CAJ | 학술논문

载荷识别中存在病态矩阵求逆的不稳定性将导致解严重失真。在总体最小二乘（Total Least Squares TLS）算法的思想上进行Tikhonov正则化，构造载荷识别的目标函数。然后利用共轭梯度（Conjunction Gradient CG）法解算该目标函数的最优化问题，提出一种算法易实现、收敛性能好、存储量小，且能全面考虑随机误差影响的CG-TLS正则化算法。经仿真和试验探讨了传递函数矩阵病态产生的原因，借助条件数优选振动响应点，最终检验CG-TLS正则化算法与常用的两种正则化算法在不同噪声水平时载荷识别的效果。结果表明，CG-TLS正则化算法载荷识别效果最优，与真实值吻合好，并具有良好的鲁棒性。因此，应用CG-TLS正则化算法实现载荷识别极具实际意义。
재하식별중존재병태구진구역적불은정성장도치해엄중실진。재총체최소이승（Total Least Squares TLS）산법적사상상진행Tikhonov정칙화，구조재하식별적목표함수。연후이용공액제도（Conjunction Gradient CG）법해산해목표함수적최우화문제，제출일충산법역실현、수렴성능호、존저량소，차능전면고필수궤오차영향적CG-TLS정칙화산법。경방진화시험탐토료전체함수구진병태산생적원인，차조조건수우선진동향응점，최종검험CG-TLS정칙화산법여상용적량충정칙화산법재불동조성수평시재하식별적효과。결과표명，CG-TLS정칙화산법재하식별효과최우，여진실치문합호，병구유량호적로봉성。인차，응용CG-TLS정칙화산법실현재하식별겁구실제의의。
The accuracy of load identification is often hindered by the inversion of an ill-conditioned transfer function matrixes at frequencies near the structural resonances.To overcome this inversion instability,the total least squares (TLS)method as a successful approach for linear problems was introduced.Tikhonov regularization of the TLS led to an optimization problem of minimizing the sum of fractional quadratic and quadratic functions. Then, the conjunction gradient(CG)method was proposed for solving Tikhonov TLS optimization problem,it was called CG-TLS algorithm,its advantages were simpler to implement,smaller storage amount,better convergence performance and that can consider not only vibration response but the transfer matrix is contaminated by noise.The ill-conditioned causes of transfer function matrix were investigated with numerical simulations and tests,then choosing the locations of vibration response optimally with condition number.Finally,the CG-TLS regularization algorithm and other two methods were used to identify vibration load at different noise levels.The results demonstrated that the CG-TLS regularization algorithm has the best performance;it also has a lower noise sensitivity;therefore,the new algorithm established here has a broad prospect of engineering application.