Terahertz Based Accurate Thickness Measurement of Thermal Barrier Coatings Using the Key Time-Frequency Information Fusion

doi:10.3901/JME.2023.14.010

Abstract

Abstract: The current Terahertz (THz) thickness measurement is mainly based on the theory of time-of-flight, but the accurate thickness measurement of thermal barrier coatings requires to introduce the THz frequency signal to extract the refractive index online. To this end, a fusion method of the key time-frequency information is presented by the transmission rules of THz waves, and the deep learning is integrated to decrease the thickness measurement errors, which reduces the influence of peak distortions for refractive index extractions and improves the accuracy of uneven thermal barrier coatings thickness measurements. To begin with, an analytical model of THz signals considering the roughness of thermal barrier coatings is constructed, and it is found that time-of-flight and refractive index can be solved by time-domain and frequency-domain data. Then, the wavelet transform is utilized to enable the time-frequency fusion of THz signals. In terms of Beer-Lambert’s law, the physical mechanism of the entire time-frequency image containing redundant information is revealed. Finally, according to the thickness feature, the key time-frequency image is acquired as the input of the convolutional neural network to establish a thickness measurement method. The simulated and experimental results demonstrate that compared with the other four thickness measurement approaches, including the peak locations, machine learning with time-domain signals-based features, convolutional neural networks with the temporal data, down-sampling and entire time-frequency images, the average absolute errors of the approach with time-frequency images are reduced by 4.65 μm, 3.08 μm, 2.51 μm, 0.58 μm and 0.25 μm, respectively. In contrast to the convolutional neural network utilizing the entire time-frequency image, the training time of the convolutional neural networks with the time-frequency image is decreased about 1 446 s. The key time-frequency fusion method can be employed to improve the THz thickness measurement accuracy under the conditions of thermal barrier coatings with the uneven microstructure and peak distortions.

Key words: terahertz nondestructive testing, thermal barrier coating, time-frequency fusion, analytical model, convolutional neural network

CLC Number:

TH744

SUN Fengshan, FAN Mengbao, CAO Binghua, LIU Lin. Terahertz Based Accurate Thickness Measurement of Thermal Barrier Coatings Using the Key Time-Frequency Information Fusion[J]. Journal of Mechanical Engineering, 2023, 59(14): 10-22.

