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Characterizing the absorptivity of a rough metal surface is a difficult but important task. The uncertainty will be enlarged by using the indirect method, i.e. 1 – reflectance measurement. In contrast, the calorimetric method is of high fidelity. However, it is difficult to extract the absorptivity. The variation of temperature follows the heat conduction equation which is a differential equation. Therefore, a method based on physics-informed neural networks (PINNs) is proposed. In this method, the temperature rising curve is fitted to the differential equation by the neural network. The differential equation is incorporated into the network through the loss function. When the training is done, the absorptivity can be extracted. For demonstration, the numerical test and experimental test are performed. A set of temperature profiles with different absorptivity values is generated numerically. Then the absorptivity is extracted by PINN. The numerical results show that this method is able to determine the absorptivity and possesses the advantages of strong anti-interference capability and high accuracy. The maximum absolute error is 0.00092 in the range of 0.05 to 0.2. In the experiment, sand-blasted gold coated aluminum plates are used as the test objects, and they are heated by a continuous wave infrared laser. The temperature is measured by a K thermocouple. Then the absorptivity values of different samples are determined by the PINN, ranging from 2% to 10% because of the differences in roughness and electroplating process. The measurement repeatability is < 1%. The proposed method is very promising to become a powerful tool for measuring the absorptivity of rough metal surface.
[1] Indhu R, Vivek V, Sarathkumar L, Bharatish A, Soundarapandian S 2018 Lasers Manuf. Mater. Process. 5 458
Google Scholar
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Zhang R M, Li L, Li Z H, Guan L, Hou S P, Tan X Y 2005 Acta Phys. Sin. 54 1283
Google Scholar
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Google Scholar
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Google Scholar
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Su B R, Wang Z E, Luo N C, Hu W F, Xi Q X 1982 Laser 9 533
[7] 陶文栓 2022 传热学 (第四版) (北京: 高等教育出版社) 第100—106页
Tao W S 2022 Heat Conduction (4th Ed.) (Beijing: Higher Education Press) pp100–106
[8] Haag M, Hügel H, Albright C E, Ramasamy S 1996 J. Appl. Phys. 79 3835
Google Scholar
[9] 蔺秀川, 邵天敏 2001 50 856
Google Scholar
Lin X C, Shao T M 2001 Acta Phys. Sin. 50 856
Google Scholar
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Google Scholar
[11] Raissi M, Perdikaris P, Karniadakis G E 2019 J. Comput. Phys. 378 686
Google Scholar
[12] Chang C W, Liu C H, Wang C C 2018 Smart Sci. 6 94
Google Scholar
[13] Cai S Z, Mao Z P, Wang Z C, Yin M L, Karniadakis G E 2021 Acta Mech. Sin. 37 1727
Google Scholar
[14] Cai S, Wang Z, Wang S, Perdikaris P, Karniadakis G E 2021 J. Heat Transfer 143 060801
Google Scholar
[15] Mao Z P, Jagtap A D, Karniadakis G E 2020 Comput. Methods Appl. Mech. Eng. 360 112789
Google Scholar
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Google Scholar
[17] Wang S, Yu X, Perdikaris P 2020 J. Comput. Phys. 449 110768
Google Scholar
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Google Scholar
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Google Scholar
[21] Ge S Y, Na H Y 1989 Properties of Thermal Radiation and its Measurement (Beijing: Science Press) pp132–137 [葛绍岩, 那鸿悦 1989 热辐射性质及其测量 (北京: 科学出版社) 第132—137页]
Ge S Y, Na H Y 1989 Properties of Thermal Radiation and its Measurement (Beijing: Science Press) pp132–137
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图 1 吸收率参数识别物理信息神经网络
Figure 1. Physics informed neural network for absorptivity identification.
图 2 不同吸收率下的温度变化历程
Figure 2. Temperature profiles under different absorptivity.
图 3 权重对吸收率预测精度的影响
Figure 3. Effect of function loss weight on absorptivity predication.
图 4 不同吸收率解析结果
Figure 4. Absorptivity resolved results for different preset values.
