摘要
Tikhonov正则化方法是求解载荷辨识问题的有效方法,正则化参数的确定是影响求解准确性的关键问题。提出了一种新方法——虚拟载荷法,以虚拟载荷向量的范数最小作为正则化参数确定准则,将载荷辨识问题转化为单参数优化问题,用一维搜索法求得最优解。通过将法方程的系数矩阵预先进行三对角化,建立了高效的求解算法。通过两个数值算例对新方法进行了检验,结果表明新的参数确定准则是有效的,基于该准则得到的载荷辨识结果具有满意的精度。
Tikhonov regularization method is effective in solving load identification problems,and proper selection of the regularization parameter is a key point that determines the solution accuracy.In this work,a new method which is named fictitious load method is proposed.Taking the minimization of the norm of the fictitious load is as the criterion of regularization parameter selection,the load identification problem isthus converted into a one-variable optimization problem which can be solved by one dimension search technique.By transforming the coefficient matrix of the normal equation into tridiagonal matrix,an efficient algorithm is developed.Two numerical examples are presented to validate the new method,and the results show that the new regularization parameter selection criterion is effective to revover the loads on structures with good accuracy.
出处
《振动工程学报》
EI
CSCD
北大核心
2016年第1期31-37,共7页
Journal of Vibration Engineering
基金
国家自然科学基金资助项目(11372339)
高超声速冲压发动机技术重点实验室基金资助项目(STSKFKT2012001)
关键词
载荷辨识
反问题
TIKHONOV正则化
正则化参数
load identification
inverse problem
Tikhonov regularization
regularization parameter
