The ill-posed phenomenon exists in the load identification of multi-support bearing structure, which leads to the solution seriously deviating from the original value. The Generalized Cross Validation (GCV) method of selecting regularization parameters has the problems of inaccurate positioning, large search range, and long calculation time when solving the ill-posed problem of the system. In this paper, the measurement point optimization and Tikhonov method are used. Furthermore, a GCV regularization parameter selection method combined with the gradient descent (G-GCV) method is proposed to effectively improve the load identification accuracy and significantly shorten the calculation time. On this basis, the median solution method is proposed by using the alternative measurement points to further improve the accuracy of load identification. In order to verify the effectiveness and accuracy of the method proposed in this paper, the load identification results of the proposed method and the traditional method are compared and analyzed based on the multi-support bearing model simulation. The feasibility and accuracy of the proposed method are further verified by the multi-excitation load identification experiment of the plate structure. The results show that the G-GCV method can not only reduce the number of calculation iterations and calculation time, but also improve the accuracy of load identification. The median method can make full use of the information from the measurement points and further improve the accuracy of load identification.
AbdelLWAbdenourSKamalM, et al. (2024) New health indicators for the monitoring of bearing failures under variable loads. Structural Health Monitoring23(5): 2922–2941.
2.
ChenBYChengYZhangW, et al. (2022) Investigations on improved Gini indices for bearing fault feature characterization and condition monitoring. Mechanical Systems and Signal Processing176: 109165.
3.
FengYP (2020) Research on Regularization Method of Dynamic Load Identification Under High Level Noise. PhD Thesis. Daqing: Northeast Petroleum University.
4.
FioriSWangJ (2023) External identification of a reciprocal lossy multiport circuit under measurement uncertainties by Riemannian gradient descent. Energies16(6): 2585.
5.
GaoYXiaoLZWuBS (2020) TSVD and Tikhonov methods and influence factor analysis for NMR data in shale rock. Journal of Petroleum Science and Engineering194: 107508.
6.
GruberHFuchsABaderM (2024) Evaluation of a condition monitoring algorithm for early bearing fault detection. Sensors24(7): 2138.
7.
GuoRQiuSFangHQ, et al. (2013) Advance in studying on transfer path analysis methods in frequency domain. Journal of Vibration and Shock32(13): 49–55.
8.
GuoRFangHQQiuS, et al. (2014) Novel load identification method based on the combination of Tikhonov regularization and singular value decomposition. Journal of Vibration and Shock33(6): 53–58.
9.
HuYY (2011) Application Research of Force Identification Based on Least Squares Method in Frequency Domain. PhD Thesis. Harbin: Harbin Engineering University.
10.
JieLKunL (2021) Sparse identification of time-space coupled distributed dynamic load. Mechanical Systems and Signal Processing148: 107177.
11.
JohnOPiergentiliF (1996) Force estimation using operational data. In Proceedings of 8th IMAC 2768 (2): 1586–1592.
12.
LageYENevesMMMaiaNMM, et al. (2014) Force transmissibility versus displacement transmissibility. Journal of Sound and Vibration333(22): 5708–5722.
13.
LiXWZhaoHTChenJ (2020) Force identification based on measurement point optimization and improved L-curve method. Journal of Shanghai Jiao Tong University54(6): 569–576.
14.
LiSJPengGLJiMY, et al. (2022) Impact identification of composite cylinder based on improved deep metric learning model and weighted fusion Tikhonov regularized total least squares. Composite Structures283: 115144.
15.
LiuJSunXSHanX, et al. (2015) Dynamic load identification for stochastic structures based on Gegenbauer polynomial approximation and regularization method. Mechanical Systems and Signal Processing56-57: 35–54.
16.
LiuCSRenCPWangNJ (2019) Load identification method based on interval analysis and Tikhonov regularization and its application. Journal of Electrical and Computer Engineering2019(1): 1–8.
17.
LiuZQChenYMShenDM, et al. (2022) Improvement of bearing dynamic load identification method and experimental verification. Noise and Vibration Control42(4): 132–137.
18.
MaCHuaHX (2015) State space load identification technique based on an improved regularized method. Journal of Vibration and Shock34(11): 146–149.
19.
PengFWangLXiaoJ, et al. (2017) A regularization approach of dynamic load identification in frequency domain based on acceleration. Journal of Hunan University44(2): 75–79.
20.
QiaoZJShuXD (2021) Coupled neurons with multi-objective optimization benefit incipient fault identification of machinery. Solitons and Fractals: The Interdisciplinary Journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena145: 110813.
21.
QiaoBJZhangXWWangCX, et al. (2016) Sparse regularization for force identification using dictionaries. Journal of Sound and Vibration368: 71–86.
22.
RahmiCUOguzKASerkanO, et al. (2019) Real time high cycle fatigue estimation algorithm and load history monitoring for vehicles by the use of frequency domain methods. Mechanical Systems and Signal Processing118: 290–304.
23.
SaadMHamadAAbdelhamidB (2022) Scaling up stochastic gradient descent for non-convex optimisation. Machine Learning111: 4039–4079.
24.
ShiXYLiuHFLLiuJX, et al. (2021) One dimensional automatic iterative inversion of electrical sounding curve based on generalized cross validation. Computational Technology of Geophysical and Geochemical Exploration43(1): 40–48.
25.
TangZHZanMZhangZF, et al. (2022) Operational transfer path analysis with generalized Tikhonov regularization method. Journal of Vibration and Shock41(24): 270–277.
26.
TaoYQGaoJXYaoYF (2016) Solution for robust total least squares estimation based on median method. Acta Geodaetica et Cartographica Sinica45(3): 297–301.
27.
WangX (2022) Survey on gradient descent and optimization algorithm. Computer Knowledge and Technology18(8): 71–73.
28.
WangLYXuRR (2020) Robust weighted total least squares algorithm for 3D coordinate transformation. Journal of Geodesy and Geodynamics40(10): 1027–1033.
29.
WangXJinHYangJY (2019) RBF network prediction algorithm based on conjugate gradient descent method. Journal of Detection and Control41(5): 106–110.
30.
XiaCN (2016) Study on Regularization Parameter Choice—Based on the L-Curve. PhD Thesis. Guangzhou: Ji’nan University.
31.
XiaoW (2021) Research on Optimization of Diesel Engine Foot Vibration Caused by Main Shaft Load. PhD Thesis. Harbin: Harbin Engineering University.
32.
XinDKQianJHeCS, et al. (2024a) Study on ill-conditioned total least squares load identification method based on the IGG weight function. International Journal of Structural Stability and Dynamics8: 2550080.
33.
XinDKZhuJCHeCS, et al. (2024b) Low frequency load identification under high noise level using weighted total least squares. Measurement236: 115125.
34.
YangZRDaiLYYuHL, et al. (2018) Research on marine intermediate bearing load identification technology. Noise and Vibration Control38(S2): 462–464.
35.
YouJYangZCSongQZ (2015) Experimental study of random dynamic loads identification based on weighted regularization method. Journal of Sound and Vibration342: 113–123.
36.
ZhouKBZhangSHuangZ, et al. (2019) An improved TSVD-GCV inversion algorithm of pore size distribution in time-domain induced polarization using migration Hankel matrix. Journal of Petroleum Science and Engineering183: 106368.
37.
ZhouKWangYNQiaoBJ, et al. (2025) Non-convex sparse regularization via convex optimization for blade tip timing. Mechanical Systems and Signal Processing222: 111764.
38.
ZhuMY (2019) Study on the Monitoring Method of Ice Load Exerted on Hull Structure. PhD Thesis. Harbin: Harbin Engineering University.
