## 1 Introduction
[10] modified the ULS method by introducing proper weighting factors in the unified error function and enhancing the iterative solving procedure. The iterative scheme in the ULS was also enhanced by [PERSON] et al. [11] using an improved stochastic search algorithm. Most of the methods mentioned above are based on least squares. The flutter derivatives are extracted by minimizing the residual between measured signals and predicted responses. In these methods, the parameters are identified from the residuals related to vertical bending and torsional motion separately [5], or the sum of them without or with weighting factors [7; 9; 10]. By utilizing weighting factors in the objective function, the accuracy of the identification results is improved. However, the weighting factors used in the previous methods are preassigned, which may not be optimal. In contrast, in this paper, the weighting factors are optimized using an iterative procedure. Generally, the flutter derivatives are extracted by solving an optimization problem, in which a good initial guess of the parameters is usually required, so that difficulties may arise to obtain a sound result when a poor initial value is used. Indeed, some researchers used the Modified Ibrahim Time Domain (MITD) approach [6; 7] or the covariance block-Hankel matrix (CBHM) method [12; 13] to determine the initial values of system parameters when identifying flutter derivatives of bridge decks. The results may not be accurate enough but are good enough to be the initial values. However, an extra step is required to determine the initial values in these methods. Therefore, methodologies based on heuristic search algorithms without initial values can be employed for this purpose. Several heuristic stochastic algorithms for global optimization have been developed in recent years, such as particle swarm optimization, harmony search algorithm, ant colony optimization, firefly algorithm, differential evolution algorithm, and gravitational search algorithm, etc. Besides the above-mentioned algorithms, in 2005, [PERSON] [14] proposed a novel swarm intelligence algorithm, i.e., the artificial bee colony (ABC) algorithm, to solve complex numerical optimization problems. ABC is a heuristic optimization algorithm with the advantage of simple structure, convenient implementation, and good stability. For a good optimization algorithm, two search capabilities of exploitation and exploration need to be balanced. Exploitation is the behavior of probing a local region of the search space by fine-tuning, with the hope of improving a promising solution that we already have at hand. Exploration is the behavior leading to disengagement from the current solution by probing a larger search space for alternatives, with the hope of finding other promising and needing to be further refined solutions. However, the standard ABC algorithm is strong in exploration but weak in exploitation, which has greatly affected its performance. In truth, it is a critical issue for such a kind of heuristic search algorithm to keep a proper balance between the exploration and exploitation. Aiming at these problems, this paper introduces a modified ABC algorithm with [PERSON]'s method (MABC-Powell) to solve the optimization problem, where the standard ABC is enhanced by several modifications [15; 16; 17; 18]. It is noted that only a single optimal estimate of flutter derivatives can be made for one set of test data for most of the methods, and repeated tests for wind tunnel tests are only limited to some cases [19]. Moreover, due to the effects of flow turbulence, measurement noise, and mathematical model error, the estimation of flutter derivatives shows dispersed results in repeated experiments. Subsequently, if mishandled, the inherent uncertainty can lead to estimation errors. Uncertainty quantification is crucial to flutter reliability analysis [19; 20; 21; 22; 23] and reliability-based optimum design [24; 25; 26] of bridges.