结构损伤识别的截断总体最小二乘法
|
摘要
基于特征对灵敏度分析,并结合总体最小二乘法,提出了一种用于结构损伤识别的截断总体最小二乘法,主要用来解决实际结构损伤识别过程中出现的病态方程组问题。以一个平面桁架结构为例,验证该方法的有效性。结果表明:在测试数据不完备的情况下,所提方法对于测试噪声仍然具有较强的鲁棒性,可供实际工程应用参考。
A method is proposed to identify structural damages based on the eigen parameter sensitivity analysis and the truncated total least squares method. The goal of this study is to solve the ill-posed least squares problem occurred in the structural damage identification due to the data missing and measurement noise. The effectiveness of the proposed method is illustrated using simulated data on a plane truss structure. The results show that the proposed method has good robustness under measurement noise and is suitable for practical engineering applications.
A method is proposed to identify structural damages based on the eigen parameter sensitivity analysis and the truncated total least squares method. The goal of this study is to solve the ill-posed least squares problem occurred in the structural damage identification due to the data missing and measurement noise. The effectiveness of the proposed method is illustrated using simulated data on a plane truss structure. The results show that the proposed method has good robustness under measurement noise and is suitable for practical engineering applications.
引文
[1]王学航,杨秋伟,赵靖芸,等.基于中性轴位置变化的再生混凝土梁损伤识别试验研究[J].机械强度,2018,DOI:10.16579/j.issn.1001.9669.2018.05.00.
[2]韩大建,王文东.基于振动的结构损伤识别方法的近期研究进展[J].华南理工大学学报(自然科学版),2003,31(1):91-96.
[3]A.Alvandi,C.Cremona.Assessment of vibration-based damage identification techniques[J].Journal of Sound and Vibration,2006,292(1):179-202.
[4]W.Fan,P.Qiao.Vibration-based Damage Identification Methods:A Review and Comparative Study[J].Structural Health Monitoring,2011,9(3):83-111.
[5]唐盛华,周楠,方志,等.基于振型加权模态柔度的桥梁损伤识别方法[J].地震工程与工程振动,2017,37(6):98-106.
[6]Z.Y.Shi,S.S.Law,L.M.Zhang.Damage localization by directly using incomplete mode shapes[J].Journal of Engineering Mechanics,2000,126(6):656-660.
[7]Q.W.Yang.A mixed sensitivity method for structural damage detection[J].Communications in Numerical Methods in Engineering,2009,25(4):381-389.
[8]杨秋伟,刘济科.结构损伤识别的柔度灵敏度方法[J].中山大学学报(自然科学版),2010,49(1):16-19.
[9]王乐洋,许才军.总体最小二乘研究进展[J].武汉大学学报(信息科学版),2013,38(7):850-856,878.
[10]H.Hu.Ridge estimation of a semiparametric regression model.Elsevier Science Publishers B.V.,2005,176(1):215-222.
[11]A.Bouhamidi.K.Jbilou.L.Reichel and et al.An extrapolated TSVD method for linear discrete ill-posed problems with Kronecker structure.Linear Algebra&Its Applications,2011,434(7):1677-1688.
[12]徐文,陈义,游为.奇异值分解法在病态问题中的应用[J].测绘通报,2016(1):62-63.
[13]R.D.Fierro,G.H.Golub,P C.Hansen,et al.Regularization by Truncated Total Leastwares[J].Siam Journal on Scientific and Statistical Computing,1997,18(1):1223-124.
[2]韩大建,王文东.基于振动的结构损伤识别方法的近期研究进展[J].华南理工大学学报(自然科学版),2003,31(1):91-96.
[3]A.Alvandi,C.Cremona.Assessment of vibration-based damage identification techniques[J].Journal of Sound and Vibration,2006,292(1):179-202.
[4]W.Fan,P.Qiao.Vibration-based Damage Identification Methods:A Review and Comparative Study[J].Structural Health Monitoring,2011,9(3):83-111.
[5]唐盛华,周楠,方志,等.基于振型加权模态柔度的桥梁损伤识别方法[J].地震工程与工程振动,2017,37(6):98-106.
[6]Z.Y.Shi,S.S.Law,L.M.Zhang.Damage localization by directly using incomplete mode shapes[J].Journal of Engineering Mechanics,2000,126(6):656-660.
[7]Q.W.Yang.A mixed sensitivity method for structural damage detection[J].Communications in Numerical Methods in Engineering,2009,25(4):381-389.
[8]杨秋伟,刘济科.结构损伤识别的柔度灵敏度方法[J].中山大学学报(自然科学版),2010,49(1):16-19.
[9]王乐洋,许才军.总体最小二乘研究进展[J].武汉大学学报(信息科学版),2013,38(7):850-856,878.
[10]H.Hu.Ridge estimation of a semiparametric regression model.Elsevier Science Publishers B.V.,2005,176(1):215-222.
[11]A.Bouhamidi.K.Jbilou.L.Reichel and et al.An extrapolated TSVD method for linear discrete ill-posed problems with Kronecker structure.Linear Algebra&Its Applications,2011,434(7):1677-1688.
[12]徐文,陈义,游为.奇异值分解法在病态问题中的应用[J].测绘通报,2016(1):62-63.
[13]R.D.Fierro,G.H.Golub,P C.Hansen,et al.Regularization by Truncated Total Leastwares[J].Siam Journal on Scientific and Statistical Computing,1997,18(1):1223-124.