结构损伤识别的一种反馈岭估计方法

杨秋伟,陆晨,罗帅,李翠红

振动与冲击 ›› 2020, Vol. 39 ›› Issue (7) : 43-50.

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PDF(1163 KB)
振动与冲击 ›› 2020, Vol. 39 ›› Issue (7) : 43-50.
论文

结构损伤识别的一种反馈岭估计方法

  • 杨秋伟,陆晨,罗帅,李翠红
作者信息 +

A feedback ridge estimate technique for structural damage recognition

  • YANG Qiuwei, LU Chen, LUO Shuai, LI Cuihong
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文章历史 +

摘要

利用含有测量噪声的数据进行结构损伤识别时,经常出现病态最小二乘问题,可能导致计算结果完全失真。为了显著提高计算精度,在岭估计的基础上,进一步提出了一种反馈岭估计方法,以获得精确并具稳定的损伤识别结果。所提的反馈岭估计方法主要分为三个步骤:对结构损伤评估中的线性方程组进行第一次岭估计计算,得到损伤参数的粗略解;根据损伤参数的粗略解,设计一个新的对角矩阵,用于随后的反馈岭估计 (即第二次岭估计) 计算中;对损伤评估线性方程组进行第二次岭估计计算(即反馈岭估计),最终获得损伤参数的高精度解,据此来对结构中的损伤位置和严重程度进行判定。以一个梁结构作为数值算例,讨论了所提方法在10%噪声水平下的有效性,并把计算结果与普通岭估计和奇异值截断法进行了比较,结果表明:所提反馈岭估计方法大幅度提高了计算精度,即使在10%的噪声水平下,该方法也能获得精度很高的计算结果。

Abstract

The ill-conditioned least squares problems often appear in structural damage recognition using noisy data to cause calculation results being fully distorted. Here, to significantly improve calculation accuracy, a feedback ridge estimate (FRE) technique was proposed to obtain accurate and stable damage recognition results. The proposed method has three steps. Firstly, the first ridge estimate (RE) calculation was done for linear equation set in structural damage evaluation to obtain the rough solution to damage parameters. Secondly, a new diagonal matrix was designed to be used in the second RE calculation according to the rough solution to damage parameters. Thirdly, the second RE calculation was done with FRE technique for linear equation set in structural damage evaluation to obtain damage parameters’ high-precision solution. A beam structure was taken as a numerical example to explore the effectiveness of the proposed method under 10% noise level. The calculation results were compared with those using the ordinary RE method and the singular value truncation (SVT) one. The results showed that the proposed FRE method can significantly improve calculation accuracy; even under 10% noise level, it can be used to obtain calculation results with very high precision.
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关键词

损伤识别 / 病态最小二乘问题 / 奇异值截断 / 反馈岭估计

Key words

damage recognition / ill-conditioned least squares problem / singular value truncation (SVT) / feedback ridge estimate (FRE)

引用本文

导出引用
杨秋伟,陆晨,罗帅,李翠红. 结构损伤识别的一种反馈岭估计方法[J]. 振动与冲击, 2020, 39(7): 43-50
YANG Qiuwei, LU Chen, LUO Shuai, LI Cuihong. A feedback ridge estimate technique for structural damage recognition[J]. Journal of Vibration and Shock, 2020, 39(7): 43-50

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