Journal of Mechanical Science and Technology 32 (3) (2018) 1125~1133 www.springerlink.com/content/1738-494x(Print)/1976-3824(Online) DOI 10.1007/s12206-018-0215-8 Damage identification of a 2D frame structure using two-stage approach † Seyed Rohollah Hoseini Vaez * and Narges Fallah Department of Civil Engineering, Faculty of Engineering, University of Qom, Qom, Iran (Manuscript Received August 3, 2017; Revised October 25, 2017; Accepted December 3, 2017) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract In this article, a two-stage damage identification approach is employed to detect the site and extent of multiple damage cases in a 2D frame structure. In the first stage, Damage locating vector (DLV) method based on a new indicator called EDS (Exponential decreased stress) is applied to localize the damaged elements. Next, the damage extents of suspected elements are quantified using two metaheuris- tic algorithms, Water evaporation optimization (WEO) and accelerated WEO. Numerical example consists of a 2D frame structure with two types of meshing elements, 35 and 105 frame elements. For every state, two multiple damage cases are tested in noisy condition. To compare performance of the two-stage method with one-stage optimization method, the studied cases are also run using these two meta- heuristic algorithms. The results indicate that the two-stage approach is more effective than one-stage because the number of intact ele- ment detected as damaged one and computational errors for actual damaged elements in one-stage method are more while the two-stage approach spends a much shorter time. Keywords: Damage detection; Water evaporation optimization (WEO); Damage locating vector (DLV); 2D frame structure; Two-stage approach; Expo- nential decreased stress (EDS) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction Many terrible accidents caused by unexpected damages in structures. SHM (Structural health monitoring) is extensively utilized to identify damage of structures and protect they better [1]. Many different methods of damage identification have been reviewed by researchers [2, 3]. Some typical methods work based on flexibility change [4, 5]. The Damage locating vector (DLV) is a kind of flexibility change method that firstly proposed by Bernal [6]. Many re- searchers developed the DLV method [7-9]. Quek et al. [8] proposed a new indicator called normalized cumulative en- ergy (nce) and extended the DLV method. Vo-Duy et al. [9] employed the DLV and nce index to localize multiple damage sites in laminated composite beams. Dinh-Cong et al. [10] proposed a two-stage assessment method using DLV and Dif- ferential evaluation (DE) algorithm for damage detection of cross-ply laminated composite beams. Nguyen-Thoi et al. [11] utilized a combination of DLV and DE algorithm for struc- tural damage assessment. Also, many researchers have tested optimization method and other methods to identify damage in engineering structures [12-17]. The DLV method can be used to localize damage sites and if the method is combined with an optimization method, the resulting method will be a two-stage damage identification approach and can be utilized to localize and quantify damages. Some researchers utilized this type and other two-stage meth- ods [18-22]. According to mentioned references, one-stage detecting damage methods have been commonly used among different methods in which researchers have allocated a long time for solving inverse optimization problem to assess dam- age of damaged elements along with disruptive healthy ele- ments. It decreases the accuracy of identifying damage extent while two-stage approaches have converted the process to two separate stages, locating damage elements and quantifying damage extent, by discriminating between damaged and healthy element and eliminating healthy elements. In the current study, the application of DLV approach and two optimization algorithms, Water evaporation optimization (WEO) and accelerated WEO, to identify damages of a 2D frame structures has been studied. In the first stage, damaged elements of the structure are localized by employing DLV and using a new index called Exponential decreased stress (EDS). The EDS index is formulated based on axial stress of frame elements. This index increases the stress of intact elements and decreases the stress of damaged elements through expo- nent of the stresses. In the second stage, a metaheuristic algo- rithm quantifies damage extent of elements introduced as sus- pected in the first stage. To show robustness and reliability of this approach and proposed EDS, a 2D-frame with two type of meshing elements has been examined with noise; also the * Corresponding author. Tel.: +98 912 1327490, Fax.: +98 2532854228 E-mail address: hoseinivaez@qom.ac.ir † Recommended by Associate Editor Daeil Kwon © KSME & Springer 2018