Sparse Reconstruction for Temperature Distribution Using DTS Fiber Optic Sensors with Applications in Electrical Generator Stator Monitoring
Abstract
:1. Introduction
2. Overview of Thermal Imaging System
3. Distributed Temperature Sensing (DTS) Acquisition Model
4. Dictionary of Hotspots
5. Imaging Reconstruction Algorithm
Algorithm 1: Image Reconstruction Algorithm |
Require: g% DTS readings, H% sensitivity matrix, D% Dictionary of hotspots, Q% finite difference matrix |
Require: % Regulariztion parameter (set empirically) |
Require: e=10–9 % avoids zero division |
Require: HD = H × D % impulse response of the dictionary |
Require: = HD′ × g % intial solution |
Require: % minimum update to stop |
1: while stop > |
2: = |
3: Wh = diag(1 ./ (abs(g − HD × ) + e)) % data term weights |
4: Wl = diag(1 ./ (abs(Q × ) + e)) % penalization term weights |
5: = (HD′ × Wh × HD + × (Q′ × Wl × Q))\(HD′ × Wh × g) % least-squares |
6: stop = norm( − )/norm() % stopping criterion |
7: end while |
8: f = reshape(D × ,209,200) % thermal image |
6. Results
6.1. Simulated Results
6.2. Experimental Results
7. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Noise Level (SNR) | MSE (mean square error) | MTD (Maximum Temperature Difference) |
---|---|---|
Noiseless | 0.5657 | 0.1 °C |
50 dB | 2.0921 | −0.5 °C |
40 dB | 6.9929 | −3.6 °C |
30 dB | 9.3758 | −12.1 °C |
20 dB | 16.595 | −20.9 °C |
10 dB | 21.8149 | −23.7 °C |
SNR | Hotspot Length | MTD (Maximum Temperature Difference) |
---|---|---|
50 dB | 15 cm | −0.5 °C |
50 dB | 14 cm | −3.7 °C |
50 dB | 13 cm | −5.1 °C |
40 dB | 22 cm | −0.9 °C |
40 dB | 21 cm | −1.6 °C |
40 dB | 20 cm | −2.4 °C |
30 dB | 27 cm | −0.7 °C |
30 dB | 26 cm | −1.8 °C |
30 dB | 25 cm | −2.6 °C |
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Bazzo, J.P.; Pipa, D.R.; Da Silva, E.V.; Martelli, C.; Cardozo da Silva, J.C. Sparse Reconstruction for Temperature Distribution Using DTS Fiber Optic Sensors with Applications in Electrical Generator Stator Monitoring. Sensors 2016, 16, 1425. https://doi.org/10.3390/s16091425
Bazzo JP, Pipa DR, Da Silva EV, Martelli C, Cardozo da Silva JC. Sparse Reconstruction for Temperature Distribution Using DTS Fiber Optic Sensors with Applications in Electrical Generator Stator Monitoring. Sensors. 2016; 16(9):1425. https://doi.org/10.3390/s16091425
Chicago/Turabian StyleBazzo, João Paulo, Daniel Rodrigues Pipa, Erlon Vagner Da Silva, Cicero Martelli, and Jean Carlos Cardozo da Silva. 2016. "Sparse Reconstruction for Temperature Distribution Using DTS Fiber Optic Sensors with Applications in Electrical Generator Stator Monitoring" Sensors 16, no. 9: 1425. https://doi.org/10.3390/s16091425