References

[1] PADTURE P,GELL M,JORDAN E. Thermal barriers coatings for gas-turbine engine applications[J]. Science,2002,296(5566):280-284.
[2] 何存富,杨玉娥,杨申,等. 毫米波检测热障涂层缺陷的方法研究[J]. 机械工程学报,2013,49(20):16-21. HE Cunfu,YANG Yue,YANG Shen,et al. Feasibility study on defects detection of thermal barrier coatings using millimeter wave[J]. Journal of Mechanical Engineering,2013,49(20):16-21.
[3] 李雪换,底月兰,王海斗,等. 基于声发射技术的热障涂层拉伸失效模式研究[J]. 机械工程学报,2020,56(14):57-64. LI Xuehuan,DI Yuelan,WANG Haidou,et al. Research on crack failure modes of thermal barrier coatings based on acoustic emission technique[J]. Journal of Mechanical Engineering,2020,56(14):57-64.
[4] MA Zhiyuan,ZHANG Wei,LUO Zhongbin,et al. Ultrasonic characterization of thermal barrier coatings porosity through BP neural network optimizing gaussian process regression algorithm[J]. Ultrasonics,2020,100(8):1-9.
[5] 龚榕,罗思琦,叶波,等. 厚度无损检测仪器的精度长期稳定性研究[J]. 机械工程学报,2019,55(21):161-169. GONG Rong,LUO Siqi,YE Bo,et al. Investigating long term stability of nondestructive testing equipment in thickness measuring[J]. Journal of Mechanical Engineering,2019,55(21):161-169.
[6] LI Yong,YAN Bei,LI Wenjia,et al. Thickness assessment of thermal barrier coatings of aeroengine blades via dual-frequency eddy current evaluation[J]. IEEE Magnetics Letters,2016,17(7):1-7.
[7] ZHU Wang,CAI Canying,YANG Li,et al. The evolution of pores in thermal barrier coatings under volcanic ash corrosion using X-ray computed tomography[J]. Surface & Coatings Technology,2019,357(15):372-378.
[8] SHI Licheng,LONG Yun,WANG Yuzhang,et al. On-line detection of porosity change of high temperature blade coating for gas turbine[J]. Infrared Physics & Technology,2020,100(8):1-11.
[9] 沈功田. 承压设备无损检测与评价技术发展现状[J]. 机械工程学报,2017,53(12):1-12. SHEN Gongtian. Development status of nondestructive testing and evaluation technique for pressure equipment[J]. Journal of Mechanical Engineering,2017,53(12):1-12.
[10] ZHOU Xu,YE Dongdong,WANG Weize,et al. Novel terahertz nondestructive method for measuring the thickness of thin oxide scale using different hybrid machine learning models[J]. Coatings,2020,10(9):805-810.
[11] UNNIKRISHNAKURUP S,DASH J,RAY S,et al. Nondestructive evaluation of thermal barrier coating thickness degradation using pulsed IR thermography and THz-TDS measurements:A comparative study[J]. NDT & E International,2020,116(11):1-9.
[12] 唐春华,李广荣,刘梅军,等. 等离子喷涂La₂Zr₂O₇热障涂层高温烧结的硬化行为[J]. 中国表面工程,2020,33(2):119-126. TANG Chunhua,LI Guangrong,LIU Meijun,et al. Sintering-stiffening behavior of plasma sprayed La₂Zr₂O₇ thermal barrier coatings during high temperature exposure[J]. China Surface Engineering,2020,33(2):119-126.
[13] KRIMI S,KLIER J,JONUSCHEIT J,et al. Highly accurate thickness measurement of multi-layered automotive paints using terahertz technology[J]. Applied Physics Letters,2016,109(2):7518-7526.
[14] CAO Binghua,WANG Mengyun,LI Xiaohan,et al. Noncontact thickness measurement of multilayer coatings on metallic substrate using pulsed terahertz Technology[J]. IEEE Sensors Journal,2020,20(6):3162-3171.
[15] FUKUCHI T,FUSE N,OKADA M,et al. Measurement of refractive index and thickness of topcoat of thermal barrier coating by reflection measurement of terahertz waves[J]. Electronics and Communications in Japan,2013,96(12):702-708.
[16] 张平,钟舜聪,张秋坤,等. 热障涂层折射率与厚度的太赫兹无损检测[J]. 机械工程学报,2021,57(20):47-56. ZHANG Ping,ZHONG Shuncong,ZHANG Qiukun,et al. Terahertz nondestructive testing of refractive index and thickness of thermal barrier coating[J]. Journal of Mechanical Engineering,2021,57(20):47-56.
[17] 代冰,王朋,周宇,等. 小波变换在太赫兹三维成像探测内部缺陷中的应用[J]. 物理学报,2017,66(8):373-379. DAI Bing,WANG Peng,ZHOU Yu,et al. Wavelet transform in the application of three-dimensional terahertz imaging for internal defect detection[J]. Acta Physica Sinica,2017,66(8):373-379.
[18] SANCHEZ A,HESHMAT B,AGHASI A,et al. Terahertz time-gated spectral imaging for content extraction through layered structures[J]. Nature Communications,2016,7(9):1-7.
