[1] Ko W L, Fleischer V, Lung S F. Curvilinear displacement transfer functions for deformed shape predictions of curved structures using distributed surface strains[EB/OL]. https://ntrs.nasa.gov/citations/20180006739

[2] Xu G H, Chen W, Huang H et al. Research on structural deformation reconstruction based on inverse finite element method[J]. Ship Science and Technology, 46, 133-140(2024).

[3] Yu S Q, Hu D, Liu W. Vision-based optical 3D reconstruction and the application in crop information perception[J]. Laser & Optoelectronics Progress, 61, 0400004(2024).

[4] Cui H H, Tian L F, Wang J R et al. Multi-objective optimization-based planning algorithm for efficient visual inspection[J]. Acta Optica Sinica, 44, 0415001(2024).

[5] Schneebeli N L, Marques C, Leal-Junior A. 2D shape reconstruction with fiber Bragg gratings embedded in rubbers using machine learning methods[J]. Optical Fiber Technology, 82, 103618(2024).

[6] Li M, Liao Y B[M]. Application technology of optical fiber sensor(2018).

[7] Foss G C, Haugse E D. Using modal test results to develop strain to displacement transformations[J]. Proceedings of SPIE, 2460, 112(1995).

[8] Grédiac M. Method for surface reconstruction from slope or curvature measurements of rectangular areas[J]. Applied Optics, 36, 4823-4829(1997).

[9] Hai X, Zhang Y N, Shen L Y et al. Three dimensional curve reconstruction based on fiber Bragg grating sensors[C], 377-382(2015).

[10] Tessler A, Spangler J L. A variational principle for reconstruction of elastic deformations in shear deformable plates and shells[EB/OL]. https://ntrs.nasa.gov/citations/20030068121

[11] Tessler A, Roy R, Esposito M et al. Shape sensing of plate and shell structures undergoing large displacements using the inverse finite element method[J]. Shock and Vibration, 2018, 8076085(2018).

[12] Ko W, Richards W, Tran V T. Displacement theories for in-flight deformed shape predictions of aerospace structures[EB/OL]. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070032936.pdf

[13] Kang L H, Kim D K, Han J H. Estimation of dynamic structural displacements using fiber Bragg grating strain sensors[J]. Journal of Sound and Vibration, 305, 534-542(2007).

[14] Kim H I, Kang L H, Han J H. Shape estimation with distributed fiber Bragg grating sensors for rotating structures[J]. Smart Materials and Structures, 20, 035011(2011).

[15] Li L, Zhong B S, Li W Q et al. Structural shape reconstruction of fiber Bragg grating flexible plate based on strain modes using finite element method[J]. Journal of Intelligent Material Systems and Structures, 29, 463-478(2018).

[16] Fanelli P, Facci A L, Jannelli E. Live crack damage detection with local strain measurement on solid bodies subjected to hydrodynamic loading[J]. Procedia Structural Integrity, 8, 539-551(2018).

[17] Si Y W, Zeng J, Xia Y B et al. Monitoring and reconstruction of wing model strain field by distributed optical fiber[J]. Journal of Vibration, 40, 800-806, 830(2020).

[18] Liang J W, Zhao D J, Zhai W J. Identification of vibration parameters of beam structures based on FBG strain sensing network[J]. Electronic Measurement Technology, 43, 155-160(2020).

[19] Zhang Q, Fu X, Ren L. Deflection estimation of beam structures based on the measured strain mode shape[J]. Smart Materials and Structures, 30, 105003(2021).

[20] Shang Q F, Zhang X X. Surface reconstruction and error compensation method based on NSGA-Ⅱ sensing position optimization[J]. Acta Photonica Sinica, 53, 0206001(2024).

[21] Yi J C, Zhu X J, Zhang H S et al. Spatial shape reconstruction using orthogonal fiber Bragg grating sensor array[J]. Mechatronics, 22, 679-687(2012).

[22] Qu D M, Sun G K, Li H et al. Optical fiber sensing and reconstruction method for morphing wing flexible skin shape[J]. Chinese Journal of Scientific Instrument, 39, 144-151(2018).

[23] Zhang X X, Song Y M, Meng F Y et al. Flexible composite skin embedded optical fiber shape sensing for variant aircraft[J]. Infrared and Laser Engineering, 48, 0622003(2019).

[24] Sun G K, Qu D M, Yan G et al. Bending deformation of optical fiber sensing and shape reconstruction of soft pneumatic driver[J]. Optics and Precision Engineering, 27, 1052-1059(2019).

[25] Jäckle S, Strehlow J, Heldmann S. Shape sensing with fiber Bragg grating sensors: a realistic model of curvature interpolation for shape reconstruction[M]. Bildverarbeitung für die medizin 2019, 258-263(2019).

[26] Luo Z H, Cheng W S, Zeng S G et al. Deformation detection of a double-clamped beam according to ultra-weak fiber Bragg grating[J]. Applied Optics, 59, 9765-9770(2020).

[27] Tan Y G, Huang B, Liu H et al. Research on deformation reconstruction algorithm of thin plate based on distributed strain[J]. Journal of Mechanical Engineering, 56, 242-248(2020).

