The generalized flexibility matrix method for structural damage detection with incomplete mode shape data

Abstract

Achieving complete data of measured mode shapes is costly during the process of structural dynamic test. This results in a challenge for the damage detection. This paper concentrates on structural damage detection problem with incomplete mode shape data. An efficient method to deal with this problem is proposed. The generalized flexibility matrix (GFM) is employed. By introducing a few new variables and partitioning the involved matrices, a nonnegative linear least square model is derived. Most of the variables in the model are the damage extents of structural elements. Our method does not involve mode shape expansion or reduction technique.

Three numerical examples show that the performance of the proposed method is superior to that of the GFM method combining with mode shape expansion, it is almost the same as that of the GFM approach with complete mode shapes data.

KEYWORDS:

• Damage detection
• generalized flexibility matrix
• incomplete mode shape
• sensitivity
• nonnegative least square

AMS SUBJECT CLASSIFICATIONS:

• 70J10
• 15A29

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by the Natural Science Foundation of China [Grant numbers 11672118 and 11401463] and the Sun Yat-sen University Research Grant for Youth Scholars.