A Combined Modal Correlation Criterion for Structural Damage Identification with Noisy Modal Data

Manolis Georgioudakis,Vagelis Plevris

doi:10.1155/2018/3183067

Abstract

Structural damage identification is a scientific field that has attracted a lot of interest in the scientific community during the recent years. There have been many studies intending to find a reliable method to identify damage in structural elements both in location and extent. Most damage identification methods are based on the changes of dynamic characteristics and static responses, but the incompleteness of the test data is a great obstacle for both. In this paper, a structural damage identification method based on the finite element model updating is proposed, in order to provide the location and the extent of structural damage using incomplete modal data of a damaged structure. The structural damage identification problem is treated as an unconstrained optimization problem which is solved using the differential evolution search algorithm. The objective function used in the optimization process is based on a combination of two modal correlation criteria, providing a measure of consistency and correlation between estimations of mode shape vectors. The performance and robustness of the proposed approach are evaluated with two numerical examples: a simply supported concrete beam and a concrete frame under several damage scenarios. The obtained results exhibit high efficiency of the proposed approach for accurately identifying the location and extent of structural damage.

Highlights

Structural damage identification has drawn increasing academic interest, as witnessed by the significant number of relevant journal and conference papers, during the recent years [1,2,3,4,5]. e necessity of detecting and repairing structural damage at its early stage has become imperative, and considerable effort has been devoted to developing nondestructive testing and evaluation (NDT&E) techniques [6]
A class of damage identification methods belonging to the second category is based on the modification of structural model properties such as mass, stiffness, and damping to reproduce as closely as possible the measured static and dynamic responses corresponding to the experimental data [4]. ese methods update the physical parameters of a finite element model of the structure by minimizing an objective function expressing the difference between finite element predicted and experimentally identified structural dynamic properties that are sensitive to damage such as natural frequencies and natural mode shapes
One limitation of the Modal Assurance Criterion (MAC) criterion is that it takes into account only the eigenvectors and not the eigenvalues of the structures. is means that, in the case of uniform-like damage, the MAC criterion will not be able to detect almost any change; as in this case, the structure becomes more flexible, but there is no significant difference in the eigenvectors which remain almost unchanged. e natural frequencies provide global information of the structure, and they can be accurately identified through dynamic measurements

Summary

Introduction

Structural damage identification has drawn increasing academic interest, as witnessed by the significant number of relevant journal and conference papers, during the recent years [1,2,3,4,5]. e necessity of detecting and repairing structural damage at its early stage has become imperative, and considerable effort has been devoted to developing nondestructive testing and evaluation (NDT&E) techniques [6]. Among the NDT&E techniques that have received significant attention in the computational mechanics field are those based on vibration signature analysis in order to obtain global information about the condition or state of health of the structural models using measured dynamic data Such techniques use vibration characteristics of the structures including frequency response functions, natural frequencies, mode shapes, modal curvatures, and modal flexibilities to identify the occurrence of the structural damage. In order to compare two sets of values for the two structures, the use of modal correlation criteria is imperative, providing a measure of consistency and correlation between estimations of mode shape vectors. Considering two mode shape vectors 􏼈φ(i)􏼉 ([n × 1]) and 􏼈ψ(j)􏼉 ([n × 1]), for structures A and B, respectively, the element MACij of the MAC matrix ([m × m]) is given by. By multiplying the n individual values of the MACF􏽢LEX vector, we obtain the MACFLEX scalar value as follows: MACFLEX 􏽙 MACF􏽢LEXi (9)

Damage Identification as an Optimization Problem

Numerical Examples

Findings

Conclusions