[19] XU Yafei,FANG Xiangdong,FAN Shuting,et al. Double Gaussian mixture model-based terahertz wave dispersion compensation method using convex optimization technique[J]. Mechanical Systems and Signal Processing,2022,164(7):1-17.
[20] XU Yafei,WANG Xingyu,ZHANG Liuyang,et al. Terahertz nondestructive quantitative characterization for layer thickness based on sparse representation method[J]. NDT & E International,2021,124(11):1-9.
[21] XU Yafei,HAO Huibo,CITRIN D S,et al. Three-dimensional nondestructive characterization of delamination in GFRP by terahertz time-of-flight tomography with sparse Bayesian learning-based spectrum-graph integration strategy[J]. Composites Part B:Engineering,2021,225(10):1-11.
[22] SUN Fengshan,FAN Mengbao,CAO Binghua,et al. Terahertz based thickness measurement of thermal barrier coatings using long short-term memory networks and local extrema[J]. IEEE Transactions on Industrial Informatics,2022,18(4):2508-2517.
[23] YE Dongdong,WANG Weize,YIN Changdong,et al. Pulsed terahertz spectroscopy combined with hybrid machine learning approaches for structural health monitoring of multilayer thermal barrier coatings[J] Optics Express,2020,28(21):34875-34893.
[24] 陈是扦,彭志科,周鹏. 信号分解及其在机械故障诊断中的应用研究综述[J]. 机械工程学报,2020,56(17):91-107. CHEN Shiqian,PENG Zhike,ZHOU Peng. Review of signal decomposition theory and its applications in machine fault diagnosis[J]. Journal of Mechanical Engineering,2020,56(17):91-107.
[25] XU Lu,YIN Xingyao,ZONG Zhaoyun,et al. Synchrosqueezing matching pursuit time-frequency analysis[J]. IEEE Geoscience and Remote Sensing Letters,2020,10(5):1-5.
[26] SHI Shuyun,LI Chao,HU Jianmin,et al. A high frequency vibration compensation approach for terahertz SAR based on sinusoidal frequency modulation Fourier transform[J]. IEEE Sensors Journal,2021,21(9):796-803.
[27] DAI Bing,WANG Peng,WANG Tianyi,et al. Improved terahertz nondestructive detection of debonds locating in layered structures based on wavelet transform[J]. Composite Structures,2017,168(3):562-568.
[28] 蒋永华,汤宝平,刘文艺,等. 基于参数优化Morlet小波变换的故障特征提取方法[J]. 仪器仪表学报,2010,31(1):56-60. JIANG Yonghua,TANG Baobing,LIU Wenyi,et al. Feature extraction method based on parameter optimized Morlet wavelet transform[J]. Chinese Journal of Scientific Instrument,2010,31(1):56-60.
[29] LONG Zhenyu,WANG Tianyi,YOU Chenwu,et al. Terahertz image super-resolution based on a deep convolutional neural network[J]. Applied Optics,2019,58(10):2731-2735.
[30] VERSTRAET D,FERRADA A,LOPEZ D,et al. Deep learning enabled fault diagnosis using time-frequency image analysis of rolling element bearings[J]. Shock and Vibration,2017,17(6):1-17.
[31] 马愈昭,王瑞松,熊兴隆. 基于BLCD分解与ACO-DBN网络的光纤振动信号识别[J]. 光子学报,2021,50(2):52-64. MA Yuzhao,WANG Ruisong,XIONG Xinglong,et al. Fiber-optic vibration signal recognition based on BLCD decomposition and ACO-DBN network[J]. Acta Photonica Sinica,2021,50(2):52-64.
[32] 郑国峰,上官文斌,韩鹏飞,等. 基于小波变换的汽车零部件加速耐久性多轴载荷谱编辑方法研究[J]. 机械工程学报,2018,54(10):156-166. ZHENG Guofeng,SHANGGUAN Wenbin,HAN Pengfei,et al. Study of load spectrum edition method based on the wavelet transform to the accelerated durability test of the vehicle component[J]. Journal of Mechanical Engineering,2018,54(10):156-166.
[33] ZHOU Yu,WANG Tianyi,DAI Bing,et al. High-precision terahertz frequency modulated continuous wave imaging method using continuous wavelet transform[J]. Optical Engineering,2018,57(2):1-7.
[34] 孙凤山,范孟豹,曹丙花,等. 基于混沌映射与差分进化自适应教与学优化算法的太赫兹图像增强模型[J]. 仪器仪表学报,2021,42(4):92-101. SUN Fengshan,FAN Mengbao,CAO Binghua,et al. The terahertz image enhancement model based on adaptive teaching-learning based optimization algorithm with chaotic mapping and differential evolution[J]. Chinese Journal of Scientific Instrument,2021,42(4):92-101.
[35] TSAI C. Confined teaching-learning-based optimization with variable search strategies for continuous optimization[J]. Information Sciences,2019,500(10):34-47.
[36] 苏海霞,张朝晖,赵小燕,等. 太赫兹谱定量测试中朗伯比尔定律表征形式分析[J]. 光谱学与光谱分析,2013,33(12):3180-3186. SU Haixia,ZHANG Zhaohui,ZHAO Xiaoyan,et al. The Lambert-Beer's law characterization of formal analysis in terahertz spectrum quantitative testing[J]. Spectroscopy and Spectral Analysis,2013,33(12):3180-3186.