船载无人机航姿与机翼形变测量技术研究

       近些年来，得益于小体积、低成本的优势，无人机的使用愈发广泛。对于船载无人机来说，由于其受到风力、气压等因素影响较大，为保障其飞行过程的稳定，需要对载体的姿态、速度、位置进行实时准确的测量。此外，为增加续航时间，船载无人机多采用大展弦比机翼，会导致机翼出现较大变形，因此还需准确测量机翼的变形程度。针对于此，本文开展了基于卡尔曼滤波的组合导航系统设计，以及基于Ko位移理论的机翼形变重构研究。

       在导航系统设计方面，为了提升导航精度，本文利用基于惯性传感器的惯性导航系统，与基于北斗和GPS的卫星导航系统进行松组合，构建组合导航系统，并设计制作导航样机。利用磁强计进行航向的测量与初始对准，通过卡尔曼滤波算法完成两种导航系统间的数据融合。为了保证系统解算的实时性，本文根据惯导器件的精度条件，对更新方程和误差方程进行了合理简化，并优化了过程、量测噪声协方差阵参数。经转台静态测量试验与多次动态跑车试验验证，与工业级组合导航系统对比结果表明，本文设计的导航系统具有良好的静态、动态测量精度。

       在机翼形变测量方面，本文以光纤光栅传感器为基础，基于Ko位移理论算法，对变截面工字梁模型进行了形变重构。利用有限元仿真建立变截面工字梁模型，将仿真结果作为真实值对形变重构误差进行分析。在同一条件下通过改变传感器的数量、外部载荷的施加方式以及大小，对算法的重构精度进行验证，仿真结果显示算法带来的重构误差不超过0.14mm。此外，由于实际测量时会引入误差，本文加入了误差分析仿真试验，在仿真时加入传感器测量误差、机翼厚度误差干扰来模拟实际情况，分析其对重构结果的影响，仿真结果表明在引入误差的情况下，该算法仍满足精度要求。

       In recent years, Unmanned Aerial Vehicles are widely used based on the advantages of small size and low cost. For ship-borne UAVs, due to the significant impact of wind, atmospheric pressure, and other factors, in order to ensure the stability the flight process, real-time and accurate measurement of the carrier’s attitude, speed, and position is required. In addition, the used of wings with large aspect ratios to increase endurance can lead to significant deformation of the wings. Therefore, it is also necessary to accurately measure the degree of deformation of the wings. In view of this, this paper carried out the design of integrated navigation system based on Kalman filtering, and the research of wing deformation reconstruction based on Ko displacement theory.
       In the aspect of navigation system design, in order to improve navigation accuracy, this paper uses inertial sensor-based inertial navigation system to loosely integrate with satellite navigation systems based on Beidou and GPS to construct an integrated navigation system. The navigation prototype is designed and manufactured. Using magnetometer for course measurement and initial alignment, data fusion between the two navigation systems is accomplished by Kalman filter algorithms. In order to ensure the real-time performance of the system, the update equation and error equation are simplified reasonably, and the parameters of the process and measurement noise covariance matrix are optimized. Compared with the industrial integrated navigation system, the results show that the navigation system designed in this paper has good static and dynamic measurement accuracy.
       Based on Fiber Bragg Grating sensor and KO displacement theory, the deformation reconstruction of variable cross-section i-beam model is presented in this paper. The finite element simulation is used to establish the variable cross-section i-beam model, and the simulation results are taken as the real values to analyze the deformation reconstruction error. Under the same condition, the reconstruction accuracy of the algorithm is verified by changing the number of sensors, the mode and the size of external load. The simulation results show that the reconstruction error of the algorithm is less than 0.14 mm. In addition, because of the error in the actual measurement, this paper adds the error analysis simulation experiment, and adds the sensor measurement error and the wing thickness error interference in the simulation to simulate the actual situation, the simulation results show that the proposed algorithm can meet the accuracy requirement even if the error is introduced.

