在航空航天领域，作用在结构上动载荷的确定对结构健康监测是非常必要和重要的。为此，本文以类似机翼结构的变截面悬臂梁结构为研究对象，提出了一种基于光纤光栅传感器与卡尔曼滤波器的动载荷识别方法。首先，根据变截面梁单元形式，推导出变截面梁的质量矩阵与刚度矩阵，建立动力学运动方程。然后，以光纤光栅传感器测得的应变信息作为观测信号，通过卡尔曼滤波器生成的增益矩阵、新息序列矩阵以及协方差矩阵，得到灵敏度矩阵和估计力的增益矩阵。在此基础上，利用广义回归模型及其最小二乘算法，估算出动载荷大小、判断出动载荷激励位置。借助数值仿真与实验手段，分别验证了该方法对于单点正弦激励、方波激励、锯齿波激励以及多点同时激励等工况下的动载荷识别效果。结果表明，本文所提算法具有较好的动载荷识别效果和噪声抑制能力，能够为未来风洞试验和真实飞行试验环境中诸如大展弦比机翼表面气动压力等载荷实时辨识、气动外形自适应控制以及结构健康监测提供技术支撑。
In the field of aerospace, it is both necessary and important to determine the dynamic load on the structure for structural health monitoring. In this paper, a method of dynamic load identification based on FBG sensors and the Kalman filter is proposed. According to the element form of variable cross-section beams, the mass matrix and stiffness matrix of variable cross-section beams are firstly derived, and the dynamic equation of motion established. Then, taking the strain information measured by FBG sensors as the observation signal, the gain matrix, innovation sequence matrix and covariance matrix generated by the Kalman filter are used to obtain the sensitivity matrix and the gain matrix of estimation force. On this basis, the generalized regression model and its least square algorithm are adopted to estimate the dynamic load and determine the excitation position of the dynamic load. By means of numerical simulation and experiments, the dynamic load identification effect of this method under single point sine excitation, square wave excitation, saw tooth wave excitation and multi-point simultaneous excitation is verified. Results show that the algorithm proposed has good dynamic load identification effect and noise suppression ability. It can also provide technical support for future wind tunnel tests and real flight test environments such as real-time load identification and aerodynamic shape adaptive control, and structural health monitoring such as high aspect ratio wing surface aerodynamic pressure.
[1] JIANG R, JIANG R J. Identification of dynamic load and vehicle parameters based on bridge dynamic responses[J]. Journal of Geophysical Research Atmospheres, 2003, 83(B7):3535-3538.
[2] PECORA R, CONCILIO A, DIMINO I, et al. Structural design of an adaptive wing trailing edge for enhanced cruise performance[C]//24th AIAA/AHS Adaptive Structures Conference.Reston:AIAA, 2016.
[3] HONG C H, QIAO S Y, WU M. Simulating study of dynamic load spectra identification method of machinery in cepstrum domain[J]. Journal of China University of Mining and Technology(English Edition), 2006, 16(1):22-24.
[4] MAES K, PEETERS J, REYNDERS E, et al. Identification of axial forces in beam members by local vibration measurements[J]. Journal of Sound and Vibration, 2013, V332:5417-5432.
[5] MA C K, CHANG J M, LIN D C. Input forces estimation of beam structures by an inverse method[J]. Journal of Sound and Vibration, 2003, 259(2):387-407.
[6] LIU J, MENG X, ZHANG D, et al. An efficient method to reduce ill-posedness for structural dynamic load identification[J]. Mechanical Systems and Signal Processing, 2017, 95:273-285.
[7] 杨智春, 贾有. 动载荷的识别方法[J]. 力学进展, 2015, 45(1):29-54. YANG Z C, JIA Y. Identification method of dynamic load[J]. Progress in Mechanics, 2015, 45(1):29-54(in Chinese).
[8] 兑红娜,王勇军,董江,等.基于飞行参数的飞机结构载荷最优回归模型[J].航空学报,2018,39(11):80-89. DUI H N, WANG Y J, DONG J, et al. Optimal regression model of aircraft structural load based on flight parameters[J]. Acta Aeronautics et Astronauctics Sinica, 2018,39(11):80-89(in Chinese).
[9] 刘铁根, 王双, 江俊峰,等. 航空航天光纤传感技术研究进展[J]. 仪器仪表学报, 2014(8):1681-1692. LIU T G, WANG S, JIANG J F, et al. Research progress of aerospace optical fiber sensing technology[J]. Journal of Instrumentation, 2014(8):1681-1692(in Chinese).
[10] WEI F F, LIU D J, MALLIK A K, et al. Magnetic field sensor based on a Tri-Microfiber coupler ring in magnetic fluid and a fiber bragg grating[J]. Sensors (Basel, Switzerland),2019,19(23):5100.
[11] XU B,HUANG J,XU X F, et al. Ultrasensitive no gas sensor based on the graphene oxide-coated long-period fiber grating[J]. ACS Applied Materials and Interfaces,2019,11(43):40868-40874.
[12] 王晓臣,蒲军平.变截面梁有限元分析[J].浙江工业大学学报,2008,36(3):312-314. WANG X C, PU J P. Finite element analysis of variable cross section beam[J]. Journal of Zhejiang University of Technology, 2008,36(3):312-314(in Chinese).
[13] 胡海岩.机械振动基础[M].北京:北京航空航天大学出版社,2018. HU H Y. Foundation of mechanical vibration[M]. Beijing:Beijing University of Aeronautics and Astronautics Press, 2018(in Chinese).
[14] 马志贵,施文龙.基于MATLAB的变截面梁单元有限元分析[J].兰州工业学院学报,2015,22(5):37-39. MA Z G, SHI W L. Finite element analysis of variable section beam element based on MATLAB[J]. Journal of Lanzhou Institute of Technology, 2015,22(5):37-39(in Chinese).
[15] 宋雪刚.基于光纤光栅传感器的动载荷识别技术研究[D].南京:南京航空航天大学,2018. SONG X G. Research on dynamic load identification technology based on FBG sensor[D]. Nanjing:Nanjing University of Aeronautics and Astronautics, 2018(in Chinese).
[16] GUO J, HUANG W, WILLIAMS B M. Adaptive Kalman filter approach for stochastic short-term traffic flow rate prediction and uncertainty quantification[J]. Transportation Research Part C:Emerging Technologies,2014, 43:50-64.
[17] SUN F, TANG L J. Cubature Kalman filter-Kalman filter algorithm[J]. Control & Decision, 2012, 27(10):1561-1565.
[18] 侯康.基于卡尔曼滤波器的桥梁损伤快速诊断方法研究[D].哈尔滨:哈尔滨工业大学,2016. HOU K. Research on fast diagnosis method of bridge damage based on Kalman filter[D]. Harbin:Harbin University of Technology, 2016(in Chinese).
[19] AZIZ K,EMRE K. Optimizing a Kalman filter with an evolutionary algorithm for nonlinear quadrotor attitude dynamics[J]. Journal of Computational Science,2020,39:101051.
[20] 宋雪刚,刘鹏,程竹明,等. 基于光纤光栅传感器和卡尔曼滤波器的载荷识别算法[J].光学学报,2018,38(3):2-3. SONG X G, LIU P, CHENG Z M, et al. Load identification algorithm based on FBG sensor and Kalman filter[J]. Acta Optica Sinica, 2018, 38(3):2-3(in Chinese).
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