A Multi-Spectral Temperature Field Reconstruction Technology under a Sparse Projection
Abstract
:1. Introduction
2. Basic Principles
2.1. Objective Function
2.2. Constraints
2.3. Reconstruction of the Field
- (1)
- (2)
- Build a function model. As shown in Figure 5b, according to the temperature measurement method described in [15], the sum of squares of temperature differences in a single sub-region in different bands is established by using the radiation information in ; that is, the temperature correlation between different bands is used to measure the temperature, and the temperature correlation between different sub-regions is coupled to establish the function model F, as shown in Equation (8).
- (3)
- Data measurement. As shown in Figure 5c, a distributed network composed of multiple temperature-measuring units is used to collect projection data from multiple angles of the measuring field, and it is used as the constraint condition to measure the reconstruction of the field. The projection data are shown in Figure 5d.
- (4)
- Function optimization. The equation constraints obtained in step (3) are used to optimize the field reconstruction objective function, and the function solution is judged to reach the optimal value according to the convergence condition of the algorithm; otherwise, return to step (1), and the radiation value of each band of the field to be measured is optimized until the optimal solution is obtained. The optimization algorithm can be realized through the use of gradient descent, particle swarm, and neural networks. In Figure 5, there are no specific requirements for the use of neural networks. In this paper, a BP neural network has been adopted to achieve optimization. The input layer is m × j neurons, the output layer is m × j neurons, and there are three hidden layers.
- (5)
- Temperature field reconstruction. Combined with Equation (7) and using the temperature measurement method in [15], the optimal solution of the function is substituted, and the temperature value of the sub-region is calculated to realize the reconstruction of the temperature field.
3. Experimental Verification
3.1. Experimental Setup
3.2. Simulation Results
3.3. Experimental Test
3.4. Advantages of This Method
4. Discussion
4.1. The Influence of the Angle between Two Projections on the Reconstruction Results
4.2. The Influence of the Number of Sub-Regions on the Reconstruction Results
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Temperature (K) | Wavelength (nm) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
5066 | 5126 | 5185 | 5244 | 5304 | 5363 | 5422 | 5481 | 5541 | 5600 | 5659 | |
600 | 0.32 | 0.6 | 0.52 | 0.4 | 0.39 | 0.52 | 0.47 | 0.31 | 0.21 | 0.16 | 0.12 |
1200 | 0.19 | 0.29 | 0.43 | 0.35 | 0.31 | 0.31 | 0.37 | 0.41 | 0.39 | 0.24 | 0.19 |
2400 | 0.13 | 0.28 | 0.36 | 0.36 | 0.32 | 0.28 | 0.24 | 0.24 | 0.25 | 0.28 | 0.29 |
