Wall emissivity solved by bidirectional reflection distribution function combined with Bi-LSTM network

Li Fu; Jinhao Fan; Zhaoyi Zhang; Lei Zhang

doi:10.3788/IRLA20220355

Journals >Infrared and Laser Engineering >Volume 52 >Issue 2 >Page 20220355 > Article

Infrared and Laser Engineering
Vol. 52, Issue 2, 20220355 (2023)

Wall emissivity solved by bidirectional reflection distribution function combined with Bi-LSTM network

Li Fu¹, Jinhao Fan¹, Zhaoyi Zhang¹, and Lei Zhang²

Author Affiliations

¹School of Automation, Shenyang Aerospace University, Shenyang 110136, China

²Shenyang Aircraft Design Research Institute, Shenyang 110136, China

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DOI: 10.3788/IRLA20220355 Cite this Article

Li Fu, Jinhao Fan, Zhaoyi Zhang, Lei Zhang. Wall emissivity solved by bidirectional reflection distribution function combined with Bi-LSTM network[J]. Infrared and Laser Engineering, 2023, 52(2): 20220355 Copy Citation Text

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Abstract

Wall spectral emissivity solution is one of the key techniques for infrared stealth of aircraft. Firstly, the wall reflected light path and light source were designed, and the brightness sequence of wall reflected radiation was obtained by spectral radiometer. In order to eliminate the influence of external interference on the solving accuracy of spectral emissivity as much as possible, Bi-LSTM brightness regression network model was designed based on bidirectional LSTM network, and the test samples were trained and learned. The wall emissivity solution model based on BRDF and the luminance regression model based on Bi-LSTM network were used to solve the wall emissivity. The calculation results show that the relative error of the proposed wall emissivity solution method based on BRDF is 12.21%, which meets the requirements of engineering test.

Keywords

BRDF LSTM network radiance spectral emissivity

$ {f_i}\left( {{\theta _i},{\varphi _i},{\theta _r},{\varphi _r},\lambda } \right) = \frac{{{\text{d}}L\left( {{\theta _i},{\varphi _i},{\theta _r},{\varphi _r},\lambda } \right)}}{{{\text{d}}E\left( {{\theta _i},{\varphi _i},\lambda } \right)}} $

(1)

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$ {\varepsilon _h}\left( T \right) = \frac{{M\left( T \right)}}{{{M_{bb}}\left( T \right)}} $

(2)

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$ {\varepsilon _{\lambda h}}\left( T \right) = \frac{{{M_\lambda }\left( T \right)}}{{{M_{\lambda bb}}\left( T \right)}} $

(3)

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$ \text{d}P\text={{\displaystyle \int }}_{半球空间}{\text{d}}^{\text{2}}P=\left[{{\displaystyle \int }}_{2\pi 球面度}L\mathrm{cos}\theta \mathrm{d} \varOmega \right]\text{d}A $

(4)

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$ M=\frac{\text{d}P}{\text{d}A}={{\displaystyle \int }}_{2\pi 球面度}L\mathrm{cos}\theta \mathrm{d} \varOmega $

(5)

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$ \text{d}{P}_{r}=\left[ { {\displaystyle {\int }_{2\pi 球面度}{L}_{in}\rho (\theta )\mathrm{d} \varOmega } } \right]\text{d}A $

(6)

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\begin{aligned} M_{r} = & \frac{d P_{r}}{d A} = \int_{2 π 球 面 度} L_{i n} ρ (θ) d Ω = \\ \int_{φ} \int_{θ} L_{r} (θ) sin θ d φ d θ \end{aligned}

(7)

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$ \rho = \frac{{{M_r}}}{{{E_{in}}}} $

(8)

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$ \rho = \frac{{{M_r}}}{{{M_{bb}}}} = \dfrac{{ \displaystyle \int_\varphi \displaystyle \int_\theta {L_r}\left( \theta \right)\sin \theta {\text{d}}\varphi {\text{d}}\theta }}{{{M_{bb}}}} $

(9)

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$ \rho = \frac{{{M_r}}}{{{M_{bb}}}} = \frac{{ \displaystyle \sum\nolimits_{k = 1}^n \int_\varphi \int_{{\theta _{k1}}}^{{\theta _{k2}}} {L_r}\left( {{\theta _k}} \right)\sin \theta {\text{d}}\varphi {\text{d}}\theta }}{{{M_{bb}}}} $

(10)

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$ \rho = \frac{{{M_r}}}{{{M_{bb}}}} = \frac{{\displaystyle \sum\nolimits_{k = 1}^n \displaystyle \int_\varphi \displaystyle \int_{{\theta _{k1}}}^{{\theta _{k2}}} \left( {{L_r}\left( {{\theta _k}} \right) - {L_g}} \right)\sin \theta {\text{d}}\varphi {\text{d}}\theta }}{{{M_{bb}} - {M_g}}} $

(11)

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