12 | 8.36 × 10−15 | 6.85 × 10−14 | 1.08 × 10−12 | 5.37 × 10−15 | 1.50 × 10−13 |
M5 | 4.79 × 10−24 | 2.60 × 10−29 | −5.03 × 10−27 | 8.05 × 10−25 | 9.31 × 10−3° | 3.09 × 10−27 |
M6 | 1.95 × 10−15 | −1.14 × 10−18 | −2.39 × 10−17 | 4.37 × 10−17 | 1.49 × 10−18 | 4.55 × 10−17 |
M7 | −3.11 × 10−24 | 5.68 × 10−29 | 2.84 × 10−27 | 3.69 × 10−25 | −9.77 × 10−31 | −2.19 × 10−27 |
Spread | Maximum Error | Average Broken Wires Error | Training Accuracy | Recognition |
---|---|---|---|---|
0.05 | 5 | 1.25 | 1 | 78.13% |
0.10 | 5 | 1.0313 | 96.70% | 84.38% |
0.12 | 5 | 0.7813 | 95.60% | 93.75% |
0.15 | 5 | 1 | 86.81% | 87.50% |
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Zhang, J.; Tan, X.; Zheng, P. Non-Destructive Detection of Wire Rope Discontinuities from Residual Magnetic Field Images Using the Hilbert-Huang Transform and Compressed Sensing. Sensors 2017, 17, 608. https://doi.org/10.3390/s17030608
Zhang J, Tan X, Zheng P. Non-Destructive Detection of Wire Rope Discontinuities from Residual Magnetic Field Images Using the Hilbert-Huang Transform and Compressed Sensing. Sensors. 2017; 17(3):608. https://doi.org/10.3390/s17030608
Chicago/Turabian StyleZhang, Juwei, Xiaojiang Tan, and Pengbo Zheng. 2017. "Non-Destructive Detection of Wire Rope Discontinuities from Residual Magnetic Field Images Using the Hilbert-Huang Transform and Compressed Sensing" Sensors 17, no. 3: 608. https://doi.org/10.3390/s17030608