[1] 刘天刚. 基于小型无人机的航姿测量系统研究与设计[D]. 重庆大学, 2015.
[2] 路小燕. 基于自适应扩展卡尔曼滤波的微小型航姿系统设计与实现[D]. 南京航空航天大学, 2018.
[3] 周建民, 康永, 刘蔚. 无人机导航技术应用与发展趋势[J]. 中国电子科学研究院学报, 2015, 10(3): 274-277.
[4] 张科. 基于逆向有限元法的结构变形重构方法研究[D]. 南京航空航天大学, 2020.
[5] 吴慧峰. 基于光纤光栅传感技术的机翼形变测量方法研究与分析[J]. 桂林航天工业学院学报, 2017, 22(4): 359-364.
[6] 苗青. 无人机导航技术研究分析[J]. 中国新通信, 2020, 22(6): 55-56.
[7] 江文. 小型无人机MIMU/GNSS 组合导航技术研究[D]. 哈尔滨工业大学, 2020.
[8] VOUCH O, MINETTO A, FALCO G, et al. On the adaptivity of unscented particle filter for gnss/ins tightly-integrated navigation unit in urban environment[J]. IEEE Access, 2021, 9: 144157-144170.
[9] SUN R, ZHANG Z, CHENG Q, et al. Pseudorange error prediction for adaptive tightly coupled GNSS/IMU navigation in urban areas[J]. GPS Solutions, 2022, 26: 1-13.
[10] 董亮, 许东欢, 臧中原, 等. 时钟模型辅助的惯性/卫星紧组合导航算法研究[J]. 导航定位与授时, 2022, 9(2): 112-117.
[11] 高威, 李亚峰, 王可东. 信号级GNSS/SINS 超紧组合导航仿真平台设计[J]. 系统工程与电子技术, 2023, 45(1): 184-192.
[12] FENG W, DENG Y, XIE Y. IMU/GPS Integrated Navigation Algorithm Based on Adaptive Kalman filter[J]. Scientific Journal of Intelligent Systems Research, 2021, 3(12): 208-213.
[13] 梁娜, 丁丹. SINS/GPS 组合导航系统研究[J]. 计算机仿真, 2022, 39(12): 34-37.
[14] MAHONY R, HAMEL T, PFLIMLIN J. Nonlinear complementary filters on the special orthogonal group[J]. IEEE Transactions on automatic control, 2008, 53(5): 1203-1218.
[15] MADGWICK S O, WILSON S, TURK R, et al. An extended complementary filter for fullbody MARG orientation estimation[J]. IEEE/ASME Transactions on mechatronics, 2020, 25(4): 2054-2064.
[16] 王健, 厉彦一. 基于重力和磁场双重互补滤波的无人机姿态解算算法[J]. 中国科技论文, 2021, 16(1): 1-6.
[17] YUFEI L, NOGICHI N, ISHII K. Development of a small-sized and low-cost attitude measurement unit for agricultural robot application[J]. Journal of Agricultural Sciences, 2018, 24(1): 33-41.
[18] 王鼎杰. 卫星辅助增强微惯性导航精度方法研究[D]. 国防科技大学, 2018.
[19] RONG H, ZHU Y, LV J, et al. Conditional equivalence between Extended Kalman filter and complementary filter for two-vector gyro-aided attitude determination[J]. Measurement, 2021, 168: 108428.
[20] LIU F, LIU Y, SUN X, et al. A new multi-sensor hierarchical data fusion algorithm based on unscented Kalman filter for the attitude observation of the wave glider[J]. Applied Ocean Research, 2021, 109: 102562.
[21] LIU Y, FAN X, LV C, et al. An innovative information fusion method with adaptive Kalman filter for integrated INS/GPS navigation of autonomous vehicles[J]. Mechanical Systems and Signal Processing, 2018, 100: 605-616.
[22] WEI X, LI J, FENG K, et al. A mixed optimization method based on adaptive Kalman filter and wavelet neural network for INS/GPS during GPS outages[J]. IEEE Access, 2021, 9: 47875-47886.
[23] TANG Y, JIANG J, LIU J, et al. A GRU and AKF-Based Hybrid Algorithm for Improving INS/GNSS Navigation Accuracy during GNSS Outage[J]. Remote Sensing, 2022, 14(3): 752.
