针对目前多数重构位移场的方法在实际工程应用中存在测点数量多、位置要求高等问题，引入机器学习建立了应变与位移之间的关系，实现了位移场的重构。分析LSTM、Transformer Encoder在动态变形重构中的精度和鲁棒性；然后设计加工槽型结构搭建实验平台，对槽道侧壁进行动态加载，通过采集系统和激光位移传感器对应变、位移信息进行采集，对比分析测试集的动态预测结果与传感器的测试结果；最后，融合LSTM和Transformer Encoder这2种神经网络，提出一种新的LSTM-Transformer Encoder（LTE）网络。结果表明：测试集上LSTM网络重构的节点最大平均误差为0.610%，Transformer Encoder重构的节点最大平均相对误差为1.010%。LSTM网络相比Transformer Encoder网络具有更好鲁棒性的同时重构精度更高，提出的LTE网络在测试集上具有更小的MSE（均方误差）及更大的R2（模型拟合系数），在整体的表现上优于LSTM和Transformer Encoder。
Aiming at the problems of large number of measurement points and high location requirements in most of the current methods for reconstructing displacement field in practical engineering applications, machine learning is introduced to establish the relationship between strain and displacement and realize the reconstruction of displacement field. We analyzed the accuracy and the robustness of the algorithms of LSTM and Transformer Encoder in dynamic deformation reconstruction; then we design and process the slot structure to build an experimental platform, dynamically load the sidewall of the slot channel, collect the strain and displacement information through the acquisition system and the laser displacement sensor, and transmit it to the computer, and then compare and analyze the dynamic prediction results of the test set with the test results of the laser displacement sensor; finally, a new LSTM-Transformer Encoder (LTE) network is proposed by fusing two neural networks, LSTM and Transformer Encoder. The results show that the maximum average error of the nodes reconstructed by the LSTM network on the test set is 0.610%, and the maximum average relative error of the nodes reconstructed by the Transformer Encoder is 1.010%.The LSTM network has better robustness than the Transformer Encoder network with higher reconstruction accuracy, and the proposed LTE network has smaller MSE (mean squared error)and larger R2 (model fit coefficient) on the test set, which is better than the LSTM and Transformer Encoder in the overall performance.
2025,47(22): 38-45 收稿日期：2025-2-27
DOI：10.3404/j.issn.1672-7649.2025.22.006
分类号：U661.43
基金项目：国家自然科学基金资助项目（51839005）
作者简介：白金川（2002 – ），男，硕士研究生，研究方向为机器学习、减振降噪
参考文献：
[1] 邢雪, 朱贺, 马炳杰, 等. 基于临界平面法的试验件随机振动疲劳寿命预测[J]. 舰船科学技术, 2025, 47(6): 1-6.
XING X, ZHU H, MA B J, et al. Random vibration fatigue life prediction of test parts based on critical plane method. Ship Science and Technology, 2025, 47(6): 1-6.
[2] BERNASCONI O, EWINS D J. Application of strain modal testing to real structures[C]//7th International Modal Analysis Conference, 1989.
[3] FOSS G, HAUGSE E. Using modal test results to develop strain to displacement transformations. nashvile tennessee[J]. Energy Geoscience, 1995, 112-128.
[4] 程光辉, 施亮, 张振海, 等. 基于应变信息的大型浮筏结构位移重构方法[J]. 舰船科学技术, 2022, 44(15): 75-79+144.
CHENG G H, SHI L, ZHANG Z H, et al. Research on displacement reconstruction algorithm of large floating raft based on strain information[J]. Ship Science and Technology, 2022, 44(15): 75-79+144 .
[5] KO W L, RICHARDS W L, TRAN V T. Displacement theories for in-flight deformed shape predictions of aerospace structures[J]. Armstrong Flight Research Center, 2007.
[6] 赵飞飞, 曹开拓, 保宏. Timoshenko梁的变形场重构及传感器位置优化[J]. 机械工程学报, 2020, 56(20): 1-11.
ZHAO F F, CAO K T, BAO H. Deformation field reconstruction of timoshenko beam and optimization of sensor placement[J]. Journal of Mechanical Engineering, 2020, 56(20): 1-11.
[7] 冯荻. 基于光纤光栅应变传感的结构变形重构技术研究[D]. 大连: 大连理工大学, 2020.
[8] 夏力, 王大鹏. 结合OFDR与Ko位移理论的变形估算研究[J]. 光通信技术, 2021, 45(7): 53-55
XIA L, WANG D P. Research on deformation estimation combining OFDR and Ko displacement theory[J]. Optical Communication Technology, 2021, 45(7): 53-55
[9] 李恒春. 基于光纤光栅的高温涡轮叶片变形重构研究[D]. 武汉: 武汉理工大学, 2021.
[10] TESSLER A, SPANGLER J L. A variational principle for reconstruction of elastic deformations in shear deformable plates and shells number[J]. 2003.
[11] TESSLER A, SPANGLER J L. Inverse FEM for full-field reconstruction of elastic deformations in shear deformable plates and shells[J]. 2004.
[12] TESSLER A, SPANGLER J L. A least-squares variational method for full-field reconstruction of elastic deformations in shear-deformable plates and shells[J]. Computer Methods in Applied Mechanics and Engineering, 2005, 194(2-5): 327-339.
[13] 雷雨恒. 基于逆有限元形状传感的桥梁挠度分布式监测方法研究[D]. 大连: 大连理工大学, 2022.
[14] 闫宏生, 白超迪, 贾同宇. 逆有限元法在船体加筋板结构变形重构中的应用[J]. 中国造船, 2023, 64(1): 168-179.
YAN H S, BAI C D, JIA T Y. Application of inverse finite element method in deformation reconstruction of hull reinforced plate structure[J]. Shipbuilding of China, 2023, 64(1): 168-179.
[15] 陈安东. 基于神经网络改进逆有限元法的结构变形重构[D]. 武汉: 华中科技大学, 2022.
[16] MATHIA K, PRIDDY K. Real-time geometrical approximation of flexible structures using neural networks[J]. Vancouver, BC, 1995.
[17] SWISCHUK R, MAININI L, PEHERSTORFER B. Projection-based model reduction: Formulations for physics-based machine learning[J]. Computers & Fluids, 2019, 179: 704-717.
[18] MOON H S, OK S, CHUN P, et al. Artificial neural network for vertical displacement prediction of a bridge from strains (Part 1): girder bridge under moving vehicles[J]. Applied Sciences, 2019, 9(14): 2881.
[19] 李生鹏, 韦朋余, 刘豪, 等. 船舶板架结构变形场测量技术研究[J]. 船舶力学, 2024, 252(10): 1599-1610.
LI S P, WEI P Y, LIU H, et al. Deformation field measuring technique of ship grillage structure[J]. Journal of Ship Mechanics, 2024, 252(10): 1599-1610.
[20] 潘兴琳. 基于光纤光栅的结构变形测量系统研究[D]. 西安: 西安电子科技大学, 2018.
[21] 王建颖. 基于FBG传感网络的复杂面形应变场检测系统研究[D]. 长春: 长春理工大学, 2020.
[22] 陈国材, 汪雪良, 杨华伟, 等. 基于iFEM和虚实结合的加板应变场构建研究[J]. 船舶力学, 2024, 28(3): 409-421.
CHEN G C, WANG X L, YANG H W, et al. Strain field construction method of stiffened plate based on iFEM and virtual-real combination method[J]. Journal of Ship Mechanics, 2024, 28(3): 409-421.
