摘要
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。
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.
出处
《振动与冲击》
EI
CSCD
北大核心
2014年第9期159-164,共6页
Journal of Vibration and Shock
基金
武器装备预研基金
总装十二五预研基金
