POD-Based Constrained Sensor Placement and Field Reconstruction from Noisy Wind Measurements: A Perturbation Study
Abstract
:1. Introduction
2. A POD-Based Sensor Placement Strategy
2.1. A Review of Gappy-POD
2.2. Constrained Sensor Placement
3. Uncertainty in Measurements
3.1. Results for Uniform Measurement Errors
3.2. Results for Non-Uniform Measurement Errors
4. Detecting the Malfunctioning Sensor
- For each sensor location , we use the data from , , …, , , …, to reconstruct the field and denote the reconstructed valued at this point as . Here, we take as we consider only the first 24 snapshot from our data.
- Compute the difference between the reconstructed value and the observed value at each : , .
- Compare the sum of over all snapshots at each . When is large, we claim that the i-th sensor is not functioning well.
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Four Modes | Six Modes | Eight Modes |
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6s-6s-6s-6s | 4s-4s-4s-4s-4s-4s | 3s-3s-3s-3s-3s-3s-3s-3s |
R Value | ||||
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Cond(M) |
R Value | ||||
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maximum of | ||||
average of |
R Value | ||||
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maximum of | ||||
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Zhang, Z.; Yang, X.; Lin, G. POD-Based Constrained Sensor Placement and Field Reconstruction from Noisy Wind Measurements: A Perturbation Study. Mathematics 2016, 4, 26. https://doi.org/10.3390/math4020026
Zhang Z, Yang X, Lin G. POD-Based Constrained Sensor Placement and Field Reconstruction from Noisy Wind Measurements: A Perturbation Study. Mathematics. 2016; 4(2):26. https://doi.org/10.3390/math4020026
Chicago/Turabian StyleZhang, Zhongqiang, Xiu Yang, and Guang Lin. 2016. "POD-Based Constrained Sensor Placement and Field Reconstruction from Noisy Wind Measurements: A Perturbation Study" Mathematics 4, no. 2: 26. https://doi.org/10.3390/math4020026
APA StyleZhang, Z., Yang, X., & Lin, G. (2016). POD-Based Constrained Sensor Placement and Field Reconstruction from Noisy Wind Measurements: A Perturbation Study. Mathematics, 4(2), 26. https://doi.org/10.3390/math4020026