Identification of structural models using a modified Artificial Bee Colony algorithm Hao Sun a , Hilmi Lus ß b , Raimondo Betti a,⇑ a Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA b Department of Civil Engineering, Bog ˘aziçi University, 34342 Bebek, Istanbul, Turkey article info Article history: Received 15 June 2012 Accepted 17 October 2012 Available online 13 November 2012 Keywords: Parameter estimation Structural system identification Artificial Bee Colony algorithm Optimization abstract A modified version of the Artificial Bee Colony (ABC) algorithm is presented to identify structural sys- tems. ABC is a heuristic algorithm with simple structure, ease of implementation and robustness. A non- linear factor for convergence control is introduced in the algorithm to enhance the balance of global and local searches. To investigate the applicability of this proposed technique to system identification, three examples are studied under different conditions regarding data availability, noise pollution level, priori knowledge of parameters, etc. Simulation results show the proposed technique produces excellent parameter estimation, even with few measurements and high noise corruptions. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Structural system modeling and identification are extremely important areas in civil and mechanical engineering. Over the past few decades, they have been widely used for different purposes, with applications in structural health monitoring, nondestructive assessment, damage detection, active control, etc. From a compu- tational point of view, system identification (SI) can be considered as an optimization or minimization process in which the objective is to determine a model of a system so that its predicted response to a given input is close enough to the measured response from the real system. Looking at the current literature, SI can be generally classified into parametric identification and nonparametric identi- fication depending on the type of structural model used. If the SI is in terms of an assumed model defined by a set of physical param- eters, such as mass and stiffness, then it is called parametric iden- tification, while nonparametric identification is used to categorize methods that use purely mathematical representations of the sys- tem. Considerable efforts have been made in developing methods for parameter identification and state estimation of dynamical sys- tems considering either a full or partial set of input as well as out- put measurements [1–10]. There are two main categories of approaches for SI, depending on whether SI is carried out in the frequency domain or in the time domain. Frequency domain methods seek to identify natural fre- quencies, mode shapes, damping ratios, and other modal quanti- ties, using frequency domain based analyses of the time histories of the input and/or output response [1,6,11–16]. However, these tools are generally unreliable for damage assessment; in fact, fre- quencies are often more affected by environmental factors, such as temperature, than by the occurrence of structural damage, according to the experiments carried by Farrar and Doebling [17]. Moreover, mode shapes tend to be quite difficult to be accu- rately measured because of their susceptibility to noise. In addi- tion, structural masses have to be assumed in order to draw conclusions on the stiffness from modal parameters like frequen- cies [18]. By contrast, time domain methods aim to estimate sys- tem physical parameters based on observed data sampled in the time domain; some of such methodologies can even track system parameters change during the duration of the records [19]. Various techniques have been developed in the time domain for both parametric and nonparametric identification, such as the least-square based estimation methods [3,4,20–23], the extended Kalman filter (EKF) [2,24–27], the unscented Kalman filter (UKF) [5,28–30], the particle filter (PF) [5,31], the H 1 filter [32], the square-root unscented filter [33], and the sequential Monte Carlo method [5,34,35]. Lin et al., for example, used a variable trace ap- proach [3] and a variable forgetting factor approach [36] to identify non-linear hysteretic structural systems on-line, while Yang and Lin [21] proposed a method for identification of parameter’s changes based on least squares estimation and adaptive tracking technique. The EKF with a weighted global iteration procedure was applied to identify structural systems by Hoshiya and Saito [24] and Jeen-Shang and Yigong [25] using earthquake records. Yang et al. [27] developed an adaptive tracking technique based on the EKF to identify the structural parameters. Such a technique is able to track the changes of system parameters on-line. The UKF, a recently developed filtering technique with many advantages 0045-7949/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compstruc.2012.10.017 ⇑ Corresponding author. Address: Department of Civil Engineering and Engineer- ing Mechanics, Columbia University, 610 S.W. Mudd Building, 500 West 120th Street, New York, NY 10027, USA. Tel.: +1 212 854 6388; fax: +1 212 854 6267. E-mail address: rb68@columbia.edu (R. Betti). Computers and Structures 116 (2013) 59–74 Contents lists available at SciVerse ScienceDirect Computers and Structures journal homepage: www.elsevier.com/locate/compstruc