Projection (10−11 W·m−2·μm−1·sr−1) | Wavelength (nm) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
5066 | 5126 | 5185 | 5244 | 5304 | 5363 | 5422 | 5481 | 5541 | 5600 | 5659 | ||
Single-peak | P(0°,1) | 5.68 | 10.00 | 8.22 | 5.98 | 5.46 | 6.95 | 5.90 | 3.67 | 2.42 | 1.72 | 1.23 |
P(0°,2) | 4.26 | 6.97 | 7.35 | 5.51 | 4.79 | 5.24 | 5.20 | 4.45 | 3.61 | 2.24 | 1.64 | |
P(0°,3) | 4.08 | 6.93 | 7.14 | 5.55 | 4.83 | 5.17 | 4.86 | 4.03 | 3.31 | 2.33 | 1.86 | |
P(0°,4) | 4.26 | 6.97 | 7.35 | 5.51 | 4.79 | 5.24 | 5.20 | 4.45 | 3.61 | 2.24 | 1.64 | |
P(0°,5) | 5.68 | 10.00 | 8.22 | 5.98 | 5.46 | 6.95 | 5.90 | 3.67 | 2.42 | 1.72 | 1.23 | |
P(90°,1) | 5.68 | 10.00 | 8.22 | 5.98 | 5.46 | 6.95 | 5.90 | 3.67 | 2.42 | 1.72 | 1.23 | |
P(90°,2) | 4.26 | 6.97 | 7.35 | 5.51 | 4.79 | 5.24 | 5.20 | 4.45 | 3.61 | 2.24 | 1.64 | |
P(90°,3) | 4.08 | 6.93 | 7.14 | 5.55 | 4.83 | 5.17 | 4.86 | 4.03 | 3.31 | 2.33 | 1.86 | |
P(90°,4) | 4.26 | 6.97 | 7.35 | 5.51 | 4.79 | 5.24 | 5.20 | 4.45 | 3.61 | 2.24 | 1.64 | |
P(90°,5) | 5.68 | 10.00 | 8.22 | 5.98 | 5.46 | 6.95 | 5.90 | 3.67 | 2.42 | 1.72 | 1.23 | |
Multi-peak | P(0°,1) | 5.69 | 10.06 | 8.23 | 5.98 | 5.47 | 6.95 | 5.91 | 3.68 | 2.42 | 1.72 | 1.23 |
P(0°,2) | 5.70 | 10.08 | 8.25 | 5.99 | 5.48 | 6.97 | 5.92 | 3.68 | 2.43 | 1.73 | 1.23 | |
P(0°,3) | 5.69 | 10.06 | 8.23 | 5.98 | 5.47 | 6.95 | 5.91 | 3.68 | 2.42 | 1.72 | 1.23 | |
P(0°,4) | 5.70 | 10.08 | 8.25 | 5.99 | 5.48 | 6.97 | 5.92 | 3.68 | 2.43 | 1.73 | 1.23 | |
P(0°,5) | 5.69 | 10.06 | 8.23 | 5.98 | 5.47 | 6.95 | 5.91 | 3.68 | 2.42 | 1.72 | 1.23 | |
P(90°,1) | 5.69 | 10.06 | 8.23 | 5.98 | 5.47 | 6.95 | 5.91 | 3.68 | 2.42 | 1.72 | 1.23 | |
P(90°,2) | 5.70 | 10.08 | 8.25 | 5.99 | 5.48 | 6.97 | 5.92 | 3.68 | 2.43 | 1.73 | 1.23 | |
P(90°,3) | 5.69 | 10.06 | 8.23 | 5.98 | 5.47 | 6.95 | 5.91 | 3.68 | 2.42 | 1.72 | 1.23 | |
P(90°,4) | 5.70 | 10.08 | 8.25 | 5.99 | 5.48 | 6.97 | 5.92 | 3.68 | 2.43 | 1.73 | 1.23 | |
P(90°,5) | 5.69 | 10.06 | 8.23 | 5.98 | 5.47 | 6.95 | 5.91 | 3.68 | 2.42 | 1.72 | 1.23 |
Temperature Field | Aver (%) | Max (%) | Rmse (%) |
---|---|---|---|
Single-peak | 1.64 | 6.26 | 5.08 |
Multi-peak | 2.1 | 12.25 | 3.99 |
Method | Prior Knowledge | Error Distribution (%) | Projection Numbers |
---|---|---|---|
Textual method | × | 1.64–12.25 | 2 |
Method in [12] | √ | 0.5–11.87 | 6 |
Method in [13] | √ | None | 15–180 |
Method in [14] | √ | 0.21–21.57 | 2–6 |
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Zhang, X.; Han, Y. A Multi-Spectral Temperature Field Reconstruction Technology under a Sparse Projection. Photonics 2024, 11, 767. https://doi.org/10.3390/photonics11080767
Zhang X, Han Y. A Multi-Spectral Temperature Field Reconstruction Technology under a Sparse Projection. Photonics. 2024; 11(8):767. https://doi.org/10.3390/photonics11080767
Chicago/Turabian StyleZhang, Xuan, and Yan Han. 2024. "A Multi-Spectral Temperature Field Reconstruction Technology under a Sparse Projection" Photonics 11, no. 8: 767. https://doi.org/10.3390/photonics11080767