[24] 唐伏乾. 车载组合导航系统卡尔曼滤波模型误差研究[D]. 吉林大学, 2022.
[25] 蔡頔. GNSS/INS 组合导航数据融合算法研究[D]. 南京信息工程大学, 2022.
[26] XIONG L, XIA X, LU Y, et al. IMU-based automated vehicle body sideslip angle and attitude estimation aided by GNSS using parallel adaptive Kalman filters[J]. IEEE Transactions on Vehicular Technology, 2020, 69(10): 10668-10680.
[27] 吴晓倩. GNSS/INS 松组合导航滤波算法研究与实现[D]. 山东科技大学, 2020.
[28] 魏传达. 基于应变信息的飞机机翼变形测量及形变重构理论研究[D]. 西安电子科技大学, 2015.
[29] 周永兴. 飞行试验机翼变形测量的一种方法[J]. 测控技术, 2013, 32(4): 15-17.
[30] LIU T, BURNER A W, JONES T W, et al. Photogrammetric techniques for aerospace applications[J]. Progress in Aerospace Sciences, 2012, 54: 1-58.
[31] GHERLONE M, CERRACCHIO P, MATTONE M, et al. Shape sensing of 3D frame structures using an inverse finite element method[J]. International Journal of Solids and Structures, 2012, 49(22): 3100-3112.
[32] NIU S, ZHAO Y, BAO H. Shape sensing of plate structures through coupling inverse finite element method and scaled boundary element analysis[J]. Measurement, 2022, 190: 110676.
[33] ZHU Z, ZHANG M, ZHOU X. A new baseline measurement method for multinode and multibaseline interferometric SAR systems using fiber Bragg gratings[J]. IEEE Transactions on Aerospace and Electronic Systems, 2019, 58(1): 4-16.
[34] 冯荻. 基于光纤光栅应变传感的结构变形重构技术研究[D]. 大连理工大学, 2020.
[35] FOSS G, HAUGSE E. Using modal test results to develop strain to displacement transformations[C]//Proceedings of the 13th international modal analysis conference: volume 2460. 1995: 112.
[36] FREYDIN M, RATTNER M K, RAVEH D E, et al. Fiber-optics-based aeroelastic shape sensing[J]. AIAA Journal, 2019, 57(12): 5094-5103.
[37] KO W L, RICHARDS W L, TRAN V T. Displacement theories for in-flight deformed shape predictions of aerospace structures[R]. 2007.
[38] 赵飞飞, 曹开拓, 保宏, 等. 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.
[39] DING G, YUE S, ZHANG S, et al. Strain-deformation reconstruction of CFRP laminates based on Ko displacement theory[J]. Nondestructive Testing and Evaluation, 2021, 36(2): 145-157.
[40] 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.
[41] ZHU H, DU Z, TANG Y. Numerical study on the displacement reconstruction of subsea pipelines using the improved inverse finite element method[J]. Ocean Engineering, 2022, 248: 110763.
[42] 潘兴琳. 基于光纤光栅的结构变形测量系统研究[D]. 西安电子科技大学, 2018.
[43] FU Z, ZHAO Y, BAO H, et al. Dynamic deformation reconstruction of variable section WING with fiber Bragg grating sensors[J]. Sensors, 2019, 19(15): 3350.
[44] 南荣昌. 基于FBG 的相控阵天线结构形变重构方法与实验[D]. 西安电子科技大学, 2021.
[45] NICOLAS M J, SULLIVAN R W, RICHARDS W L. Large scale applications using FBG sensors: determination of in-flight loads and shape of a composite aircraft wing[J]. Aerospace, 2016, 3(3): 18.