图 5 实验装置
Figure 5. Experimental setup.
图 6 温度变化历程
Figure 6. Temperature history.
图 7 下降沿拟合结果
Figure 7. Fitting results of falling edge.
图 8 损失函数及吸收率随迭代次数的变化
Figure 8. Loss functions and absorptivity varying with iterations.
图 9 预测温度与测量温度对比
Figure 9. Comparison between predicted temperature and experimental data.
图 10 不同样品重复测量温度变化历程
Figure 10. Temperature histories of different samples.
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[1] Indhu R, Vivek V, Sarathkumar L, Bharatish A, Soundarapandian S 2018 Lasers Manuf. Mater. Process. 5 458
Google Scholar
[2] 张端明, 李莉, 李智华, 关丽, 侯思普, 谭新玉 2005 54 1283
Google Scholar
Zhang R M, Li L, Li Z H, Guan L, Hou S P, Tan X Y 2005 Acta Phys. Sin. 54 1283
Google Scholar
[3] Bergström D 2008 Ph. D. Dissertation (Sweden: Luleå University of Technology
[4] Gindele K, Kohl M, Mast M 1985 Appl. Opt. 24 1757
Google Scholar
[5] 高爱华, 王少刚, 闫丽荣 2016 应用光学 37 303
Google Scholar
Gao A H, Wang S G, Yan L R 2016 J. Appl. Opt. 37 303
Google Scholar
[6] 苏宝嫆, 王哲恩, 罗乃草, 胡文富, 奚全新 1982 激光 9 533
Su B R, Wang Z E, Luo N C, Hu W F, Xi Q X 1982 Laser 9 533
[7] 陶文栓 2022 传热学 (第四版) (北京: 高等教育出版社) 第100—106页
Tao W S 2022 Heat Conduction (4th Ed.) (Beijing: Higher Education Press) pp100–106
[8] Haag M, Hügel H, Albright C E, Ramasamy S 1996 J. Appl. Phys. 79 3835
Google Scholar
[9] 蔺秀川, 邵天敏 2001 50 856
Google Scholar
Lin X C, Shao T M 2001 Acta Phys. Sin. 50 856
Google Scholar
[10] LeCun Y, Bengio Y, Hinton G 2015 Nature 521 436
Google Scholar
[11] Raissi M, Perdikaris P, Karniadakis G E 2019 J. Comput. Phys. 378 686
Google Scholar
[12] Chang C W, Liu C H, Wang C C 2018 Smart Sci. 6 94
Google Scholar
[13] Cai S Z, Mao Z P, Wang Z C, Yin M L, Karniadakis G E 2021 Acta Mech. Sin. 37 1727
Google Scholar
[14] Cai S, Wang Z, Wang S, Perdikaris P, Karniadakis G E 2021 J. Heat Transfer 143 060801
Google Scholar
[15] Mao Z P, Jagtap A D, Karniadakis G E 2020 Comput. Methods Appl. Mech. Eng. 360 112789
Google Scholar
[16] Cuomo S, di Cola V S, Giampaolo F, Rozza G, Raissi M, Piccialli F 2022 J. Sci. Comput. 92 88
Google Scholar
[17] Wang S, Yu X, Perdikaris P 2020 J. Comput. Phys. 449 110768
Google Scholar
[18] McClenny L D, Braga-Neto U M 2023 J. Comput. Phys. 474 111722
Google Scholar
[19] Xu K, Darve E 2021 arXiv: 2105.07552 [math. NA]
[20] Dudoit S, Fridlyand J 2003 Bioinformatics 19 1090
Google Scholar
[21] Ge S Y, Na H Y 1989 Properties of Thermal Radiation and its Measurement (Beijing: Science Press) pp132–137 [葛绍岩, 那鸿悦 1989 热辐射性质及其测量 (北京: 科学出版社) 第132—137页]
Ge S Y, Na H Y 1989 Properties of Thermal Radiation and its Measurement (Beijing: Science Press) pp132–137
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