[28] Chen X Y, Yi X H, Qian J W et al. Updated shape sensing algorithm for space curves with FBG sensors[J]. Optics and Lasers in Engineering, 129, 106057(2020).

[29] Wang Y, Xu H Y, Wang J L et al. Three-dimensional surface shape reconstruction of fiber Bragg gratings in a ring arrangement[J]. Chinese Optics, 17, 398-408(2024).

[30] Peng X L, Cai J J, Gong Z P et al. Design and measurement of a parallel-dual FBG shape sensor for elastic cantilever beam structure shape reconstruction[J]. Optical Fiber Technology, 86, 103849(2024).

[31] Guo Y X, Yang Y H, Xiong L. Double-layer orthogonal fiber Bragg gratings flexible shape sensing technology[J]. Optics and Precision Engineering, 29, 2306-2315(2021).

[32] Lü J H, Dong M L, He Y L et al. Three-dimensional shape multi-core fiber reconstruction method of flexible mechanism by introducing curvature and angle correction[J]. Infrared and Laser Engineering, 50, 20200453(2021).

[33] Jiang Y, Yan J, Zhang L et al. Array FBG sensing and 3D reconstruction of spacecraft configuration[J]. Optoelectronics Letters, 18, 193-199(2022).

[34] Shang Q F, Liu F. Curvature and bending direction error correction model of FBG shape sensor[J]. Acta Optica Sinica, 43, 2228002(2023).

[35] Kefal A, Yildiz M. Modeling of sensor placement strategy for shape sensing and structural health monitoring of a wing-shaped sandwich panel using inverse finite element method[J]. Sensors, 17, 2775(2017).

[36] Kefal A, Mayang J B, Oterkus E et al. Three dimensional shape and stress monitoring of bulk carriers based on iFEM methodology[J]. Ocean Engineering, 147, 256-267(2018).

[37] Kefal A, Tabrizi I E, Yildiz M et al. A smoothed iFEM approach for efficient shape-sensing applications: numerical and experimental validation on composite structures[J]. Mechanical Systems and Signal Processing, 152, 107486(2021).

[38] Kefal A, Tabrizi I E, Tansan M et al. An experimental implementation of inverse finite element method for real-time shape and strain sensing of composite and sandwich structures[J]. Composite Structures, 258, 113431(2021).

[39] Liu M Y, Zhang X, Song H et al. Inverse finite element method for reconstruction of deformation in the gantry structure of heavy-duty machine tool using FBG sensors[J]. Sensors, 18, 2173(2018).

[40] Gherlone M, Cerracchio P, Mattone M. Shape sensing methods: review and experimental comparison on a wing-shaped plate[J]. Progress in Aerospace Sciences, 99, 14-26(2018).

[41] Fu S S, Sun G K, He Y L et al. Simulation study on wing skin deformation monitoring based on inverse finite element method[J]. Aeronautical Manufacturing Technology, 65, 107-114(2022).

[42] Wu M Q, Tan S J, Gao F X. Shape reconstruction of plane beam with finite deformation based on absolute nodal coordinate formulation[J]. Chinese Journal of Theoretical and Applied Mechanics, 53, 2776-2789(2021).

[43] Yuan S, Sun G K, Yu K et al. In-orbit thermal deformation monitoring for composite laminated structures of remote sensing satellites using temperature self-decoupling fiber optical system and inverse finite element method[J]. Applied Physics B, 130, 45(2024).

[44] Chen K Y, Fan H Z, Bao H. Discontinuous deformation monitoring of smart aerospace structures based on hybrid reconstruction strategy and fiber Bragg grating[J]. Sensors, 24, 3603(2024).

[45] Jutte C V, Ko W, Stephens C A et al. Deformed shape calculation of a full-scale wing using fiber optic strain data from a ground loads test[EB/OL]. https://ntrs.nasa.gov/api/citations/20120004140/downloads/20120004140.pdf

[46] Yuan S F, Yan M J, Zhang J J et al. Shape reconstruction method of spar wing structure[J]. Journal of Nanjing University of Aeronautics & Astronautics, 46, 825-830(2014).

[47] Liu P, Zeng J, Li X Y et al. Distributed optical fiber deformation monitoring and error correction for space truss beams[J]. Piezoelectrics & Acoustooptics, 41, 715-720, 724(2019).

[48] Ding G P, Yue S Y, Zhang S C et al. Strain - deformation reconstruction of CFRP laminates based on Ko displacement theory[J]. Nondestructive Testing and Evaluation, 36, 145-157(2021).

[49] Hu M Y, Wu S Q, Dong E L. Real-time displacement field reconstruction of typical thermal protection structures based on measured strain[J]. Journal of Southeast University (Natural Science Edition), 51, 664-671(2021).

[50] Wei L, Li H C, Wei Y H. Research on deformation detection and reconstruction of high temperature turbine blade[J]. Machinery Design & Manufacture, 66-70(2024).

[51] Li J L, Qu C Y, Zhu Z S et al. Six-dimensional deformation measurement of distributed POS based on FBG sensors[J]. IEEE Sensors Journal, 21, 7849-7856(2021).

[52] Esposito M, Gherlone M. Composite wing box deformed-shape reconstruction based on measured strains: optimization and comparison of existing approaches[J]. Aerospace Science and Technology, 99, 105758(2020).