# Structural Damage Localization by the Principal Eigenvector of Modal Flexibility Change
## 1 Introduction  
During the last decades, a large number of research papers have reported on structural defect assessment based on the changes in measured static/dynamic response. The theoretical basis of these algorithms lies in the fact that the static and dynamic responses are functions of structural material properties (such as stiffness, mass, and damping). As a result, if the material properties are changed due to structural defects, then structural responses must also be changed. The relevant literature reviews can be found in references [1; 2; 3]. Generally, defect identification algorithms can be divided into model based and non-model based procedures according to using finite element model (FEM) or not. Algorithms [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16] based on FEM assess structural defects by modifying structural FEM according to structural responses. The modifications of structural FEM will indicate the location and severity of the defect. It is well known that model-based methods are computationally intensive and highly influenced by the quality of structural FEM. However, the precise FEM is often difficult to achieve in engineering practice for the simplified assumptions in the construction of the FEM, which means that the correct results might be missed.  
The advantages of non-model algorithms lie in their easiness and straightforwardness because structural EEMs are not needed in these approaches. Damage indexes can be established directly by the variations of structural responses before and after damage for assessing structural defects. [PERSON] and [PERSON] [17] used the uniform load surface (ULS) of structural flexibility to locate defects. [PERSON] and [PERSON] [18; 19] discovered that the curvature of ULS is sensitive to local damage in the plate structure. [PERSON] and [PERSON] [20] made use of the simplified gapped-smoothing technique to improve the accuracy of the ULS algorithm. [PERSON] _et al._[21] proposed an elastic damage load theorem to locate defects in simply supported beams. [PERSON] _et al._[22] presented a normalized ULS algorithmfor damage identification in beam-like structures. Other algorithms for defect localization can be found in references [23; 24; 25; 26; 27]. In engineering practice, structural response parameters are sometimes difficult to obtain and/or depend on environmental factors (e.g., temperature, humidity, loading at the time of testing, _etc._). If the environmental impact is not considered properly, these localization algorithms will probably give incorrect results. In view of this, [PERSON] _et al._[9; 28; 29] proposed the interpolation damage detection method (IDDM) to considering the environmental impact. Their investigations verified the effectivity of the IDDM. [PERSON] _et al._[30; 31] proposed a new damage index and a method based on the Poincare map for structural damage localization. Numerical and experimental studies confirm the applicability and sensitivity of their method in application.  
This study proposes a defect localization algorithm based on the principal eigenvector (PE) obtained from structural flexibility variation. The presented algorithm uses PE as a new damage indicator to locate structural defects without FEM. A three-span continuous beam is used as an example to demonstrate the efficiency of the presented PE algorithm in structural defect localization. For several damage scenarios in the structure, defect localization results obtained by the PE algorithm and the ULS procedure are both given for comparison. The numerical result demonstrated that the PE algorithm can locate structural defects with good accuracy, whereas the ULS approach occasionally missed one or two defect locations. It has been shown that the proposed PE algorithm may be more effective at identifying structural damage locations than the ULS approach.